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f(x)=2x+3/5. Find the inverse.
Answers
[tex]f^{-1} (x)=\frac{x}{2} -\frac{3}{10} }.[/tex]
Step-by-step explanation:1. Write the function.[tex]f(x)=2x+\frac{3}{5} \\ \\[/tex]
2. Rewrite "f(x)" as "y".[tex]y=2x+\frac{3}{5} \\ \\[/tex]
3. Switch positions between "y" and "x".[tex]x=2y+\frac{3}{5} \\ \\[/tex]
4. Now solving for x: Subtract "3/5" from both sides of the equation.[tex]x-\frac{3}{5} =2y+\frac{3}{5} -\frac{3}{5} \\\\x-\frac{3}{5} =2y[/tex]
5. Divide both sides by "2".[tex]\frac{x-\frac{3}{5}}{2} =\frac{2y}{2} \\ \\\frac{x-\frac{3}{5}}{2} =y[/tex]
6. Move the terms.[tex]y =\frac{x-\frac{3}{5}}{2}[/tex]
7. Rewrite as 2 independent fracions.[tex]y =\frac{x}{2} -\frac{\frac{3}{5} }{2}[/tex]
8. Solve the fraction division.[tex]y =\frac{x}{2} -\frac{3}{5} }*\frac{1}{2} \\ \\y =\frac{x}{2} -\frac{3*1}{5*2} }\\ \\y =\frac{x}{2} -\frac{3}{10} }[/tex]
9. Express the answer.[tex]f^{-1} (x)=\frac{x}{2} -\frac{3}{10} }[/tex].
-Extra step- 10. Verify the answer.To verify if this is the correct expression for the inverse of the function, simply see if the "x" values and "y" values of the function are inverses as well. For example, a value of x = 2 returns 4.6 on the original function. Therefore, the inverse function should return 2 when a value of x = 4.6 is used. Check the attached image to see this comparison using the table of values of the original function and it's inverse.
Hello and greetings KingDanny2xx.
Therefore, the inverse of f(x)=2x+3/5 is f⁻¹ (x) = x/2 - 3/10.
Step-by-step explanation:[tex]\boldsymbol{\sf{f(x)=2x+\dfrac{3}{5} }}[/tex]
We substitute f(x) for y.
[tex]\boldsymbol{\sf{y=2x+\dfrac{3}{5} }}[/tex]
We interchange x and y.
[tex]\boldsymbol{\sf{x=2y+\dfrac{3}{5} }}[/tex]
We interchange the sides of the equation. We want to swap sides because mathematicians agreed to the convention that the unknown variable in equations and inequalities must always be on the left-hand side.
If there is a variable on both sides, we do it to facilitate a later calculation.
[tex]\boldsymbol{\sf{2y+\dfrac{3}{5}=x }}[/tex]
We multiply both sides of the equation by 5. We want to multiply an equation to get rid of fractions and/or rational expressions, doing a lot more calculations later.
Both sides of the equation must be multiplied by the same value to preserve equality between all sides, according to the Multiplication Property of Equality.
[tex]\boldsymbol{\sf{5\left(2y+\dfrac{3}{5}\right)=5x }}[/tex]
We distribute the 5 to the terms in parentheses. The distributive property is that each term in an expression between parentheses is multiplied by the expression outside the parentheses.
[tex]\boldsymbol{\sf{5x2y+5x\dfrac{3}{5} =5x}}[/tex]
We calculate the product.
[tex]\boldsymbol{\sf{10y+\not{5}x\dfrac{3}{\not{5}}=5x }}[/tex]
We cancel the greatest common divisor 5.
[tex]\boldsymbol{\sf{10y+3=5x}}[/tex]
We move the constant to the right side and change its sign. We want to move a constant to the right because it is customary for constants in equations to be on the right hand side.
The sign of the constant must be changed because in the process of "moving the constant", we are adding its opposite to both sides.
We move the constant to the right by adding its opposite to both sides.
[tex]\boldsymbol{\sf{10y+3-3=5x-3}}[/tex]
Since two opposite numbers add up to 0, we remove them from the expression. The additive inverse property states that two opposite numbers add up to 0.
Since adding or subtracting 0 doesn't change the value of the expression, we can simply remove them.
