Given the expressions, f(x)=√x+5, g(x)=3x-7, and h(x)=5x, the answer to f(g(5)) is 8. This is because when g(5) is substituted into f(x) we get f(g(5))=f(3x-7)=√(3x-7)+5. When 5 is substituted for x, this simplifies to f(g(5))=√(-2)+5 which equals 8.
The answer to g(f(78)) is 60. This is because when 78 is substituted into f(x) we get f(78)=√78+5 which simplifies to f(78)=9. When 9 is substituted into g(x) we get g(f(78))=3x-7 which simplifies to g(f(78))=3(9)-7 which equals 60.
Finally, the answer to h(g(f(2))) is 83. This is because when 2 is substituted into f(x) we get f(2)=√2+5 which simplifies to f(2)=3. When 3 is substituted into g(x) we get g(f(2))=3x-7 which simplifies to g(f(2))=3(3)-7 which equals 8. When 8 is substituted into h(x) we get h(g(f(2)))=5x which simplifies to h(g(f(2)))=5(8) which equals 83.
In summary, the answers to f(g(5)), g(f(78)), and h(g(f(2))) are 8, 60, and 83 respectively.
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the long leg of a right triangle is 71 feet longer than the short leg. the hypotenuse is 85 feet long. how long are the legs of the right triangle?
The right triangle Short leg: 14 feet and Long leg: 85 feet.
Because you have a right triangle, and you know the hypotenuse, you can use the Pythagorean Theorem:
x2 + y2 = 852
You are told the difference between the 2 sides:
x = y + 71
Now you have 2 equations. Use the expression for x in the 2nd equation, and substitute into the first:
(y + 71)2 + y2 = 852
Originally known as a rectangle triangle , a right triangle or right-angled triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle), i.e., It has two perpendicular sides.
The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
The hypotenuse is the side that is opposite the right angle (side c in the figure). Legs are the sides that are close to the correct angle (or catheti, singular: cathetus).
The side b that is adjacent to angle B and opposite to angle A is known as side a, while the side a that is adjacent to angle A and opposite to angle B is known as side b.
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The value of the short leg of the right angle triangle is 14 feet while the value of the long leg will be 85 feet.
You may apply the Pythagorean Theorem since you have a right triangle and know the hypotenuse:
x^2 + y^2 = 852
You are told the difference between the 2 sides:
x = y + 71
Now we have 2 equations.
Now, we will use the expression for x in the 2nd equation, and substitute into the first:
Thus we will get it as:
(y + 71)^2+y^2=852
A right triangle, also known as a right-angled triangle, is a triangle with one angle that is a right angle (that is, a 90-degree angle), i.e., it has two perpendicular sides.
The connection between the sides and angles of a right triangle is the basis of trigonometry.
The hypotenuse is the opposite side of the right angle.
Legs are the sides that are nearly at the right angle
The side b that is adjacent to angle B and opposite to angle A is known as side a, while the side a that is adjacent to angle A and opposite to angle B is known as side b.
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Which sentence uses correct punctuation?
A. Exercise and diet; these are the keys to living a long life.
O
B. There are three places I want to visit: Japan, India, and France.
C. Mara wished she could visit the stars: she often dreamed of it.
D. Dr. Chu has this to say about sugar; "Only eat small amounts."
Answer:
C. Mara wished she could visit the stars: she often dreamed of it.
Write your answer as a fraction or whole number without exponents.
4 ^–1 =
The index form 4 ^–1 as a fraction or whole number without exponents is 1/4
What are index forms?The index form of a number described as the number that is written as an exponential expression
Index forms are also described as a single number that is raised to another number or variable.
The index or exponent of an exponential expression shows how many times to multiply the base by itself in the expression.
From the information given, we have the index form as;
4^-1
This is represented as a fraction;
1/4^1
Note that any number that is raised to 1 is equal to the number
1/4
Hence, the value is 1/4
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Solve by using a proportion. Round answer to the nearest hundredth of necessary.
