A cafeteria is in the shape of a rectangle. The length of the rectangle is four times its width. The area of the cafeteria is 14,800 square feet. What is the length of the cafeteria? Round to the nearest foot.
Hint: Use A = LW.
A. 243 Ft.
B. 61 FT.
C. 370 FT.
D.121 FT.

Answers

Answer 1

Answer:

Option A, [tex]L = 243\ ft[/tex]

Step-by-step explanation:

Step 1:  Create an equation

[tex]Length = 4 * Width[/tex]

[tex]Area = (4 * W) * W[/tex]

[tex]Area = 4 W^2[/tex]

Step 2:  Solve for W

[tex]14800\ ft^2 = 4 W^2[/tex]

[tex]\frac{14800\ ft^2}{4} = W^2[/tex]

[tex]3700\ ft^2 = W^2[/tex]

[tex]\sqrt{3700\ ft^2} = \sqrt{W^2}[/tex]

[tex]61\ ft = W[/tex]

Step 3:  Solve for L

[tex]Length = 4 * Width[/tex]

[tex]L = 4 * 61\ ft[/tex]

[tex]L = 243\ ft[/tex]

Answer:  Option A, [tex]L = 243\ ft[/tex]


Related Questions

Select the correct answer.
A polygon is translated and then stretched vertically. Which statement is correct?

A.
The translation does not preserve side lengths and angles, but the vertical stretch preserves side lengths and angles of the preimage.
B.
Neither the translation nor the vertical stretch preserves side lengths and angles of the preimage.
C.
The translation preserves side lengths and angles, but the vertical stretch does not preserve side lengths and angles of the preimage.
D.
Both the translation and the vertical stretch preserve side lengths and angles of the preimage.

Answers

C: The translation preserves side lengths and angles, but the vertical stretch does not preserve side lengths and angles of the preimage.

How to explain translation of a polygon?

When we talk about the concept of translation in transformations, it means that the side lengths remain the same. This means the object is just moved from one place to another and the lengths are preserved.

However, when we stretch the polygon, it means we are increasing or decreasing at least one side length.

Thus, we can conclude that The translation preserves side lengths and angles, but the vertical stretch does not preserve side lengths and angles of the preimage.

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please help
i cant do this

Answers

Answer:

42 sq. cm

Step-by-step explanation:

Answer: 42 sq. cm

Length of Big Rectangle: 7

Width of Big Rectangle 7+0.5+0.5 = 8

Area of Big Rectangle: 56

Area of Small Rectangle = 0.5*7 = 3.5

Area of 4 Small Rectangles = 3.5 *4 = 14

Shaded Area = Big Rectangle - 4 Small Rectangles = 56 - 14 = 42 sq. cm

To reassure the answer above is correct

PLEASE ANYONE I NEED HELP

Answers

Answer:

Number 1, or letter H should be 3 and 3.

Step-by-step explanation:

There's 1 hamburger, 1 hot dog and 1 chicken sandwich. Sandwich wise it's 3.

There's 1 cola, 1 diet cola and 1 lemonade, thus making it 3 as well.

what is the diffrence of (x+5) and (2x+3)

Answers

Answer:

2-x

Step-by-step explanation:

When my pot of paint is half full, it weighs 5.8 kg. When my pot of paint is one quarter full, it weighs 3.1 kg.
What is the weight of the full pot?

Answers

The paint in the pot is an illustration of a linear equation and the weight of the full pot is 11.2 kg

How to determine the weight of the full pot?

The given parameters can be represented using the following ordered pairs:

(x,y) = {(0.5, 5.8) and (0.25, 3.1)}

The slope of the equation is calculated using:

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

This gives

m = (3.1 - 5.8)/(0.25 - 0.5)

Evaluate

m = 10.8

The equation is then calculated using:

y = m(x - x1) + y1

This gives

y =  10.8(x - 0.5) + 5.8

Expand

y =  10.8x + 0.4

When the pot is full, we have x = 1

So, the equation becomes:

y =  10.8 * 1 + 0.4

Evaluate

y =  11.2

Hence, the weight of the full pot is 11.2 kg

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Tori invests $1,500 into the stock market which earns 9% per year. In 20 years, how much will Tori's investment be worth if interest is compounded semiannually (twice a year)?​

Answers

[tex]\bold{ANSWER:}[/tex]
$8725

[tex]\bold{EXPLANATIONS:}[/tex]

During a​ 6-week weight-loss​ regimen, Tony lost weight at a rate of 1.1 pounds per day. How much did he lose after 16 ​days? After ​weeks?

Answers

Answer:

After 16 days:  17.6 pounds

After 6 weeks: 46.2

Step-by-step explanation:

1.1 x 16 = 17.60

42 x 1.1 = 46.2  (6 weeks x 7 days a week = 42)

The weight loss after 16 days will be 17.6 pounds and after 6 weeks will be  46.2.

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that during a​ 6-week weight-loss​ regimen, Tony lost weight at a rate of 1.1 pounds per day.