[tex]\boldsymbol{\sf{10y=5x-3}}[/tex]
We divide both sides of the equation by 10. We want to divide an equation to isolate the unknown variable on one side or to transform the equation in a certain way.
Both sides of the equation must be divided by the same number to preserve equality between the sides, according to the Division Property of Equality.
[tex]\boldsymbol{\sf{10y\div10=(5x-3)\div10}}[/tex]
Any equation divided by itself is equal to 1.
[tex]\boldsymbol{\sf{y=(5x-3)\div10}}[/tex]
We distribute the 10 to the terms in parentheses. The distributive property is that each term of an expression between the parentheses is multiplied by the expression that is outside the parentheses.
[tex]\boldsymbol{\sf{y=5x\div10-3\div10 }}[/tex]
We write the division as a fraction. A fraction is another way of writing division.
One more way to remember it is the division symbol.
÷We notice that the division symbol looks like a fraction where the dots represent the numerator and denominator.
[tex]\boldsymbol{\sf{y=\dfrac{5}{10}x-3\div10 \iff y=\dfrac{\not{5}}{\not{10}}x-\dfrac{3}{10} }}[/tex]
We divide by the common factor 5. The object of canceling a common factor is to rewrite a fraction in the simplest form to facilitate a later calculation.
We can cancel a common factor because it will still represent the same value.
[tex]\boldsymbol{\sf{y=\dfrac{1}{2}x-\dfrac{3}{10} }}[/tex]
Substitute y for f⁻¹ (x). Substitution means to replace one algebraic expression with another or with a specific value.
[tex]\boldsymbol{\sf{f^{-1}(x)=\dfrac{x}{2}-\dfrac{3}{10} }}[/tex]
Therefore, the inverse of f(x)=2x+3/5 is f⁻¹ (x) = x/2 - 3/10.
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Related Questions
A coin purse contains five 10-peso coins, three 5-peso coins, and nine 1-peso coins. If a coin is randomly picked from the purse, find the probability that it is.
a. not a 10-peso coin.
b. a 5-peso coin.
Answers
a. The probability that it is not a 10-peso coin is [tex]\frac{12}{17}[/tex].
b. The probability that it is a 5-peso coin is [tex]\frac{3}{17}[/tex] .
What is probability?
The mathematical notion of probability is used to determine the likelihood of an event. It is only helpful for estimating the likelihood that an event will happen. A scale from 0 to 1, where 0 denotes impossibility and 1 denotes a specific occurrence.
We are given that a purse contains five 10-peso coins, three 5-peso coins, and nine 1-peso coins.
Total coins = 5 + 3 + 9 = 17
a. Probability of getting a 10 peso coin is
P (A) = [tex]\frac{5}{17}[/tex]
Probability of not getting a 10 peso coin is
⇒Probability = 1 - P (A)
⇒Probability = 1 - [tex]\frac{5}{17}[/tex]
⇒Probability = [tex]\frac{12}{17}[/tex]
b. Probability of getting a 5 peso coin is [tex]\frac{3}{17}[/tex] .
Hence, the required probabilities have been obtained.
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Solve four-sixths minus three-twelfths equals blank.
one-sixth
five-twelfths
seven-twelfths
thirty-six seventy-seconds
Question 4(Multiple Choice Worth 2 points)
(05.04 LC)
Solve seven-eighths minus nine-sixteenths equals blank.
two-sixteenths
two-eighths
five-sixteenths
sixteen thirty-seconds
Question 5(Multiple Choice Worth 2 points)
(05.04 LC)
Solve two-fifths minus one-seventh equals blank.
one-fifth
one-seventh
nine thirty-fifths
three-twelfths
Answers
By answering the presented question, we may conclude that As a result, fraction the answer is nine thirty-fifths.
what is fraction?A whole can be represented by any number of equal sections or fractions. In standard English, fractions represent the number of units of a specific size. 8, 3/4. A whole contains fractions. In mathematics, numbers are stated as the ratio of the numerator to the denominator. Each of these is an integer in simple fractions. A fraction exists in the numerator or denominator of a complex fraction. True fractions have numerators that are smaller than their denominators. A fraction is a sum that represents a piece of a total. You may assess it by dividing it up into smaller chunks. Half of a whole number or object, for example, is represented as 12.