A map scale designates 0.75 inch = 50 miles. If the distance between two towns on the map is 2.75 inches, how many miles must you drive
to go from the first town to the second town?
Answer:
miles
To go from the first town to the second town, you must drive 137.5 miles.
What is an proportion?
A proportion is a mathematical equation that compares two ratios. It is usually written as two equal fractions or ratios, one on each side of the equation. A proportion can be used to compare the relationship between different quantities, such as measurements, rates, or even time.
We can use proportion to solve this problem. The proportion relates the map scale to the actual distance:
0.75 inch / 50 miles = x / distance
where x is the actual distance we want to find.
We can cross-multiply and solve for x:
0.75 inch * distance = 2.75 inches * 50 miles
x = (2.75 inches * 50 miles) / 0.75 inch
x = (137.5 miles)
To go from the first town to the second town, you must drive 137.5 miles.
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For the following right traingle, find the side length x. Round your answer to the nearest hundredth
Answer:
20
Step-by-step explanation:
(Hypotenuse)²=(Opposite)²+(Adjacent)²
(25)²=(15)²+(A)²
A²=625-225
A=✓400
A=20.00
Help me please! (Worth 50 points!!!!)
Question 8: A system of equations is given.
-2y = 2 - 3x
-5y = 10 - 5x
Part 1: Use elimination to solve the system of equations & show all work.
Part 2: Identify the values for x & y by filling in the blanks below.
x = ______
y = ______
Answer:
Step-by-step explanation:
-2y=2-3x-5y=10-5x
-2y=10-5x
2-3x-5y-5x
(SIMPLIFY)
5x-2y=10
2x-5y=8
(MULTIPLY BOTH SIDES)
-25x-10y=-50
4x-10y=16
(ELIMINATE ONE VARIABLE BY ADDING THE EQUATIONS)
-21x=-34
(DIVIDE BOTH SIDES)
X=34/21
(SUBSTITUTE THE VALUE OF X)
2x34/21-5y=8
(SOLVE EQUATION)
Y=-20/21
(A POSSIBLE SOLUTION IS)
(X,Y)=(34/21 , -20/21)
(CHECK THE SOLUTION)
-2x(-20/21)=2-3x 34/21 - 5x (-20/21)=10-5 X 34/21
(SIMPLIFY)
40/21=40/21=40/21
(X,Y)= (34/21 , -20/21)
(SOLUTION)
PLEASE HELP!! GIVING 50 POINTS. NEED DONE ASAP
Answer:
1. T, W, E, G
2. C, B, D, A
Step-by-step explanation:
For question 1:
G passes through (2, 3) and (0, -1). So, the slope is [tex]\frac{-1-3}{0-2}[/tex] = 2.
T passes through (0, 3) and (4, 4) so the slope is (4-3)/(4-0) = [tex]\frac{1}{4}[/tex].
E has a slope of [tex]\frac{5}{3}[/tex] because the equation is y = mx+b where m is the slope.
W has a slope of [tex]\frac{1}{3}[/tex] since slope is increase in y divided by increase in x.
The order of these from least to greatest is [tex]\frac{1}{4}[/tex], [tex]\frac{1}{3}[/tex], [tex]\frac{5}{3}[/tex], and 2.
Therefore, the answer is T, W, E, G.
For question 2:
A passes through (0, -1) and (2, 2), so the slope is (2- -1)/(2-0) = [tex]\frac{3}{2}[/tex].
B passes through (2, 0) and (4, 1), so the slope is (1-0)/(4-2) = [tex]\frac{1}{2}[/tex].
C has a slope of [tex]\frac{1}{4}[/tex] since the equation is y=mx+b where m is the slope.
D has a slope of [tex]\frac{3}{4}[/tex] since the slope is increase in y divided by increase in x.
