A rectangle and a square have the same area. a. The width of the rectangle is w inches. The length of the rectangle is 15 inches less than 4 times the width of the rectangle. Write a polynomial to represent the area of the rectangle. b. The side of the square is w inches. Write a polynomial to represent the area of the square. c. Write an equation such that the area of the rectangle is equal to the area of the square. d. Solve the equation in part (c) to find the side length of the square. e. What are the length and the width of the rectangle?

Answers

Answer 1

9514 1404 393

Answer:

  a) w(4w-15)

  b) w²

  c) w(4w -15) = w²

  d) w = 5

  e) 5 by 5

Step-by-step explanation:

a) If w is the width, and the length is 15 less than 4 times the width, then the length is 4w-15. The area is the product of length and width.

  A = w(4w -15)

__

b) If w is the side length, the area of the square is (also) the product of length and width:

  A = w²

__

c) Equating the expressions for area, we have ...

  w(4w -15) = w²

__

d) we can subtract the right side to get ...

  4w² -15w -w² = 0

  3w(w -5) = 0

This has solutions w=0 and w=5. Only the positive solution is sensible in this problem.

The side length of the square is 5 units.

__

e) The rectangle is 5 units wide, and 4(5)-15 = 5 units long.

The rectangle and square have the same width and the same area, so the rectangle must be a square.


Related Questions

I NEED HELP PLEASE NO LINKS OR U WILL GET REPORTED. I WILL GIVE BRAINLY THING, make sure you are correct ​

Answers

Answer:

D

Step-by-step explanation:

French colonies were north of the US. Portugal only owned Brazil, and Germany had no colonies.

5+5(6*7)Easy points cause I love y’all pur

Answers

tysmmm ilyyyyyyyyyyyyyyyy

Shawn bought 3 items at the grocery store that cost $3.35, $6.85, and $2.90. After paying the cashier, Shawn received $2.15 in change.

How much did Shawn give the cashier to pay for his purchase?

Answers

Answer:  Shawn payed the cashier $15.25

Step-by-step explanation:

someone please help me answer this!!

Answers

Answer:

-5 63/100

Step-by-step explanation:

BRAINLIEST AND ACED+ PLEASE HELP ME :c

Answers

Answer:

1 1/2 x 4 1/2 x 5 =  33 3/4

63°
13°
Choose the equation that best describes the image.

Answers

Answer:

13+63 if I'm not wrong......

A color printer prints 8 pages in 5 minutes.
How many minutes does it take per page?

Answers

Answer:

It takes 5/8 minutes or 0.625 minutes to print per page.

Step-by-step explanation:

The find the singular unit value of how long it would take per page you simply divide the amount that you are trying to figure out by the total amount of time you are taking and in this case it would be 5 divided by 8 in order to solve for the amount of minutes it takes per page.


Find how many quarts of 5% butterfat milk and 2% butterfat milk should be mixed to yield 45 quarts of 3% butterfat milk.
The mixture should contain quarts of the 5% butterfat milk.

Answers

Answer:

It would take 4 quarts of 5% buttermilk and 41 quarts of 2% buttermilk to make 45 quarts of 3% buttermilk.

Step-by-step explanation:

Let the number of 5% quarts = x

Let the number of 2% quarts = y

x+y=45

y=45-x

(.05)x+(.02)y=(0.03)45

5x+2y=102

5x+2(45-x)=102

5x+90-2x=102

3x=12

x=4

y=45-x=45-4=41

So it would take 4 quarts of 5% buttermilk and 41 quarts of 2% buttermilk to make 45 quarts of 3% buttermilk.

P+p+p/2+p/4+1=100
Polinomios

Answers

Answer:

=

3

6

Step-by-step explanation:

+

+

2

+

4

+

1

=

1

0

0

{\color{#c92786}{p}}+{\color{#c92786}{p}}+\frac{p}{2}+\frac{p}{4}+1=100

p+p+2p​+4p​+1=100

2

+

2

+

4

+

1

=

1

0

0.         2

+

2

+

4

+

1

=

1

0

0

2p+\frac{p}{2}+\frac{p}{4}+1=100

2p+2p​+4p​+1=100

2

+

2

+

4

+

1

1

=

1

0

0

1.              Subtract the numbers

Subtract the numbers

2

+

2

+

4

=

9

=

3

6

.        

A number between 0 and 1, expressed as one number over another, is called a

Answers

Answer:

its called a frcaction

Step-by-step explanation:

Fraction po

#carryonlearning

Simplify the expression and write your answer as a power
10

Answers

Answer:

10^88

Step-by-step explanation:

You have to multiply the exponents since they are in parenthesis.

Good Luck!

Answer:

The answer is C. 10^88

Step-by-step explanation

Whenever you have an exponent written like this, you must multiply the 8 and 11.  Which will give you 10^88.  I hope this has helped you!   :3    Sorry if it is incorrect.

