Optiοn B. is cοrrect, the result οf substituting fοr y in the given equatiοns is x - 3 =x² + 2x - 4.
What is the equivalent expression?Equivalent expressiοns are expressiοns that wοrk the same even thοugh they lοοk different. If twο algebraic expressiοns are equivalent, then the twο expressiοns have the same value when we plug in the same value fοr the variable.
Tο substitute fοr y in the secοnd equatiοn, we can replace y with its equivalent expressiοn in terms οf x frοm the first equatiοn, which gives us:
x - 3 = x² + 2x - 4
This is option B.
Optiοn A is incοrrect because it substitutes y fοr its expressiοn in terms οf x in the wrοng equatiοn.
Optiοn C is incοrrect because it subtracts (x-3) instead οf adding it tο the secοnd equatiοn.
Optiοn D is incοrrect because it sets the expressiοn fοr y in the first equatiοn equal tο x² instead οf the expressiοn fοr y in the secοnd equatiοn.
Hence, οptiοn B. is cοrrect, the result οf substituting fοr y in the given equatiοns is x - 3 = x² + 2x - 4.
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Complete question:
What is result of substituting for y in the bottom equation?
y = x – 3,
y = x² + 2x – 4
A. y=(x-3)²+2(x-3)-4
B. x-3=x²+2x-4
C. y=x²+2x-4-(x-3)
D. (x-3)=x²
Which of the following values are solutions to the inequality 2 < 8 + 5 x ? 6, 0, or -8
Answer:
x > -6/5
Step-by-step explanation:
2 < 8 + 5x
-6 < 5x
x > -6/5
This is the correct answer, but I don't see it in the options list.
The sum of a number x and twice another is 20. If the product of these numbers is not more than 48 what are the possible values of x
The possible value of x that is here, a are 8 and 12, when the sum of two number and product is given.
A system of equations is what?A group of two or more equations that must be solved all at once is known as a system of equations. The values of the variables in a system of equations that make all of the equations in the system true are known as the solutions. Several approaches, including substitution, elimination, and graphing, can be used to solve systems of equations. Several branches of mathematics, science, and engineering employ systems of equations to represent and solve issues that arise in the real world.
Let us suppose the two numbers = a and b.
Thus, from the given statement we have:
a + 2b = 20 (Equation 1)
and
ab ≤ 48 (Equation 2)
Using equation 1:
a = 20 - 2b
Substituting this expression for "a" into Equation 2, we get:
(20 - 2b)(b) ≤ 48
-2b² + 20b - 48 ≤ 0
b² - 10b + 24 ≥ 0
This inequality can be factored as:
(b - 4)(b - 6) ≥ 0
Since we want the product of the two numbers to be less than or equal to 48, both "a" and "b" must be positive.
We only need to consider the values of "b" that make this inequality true:
b ≤ 4 or b ≥ 6
Plug each of these values of "b" back into Equation 1:
When b = 4, we get:
a + 2(4) = 20
a = 12
When b = 6, we get:
a + 2(6) = 20
a = 8
Therefore, the possible values of "a" are 8 and 12.
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A contractor needs to buy nails to build a house. The nails come in small boxes and large boxes. Each small box has 100 nails and each large box has 450 nails. The contractor bought 3 more small boxes than large boxes, which all together had 2500 nails. Determine the number of small boxes purchased and the number of large boxes purchased. PLEASE HELP!!
Answer: Let's call the number of large boxes purchased "L" and the number of small boxes purchased "S".
From the problem, we know that:
Each small box has 100 nails, so the total number of nails from the small boxes is 100S.
Each large box has 450 nails, so the total number of nails from the large boxes is 450L.
The contractor bought 3 more small boxes than large boxes, so S = L + 3.
The total number of nails purchased is 2500, so 100S + 450L = 2500.
We can use the second equation to solve for one of the variables in terms of the other. For example, we can solve for L:
100S + 450L = 2500
Substituting S = L + 3:
100(L + 3) + 450L = 2500
Expanding the parentheses:
100L + 300 + 450L = 2500
Combining like terms:
550L + 300 = 2500
Subtracting 300 from both sides:
550L = 2200
Dividing both sides by 550:
L = 4
So the contractor purchased 4 large boxes of nails.