The order of these from least to greatest is [tex]\frac{1}{4}[/tex], [tex]\frac{1}{2}[/tex], [tex]\frac{3}{4}[/tex], and [tex]\frac{3}{2}[/tex].
Therefore, the answer is C, B, D, A.
I hope this helps! :)
Didn't understand something? Some important formulas/things to remember that I used:
The equation of a linear function can be written as y=mx+b. m represents the slope.
The slope is the change/increase (decrease, in some cases), in y, divided by the change/increase in x.
The formula for the slope is [tex]\frac{Y2 - Y1}{X2 - X1}[/tex], where Y2 is the y coordinate of the second point, Y1 is the y coordinate of the first point, X2 is the x coordinate of the second point, and X1 is the x coordinate of the first point.
I think of a number. I halve it and multiply it by 4. my answer is 40. What is the number? pls it's needed urgently due in 10mins
Answer:
The number is 20
Step-by-step explanation:
First we have n, then n/2, then 4n/2, which equals 40. Thus, we have 2n=40, or n=20 which is the number.
Answer:
20
Step-by-step explanation:
A number increased by 7 gives 20, what is the number?with steps pls
Answer: 13
Step-by-step explanation:
13+7= 20
Answer:
The number is 13.
Step-by-step explanation:
"A number" is a number we don't know to begin with. It should be represented by a variable. Let's use n. We'll probably be trying to find this number.
"increased by" usually means that there is adding going on here.
So far, we have:
n + 7
that is algebra for "A number increased by 7"
"gives 20" is a little strange wording, but it means yields or equals.
So now we have the whole equation:
n + 7 = 20
To solve, subtract 7 from both sides (of the equal sign)
n = 20 - 7
n = 13
The number is 13.
Check:
13 increased by 7 gives 20?
13 + 7 = 20 ?
20 = 20 ✔Yes! Done!
find an equation of a plane containing the three points (3, -1, -2), (1, -6, -4), (1, -5, -2) in which the coefficient of is -8.
Which decimal number is less than 1.4 and greater than 1.35?
A. 1.34
B. 1.39
C.1.40
D. 1.53
Answer:
B
Step-by-step explanation:
The decimal number less than 1.4 and greater than 1.35 is A = 1.39
What are decimal numbers?The decimal numbers can only be expressed as fractions since they contain a fractional component. The accepted method for representing both integer and non-integer numbers is the decimal numeral system. There are 10 single-digit numbers in the decimal system:
0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. After the number 9, comes 10, then comes 11, then 12, and so on. Each time the digit to the right exceeds 9, the number on the left is increased by 1.
Given data ,
Let the decimal number be represented as A
Now , the value of A is
Let the first number be p = 1.4
Let the second number be q = 1.35
Now , q < A < p
The value of A is less than 1.4 and greater than 1.35
So , A = 1.39
Hence , the decimal number is A = 1.39
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if x, y, and z are integers and xy z is an odd integer, is x an even integer? (1) xy xz is an even integer. (2) y xz is an odd integer. a) statement (1) alone is sufficient, but statement (2) alone is not sufficient. b) statement (2) alone is sufficient, but statement (1) alone is not sufficient. c) both statements together are sufficient, but neither statement alone is sufficient. d) each statement alone is sufficient. e) statements (1) and (2) together are not sufficient.
c) both statements together are sufficient, but neither statement alone is sufficient.
According to the question
The query asks if statements (1) and (2) by themselves are sufficient to determine whether x is an even number. The answer is that neither assertion by itself is adequate to ascertain what x is worth. However, when both claims are taken into account, they are adequate to decide whether or not x is an even number. This is due to the fact that if xyz is even and yz is odd, x must be even. If x were odd, both xy xz and y xz would be strange as well. Due to this, the proper response is "c) neither statement is adequate when read alone, but both assertions taken together are sufficient."
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A large school district employs 3,461 teacher. If there are 28 students per teacher, how many students are there?
Answer: To find the number of students, you can multiply the number of teachers by the number of students per teacher.