We can simplify both fractions to have a common denominator of 12 for the first problem:
Four-sixths = Eighteenths
Three-twelfths + three-twelfths = three-twelfths
As a result, the phrase becomes: 8/12 - 3/12 = 5/12
As a result, the answer is five-twelfths.
For the second case, we may reduce both fractions again such that they have a common denominator of 16:
Seventy-eighths = fourteenteenths
Nineteenths + nineteenths = nineteenths
As a result, the equation becomes: 14/16 - 9/16 = 5/16.
As a result, the answer is five-sixteenths.
We can simplify both fractions to obtain a common denominator of 35 for the third problem:
Two-fifths = 14-thirty-fifths
One-seventh Equals thirty-fifths
As a result, the phrase becomes: 14/35 - 5/35 = 9/35
As a result, the answer is nine thirty-fifths.
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Help with math problems
Answers
Answer:
I think
Step-by-step explanation:
the length of a rectangle is 5 inches more than twice a number. The width is 4 inches less than the same number. If the area of the rectangle is 15, find the number
Answers
Answer: 5
Step-by-step explanation:
A = Lw (area of rectangle is length times width)
A = 15 (Area is 15)
L = 2x + 5 (length is 2 times a number plus another 5)
w = x - 4 (width is 4 less than that number
Plug in the values:
15 = (2x + 5)(x - 4)
FOIL
15 = 2x2 - 8x + 5x - 20
simplify:
15 = 2x2 - 3x - 20
Subtract 15
0 = 2x2 - 3x - 35
Factor out the quadratic. We know that one number has to be 7 and the other 5 so that they multiply together to make 35, and that one of them has to be negative so that it's actually -35.
That means we have m * n = -35
We also need it set up so that so that 2m + n = -3:
2 * -5 + 7 = -3
0 = (2x + 7)(x - 5)
So:
0 = 2x + 7, or 0 = x - 5
x = -7/2 or 5
We cannot have a negative length, so x = 5
Check:
15 = (2 * 5 + 5) (5 - 4)
15 = 15 * 1
15 = 15
pls help with number 5 a through d
Answers
The surface area of the following solids is:
a.54cm².
b. 43.32cm².
c. 21.2cm².
d. The figures b and c are smaller than a.
Explain surface area?In contrast to the lateral surface area, which is used to determine the area occupied by the shape's curved surface, the total surface area takes into account all faces of the 3D shape, including both flat and curved surfaces.
The area around the bases is not included. One 3D shape called a sphere has just one round surface and no flat base.
In the given question,
In the 1st figure,
Total surface area = Total surface area of 6 squares.
= 6 × 3²
= 54cm².
In the 2nd figure,
Total surface area = Total surface area of 2 triangles + Total surface area of 3 squares + Total surface area of larger triangle.
= 2 × 1/2 × 3 × 3 + 3 × 3² + 1/2 × 3.96 × 3.7
= 9 + 27 + 7.32
= 43.32cm².
In the 3rd figure,
Total surface area = Total surface area of 4 triangles
= 1/2 × 3 × 3 + 1/2 × 3 × 3 + 1/2 × 4.2 × 3.7 + 1/2 × 3 × 3
= 9 + 7.77 + 4.5
= 21.2cm².
Hence, the figures b and c are smaller than the figure a.
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GIFTS Joel has $96 to spend on at least 9 gifts for the holidays. He plans to buy puzzles that cost $8 or games that cost $12. How many of each can he buy? Part A Create a system of inequalities that represents the constraints in the problem. Let x be the number of puzzles Joel can buy and y be the number of games Joel can buy. Can Joel buy 2 games and 6 puzzles and satisfy the constraints?
Answers
Joel cannot buy 2 games and 6 puzzles and satisfy the constraints was solved by using inequality.
The total cost of x puzzles and y games must be less than or equal to $96, which gives us the first inequality: 8x + 12y ≤ 96
The second inequality: x + y ≥ 9.
What is inequality function?An inequality is a mathematical statement that compares two quantities or expressions and shows the relationship between them using one of the following symbols: <, >, ≤, or ≥. For example, "x > 5" is an inequality that states that x is greater than 5.
In the given question,
Part A:
Let x be the number of puzzles Joel can buy and y be the number of games Joel can buy.