We can use the equation S = L + 3 to find the number of small boxes purchased:
S = L + 3 = 4 + 3 = 7
So the contractor purchased 7 small boxes of nails.
Therefore, the contractor purchased 4 large boxes and 7 small boxes of nails.
Step-by-step explanation:
A clothing designer is interested in determining if there is a relationship between a person’s age and their preference for a particular style of dress. A survey is written and asks questions including questions about age and dress size. Should these questions be included in the survey?
A. The questions are acceptable because the researcher is studying the relationship between age and preferred dress style.
B. The questions should not be included because people may not want to answer questions about age and dress size.
C. The questions can be included but there should be an option where the participant can choose not to respond to the questions.
D. The questions should not be included because surveys should never ask for personal information.
Option (a) is correct i.e., the questions are acceptable because the researcher is studying the relationship between age and preferred dress style.
What is the age in math?Age is any person time he live till time calculated. Use age we solve different math problems.
Like calculate the age of a person or what was his age 5 year ago.
If the age is given in the form of a ratio, for example, a:g, then the age shall be considered as g h and a h. If you are assuming the current age to be h, then n times the current age will be (h × n) years. If you are assuming the current age to be h, then 1/n of the age shall be equal to ( h / n) years.
Option (a) is correct i.e., the questions are acceptable because the researcher is studying the relationship between age and preferred dress style.
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The researcher is investigating the association between age and favourite dress style, thus the questions are appropriate. The assertion is true.
What exactly is my age?Days are calculated as the difference between both the current day and the person's birth day. Age is calculated as follows: aged = (years x 365) + (months x 31) + days. The person's age is expressed in days. For the age in years, divide the figure by 365.
How do you determine age manually?Age is determined by comparing a person's birthdate to the day on which age must be determined. The age of a person is determined by subtracting the provided date from the individual's birthdate. Provided date minus birthdate equals age of a person.
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3. True or False: The percentage distribution cannot be constructed from the frequency distribution directly. 7. True or False: The coefficient of variation is a measure of relative variation. 9. True or False: The number of males selected in a sample of 5 students taken without replacement from a class of 9 females and 18 males has a hypergeometric distribution.
the sample is drawn without replacement from a class of 9 females and 18 males, so the number of males selected follows a hypergeometric distribution.
3. False: The percentage distribution can be constructed from the frequency distribution directly. A frequency distribution is a summary of the number of times each score occurs in a set of data. It shows the distribution of scores into classes or groups of equal size. It is useful in understanding the pattern of data. A percentage distribution is a distribution of data as a percentage of the total data. This distribution is constructed by dividing the frequency of each class by the total frequency and multiplying by 100.7. True: The coefficient of variation is a measure of relative variation. The coefficient of variation is a ratio of the standard deviation to the mean of the distribution expressed as a percentage. It is used to compare the variability of two or more sets of data with different means. The formula for coefficient of variation is given as CV= (standard deviation/mean) *100.9. True: The number of males selected in a sample of 5 students taken without replacement from a class of 9 females and 18 males has a hypergeometric distribution. A hypergeometric distribution is a probability distribution used to calculate the probability of obtaining a specific number of successes in a fixed number of draws from a finite population. It is used to find the probability of obtaining a certain number of successes in a sample without replacement from a finite population with a specified number of successes and failures. In this case, the sample is drawn without replacement from a class of 9 females and 18 males, so the number of males selected follows a hypergeometric distribution.
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Ramundo had some money in his pocket to take to the mall with his friends. His mom gave him an extra $10. He now has no more
than $40 in his pocket.
8) Select the inequality that represents the possible amount of money Ramundo originally had in his pocket.
a) − 10 ≥ 40
b) − 40 ≥ 10
c) + 10 ≤ 40
d) + 40 ≤ 10
I need help with the back of the geometric mean maze :(
In the back of the maze, you will see two numbers at the start and end points of the maze. Let's call these numbers a and b.
To solve the maze, we need to find the geometric mean of a and b, which is the value that, when multiplied by itself, gives us the product of a and b.
The formula for the geometric mean is:
Geometric Mean = √(a × b)
So, to solve the maze, we need to find the geometric mean of the starting and ending numbers, and then follow the path in the maze that matches that value. This path will lead us to the end of the maze.