3,461 teachers * 28 students/teacher = 96,668 students
So, there are 96,668 students in the school district.
Step-by-step explanation:
your colleague has built a model to show how the weather has an impact on daily sales of ice cream in your shop. the variable that tells you what the weather was like, is known as what?
Answer:
Independent variable. cause the sales will be depending upon the weather.
Step-by-step explanation:
help please all 4 problems
The equation of the slope is y = -5x + 72.
What is slope?A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
Any two different points on a line may be used to compute the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.
Given that:
72 inches is the depth of the liquid level in water tank.
Water drains at a rate of 5 inches per minute.
Let y represent the tank's height, which is given as 72.
Let x be the total number of minutes, here x = 0.
Therefore, the slope's equation is the rate at which the water drains, that is:
m = -5
The equation of the line is given by the formula:
y = mx + c
Substitute the values:
72 = -5(0) + c
c = 72
And the equation is:
y = -5x + 72
Hence, the equation of the slope is y = -5x + 72.
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The group of linear function is shown on the coordinate grid. What is the slope of the line?
Answer:
what grid
Step-by-step explanation:
What is the probability of flipping a coin 8 times and getting heads 2 times?
Round your answer to the nearest tenth of a percent.
OA. 21.9%
OB. 27.3%
OC. 3.1%
OD.
10.9%
SUBMIT
Answer:
10.9%
Step-by-step explanation:
You want to do the number of ways that can happen, which is [tex]_8C_2 = 28[/tex] divided by the total number of possibilities which is [tex]2^8[/tex] to get 10.9%
h. Write a decimal number and a fraction commonly used as
approximations
for pi.
The decimal number and the fraction commonly used as approximations for pi are 3.142 and 22/7
How to determine the decimal and the fraction?from the question, we have the following parameters that can be used in our computation:
pi
The pi variable is a mathematical constant that has the following fractional value
pi = 22/7
When converted to decimal in 3 decimal places, we have
pi = 3.142
Hence, the representations are 22/7 and 3.142
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In which number does the digit 8 have a value that is 1/10 10 1 start fraction, 1, divided by, 10, end fraction times as great as the digit 888 in the number 2{,}980. 72,980. 72, comma, 980, point, 7?
The digit 8 has a value that is 1/10 times as great as the digit 8 in the number 2,980.7 will be 548
The 8 in our number, 2,980.7, is in the tens place and hence represents an 80.
The value of the digit 8 is equal to 1/10 of 10 divided by 1, which is 10 times greater than the value of the digit 888.
We need a number that contains an 8 and has a value that is 1/10 of the previous number, hence we need:
1/10*80 = 8
So, the number we're seeking has an 8 in the position of the one.
Option C: 548 would be this.
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I'm a bit Confused on this math problem could someone help me please? thanks if you do! :D
Answer:
Step-by-step explanation:
Alright so let me try and explain this as best as I can:
So the graph isn't linear because the graph shows a parabola (a boomerang kind of shape that happens if you use an exponent somewhere in a y=mx+b formula if I remember correctly) and not a straight line. Linear graphs cannot curve, and this one does. Not sure why it it would be a function though. Assuming the answer chosen is correct, my best guess as to why it might be a function is because it continues to go in the same direction forever, there is a predictable amount of change between each point and you can follow a formula to find every point on the graph.
I really hope this helps a little!
Nolan invested $5,300 in an account paying an interest rate of 3.8% compounded annually. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $6,880?
With compound interest of 3.8% compounded annually it will take 7 years for the value of the account to reach $6,880.
What is Compound interest?
Compound interest is the interest imposed on a loan or deposit amount. It is the most commonly used concept in our daily existence. The compound interest for an amount depends on both Principal and interest gained over periods. This is the main difference between compound and simple interest.
Formula to find compound interest:
A=P(1+r/n)^nt
Where,
A = amount
P = principal
r = rate of interest
n = number of times interest is compounded per year
t = time (in years)
Alternatively, we can write the formula as given below:
CI = A – P
Where CI=Compound Interest
Now,
As given
A=$6880
P=$5300
r=3.8%
n=1
t=?
