A school gym has an area of 4,641 square feet and a perimeter of 284 feet. What are the dimensions of the gym?

Answers

Answer 1

Answer:

dimensions are 51x91

Step-by-step explanation:

Assuming that the gym is rectangular in shape, then...

l*w=4641

and 2l+2w=284

We have two variables and two equations so to solve this we plug one equation into another.

Solve for one variable:

l*w=4641

w=4641/l

Plug into the other equation...

2l+2(4641/l)=284

Solve

l*(2l+9282/l)=284

2l^2+9282=284l

2l^2-284l+9282=0

Factor the trinomial:

2(l−51)(l−91)=0

l−51=0 or l−91=0(Set factors equal to 0)

l=51 or l=91

now, lets plug it into one of the equations to find w

51*w=4641

w=91, l=51

or...

91*w=4641

w=51, l=91

Answer 2

Answer:

91 ft × 51 ft

Step-by-step explanation:

while the other answer is basically correct, it makes a to at the beginning of the calculation (but the continues correctly).

and it assumes you can find the right factoring of the expression.

so, I will show you here how to generally solve this, even if you cannot find the right factorization :

l×w = 4,641 ft²

w = 4641/l

2l + 2w = 284

2l + 2(4641/l) = 284

2l + 9282/l = 284

2l² + 9282 = 284l

2l² - 284l + 9282 = 0

to make things easier let's divide everything by 2

l² - 142l + 4641 = 0

the general solution to a squared equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = l

a = 1

b = -142

c = 4641

l = (142 ± sqrt((-142)² - 4×1×4641))/(2×1) =

= (142 ± sqrt(20,164 - 18,564))/2 =

= (142 ± sqrt(1600))/2 = (142 ± 40)/2 = 71 ± 20

l1 = 71 + 20 = 91

l2 = 71 - 20 = 51

w1 = 4641/91 = 51

w2 = 4641/51 = 91

so, they are interchangeable (it does not matter which we call length and which width).

the dimensions are 91 ft × 51 ft


Related Questions

The surface of an office desk has a perimeter of 20 feet and an area of 21 square feet. what are the dimensions of the desk?

Answers

Answer:

3 feet by 7 feet

Step-by-step explanation:

perimeter = 20 feet

area = 21 feet²

If the desk is a rectangle:

perimeter = 2l + 2w = 2 (l+w) = 20

                                    2 (l+w) = 20 , divide both sides by 2

                                          l+w = 10

area = l · w = 21

What numbers we know that have sum as 10 and their product as 21?

l + w = 10

l · w = 21

factors of 21 are 1,3,7

3+7 = 10

3 ·7 = 21

The dimensions of the desk could be 3 feet by 7 feet.

Line n goes through points A and B. What is the slope of line n?
Point A;(4,7)
Point B:(18,17)

Answers

Answer:

The slope is 5/7.

Step-by-step explanation:

Use a slope formula.

Slope:

[tex]\sf{\dfrac{y_2-y_1}{x_2-x_1} }[/tex]

y₂ = (17)

y₁ = (7)

x₂ = (18)

x₁ = (4)

Rewrite the problem down.

[tex]\sf{\dfrac{17-7}{18-4}=\dfrac{10}{14}={\dfrac{10\div2}{14\div2}=\boxed{\sf{\dfrac{5}{7}}}[/tex]

Therefore, the slope is 5/7.

I hope this helps! Let me know if my answer is wrong or not.

Answer:

5/7

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(17-7)/(18-4)

m=10/14

simplify

m=5/7

help me quickly
102% of 120=

Answers

102 is what percent of 120? = 85.

Answer:

122.4

Step-by-step explanation:

this is easy, all we need to do is multiply 120 by 1.02, since it is 2%, and it is increasing not decreasing. when we do that, we get 122.4. to check, you can also do .02x120, to get 2.4. please mark as brainlest.

answer fast its a test q.
based on the statement is true?

Answers

Answer:

the right answer is F (exterior angle of triangle is equal to its sum of opposite interior angle of a traingle)

Answer: W = 40 degrees.

Step-by-step explanation: When you're finding a missing interior angle, all you need is the angle measurements of the other two angles.  According to the picture, we have two 70's given, which both add up to 140.  All the interior angles of a triangle need to add up to 180, and we have 140 so far.  That's where the missing angle comes in.  When you subtract 140 from 180, you get 40, which is your missing angle.