The total cost of x puzzles and y games must be less than or equal to $96, which gives us the first inequality: 8x + 12y ≤ 96
Joel needs to buy at least 9 gifts, which means that the total number of gifts must be greater than or equal to 9. Since x represents the number of puzzles and y represents the number of games, the total number of gifts is x + y. This gives us the second inequality: x + y ≥ 9
We also know that Joel can only buy puzzles or games, not both. Therefore, x and y must be either both integers or both half-integers (such as 1.5 or 2.5), but they cannot be mixed. This gives us the third inequality:
x, y are both integers or both half-integers
Part B:
To see if Joel can buy 2 games and 6 puzzles and satisfy the constraints, we can substitute x = 6 and y = 2 into the inequalities:
8x + 12y ≤ 96
8(6) + 12(2) ≤ 96
72 ≤ 96
This inequality is true, so the first constraint is satisfied.
x + y ≥ 9
6 + 2 ≥ 9
8 ≥ 9
This inequality is not true, so the second constraint is not satisfied. Therefore, Joel cannot buy 2 games and 6 puzzles and satisfy the constraints.
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Find x correct to 2 decimal places.
Answers
Answer:
216.49
Step-by-step explanation:
you have two right triangles, for the left one
[tex]tan(64)=\frac{113}{a}[/tex]
[tex]a=\frac{113}{tan(64)}[/tex]
for the one on the right
[tex]tan(35)=\frac{113}{b}[/tex]
[tex]b=\frac{113}{tan(35)}[/tex]
The total value of X is the sum
[tex]\frac{113}{tan(35)} +\frac{113}{tan(64)}=216.4945073[/tex]
so 216.4945073
Find the area of the regular polygon below.
Answers
The area of the regular polygon which is given above would be = 64.5 cm². That is option D.
How to calculate the area of the regular polygon?To calculate the area of the given regular polygon will require the use of this formula such as:
Area = 1/2(a×p)
where;
a = length of an apothem = 4.3 cm
p = perimeter = 6×5 = 30cm
Area = 1/2 ( 4.3×30)
= 129/2
= 64.5 cm²
Therefore, in conclusion the area of the regular polygon which is a hexagon with 6 sides would be = 64.5 cm².
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Here is the problem.
Answers
a) The speed at which the car gets maximum gas mileage is given as follows: 48 miles per hour.
b) The max gas mileage is given as follows: 29.5 miles per gallon.
How to obtain the maximum gas mileage?The gas mileage is modeled as a function of the velocity x according to the quadratic function presented as follows:
m(x) = -0.028x² + 2.688x - 35.012.
The coefficients are given as follows:
a = -0.028, b = 2.688, c = -35.012.
The leading coefficient a is negative, hence the vertex represents the point at which the maximum mileage is obtained.
The velocity is given as follows:
x = -b/2a
x = -2.688/[2(-0.028)]
x = 48 miles per hour.
The max gas mileage is obtained as follows:
m(48) = -0.028(48)² + 2.688(48) - 35.012.
m(48) = 29.5 miles per gallon.
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write a linear equation based on the given information.
through: (5,-1) and (2,2)
Answers
Answer:
y = (-1/3)x + 2/3
Step-by-step explanation:
We can use the slope-intercept form of a linear equation to find the equation of the line passing through the points (5, -1) and (2, 2). The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:
slope = (y2 - y1) / (x2 - x1)
Substituting the coordinates of the given points, we have:
slope = (2 - (-1)) / (2 - 5) = -1/3
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. We can use the point-slope form of a linear equation to find the y-intercept.
Using the point (5, -1), we have:
-1 = (-1/3)(5) + b
Solving for b, we get:
b = -1 + 5/3 = 2/3
Therefore, the equation of the line passing through the points (5, -1) and (2, 2) is:
y = (-1/3)x + 2/3
Which solid figure could be formed from the net shown?
(A) cube
(B) triangular prism
(C) rectangular pyramid
(D) square pyramid
_______________________________
(reporting wrong/spam answers)
(giving brainliest to correct answers)
_______________________________
Answers
A) Cube
the two squares will form the top and one side.