Once we find the geometric mean of the starting and ending numbers, we can use a calculator or mental math to simplify the expression and find the value.
I need help with the back of the geometric mean maze
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2b+8-5b+3=-13+8b-5 solve the equation
Answer:
b ≈ 2.636.
Step-by-step explanation:
First, we can simplify both sides of the equation by combining like terms:
2b + 8 - 5b + 3 = -13 + 8b - 5
-3b + 11 = 8b - 18
Next, we can isolate the variable term on one side of the equation by adding 3b to both sides:
-3b + 3b + 11 = 8b - 18 + 3b
11 = 11b - 18
Then, we can isolate the variable term again by adding 18 to both sides:
11 + 18 = 11b - 18 + 18
29 = 11b
Finally, we can solve for b by dividing both sides by 11:
29/11 = b
b ≈ 2.636
Therefore, the solution to the equation is b ≈ 2.636.
Answer:
b = 29/11
Step-by-step explanation:
2b + 8 - 5b + 3 = -13 + 8b - 5
-3b + 11 = -18 + 8b
-11b + 11 = -18
-11b = -29
b = 29/11
Multiply. State any restrictions on the variable. (x^(2)+5x-36)/(x^(2)+4x-32)*(4x+32)/(x+6)
When simplified, the above expression translates to = 4(x + 9) / (x + 6) where the restrictions are stated as: x ≠ -8, 4, -6.
What is a restriction in math?In mathematics, restrictions refer to conditions or limitations placed on the values that a variable can take, either to ensure the validity of a mathematical expression or to satisfy a particular requirement.
With regard to the above,
We can simplify the given expression as follows:
(x^2 + 5x - 36) / (x^2 + 4x - 32) * (4x + 32) / (x + 6)
= [(x + 9)(x - 4) / (x + 8)(x - 4)] * [4(x + 8) / (x + 6)]
= (x + 9) * 4 / (x + 6)
= 4(x + 9) / (x + 6)
The restrictions on the variable are:
x cannot be equal to -8 or 4, since these values would make the denominator of the first fraction equal to zero.x cannot be equal to -6, since this value would make the denominator of the second fraction equal to zero.Learn more about restriction in math:
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A basketball team has II players, 5 of whom are in the starting line up. How many different starting line ups are possible if the star be in the time line up?
After answering the presented question, we can conclude that If the star equation player is in the starting lineup, there are 210 distinct starting lineups imaginable.
What is equation?In mathematics, an equation is a proposition that states the equivalence of two expressions. An equation consists of two sides separated by a system of equations (=). For instance, the statement "2x + 3 = 9" states that the word "2x Plus 3" equals the integer "9". The goal of solving equations is to find the value or amounts of the variable in the model) that will permit the calculation to be accurate. Mathematics can be simple or complex, linear or nonlinear, and contain one or more parts. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the power of 2. Lines are used in many areas of mathematics, including algebra, arithmetic, and geometry.
If the starting lineup includes the star player, there are only four spaces left to fill with the remaining ten players. The number of possible starting lineups is the number of ways to select four players from the remaining ten, which may be calculated using the combination formula:
C(10,4) = 10! / (4! * 6!) = 210
If the star player is in the starting lineup, there are 210 distinct starting lineups imaginable.
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Colette is using homegrown cucumbers to make pickles. The number of pickles she can make is determined by how many cucumbers she has on hand. p = the number of pickles Colette can make c = the number of cucumbers Colette has Which of the variables is independent and which is dependent?
The number of pickles (p) is the dependent variable, while the number of cucumbers (c) is the independent variable.
What is the dependent variable?The dependent variable is the variable that is being measured or observed and is affected by the independent variable. The independent variable is the variable that is being manipulated or changed by the researcher to determine its effect on the dependent variable.
In this scenario, the number of pickles Colette can make depends on the number of cucumbers she has. Therefore, the number of pickles (p) is the dependent variable, while the number of cucumbers (c) is the independent variable.
The independent variable is the one that can be freely chosen or manipulated, and which affects the dependent variable. In this case, Colette has control over how many cucumbers she grows, and the number of pickles she can make is affected by the number of cucumbers she has. Therefore, the number of cucumbers is the independent variable, and the number of pickles is the dependent variable.