Let me know if this is right! :)

enter the value of 4 1/4 - 5/7 + (-2/7) - (-3)

Answers

Answer:

[tex]=6\frac{1}{4}[/tex]

Step-by-step explanation:

[tex]4\frac{1}{4}-\frac{5}{7}+\left(-\frac{2}{7}\right)-\left(-3\right)[/tex]

[tex]4\frac{1}{4}=\frac{4\cdot 4+1}{4}[/tex]

[tex]=\frac{17}{4}[/tex]

[tex]=\frac{17}{4}-\frac{5}{7}+\left(-\frac{2}{7}\right)-\left(-3\right)[/tex]

[tex]=\frac{99}{28}+\left(-\frac{2}{7}\right)-\left(-3\right)[/tex]

[tex]=\frac{99}{28}-\frac{2}{7}-\left(-3\right)[/tex]

[tex]=\frac{13}{4}-\left(-3\right)[/tex]

[tex]=\frac{13}{4}+3[/tex]

[tex]=\frac{25}{4}[/tex]

[tex]\frac{25}{4}=6\frac{1}{4}[/tex]

[tex]=6\frac{1}{4}[/tex]

-{ModPatrol}

Which product has 4 zeros after the digit 3?
0.03 x 104
0.3 x 104
0.3 x 10
0.03 X 109

Answers

Answer:

0.03×104=3.12

0.3×104=31.2

0.3×10=3

0.03×109=3.27

these are the products

hope it helps!

What phrase is a description of 2m + 7

Answers

Answer: 7 more than 2 times a number

Step-by-step explanation:

To describe 2m it would by 2 times m since it is multiplication

When describing a variable simply call it a number

Now we have "2 times a number", but we still need to incorporate the +7

To represent +7 we can say "7 more" since that represents addition

So we end up with "7 more than 2 times a number"

Answer:

2 times m + 7

Step-by-step explanation:

2 is the coeficient

m is the y additive

An explicit rule for a sequence tells how to find an as a function of blank the first term,A1, the next term an+1,

Answers

Answer:

The correct answer is "the term number, n."

Step-by-step explanation:

Answer:

Step-by-step explanation:

on edge!! dear student... you got this.. don't procrastinate and more importantly don't doubt yourself. You CAN and WILL make it to 100%

indicate the formula for the following conditions.

P(n,r) = ?

Answers

Answer:

P (n,r)= [tex]\frac{n!}{(n-r)!}[/tex]

Step-by-step explanation:

P (n,r)= ?

complete formula for permutation of objects in a set:

P (n,r) = [tex]\frac{n!}{(n-r)!}[/tex]

hello me again, answer this question, please show work

Answers

Answer:

6x

Explanation:

A number is x. 6 x x is written as 6x

Answer:

6x or 6*x

Step-by-step explanation:

Represent the following sentence as an algebraic expression, where "a number" is the letter x.

6 is multiplied by a number

6x

6 * x

Hope this helps!

Demarcus has to wrap a gift for his friend's birthday party. The gift is in a rectangular
box with the dimensions shown below. He's trying to figure out how much gift wrap
he needs to cover the entire box. Should he calculate the total surface area or the
lateral surface area? Pick the right measurement and then calculate it for him.
In your answer, specify whether he should use total surface area or lateral surface
area. Calculate the one you choose, give that measurement of the box, and then
explain how you calculated it.
13 in
20 in
8 in

Answers

Demarcus should calculate the total surface area of the rectangular prism and the measurement is 1,048 in²

How to calculate the total surface area of a rectangular prism

Length = 20 inwidth = 8 inHeight = 13 in

Total surface area = 2(lw + hw + lh)

= 2(20×8 + 13×8 + 20×13)

= 2(160 + 104 + 260)

= 2(524)

= 1,048 in²

Learn more about surface area:

https://brainly.com/question/1310421

The seats in a movie theater are arranged so that each row has 6 more seats than the row in front of it. If the first row has 24 seats, how many seats are in the 6th row?
a. 30
b. 48
c. 54
d. 60

Answers

Answer:

54 seats

Step-by-step explanation:

To make it easier, I'll put it like this.

Row    |    Seats

 1        |      24

 2       |      30

 3       |      36

 4       |      42

 5       |      48

 6       |      54

(Add 6, because each row has 6 more seats than the row in front of it.)

So, the 6th row has 54 seats.

Hope this helped !

Kelly has some money. She spends $17.50 on clothes,
She has $6.21 left. Which model represents this?
a $17.50 -6.21 =n
b. n - 17.50 = 6.21
c. n + 17.50 = 6.21
d. n + 6.21 = 17.50
Explain.

