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3 years ago

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Mathematics

1 answer:

allsm [11]3 years ago

4 0

Answer:

Jennifer has 7 quarters

Step-by-step explanation:

<u><em>The correct question is</em></u>

Jennifer has $ 3.51 in change in her piggy bank. The change consists of 51 coins inducing pennies, nickels and quarters. If there are 3 times as many nickels as pennies, how many quarters does she have?

Remember that

$1\ penny=\$0.01\\1\ nickel=\$0.05\\1\ quarter=\$0.25$

Let

x ----> the number of pennies

y ---> the number of nickels

z ---> the number of quarters

we know that

$x+y+z=51$ -----> equation A

$0.01x+0.05y+0.25z=3.51$ ----> equation B

$y=3x$ ---> equation C

substitute equation C in equation A and equation B

$x+3x+z=51$

$4x+z=51$ -----> equation D

$0.01x+0.05(3x)+0.25z=3.51$

$0.16x+0.25z=3.51$ ----> equation E

we have

$4x+z=51$ -----> equation D

$0.16x+0.25z=3.51$ ----> equation E

Solve the system of equations D and E by graphing

Remember that the solution is the intersection point both graphs

The solution is the point (11,7)

x=11,z=7

see the attached figure

Find the value of y

$y=3(11)=33$

The number of pennies is 11

The number of nickels is 33

The number of quarters is 7

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Answer:

n<-27

Step-by-step explanation:

you have to get n by itself, to do this divide -3 from both sides of the equations.

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The quadratic regression equation that best fits the data set is y = 32.86x² - 379.14x + 1369.14

<h3>The data points </h3>

The following table of values represents the data points that would be used to solve this question:

x 3 4 5 6 7 8 9

y 470 416 403 226 314 338 693

Where:

x represents years since 2000
y represents the annual revenue of a manufacturing company in thousand dollars

<h3>The function of the dataset</h3>

The table of values illustrates a quadratic function.

The function would be calculated using a graphing calculator

From the graphing calculator, we have:

a = 32.86; b = -379.14 and c = 1369.14

A quadratic regression equation is represented as:

y = ax² + bx + c

So, we have:

y = 32.86x² - 379.14x + 1369.14

Hence, the quadratic regression equation that best fits the data set is y = 32.86x² - 379.14x + 1369.14

<h3>Why the function type was chosen?</h3>

From the table of values in (a), we can see that as x increases; the value of y decreases and then increases after it reaches a minimum.

This illustrates the behavior of a quadratic regression function

See attachment for the scatter plot

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2 years ago

5. Which polynomial is equal to (x5 + 1) divided by (x + 1)?

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Answer:

B $x^4-x^3+x^2-x+1$

Step-by-step explanation:

Given,

Dividend = $(x^5+1)$

Divisor = $(x+1)$

Step 1: First The dividend is $(x^5+1)$ and Divisor is $(x+1)$ when divided first time the quotient will be $x^4$ and remainder will be $-x^4+1$

Step: 2 Now the new dividend is $-x^4+1$ and Divisor is $(x+1)$ when divided the quotient will be $x^4-x^3$ and remainder will be $x^3+1$

Step: 3 Now the new dividend is $x^3+1$ and Divisor is $(x+1)$ when divided the quotient will be $x^4-x^3+x^2$ and remainder will be $-x^2+1$

Step: 4 Now the new dividend is $-x^2+1$ and Divisor is $(x+1)$ when divided the quotient will be $x^4-x^3+x^2-x$ and remainder will be $x+1$

Step: 5 Now the new dividend is $x+1$ and Divisor is $(x+1)$ when divided the quotient will be $x^4-x^3+x^2-x+1$ and remainder will be 0.

Hence When the polynomial $(x^5+1)$ is divided by $(x+1)$ the answer or quotient will be equal to $x^4-x^3+x^2-x+1$ and remainder will be 0.

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