The weight loss after 16 days will be calculated as,

1.1 x 16 = 17.60 pounds

The weight loss after 6 weeks will be calculated as,

42 x 1.1 = 46.2  (6 weeks x 7 days a week = 42)

Therefore, the weight loss after 16 days will be 17.6 pounds and after 6 weeks will be  46.2.

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Two math classes took the same quiz. The scores of 10 randomly selected students from each class are listed below.

Sample of Class A: 75, 80, 60, 90, 85, 80, 70, 90, 70, 65

Sample of Class B: 95, 90, 85, 90, 100, 75, 90, 85, 90, 85

Based on the medians of the scores for each class, what inference would you make
about the quiz scores of all the students in Class A compared to all the students in
Class B? Explain your reasoning to justify your answer.
(written answer)

Answers

Answer:

The score of class b were better than the scores of class a.

the median for class a was 77.5

the median for class b was 90

therefore class b overall scored better on the quiz than class a

Step-by-step explanation:

hope this helps :)

Hi can someone help me find domain and range

Answers

Answer:

Step-by-step explanation:

Domain is ( - ∞ , ∞ )

Range is [ 0 , 1 ] ∪ ( 2 , ∞ )

need help with #10 :’)

the # is “Which of the following expressions is equivalent to 42 + 63?

A- 3(15+21)

B- 6(7+9)

C- 7(6+9)

D- 14(3+3)

8

Answers

Answer:

the answer is c

Step-by-step explanation:

first add : 42+63=105

so you need to solve the expressions until you find the one that equal the same amount.

start with the problem in the parenthesis then multiply.

you will find that C equals 105

6+9=15

15×7=105

ILL GIVE BRAINLIEST!! ANSWER PLEASEEE :,((

Last year, Dan opened an investment account with $6600. At the end of the year, the amount in the account had increased by 26.5%. How much is this increase
in dollars? How much money was in his account at the end of last year?

Answers

Answer:

5600*.065=364

5600+364=$5964 in the account at the end of the year.

Step-by-step explanation:

Answer:

22.5% = 22.5/100

(22.5/100)*6600

How much money was in his account at the end of last year?

$2200 plus the increase

brainliest?

The value of 30 is between which two integers


Answers

Answer:

[tex]5 < \sqrt{30} < 6[/tex]

Step-by-step explanation:

[tex]Locate\ \sqrt{30}\ between\ two\ integers:\\ \downarrow\\ 5 < \sqrt{30} < 6[/tex]

I hope this helps you

:)

What is the measure of angle c?

Answers

Answer:

∠ c = 29°

Step-by-step explanation:

∠ b and 97° are vertically opposite angles and are congruent , so

∠ b = 97°

the 3 angles in the triangle sum to 180° , that is

54° + b + c = 180°

54° + 97° + c = 180°

151° + c = 180° ( subtract 151° from both sides )

c = 29°

Answer:

•SEE ABOVE ATTACHMENT•

HOPE IT HELPS!

MARK AS BRAINLIAST.

32 divided by 1.6 how to work out

Answers

Answer:

20

Step-by-step explanation:

[tex]\frac{32}{1.6} =\frac{32}{\frac{16}{10}} =32*\frac{10}{16} =\frac{320}{16} =20[/tex]

So the answer is 20

find the vaule of 3x + 2 when 7 +x =5

Answers

Answer:

=> -4

Step-by-step explanation:

7 + x = 5

=> x = 5 - 7

=> x = -2

Putting the value of x = -2 in equation 3x + 2

=> 3(-2) + 2

=> -6 + 2

=> -4

Answer:

-4

Step-by-step explanation:

when 7 +x =5   solve for x by subtracting 7

x=5-7 =-2

3x+2 =               substitute (-2) for x

3(   )+2

3(-2)+2

-6+2=-4

Help me, paid well just answer

Answers

Answer:

30.67

Step-by-step explanation:

[tex] \frac{9}{ \sin(x) } \: = \frac{16}{ \sin(115) } \\ \\ \frac{9}{ \sin(x) } \: = \frac{16}{ 0.91 } \: \: \\ \\ \frac{9 \times 0.91}{16} = \sin(x) \\ x = 30.67[/tex]

Why is circle 1 similar to circle 2?

Circle 1: center (2, 3) and radius 4

Circle 2: center (2, 3) and radius 12

Circle 1 and circle 2 have the same center.

Circle 2 is a dilation of circle 1 with a scale factor of 3.

Circle 1 and circle 2 are reflections of each other.

Circle 2 is a dilation of circle 1 with a scale factor of 8.

Answers

circle 2 is a dial at ion of circle 1

Which function is represented by the graph below?