Each square right, top and bottom of the square will form the sides
Round 0.652 to the nearest tenth
Pls help
Answers
Answer:
0.7
Step-by-step explanation:
Answer: 0.7
Step-by-step explanation: The tenths place in decimals is the number directly to the right of the decimal. the 5 next to the six is greater than or equal to 5 meaning you can round up the 6 to a 7.
Jordan is on a road trip across the country with their family. In one day of traveling, they drove a total of 666.9 miles. Assume the same distance is driven each day of the trip and that the road trip consists of 7 days of traveling. Estimate the total number of miles Jordan will drive.
Answers
We estimate that Jordan will drive a distance of approximately 4668.3 miles during the entire 7-day road trip.
What is distance?Distance and displacement are two key words in mechanics that, although having similar sounds, have distinct definitions and meanings. How much of an object's path is covered by a moving object is measured in terms of distance. Whereas "How much route is covered by the item in a specific direction" is measured by displacement, The main distinction between distance and displacement is therefore that the former is a scalar quantity while the latter is a vector quantity.
Given that, the distance travelled is 666.9 miles.
The same distance is travelled for 7 days thus,
distance = Distance per day x Number of days
distance = 666.9 miles/day x 7 days
distance = 4668.3 miles
Hence, we estimate that Jordan will drive approximately 4668.3 miles during the entire 7-day road trip.
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find the real cube root of the perfect cube
Answers
Answer:
-3/2
Step-by-step explanation:
cubed roots of -27 is -3
cubed root of 8 is 2
What is
2+3(3x9)
Someone pls explain this to me
Answers
Answer:
83
Step-by-step explanation:
The expression follows the order of operations (PEMDAS): Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction, in that order.
First, simplify what is inside the parentheses: 3 x 9 = 27
Next, multiply 3 by 27: 3 x 27 = 81
Finally, add 2 to 81: 2 + 81 = 83
Therefore, the expression 2+3(3x9) equals 83.
The result of this expression is 83
Basic rules for expressionsTo solve them we have to start from the inside to out, that is, parentheses, brackets...
And proceed to signal resolution:
[tex]\begin{array}{l}\sf 2+3\tiny\text{$\times$}(3\times9)\\\sf 2+3\tiny\text{$\times$}(27)\\\sf 2+81\\\bf 83\end{array}[/tex]
We get the result 83
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22. A small coffee company claims to include 11 ounces of coffee in every bag of ground coffee it produces. Out of a random sample of 250 bags, 50 of the bags contain only 10.9 ounces. Which inferences from the results of the random sample are reasonable? Choose all that are correct.
A. It can be inferred that 5% of the bags from a second random sample will contain more than 11 ounces.
B. It is likely that a second random sample of bags will show a much lower percentage of bags with only 10.9 ounces.
C. The percentage of all bags produced that contain less than 11 ounces is likely to fall between 15% and 25%.
D. It is likely that the company's claim is true because 20% of the bags in the sample contain 10.9 ounces.
E. It is unlikely that the company's claim is true because 20% of the bags in the sample contain 10.9 ounces.
Answers
The inferences from the results of the random sample that are reasonable is: C. The percentage of all bags produced that contain less than 11 ounces is likely to fall between 15% and 25%.
Which inferences from the results of the random sample are reasonable?From the sample of 250 bags, we know that 50 of them contain only 10.9 ounces of coffee. Let's calculate the percentage of bags in the sample that contain less than 11 ounces:
50/250 = 0.2 = 20%
Now let's consider each inference:
A. It cannot be inferred that 5% of the bags from a second random sample will contain more than 11 ounces. The sample only provides information about the bags in the sample, not the entire population.
B. It is possible that a second random sample of bags will show a lower percentage of bags with only 10.9 ounces, but it cannot be concluded with certainty based on the given information.
C. It is reasonable to estimate that the percentage of all bags produced that contain less than 11 ounces is likely to fall between 15% and 25%. This is because out of a sample of 250 bags, 50 bags contained 10.9 ounces, which is 20% of the sample.
D. It is not necessarily likely that the company's claim is true because 20% of the bags in the sample contain 10.9 ounces. The sample provides information about the bags in the sample, not the entire population.
E. It is not necessarily unlikely that the company's claim is true because 20% of the bags in the sample contain 10.9 ounces. The sample provides information about the bags in the sample, not the entire population.