Find the area of the triangle

Answers

Answer:

[tex] \frac{4 \times 5}{2} = 10[/tex]

Many businesses and organizations insist that official communications use professional-looking fonts, such as Times New Roman. Fonts characterized as less professional, such as Comic Sans, should be avoided. A student would like to determine if font choice makes a difference in the average grade on a typed response in English classes. There are currently four English classes available from which the student can collect data, and each class has a similar writing assignment. That the start of the assignment, students are randomly assigned a font, either times new Roman or comic sans, and then complete the assignment the teachers grade the assignment and the mean grade for each font is found.


What is the response variable in this experiment?

A the font used by each h student
B, the teachers grading the responses
C the grade received on each assignment
D the length of the student response on the assignment

Answers

Answer:

C.

Step-by-step explanation:

The response variable can be defined as those variables that are considered to be the focus of a question in research or experiment. It is also known as a dependent variable and is marked on the y-axis. The response variable is explained with the help of an explanatory variable, marked on the x-axis. The other names for response variables are y-variables or outcome variables.

In the given case, the response variable is the grade received on each assignment. The grades received by students on each assignment are the main focus of this research.

Therefore, option C is correct.

Liam invests $5,000 in an account that pays 2.5% compound interest annually. He uses the expression P(1+r)t to find the total value of the account after t years. What will be the total value of the account after 3 years?

Answers

Answer:

The final balance is $5,389.

The total compound interest is $389.

Step-by-step explanation:

HELP I BEG
Solve the linear equation and explain why it’s either one solution, infinite solution or no solution

2(4+2.5x)+7 = -3(x-5)

Answers

Answer:

infinite solution , b/c when i graphed it , it showed a line that went on & on

Step-by-step explanation:

2(4+2.5x)+7 = -3(x-5)

8+5x+7=-3x+15

15+5x=-3x+15

2x=0

Lauren bought 20 oz of sliced ham. She used 3/4 of the ham to make sandwiches for her friends. She used 1/5 of the ham in an omelet. How many ounces of ham were left?

Answers

Answer:

19 oz

Step-by-step explanation:

Lauren bought 20 ounces of sliced ham, out of which she used three-fourth of the ham to make sandwiches for her friends and one fifth of the ham in an omelette. We are to find the ounces of ham that were left. So, total ounces of ham that were used = 15 + 4 = 19 ounces.

Hope this helped!

a certain vehicle can drive 300miles on a tank of 20 gallons. how far can it drive on 30 gallons?

what is the answer in miles ??

PLEASE HELP ME !!!!

Answers

Answer:

450 miles

Step-by-step explanation:

First you calculate miles per gallon, which you do by dividing 300/20. This gives us 15. So you can go 14 miles on one gallon.

From there you multiply 15 by 30, since you'll be driving 30 miles. This gives us 450 miles.

Step-by-step explanation:

[tex] \frac{300}{x} \times \frac{20}{30} = \frac{20x}{20} \frac{9000}{20} x = 450miles[/tex]

no links plz help
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

the answer is essentially d

How many favorable outcomes will there be for spinning the same color twice?

Answers

Answer:

3 favorable outcomes

There are three paths that end up with spinning the same color twice

Answer:

should be 3

Step-by-step explanation:

Order the numbers from least to greatest.
= –1.5
- (-2)
2.5
8/3

HELPP

Answers

Answer:

-1.5, -(-2), 2.5, 8/3

Step-by-step explanation:

pretty sure this is right

-1.5, -(-2), 2.5, 8/3

Use the graph. How does the diagram show that the slope between any two points on a line is the same? A. It does not show this because the triangles are not the same size. B. The triangles have the same vertical heights and horizontal lengths. C. The distance between A and B is the same as the distance between B and C. D. The triangles are similar so the ratios of their vertical heights to their horizontal lengths are equivalent.

Answers

Answer:

the answer is D The triangles are similar so the ratios of their vertical heights to their horizontal lengths are equivalent.

Step-by-step explanation:

The triangles are similar so the ratios of their vertical heights to their horizontal lengths are equivalent. Therefore, option D is the correct answer.

What is slope of a line?

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

We know that, slope = Rise/Run.

Here, slope of a line AB = 3/6

= 1/2

Now, slope of a line BC = 2/4

= 1/2

Therefore, option D is the correct answer.

To learn more about the slope of a line visit:

https://brainly.com/question/14511992.

#SPJ3

Please please help no scams please ​

Answers

Answer:

between 6 and 7

Step-by-step explanation:

√39 = 6.244... which is between 6 and 7

also, you do not need a calculator if you know that the sq. rt. of 36 is 6 and the sq. rt. of 49 is 7. 39 is between 36 and 49.



5 Bill's trail mix has 6 cups of walnuts
and 10 cups of cranberries. Using
the same recipe, how many cups
of walnuts go with 15 cups of
cranberries?

Answers

Answer:

Umm, I will do my best to comment on this. I feel so bad for all the people that I hit answer and I don´t know it. =( !