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Solve the compound inequality
-2<-x ≤3
Answer:2>x[tex]\geq[/tex]-3
Step-by-step explanation:
when we divide each side with a negative number "<" turns into ">",">" turns into "<" and so on.
we can divide each side with -1, the we get,
2>x[tex]\geq[/tex]-3
[tex]-2 < -x \leq 3 \iff 2 > x \geq -3[/tex]
[tex]-3 \leq x < 2 \implies x \in [-3;2)[/tex]
HELP WOULD BE APPRECIATED
Answer:
Below
Step-by-step explanation:
Domain 'x' can be any value except 10 <====which would make the denominator = 0 which is not allowed
(-∞, 10 ) U (10 , +∞)
Range : horizontal asymptote the degree of the numerator and the denominator is the same : 1 so the horizontal asymptote will be
3 / -1 = -3 ( The coefficients of 'x' in the num and den)
the vertical asymptote occurs at x = 10 ...then the value of y goes to + inf
so range is ( -3, +∞)
Inverse Does exist , switch x's and y's in the original equation
x = (3y+1) / (10-y) now solve for y
and you will get f^-1 (x) = (10x-4) / (x+3)
Here is graph of f(x) , f^-1(x) and x=y :
y=tanx,thendy/dx is equal to what
The derivative of y = tan(x) is sec²(x).
What is Trigonometric Functions?
Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.
y=tanx
dy/dx = dy/dx = cos x.cos x - sin x(-sin x) / cos² x
⇒ dy/dx = (cos² x + sin² x) / cos² x
⇒ dy/dx = 1 / cos²x
⇒ dy/dx = sec²(x)
Thus, the derivative of y = tan(x) is sec²(x).
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ayuda porfa está demasiado difícil:'(
The number of weeks until Riley and Amari would have earned the same, would be 10 weeks.
How to find the number of weeks ?Variables:
Let x be the number of weeks they work.
Let y be their total earnings in dollars.
System of equations:
For Riley: y = 5x
For Amari: y = 20 + 3x
Setting the two expressions for y equal to each other, we get:
5x = 20 + 3x
5x - 3 x = 20
x = 20 / 2
x = 10 weeks
Therefore, their earnings will be the same after 10 weeks of work.
We can also solve the system of equations graphically by plotting the two equations and finding the point of intersection. The point of intersection is (10,50). Therefore, their earnings will be the same after 10 weeks of work and their total earnings will be $50.
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The question, when translated to English is:
Riley and Amari earn weekly chore allowances for the summer, Riley is paid $5 a week and Amari is paid $20 at the beginning of the summer and then earns $3 a week.
When will their earnings be the same?
What is the amount?Define your variables.Write a system of equationsUse at least two different methods to solve the system.
In ΔLMN, m = 5. 9 cm, n = 8. 7 cm and ∠L=163°. Find the length of l, to the nearest 10th of a centimeter
Using the Law of Cosines the length of l, to the nearest 10th of a centimeter is 4.6 cm.
To find the length of side l in triangle LMN, we can use the Law of Cosines, which states that c² = a² + b² - 2ab cos(C), where c is the side opposite the angle C.
In this case, we have:
a = 5.9 cm
b = 8.7 cm
C = 163°
First, we need to convert the angle from degrees to radians by multiplying it by π/180:
C = 163° × π/180 = 2.847 radians
Now we can plug in the values into the Law of Cosines:
l² = 5.9² + 8.7² - 2(5.9)(8.7)cos(2.847)
Simplifying the right-hand side:
l² = 68.81 - 60.83 × cos(2.847)
Taking the square root of both sides:
l ≈ 4.6 cm
Therefore, the length of l to the nearest 10th of a centimeter is 4.6 cm.
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parallelogram has a height of 7 inches and a base length of 5 inches. What is the area of the parallelogram?
Answer:
7 times 5 = 35
Step-by-step explanation:
7 less Than the quotient of six and b algebraic expression
Answer:
6 / b - 7
Step-by-step explanation:
A student project involved collecting data to see if there was a difference in the amount of time one had to wait at the drive-thru between two fast food restaurants, A and B. She randomly selected 17 cars at fast food restaurant A and 17 cars at fast food restaurant B. For each car chosen, she recorded how much time passed from the placement of the order to receiving their food at the pick-up window. The data is given in the table below.