Answers

Answer:

b

Step-by-step explanation:

because we dont know what she started with.

Answer:

b) I guess

Step-by-step explanation:

she has n. she spends $17.50 (-). she has $6.21 left

n                -                      17.50               =$6.21

n-17.50=$6.21

Calculator
40%Increased in 360

Answers

Answer:

504

Step-by-step explanation:

40%=.40

360*.40=144

original number + increase = x

360+144=504


A sector with arc measure 72º has an
area of 80 square feet. Determine
the radius of the circle.
A 18 ft
C 12 ft
B 20 ft
D 16ft

Answers

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's find the Radius ~

[tex]\qquad \sf  \dashrightarrow \: area = \frac{ \theta}{360} \times \pi {r}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 80= \frac{ 72}{360} \times \pi {r}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: {r}^{2} = \frac{80 \times 360}{72 \times \pi} [/tex]

[tex]\qquad \sf  \dashrightarrow \: {r}^{2} = \frac{80 \times 5}{ \pi} [/tex]

[tex]\qquad \sf  \dashrightarrow \: {r}^{} = \sqrt\frac{400}{ \pi} [/tex]

[tex]\qquad \sf  \dashrightarrow \:r = \frac{20}{ \sqrt{\pi} } [/tex]

or

[tex]\qquad \sf  \dashrightarrow \:r \approx 11.28 \: ft[/tex]

I hope you understood the whole procedure, let me know if you have doubts ~

➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖

5547x94
what is the answer

Answers

Answer:

521418

Step-by-step explanation:

The answer should be 521418

hey who knows this? i need help

Answers

Answer:

I don't see any thing there

Step-by-step explanation:

u need to include the picture

Find the length of the altitude.

Answers

[tex]135 = \frac{22 + 8}{2} \times h \\ 135 = \frac{30}{2} \times h \\ 135 = 15 \times h \\ h = \frac{135}{15} \\ h = \frac{27}{3} = 9cm[/tex]

Answer:

Area of a trapezoid :

[tex]area = \frac{a + b}{2} h[/tex]

The measures given are trapezoid

Area = 135

base 1 = 22

base 2 = 8

[tex]135 = \frac{22 + 8}{2} h \\ \\135 = \frac{30}{2} h \\ 2(135) = ( 2)\frac{30}{2} h \\ 270 = 30h \\ \frac{270}{30 } = \frac{30h}{30} \\ 9 = h[/tex]

Step-by-step explanation:

We can check if the answer is right

[tex] \frac{22 + 8}{2} \times 9 \\ \frac{30}{2} \times 9 \\ 15 \times 9 = 135[/tex]

The radius of a quarter circle is 3 what is the quarter circle's perimeter?

Answers

Answer:

21.42

Step-by-step explanation:

Imagine it as a full circle. 3 x 4 will give you the diameter of a full circle, which is 12. circumference = pi x diameter. so 12 pi (we can work that out later). now for the quater circle, divide it by 4, so 3 pi. Then you have the 2 extra edges which are both 2r, so 6 each. finally, you have 3 pi plus 12 which = 21.42

PLSSS HELP IF YOU TURLY KNOW THISS

Answers

Answer:

answer "Less than"

Step-by-step explanation:

a) 1 2/3 = 5/3 = 1.666 ...

b) 1 5/6 = 11/6 = 1.833 ...

a < b

Answer:

1 5/6 > 1 2/3

Step-by-step explanation:

=>        1 5/6 = (1*6)+5/6

=>        1 5/6 = 6+5/6

=>        1 5/6 = 11/6

so like that, 1 2/3 = 5/3

now the denominators should be the same

for that,

5*2/3*2 = 10/6

11/6 and 10/6

=>          11/6 > 10/6

=>          1 5/6 > 1 2/3

What is the number halfway between 8516 and 8586?

Answers

Answer:

8551

Step-by-step explanation:

The midpoint of two numbers can be found by finding the mean of the two numbersMidpoint = 8516 + 8586 / 2We clearly see both numbers start with the digits '85' therefore their midpoint will also start with '85'The remaining two digits on those two numbers should be added and divided by 2⇒ 16 + 86 / 2 = 102/2 = 51Midpoint = 8551

32 is what percent of 50?
64%
70%
1.5%
156%

Answers

Answer:

64% hope this helps

Step-by-step explanation:

I'm just smart

Answer:

The answer is 64%

Step-by-step explanation:

5= 10% multiply 5 by 6 and you get 30. the 2 equals 4 percent so the percent is 64%. I hope this helps.