Answer:

25.5

Step-by-step explanation:

10÷6=1.7

1.7x15=25.5

2.) What is another way to write 700,562? Select all the ways to write this number, A) (7 +100,000) + (5+ 1,000) + (6 +10) + (2 +1) B) seven hundred thousand, five hundred sixty-two C) 700,000 +500 + 60 + 2 D) 7 hundred thousands +5 hundreds +62 tens. E) 7 hundred thousands +5 thousands + 6 tens + 2 ones​

Answers

Answer:

b,c

Step-by-step explanation:

b is written  in the written form properly and  is is extended using the right place values

Need help asap 10 points, provide explanation please.

Answers

Answer:

Step-by-step explanation:

Use the distance formula between points to find all sides:

[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]

AB=[tex]\sqrt{13}[/tex]

BC=[tex]\sqrt{13}[/tex]

CA=[tex]\sqrt{26}[/tex]

This is a 45° 45° 90° triangle, where two of the sides are equal and the other side is the first two sides times [tex]\sqrt{2}[/tex], so yes, it is a right triangle.

Answer:

Answer D is correct.

Step-by-step explanation:

By inspection, the side lengths are {3, 4, 5}, and this triplet satisfies the Pythagorean Theorem:  3^2 + 4^2 = 5^2.  Thus this IS a right triangle.  

One could also find the lengths of the three sides using the distance formula and the endpoints of each line segment forming the triangle.

Answer D is correct.

Find the circumference of the circle P. Find the length of arc AB.

Answers

Answer:

A) 56.549

B) 9.425

Step-by-step explanation:

2(pi)r=56.54867

60/360x56.54867=9.425

1.Write the expression in expanded form. The subscript number can be write in
normal form. E.g. X1 + X1Y1, do not forget the correct parenthesis and the correct
order. *



2.For the equation in above evaluate the notation using the values below. Please
enter the exact value.
X1 =0
Y1 = 5
Z1 = 0
X2 = 1
Y2 = 26
Z2 = -2
X3 = 12
Y3 = -2
Z3 = 3
X4 = -1
Y4 = 25
Z4 = 24​

Answers

Answer:

(a) Expanded form:

[tex]((X_1 + X_1Y_1) - X_1Z_1) + ((X_2 + X_2Y_2) - X_2Z_2) + ((X_3 + X_3Y_3) - X_3Z_3) + ((X_4 + X_4Y_4) - X_4Z_4)[/tex]

(b) The value of the expression: -21

Step-by-step explanation:

Given

[tex]\sum \limit^4_{i=1}\ ((X_i+X_iY_i) - X_iZ_i)[/tex]

Solving (a): The expanded form:

This means that we substitute the values of i from 1 to 4 in the above expression.

So, the expression becomes:

[tex]((X_1 + X_1Y_1) - X_1Z_1) + ((X_2 + X_2Y_2) - X_2Z_2) + ((X_3 + X_3Y_3) - X_3Z_3) + ((X_4 + X_4Y_4) - X_4Z_4)[/tex]

Solving (b): The value of the expression

To do this, we simply substitute the given values of X1, X2....... in the expression.

This gives:

So, the expression becomes:

[tex]((0 + 0*5) - 0*0) + ((1 + 1*26) - 1*-2) + ((12 + 12*-2) - 12*3) + ((-1 + -1*25) - -1*24)[/tex]

Simplify each bracket

[tex]((0 + 0) - 0) + ((1 + 26) +2) + ((12 -24) - 36) + ((-1 -25) +24)[/tex]

[tex]0 + 29 -48 -2[/tex]

[tex]-21[/tex]

Hence, the result of the expression is -21

Plzz help will mark brainleast

Answers

The last one, it will be easier for more readers that way. Plus the message should get to as many people.

Solve each equation 24 = 5k - 8k

Answers

Answer:

k = -8

Step-by-step explanation:

24 = 5k - 8k

24 = -3k

k = 24/(-3)

k = -8

Answer:

k = -8

Step-by-step explanation:

Solve for k

First we re arrange our equation so that it look simple to calculate.

24=5k-8k

5k-8k = 24

-3k = 24

Divide -3 both side to get the value of k

 k = -8

To prove substitute k into formula:

5k-8k = 24

5 (-8) - 8 (-8) = 24

-40 + 64 = 24

24 = 24

expand the square of a binomial (y^7-11)^2​

Answers

Answer:

[tex]y^{14} -22y^7+121[/tex]

Step-by-step explanation:

This equation should help:

[tex](a+b)^2=a^2+2ab+b^2[/tex]

[tex](y^{7}-11)^2\\\\=y^{14} +2*y^7*-11+11^2\\\\=y^{14} -22y^7+121[/tex]

Answer:

[tex] {y}^{14} - 22 {y}^{7} + 121[/tex]

Step-by-step explanation:

[tex](y {}^{7 } - 11)( {y}^{7} - 11)[/tex]

First terms,

[tex]{y}^{14} [/tex]

Outer,

[tex] {y}^{7} \times - 11 = - 11 {y}^{7} [/tex]

Inner,

[tex] {y}^{7} \times - 11 = - 11 {y}^{7} [/tex]

Last,

[tex] - 11 \times - 11 = 121[/tex]

Add all terms up

[tex] {y}^{14} - 22 {y}^{7} + 121[/tex]

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