Fast Food A Fast Food B
163.3 71
186.8 126.5
140.7 140.7
120.1 148
124.1 163.2
182.7 168.1
193 173.8
91.8 177.1
156.1 204.9
73.6 221.3
94.4 225
175 230
111.7 297.3
77.6 305.2
129.1 313.8
134.7 345.2
139 288.4
(b) Test the statistical hypotheses in (a) by carrying out the appropriate statistical test. Find the value of the test statistic for this test, use two decimals in your answer.
Test Statistic =
(c) Determine the P-value for this test, to three decimal places.
P=
(d) Based on the above calculations, we should ? reject OR not reject the null hypothesis? Use α=0.05
The reject the null hypothesis with α=0.05.
Based on the above calculations, we should reject the null hypothesis with α=0.05.
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Please help (Look at image) QUICKLY
Answer:
See below.
Step-by-step explanation:
We are asked to identify the Proof for Statement 7.
To start, we already have 2 sides and 1 angle proven, meaning that we can prove ΔABX ≅ ΔABY by the Side-Angle-Side Triangle Congruency Theorem. (SAS).
Because both Triangles are congruent, every side, and angle of the triangles are congruent. ASA, and SAS are incorrect choices, they're only used to prove that 2 triangles are congruent. HL is incorrect as well, the HL (Hypotenuse - Leg Theorem) is only used to prove that 2 triangles are congruent also. Our only option is CPCTC (Corresponding parts of congruent triangles are congruent); Meaning that every angle and every side of the 2 triangles are congruent.
For Statement 7, AX ≅ AY proved by CPCTC.
5. Claude is wrapping cylindrical bug spray containers in tissue paper to put them inside a box.
Each container has a height of 12. 7 centimeters and a radius of 3 centimeters.
If he is wrapping a total of 5 bug spray containers, how many square
centimeters of tissue paper will he need?
Claude will need approximately 1202.3 square centimeters of tissue paper for wrapping a total of 5 bug spray containers.
To calculate the amount of tissue paper needed, we need to find the lateral surface area of one cylinder and then multiply it by the number of cylinders being wrapped.
The lateral surface area of a cylinder can be found using the formula 2πrh, where r is the radius and h is the height of the cylinder. In this case, r = 3 cm and h = 12.7 cm.
Lateral surface area of one cylinder = 2π(3 cm)(12.7 cm) = 239.38 cm² (rounded to two decimal places)
Since Claude is wrapping 5 bug spray containers, we need to multiply the lateral surface area of one cylinder by 5:
Total tissue paper needed = 5 × 239.38 cm² = 1196.9 cm²Therefore, Claude will need approximately 1202.3 square centimeters of tissue paper.
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Suppose that 1000 customers are surveyed and 850 are satisfied or very satisfied with a corporation's products and services. Test the hypothesis Upper H Subscript 0 Baseline colon p equals 0. 9 against Upper H Subscript 1 Baseline colon p not-equals 0. 9at. Find the P-value
The p-value is 0.1138 for the given hypothesis.
What exactly is a p-value?
A p-value, or probability value, is a statistical measure that helps to determine the strength of evidence against a null hypothesis in a hypothesis test. In hypothesis testing, a null hypothesis is a statement or assumption about a population parameter that we want to test using sample data. The p-value is the probability of obtaining a test statistic as extreme as, or more extreme than, the observed test statistic, assuming the null hypothesis is true.
Now,
To test the hypothesis,
we need to perform a hypothesis test using a significance level (α) to determine whether the sample proportion of satisfied customers is significantly different from 0.9.
The null hypothesis (H0) is that the true proportion of satisfied customers is equal to 0.9. The alternative hypothesis (H1) is that the true proportion is not equal to 0.9.
We can use the normal approximation to the binomial distribution to test this hypothesis, since the sample size is large (n = 1000) and both np and n(1-p) are greater than or equal to 10, where p is the true proportion of satisfied customers.
The test statistic is given by:
z = (P - p0) / √(p0(1 - p0) / n)
where p0 is the proportion (0.9), P is the sample proportion (850/1000 = 0.85), and n is the sample size.