Therefore,
The time it would take to become $6880 will be
6880=5300(1+3.8/100)^t
From here t=7 years
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solve (4+8x) over 12x
Answer:
C
Step-by-step explanation:
(4+8x)/12 simplifies to (1+2x)/3x
Which of these triangle pairs can be mapped to each other using both a translation and a reflection across the line containing AB?
Triangles X Y Z and A B C are congruent. Triangle X Y Z is reflected across a line to form triangle A B C. It is also slightly higher than triangle A B C.
Triangles A B C and A Y C are congruent and share common side A C. Triangle A B C is reflected across line A C to form triangle A Y C.
Triangles A B C and X Y Z are congruent. Triangle X Y Z is slightly higher and to the right of triangle A B C.
Triangles A B C and X Y Z are congruent. Triangle A B C is rotated to the right to form triangles X Y Z. Triangle X Y Z is also higher and to the right of triangle A B C.
( the answer is not B )
The triangle pairs that can be mapped to one another using both a translation and a reflection across the line containing AB will be A based on the provided information. Triangles A B C and X Y Z are similar. Triangle A is created by reflecting triangle X, Y, and Z across a line. The correct option is A.
What is the Triangles about?The first triangle pair is a pair that can be mapped to one another using both translation and reflection across a line containing AB.
The first figure is made up of the coordinates XYZ and ABC, which are translations and reflections of one another across the line AB.
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Answer: it is A
Step-by-step explanation: just took the test
6/7 of a number is 5400. find 7/9 of the same money
Answer:
7/9 of the same money is 4900
Step-by-step explanation:
If 6/7 of a number is 5400, we can set up an equation to find the value of the number:
(6/7)x = 5400
To solve for x, we can multiply both sides by 7/6:
x = 5400 * (7/6)
x = 6000
Now that we know the number is 6000, we can find 7/9 of that value:
(7/9) * 6000 = 4900
So 7/9 of the same money is 4900.
Identify the lower class​ limits, upper class​ limits, class​ width, class​ midpoints, and class boundaries for the given frequency distribution. Also identify the number of individuals included in the summary. Blood Platelet Count of Males ​(1000 ​cells/mu​L) Frequency 0​-99 3 100​-199 54 200​-299 76 300​-399 21 400​-499 0 500​-599 0 600​-699 1 Identify the lower class limits​ (in 1000 ​cells/mu​L).
1) The lower class limits: 100, 200, 300, 400, 500, 600 .
2) The upper class limits: 199, 299, 399, 499, 599, 699.
3) The class width: 100.
4) Class midpoints: 149.5, 249.5, 349.5, 449.5, 549.5, 649.5.
5) Class boundaries : 99.5, 199.5, 299.5, 399.5, 499.5, 599.5, 699.5.
6) The number of individuals included in the summary : 155
The lower class limit in each class: 0,100, 200, 300, 400, 500, 600.
The upper-class limit is the biggest value in each class.
so the upper-class limit is: 99, 199, 299, 399, 499, 599, 699.
As we know the class width is the difference between the lower limit of one class and the lower limit of the previous class.
For example, 300 is the lower limit of one class and the lower limit of the previous class is 200 , so 300 - 200 = 100.
We know that, the class midpoints are the average of the limits of a class.
So, using midpoint formula the class midpoints are:
[tex]\frac{100+199}{2} = 149.5\\\\\frac{200+299}{2} = 249.5\\\\\frac{300+3199}{2} = 349.5\\\\\frac{400+499}{2} = 449.5\\\\\frac{500+599}{2} = 549.5\\\\\frac{600+699}{2} = 649.5\\[/tex]
We know that the class boundaries are nothing but the end points of an open interval which contains the class interval.