Therefore, the correct inferences from the given information are C. The percentage of all bags produced that contain less than 11 ounces is likely to fall between 15% and 25%.
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What are the foci of the graph x^2/40-y^2/81=1
Answers
Answer:
Step-by-step explanation:
(y^2)/1600-(x^2)/81=1. y21600−x281=1 y 2 1600 - x 2
Answer: y21600x281=1 y 2 1600 - x 2
Step-by-step explanation: for sure chfjjgffjfj ;)
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One of the sides of a rectangle has the length of 7. Which of the following points, when paired with (6, 5), will make a side equal to this length?
A) (7, 5)
B) (6, 12)
C) (6, 7)
D) (12, 5)
Answers
Answer:its b 6,12
Step-by-step explanation:
Please solve these 2 problems for me
Answers
The value of the perimeter:
1. 97. 3 units
2. 27. 8 units
How to determine the perimeter of the shapesThe formula for the perimeter of a triangle is expressed as;
P = a + b + c
Given that;
P is the perimeter of the trianglea, b and c are the length of the sidesFrom the diagram shown, we have that;
Using the tangent identity;
tan 44 = BC/29
find the value and cross multiply
BC = 28. 00
Also, AC ²= 29² + 28²
AC = √1625 = 40. 3
Then, the perimeter = 29 + 28. 00 + 40. 3 = 97. 3 units
For the second diagram;
Note that the perimeter of a rectangle is expressed as 2(length + width)
Substitute the values
Perimeter =2 ( 4 + 3) = 14 units
For triangle;
sin 45 = 4/t
cross multiply
t = 5. 7 units
To determine the adjacent side;
5.7² - 4² = x²
32. 5 - 16 = a²
a = √16. 49
a = 4. 1
Then, the perimeter = perimeter of rectangle + perimeter of triangle
= 14 + 13. 8
= 27. 8 units
Note that no specific unit was given as thus, we used 'units' as the measuring scale.
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uploaded
Screenshot 2023-03-06 9.
57.19 AM.pn
Answers
The relationship between the diameter of a circle and it's circumference is presented in this problem.
What is the measure of the circumference of a circle?The circumference of a circle of radius r is given by the equation presented as follows:
[tex]C = 2\pi r[/tex]
The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, while the diameter of the circle is the distance between two points on the circumference of the circle that pass through the center. Hence, the diameter’s length is twice the radius length.
The diameter is twice the radius, hence, for a circle with diameter 35 in, the radius is given as follows:
r = 0.5 x 35
r = 17.5 in.
Then the circumference of the circle is given as follows:
C = 2 x pi x 17.5
C = 109.9 in.
Missing InformationThe problem is incomplete, hence the relation between the diameter of a circle and it's circumference is presented.
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15 ) Ian throws a ball up in the air and lets it fall to the ground.
The height of the ball, h(t), is modeled by the equation
h(t) = -16t² + 6t+ 3, with h(t) measured in feet, and time, t,
measured in seconds. The number 3 in h(t) represents
(1) the maximum height of the ball
(2) the height from which the ball is thrown
(3) the number of seconds it takes for the ball to reach the ground
(4) the number of seconds it takes for the ball to reach its maximum
height
Answers
The number 3 in the equation h(t) = -16t² + 6t+ 3 represents option 2 - the height from which the ball is thrown.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
The equation h(t) = -16t² + 6t+ 3 gives the height of the ball as a function of time.
The constant term in this equation is 3, which represents the initial height of the ball when it is thrown.
Therefore, the correct answer is (2) the height from which the ball is thrown.
Option (1) cannot be correct, because the maximum height of the ball occurs when the derivative of h(t) is zero, which is not necessarily equal to the constant term in the equation.
Option (3) cannot be correct, because the ball reaches the ground when h(t) = 0, which requires solving a quadratic equation.
Option (4) cannot be correct, because the time it takes for the ball to reach its maximum height is given by the formula t = -b/2a, where a and b are the coefficients of the quadratic equation, and it does not depend on the constant term.
Therefore, option 2 is the correct answer.
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Eli has a trophy case that is 4 3/5 feet by 2 feet by 3 1/2feet. What is the volume of Eli’s trophy case?
Answers
The volume of Eli's trophy case is 64.4 cubic feet.