Plugging in the values, we get:
z = (0.85 - 0.9) / √(0.9 * 0.1 / 1000) = -1.5811
The P-value is the probability of getting a test statistic as extreme as -1.5811 or more extreme, assuming the null hypothesis is true. Since this is a two-tailed test (H1: p ≠ 0.9), we need to find the area in both tails of the standard normal distribution.
Using a standard normal distribution table, we find that the area to the left of -1.5811 is 0.0569, and the area to the right of 1.5811 is also 0.0569. Therefore, the total area in both tails is:
p-value = 0.0569 + 0.0569 = 0.1138
So,
the p-value is 0.1138.
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Give 5 reasons why someone would believe in God.
pls answer this
The numinous
Answered Prayers
They are taught about the faith
Through their own experience
The teachings from the Bible
Answer:
Nobody ever said having faith would be easy, but it will be worth it and here is why.
He knows better than we do. God knows everything we are going through at this very moment and everything we will go through in the future. ...
All Things Are Possible With God.
He Is Worthy Of Our Trust.
He Knows What He Is Doing.
He is the creator of the universe
he exited before the heavens and earth
He is our father and the father of our ancestors
He has performed many miracles
He is the God who answers all prayers if you believe.
He is the one who stands by you in any situation, in good times and bad
He is a merciful, understandable and dependable God
What he says he'll do, that is what he'll do
Find the surface area , curved surface area and volume of cylinder with radius 14cm
and height 25cm?
STEP BY STEP PLEASE!!!!!
The surface area of the cylinder is 3,428 square centimeter, the curved surface area of the cylinder is 2,198 square centimeter and the volume of the cylinder is 15,386 cubic centimeter.
What is area and volume?
A flat, two-dimensional object's area is the space it takes up in a plane. A three-dimensional object's volume is the area it takes up in space.
We know that
Curved surface area = 2πrh
So, using this we get
⇒Curved surface area = 2 × 3.14 × 14 ×25
⇒Curved surface area = 2,198 square centimeter
Similarly,
Total surface area = 2πr (r + h)
So, using this we get
⇒Total surface area = 2 × 3.14 × 14 (14 + 25)
⇒Total surface area = 2 × 3.14 × 14 (39)
⇒Total surface area = 3,428 square centimeter
Similarly,
Volume = π[tex]r^{2} h[/tex]
So, using this we get
⇒Volume = 3.14 × [tex]14^{2}[/tex] × 25
⇒Volume = 15,386 cubic centimeter
Hence, the area and volume of the cylinder have been obtained.
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If f(x)f(x) is an exponential function where f(4.5)=16f(4.5)=16 and f(9.5)=60f(9.5)=60, then find the value of f(15)f(15), .
The value of f(15) is approximately 346.42.
What is an exponential function?An exponential function is a mathematical function of the form f(x) = abˣ, where a and b are constant and b is greater than zero and not equal to 1. An example is f(x) = 2ˣ
We can use the properties of exponential functions to find the value of f(15). Since f(x) is an exponential function, we can write it in the form:
f(x) = a × bˣ
f(4.5) = 16 = a × b⁴.5
f(9.5) = 60 = a × b⁹.5
Dividing second equation by first equation gives:
f(9.5)/f(4.5) = (a × b⁹.5)/(a × b⁴.5) = b⁵
Substituting the given values, we get:
60/16 = b⁵
b = (60/16)¹/⁵
b ≈ 1.46
Substituting b into the first equation gives:
16 = a × 1.46⁴.5
a ≈ 0.30
Therefore, the exponential function is:
f(x) = 0.30 × 1.46ˣ
To find f(15), we can substitute x = 15 into the function:
f(15) = 0.30 × 1.46¹⁵
f(15) ≈ 346.42
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Question 9, please help
9/10
Answer:A
Step-by-step explanation:
can someone please help me answer these questions and show me how you got the answer. thank you!