help please this assignment is due in a few minutes

Answers

200 miles. If their traveling 400 miles per hour. 30 minutes is half so u cut the miles in half

Answer:

C. 200 hours

Step-by-step explanation:

According to the given Question ,

Speed of Aeroplane is 400miles/hour

It means that the aeroplane covers 400 miles in 60 minutes.

and it is asked for 30 minutes , so

We know that 30 minutes is equal to 0.5 hours

By the formula ,

Distance = Speed × Time

putting the values given , we get

= 400×0.5

Distance = 200 miles

PLEASE HELP ASAP
a. write the first four terms of the series
b. does the series diverge or converge?
c. if the series has a sum, find the sum

Answers

Answer:

i think it B

Step-by-step explanation:

A recycling bin is in the shape of a right rectangular prism. The bin is 9 meters long, 5 meters wide, and 313 meters tall.

What is the volume of the recycling bin?

Enter your answer in the box.

V = m³

Answers

Answer:

14,085m³

Step-by-step explanation:

9*5*13

9*5=45

45*313=14,085

14,085

The ratio of the number of dolls Jacky had to the number of dolls Peter had was 5 : 2 but, after Jacky gave 15 dolls to Peter, they have an equal number of dolls. How many dolls did they have altogether?
PLS HELP MEEE

Answers

The number of dolls Jacky is 50 and the number of dolls Peter is 20. Then the total number of dolls is 70.

What are ratio and proportion?

A ratio is an ordered couple of numbers a and b, written as a/b where b can not equal 0. A proportion is an equation in which two ratios are set equal to each other.

The ratio of the number of dolls Jacky had to the number of dolls Peter had was 5: 2.

[tex]\rm \dfrac{x}{y}=\dfrac{5}{2}[/tex]

Let the number of dolls Jacky be x and the number of dolls Peter be y.

But, after Jacky gave 15 dolls to Peter, they have an equal number of dolls. Then we have

x - 15 = y + 15

     x = y + 30

Then we have

[tex]\begin{aligned} \rm \dfrac{y+30}{y} &=\dfrac{5}{2}\\\\2y + 60 &= 5y \\\\3y &= 60 \\\\y &= 20 \end{aligned}[/tex]

Then x will be

x = y + 30

x = 20 + 30

x = 50

Then the total number of dolls they have altogether will be 70.

More about the ratio and the proportion link is given below.

https://brainly.com/question/14335762

Answer:

70

Step-by-step explanation:

BECAUSE

table:
0 16
2 23
4 33
6 48
8 69
10 99
is this linear or exponential?

Answers

Answer:

exponential

Step-by-step explanation:

it is an exponential function

+7

+10

+15

+21

+30

What is the slop of the line?
5(y+2)=4(x-3)

A. 3/2
B. 2/3
C. 4/5
D. 5/4

Answers

Answer:

c. 4/5

Step-by-step explanation:

help me out i will give brainlist

Answers

Answer:

no

Step-by-step explanation:

0.06 = [tex]\frac{6}{100}[/tex] ← that is 6 books out of 100

she requires to have 60 out of 100 , that is

[tex]\frac{60}{100}[/tex] = 0.6

Julia was creating similar triangles in the coordinate plane. The first triangle had a rise of 3 and a run of 10. The second triangle had a rise of 7. 5. Analyze Julia’s work to see if she found the correct length of the run for the second triangle to be similar to the first triangle. 1. 3 10 = 7. 5 x 2. 75 = 3x 3. X = 25 Is Julia correct? If not, what was her mistake? Yes, she is correct. No, her proportion does not have the corresponding measures from corresponding figures in the same positions in the ratios. No, she needed to have the product of the numerators equal to the product of the denominators. No, she needed to multiply 7. 5 to both sides.

Answers

Yes julia is correct the run of the scond similar triangle will be b2=25.

What are simlilar traingles?

The similar triangle are those whose three sides or one angle or two sides or two angles one side are equal.

In the given:

Height of first triangle h=3

Base of first traingle =10

Height of second triangle =7.5

The base of second triangle b2 = ?

From the triangle similarity

[tex]\dfrac{h_1}{b_1}=\dfrac{h_2}{b_2}[/tex]

[tex]\dfrac{3}{10}=\dfrac{7.5}{b_2}[/tex]

[tex]b_2=\dfrac{7.5\times 10}{3}[/tex]

[tex]b_2=25[/tex]

Thus julia is correct the run of the scond similar triangle will be b2=25.

To know more about similar triangle follow

https://brainly.com/question/2644832

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