Eli's trophy case's length, breadth, and height must be multiplied to determine its volume. The case has the following measurements:
Length = 4 3/5 feet
Width = 2 feet
Height = 3 1/2 feet
We can sum the improper fractions after converting the mixed integers to fractions to arrive at:
Length = 4 3/5 feet = (5*4 + 3)/5 = 23/5 feet
Height = 3 1/2 feet = (2*3 + 1)/2 = 7/2 feet
Now that we have the volume, we can multiply the length, width, and height:
Volume equals length, width, and height
= (23/5) feet x 2 feet x (7/2) feet
= (23 x 2 x 7)/(5 x 2) cubic feet
= (644/10) cubic feet
= 64.4 cubic feet
Eli's trophy case therefore has a 64.4 cubic foot volume.
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The box plots display data collected when two teachers asked their classes how many pencils they lose in a school year.
A box plot uses a number line from 5 to 47 with tick marks every one unit. The box extends from 8 to 14 on the number line. A line in the box is at 11. The lines outside the box end at 7 and 45. The graph is titled Mr. Johnson's Class, and the line is labeled Number Of Pencils.
A box plot uses a number line from 2 to 52 with tick marks every one unit. The box extends from 8 to 26 on the number line. A line in the box is at 16. The lines outside the box end at 5 and 50. The graph is titled Mrs. Cheng's Class, and the line is labeled Number Of Pencils.
Which class lost fewer pencils overall based on the data displayed?
Mrs. Cheng's class; it has a narrow spread in the data
Mr. Johnson's class; it has a wide spread in the data
Mrs. Cheng's class; it has a smaller median value 16 pencils
Mr. Johnson's class; it has a smaller median of 11 pencils
Answers
Answer: Based on the data displayed, Mrs. Cheng's class lost fewer pencils overall as it has a smaller spread in the data compared to Mr. Johnson's class. The box plot of Mrs. Cheng's class has a smaller spread, with a larger interquartile range and smaller range compared to Mr. Johnson's class, indicating that the data is more concentrated and consistent. Additionally, the median value of Mrs. Cheng's class is higher than Mr. Johnson's class, indicating that half of the students in Mrs. Cheng's class lost fewer pencils than half of the students in Mr. Johnson's class. Therefore, the correct answer is "Mrs. Cheng's class; it has a narrow spread in the data".
Step-by-step explanation:
can someone hel-p me
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Which is the best first step when solving the following system of equations?
x + y = 3. 4 x minus y = 7.
Multiply the first equation by 4.
Add the first equation to the second equation.
Multiply the second equation by Negative 1.
Subtract the second equation from the first equation.
Mark this and return
Answers
On solving the provided question, we can say that Hence, the solution to the system of equations is x = 19/8 and y = 5/8.
What is equation?A math equation is a technique that links two statements and utilises the equals sign (=) to express equivalence. In algebra, an equation is a mathematical statement that proves the equivalence of two mathematical expressions. For example, in the computation 3x + 5 = 14, the equal sign inserts a gap between the numbers 3x + 5 and 14. A mathematical formula may be used to explain the link between the two phrases written on either side of a letter. The logo and the programme are usually the same. For example, 2x - 4 equals 2.
4x + 4y = 12 is obtained by multiplying the first equation by four.
To remove y, combine the first and second equations: (4x + 4y) + (4x - y) = 12 + 7, which simplifies to 8x = 19.
Divide both sides of the equation by 8 to find x: x = 19/8.
To find y, plug the value of x into either equation: y = 3 - x = 3 - 19/8 = 5/8.
Hence, the solution to the system of equations is x = 19/8 and y = 5/8.
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suppose 2 bakers make 30 loaves of bread in 1 hr. how many hours would 3,5,6,and 15 bakers need to make 30 loaves
Answers
Answer:
Therefore, 3 bakers can make 30 loaves of bread in 2 hours.
Therefore, 5 bakers can make 30 loaves of bread in 2 hours.
Therefore, 6 bakers can make 30 loaves of bread in 1.25 hours.
Therefore, 15 bakers can make 30 loaves of bread in 2 hours.
Step-by-step explanation:
In the number of bakers, it would take 2 hours to make 30 loaves of bread.
What is proportion?A proportion is an equation in which two ratios are set equal to each other.