1.) write an equation for a line perpendicular to y=2x+3 and passing through the point (4-6)
2.) (11-3i)(7-12i)
3.) (185-72i) divided by (11+10i)
4.) solve the equation by completing the square: y^2-6y+19=5
1) y + (1/2)x = 2
2)-59 - 153i
3)1315 - 62i
4)No real solutions
1) Equation for a line perpendicular to y=2x+3 and passing through the point (4-6)A line perpendicular to y = 2x + 3 would have a slope of -1/2 (the negative reciprocal of 2). To find the equation of the line, we use point-slope form. We substitute the point (4, -6) and the slope of -1/2:We know that the line must pass through the point (4, -6) and be perpendicular to the line y = 2x + 3, so we can write its equation in point-slope form as follows:y - (-6) = (-1/2)(x - 4)y + 6 = (-1/2)x + 2The answer is y + (1/2)x = 2.
2) Multiplying the complex numbers (11-3i)(7-12i)We will be using the FOIL method (first, outer, inner, last) for multiplying two binomials:First, we multiply 11 and 7 to get 77.Then, we multiply 11 and -12i to get -132i.Next, we multiply -3i and 7 to get -21i.Last, we multiply -3i and -12i to get 36i² (remembering that i² is equal to -1).Finally, we combine like terms:77 - 132i - 21i + 36i² = 77 - 153i - 36 = -59 - 153iThe answer is -59 - 153i.
3) Dividing complex numbers (185-72i) divided by (11+10i)To divide complex numbers, we need to multiply the numerator and denominator by the conjugate of the denominator (in which the sign of the imaginary part is changed):We multiply the numerator and denominator by the conjugate of 11 + 10i, which is 11 - 10i in this case, to eliminate the imaginary part from the denominator:(185 - 72i)(11 - 10i) = (185 × 11 - 72i × 11) - (185 × 10i + 72i × 10i) = (2035 - 792i) - (1850i + 720i²)Simplifying, we get:(2035 - 792i) - (1850i + 720i²) = (2035 - 792i) - (1850i + 720(-1)) = (2035 - 792i) - (1850i - 720) = 1315 - 62iThe answer is 1315 - 62i.
4) Solving an equation by completing the square: y² - 6y + 19 = 5First, we isolate the y terms and move the constant to the other side:y² - 6y + 14 = 0Next, we divide both sides by the leading coefficient (1 in this case):y² - 6y = -14To complete the square, we take half the coefficient of y, square it, and add it to both sides. In this case, that's (-6/2)² = 9:y² - 6y + 9 = -5Now, we factor the left-hand side as a perfect square:(y - 3)² = -5Finally, we take the square root of both sides:(y - 3) = ±√(-5)This expression has no real solutions because the square root of a negative number is imaginary. Therefore, the answer is "No real solutions."
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Line Equations from Poin (t)/(S)lope (Point Slope Form ) Feb 27, 3:59:34 PM Watch help video Use point-slope form to write the equation of a line that passes through the point (18,-17) with slope -(1)/(4). Answer: Submit Answer
x + 4y = -52.
The point-slope form of the equation of a line passing through the point (x1, y1) with slope m is:y - y1 = m(x - x1)Here, the point (x1, y1) = (18, -17) and the slope m = -1/4Therefore, the equation of the line in point-slope form is:y + 17 = (-1/4)(x - 18)Expanding the equation:4(y + 17) = -x + 18 => 4y + 70 = -x + 18 => x + 4y = -52The required equation of the line is x + 4y = -52.
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Elliot a mangé les 2 tiers de la pizza , et sa soeur Eve a mangé 1 cinquième de la pizza .
En reste t'il pour leur frère Tom ?
A mathematics teacher wanted to see the correlation between test scores and homework. The homework grade (x) and test grade (y) are given in the accompanying table. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. Using this equation, find the projected test grade, to the nearest integer, for a student with a homework grade of 45.
Homework Grade (x) Test Grade (y)
78
78
66
66
89
89
76
76
54
54
42
42
86
86
90
90
74
74
68
68
73
73
73
73
86
86
84
84
63
63
54
54
64
64
54
54
Answer:
First, we need to find the slope and y-intercept of the linear regression line:
Using a calculator or statistical software, we get:
Slope (b) = 0.621
Y-intercept (a) = 50.4
Therefore, the linear regression equation is:
y = 0.6x + 50.4
To find the projected test grade for a student with a homework grade of 45, we substitute x = 45 into the equation:
y = 0.6(45) + 50.4
y = 27 + 50.4
y = 77.4
Rounding to the nearest integer, the projected test grade for a student with a homework grade of 45 is 77.