So, the class boundaries for the first class = (99.5, 199.5)
the class boundaries for the second class = (199.5, 299.5)
the class boundaries for the third class = (299.5, 399.5)
the class boundaries for the fourth class = (399.5, 499.5)
the class boundaries for the fifth class = (499.5, 599.5)
The total of individuals is equal to the sum of all the frequencies of each class: 3 + 54 + 76 + 21 + 0 + 0 + 1 = 155
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The complete question is:
Identify the lower class limits, upper class limits, class width, class midpoints, and class boundaries for the given frequency distribution. Also identify the number of individuals included in the summary. Blood Platelet Count of Males (1000 cells/muL) Frequency 0-99 3 100-199 54 200-299 76 300-399 21 400-499 0 500-599 0 600-699 1 Identify the lower class limits (in 1000 cells/muL).
Write the explicit formula for each geometric sequence.
Then determine the 8th term of each sequence.
Show work below.
Part A) 4, 16, 64, 256,...
Answer: The explicit formula for a geometric sequence is given by:
an = a1 * r^(n-1)
Where a1 is the first term, r is the common ratio, and n is the term number.
Part A) In this sequence, the first term is 4, and the common ratio is 4/1 = 4.
So the explicit formula for this sequence is:
an = 4 * 4^(n-1)
To find the 8th term of this sequence, we can substitute n = 8 into the formula:
a8 = 4 * 4^(8-1)
a8 = 4 * 4^7
a8 = 4 * 16,384
a8 = 65,536
Therefore, the 8th term of this sequence is 65,536.
Step-by-step explanation:
A pair of sneakers costs $46.99. You have a coupon for 15% off. What is the total cost of the sneakers after 5% sales tax is included?
Answer:
The cost of the sneakers after the coupon is applied would be $46.99 - ($46.99 * 15%) = $39.94.
The total cost of the sneakers after 5% sales tax is included would be $39.94 + ($39.94 * 5%) = $41.94
Answer: $41.94
15% off means the sneakers are at 85% of it's original price.
85% = 0.85
$46.99 x 0.85
= $39.94 after 15% coupon
5% sales tax means you are adding 5% to the price.
105% = 1.05
$39.94 x 1.05
$41.94, after the coupon and sales tax.
A linear function passes through the points (-3, 14)
and (2, -1). What is the rate of change of the
function?
The rate of change of the linear function is the third option which is -3.
The linear function runs through the points (-3,14) and is specified in question (2,-1).
The function's rate of change must be determined.
Having said that,
The slope of a linear function determines how quickly it changes.
A line's slope
By calculating the difference between the coordinates of the two points, (x1,y1) and (x2,y2), it is simple to calculate the slope of a straight line between them. The letter "m" is frequently used to denote slope.
In light of this, the slope of a line passing through the points (-3,14) and (2,-1) is
(-1-14)/(2-(-3)) = -15/5 = -3.
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HELPPPPPPPPPPPP DUE IN 20 MIN
Answer: D
Step-by-step explanation: the amount per cashews (c) is $2.45. Therefore, its 2.45c
The amount per pounds of sugar is $0.61. Therefore, its 0.61s
And, since its "buying" (basically, adding), you gotta add them. So, the answer would be: 2.45c+0.61s
Noah drew a pentagon with sides of length 1 inches. He wants to increase the length of each side by x inches so the pentagon is still a pentagon and has a perimeter of 25 inches.
The value of x that will give a perimeter of 25 inches is 4 inches
How to find the value of x that will give a perimeter of 25 inches?
The perimeter of a pentagon is the sum of the lengths of all its sides. The formula to calculate the perimeter of a pentagon is:
P = 5L
where is the side length
Initially, the sides of length, L is 1 inches
Now, we increase L by x and perimeter is 25 inches. Thus, can write:
25 = 5(1 + x)
25 = 5 + 5x
5x = 25 - 5
5x = 20
x = 20/5
x = 4 inches
Therefore, the value of x is 4 inches
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