Let h be the number of hours needed for a given number of bakers to make 30 loaves. Then we have:
2 bakers can make 30 loaves in 1 hour, so 1 baker can make 15 loaves in 1 hour.
Therefore:
3 bakers can make 45 loaves in h hours, so 45/3 = 15 loaves can be made in 1 hour. Thus, 3 bakers can make 30 loaves in 2 hours.
5 bakers can make 75 loaves in h hours, so 75/5 = 15 loaves can be made in 1 hour. Thus, 5 bakers can make 30 loaves in 2 hours.
6 bakers can make 90 loaves in h hours, so 90/6 = 15 loaves can be made in 1 hour. Thus, 6 bakers can make 30 loaves in 2 hours.
15 bakers can make 225 loaves in h hours, so 225/15 = 15 loaves can be made in 1 hour. Thus, 15 bakers can make 30 loaves in 2 hours.
Therefore, regardless of the number of bakers, it would take 2 hours to make 30 loaves of bread.
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new food is designed to add weight to mature beef cattle. The weight in pounds is given by
W = 8xy(20 − x − 2y),
where x is the number of units of the first ingredient and y is the number of units of the second ingredient. How many units of each ingredient will maximize the weight?
x=
y=
What is max weight?
Answers
The maximum weight occurs when x = 0 and y = 0, and the maximum weight is W = 0.
Describe Derivatives?In calculus, the derivative is a fundamental concept that measures the rate of change of a function with respect to its input variable. The derivative of a function at a particular point gives the instantaneous rate of change of the function at that point.
The derivative of a function f(x) with respect to its input variable x is denoted by f'(x) or df/dx. It is defined as the limit of the difference quotient as the change in x approaches zero:
f'(x) = lim (h → 0) [(f(x+h) - f(x)) / h]
Intuitively, the derivative of a function at a particular point gives the slope of the tangent line to the graph of the function at that point. This slope can be positive, negative, or zero, depending on whether the function is increasing, decreasing, or constant at that point.
To find the maximum weight, we need to find the critical points of the function.
First, we find the partial derivatives of the weight function with respect to x and y:
∂W/∂x = 8y(20 - 2x - 2y)
∂W/∂y = 8x(20 - x - 4y)
Setting these partial derivatives equal to zero, we get:
8y(20 - 2x - 2y) = 0
8x(20 - x - 4y) = 0
Solving for x and y, we get two critical points:
x = 0, y = 0
x = 10, y = 5
To determine which of these critical points correspond to a maximum, we use the second partial derivative test.
The second partial derivatives of W with respect to x and y are:
∂²W/∂x² = -32y
∂²W/∂y² = -32x
At the critical point (0,0), both second partial derivatives are negative, which means that it is a maximum.
At the critical point (10,5), both second partial derivatives are positive, which means that it is a minimum.
Therefore, the maximum weight occurs when x = 0 and y = 0, and the maximum weight is W = 0.
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Which shape is given below?
A) a rectangle
B) a rhombus
C) a kite
D) a trapezoid
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find the root of -3x^{3\:}-21x^2+72x+540=0
Answers
15. Maggie said that she could add 8 to both sides of the equation would still be equal. Do you agree? Explain
Answers
Answer:
It depends on the equation in question. If Maggie is referring to an equation in the form of x = y, then adding 8 to both sides would still result in the same value of x and y being equal. For example, if the equation is 2x - 5 = 7, then adding 8 to both sides would result in 2x - 5 + 8 = 7 + 8, which simplifies to 2x + 3 = 15. In this case, adding 8 to both sides would not maintain equality.
However, if the equation is in the form of an inequality such as x < y or x > y, adding the same value to both sides may not maintain the inequality. For example, if the inequality is 2x - 5 < 7, then adding 8 to both sides would result in 2x - 5 + 8 < 7 + 8, which simplifies to 2x + 3 < 15. In this case, adding 8 to both sides would still maintain the inequality.
Therefore, whether or not adding 8 to both sides of an equation would still result in equality depends on the equation in question and the mathematical operation being performed.
Yes. Yes I do.
If you think of an equation as a balance, where both sides have equal weight, then adding the same amount to both sides or taking away the same amount from both sides will still maintain that balanced weight.
We call this the addition property of equality:
If a = b, then a+c = b+c for any expression c.