Answers

Answer:

[tex]f(x)=2^x[/tex]

Step-by-step explanation:

Exponential function:

[tex]f(x)=a(b^x)+c[/tex]

Step 1. Find a, y-intercept

Step 2. Find b, slope

Step 3. Find c, horizontal asymptote

a = 1

m = (y₂ - y₁)/(x₂ - x₁)

m = (3 - 1)/(1 - 0) = 2/1

b = 2

c = 0

[tex]f(x)=1(2^x)+0\\f(x)=2^x[/tex]

How to solve four hundred thirty five minus six hundred for teen

Answers

Answer:

- 179

Step-by-step explanation

There are numbers behind Zeros and they are known as negtive numbers

Write 5 1/6 as a decimal. Show your long division work

Answers

Answer:

5.1666666666667

To solve

We know that...

[tex]5\frac{1}{6} = 5 + \frac{1}{6}[/tex]

So that means

[tex]\frac{1}{6}[/tex] = 1 ÷ 6

And with that info, 5 1/6 becomes

[tex]5 + (\frac{1}{6})[/tex]

_______________________________________________________

Solve by improper fractions

We know from the last problem that...

[tex]5\frac{1}{6} = 5 + \frac{1}{6}[/tex]

Converting 5 as a whole number to a fraction, it becomes

[tex]5 = \frac{5}{1}[/tex]

Now it becomes...

[tex]\frac{5}{1} + \frac{1}{6}[/tex]

Since the fractions will not change, first find the whole, then multiply your improper fraction by the whole, and add the part

[tex]\frac{6}{6}\\\\ = (\frac{5}{1} * \frac{6}{6} ) + \frac{1}{6}[/tex]

Converting to improper fraction

[tex]\frac{30}{6}\\\\= \frac{30}{6} + \frac{1}{6}(part) = \frac{31}{6}[/tex] never add the denominators when they are equal.

We know that...

[tex]\frac{31}{6}[/tex] = 31 ÷ 6

Whose quotient is equal to

[tex]5.166[/tex]

________________________________________________________

Need more information? Ask in comments.

Here is a right angled triangle work out the value of x using trigonometry

Answers

[tex]~~~~~\sin 30^{\circ} = \dfrac{\text{Perpendicular}}{\text{Hypotenuse} }\\\\\\\implies \dfrac 12 = \dfrac{8}x\\\\\\\implies x = 8\cdot2\\\\\\\implies x = 16 ~ \text{cm.}[/tex]

The measure of the side length is 16 cm after applying the sin ratio which is the side opposite to the angle/hypotenuse.

What is a right-angle triangle?

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

It is given that:

A right-angle triangle is shown in the picture.

To find the side length of the hypotenuse apply the sin ratio

sin30 = side opposite to the angle/hypotenuse

1/2 = 8/x

x = 8(2)

x = 16 cm

Thus, the measure of the side length is 16 cm after applying the sin ratio which is the side opposite to the angle/hypotenuse.

Learn more about the right-angle triangle here:

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Simplify: 173‾√−295‾√+33‾√+115

Answers

The simplified form of the expression 173‾√−295‾√+33‾√+115 is; (1/73) (√-23/1947)

What is the simplified form of the expression?

It follows from the task content that expression given is; 173‾√−295‾√+33‾√+115.

It therefore follows that the expression can be simplified as follows;

173‾√−295‾√+33‾√+1151/173 (√(115/-295×33))

(1/73) (√-23/1947)

On this note, it follows that the simplified form of the expression is; (1/73) (√-23/1947).

Read more on simplifying an expression;

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Which statement best describes the primary duty of the judicial branch of government? A. to appropriate and pass the budget B. to interpret the laws and Constitution C. to make treaties and declare war​

Answers

Answer:

B

Step-by-step explanation:

just look up its responsibilities as a branch, and its judicial its in its name

The volume of the given figure is __ ft3

Answers

Answer:

I believe the answer is 20

if n=14 when m=4 find n when m=23

Answers

divide 14 by 4 which gives you 3.5
3.5 x 23 = 80.5
therefore n=80.5 or you round up and get 81.

What is the measure of gef

Answers

Grate elf finder because I am really

Which of the following sets of ordered pairs defines a relation that
is NOT a function?
O {(1, 5), (5, 1), (7, 9), (9, 7)}
O {(6, 7), (8, 10), (13, 9), (21, 10)}
O {(2, 2), (3, 4), (5, 8), (12, 16)}
O {(5, 14), (5, 16), (7, 23), (11, 31)}

Answers

para lang po sa points hehe

Please help i have an assignment due TODAY i need to get this done
rules:
NO LINKS! im not getting myself a virus

Answers

Answer:

Line LK is the dimameter

Step-by-step explanation:

A diameter is a line that goes through the center and goes from one end a the circle to the other end of the circle.

Hope this helps!!

A triangular window in a beach house is 48 inches in height and contains 1728 square inches of glass. Find
the measure of the base of the window.

Answers

[tex]\huge{\color{red}{\fbox{\textsf{\textbf{Answer}}}}} [/tex]

To find :-

The base of a triangle glass window

Given :-

Height of the window = 48 inches

Area of glass = Area of traingle = 1728 square inches

There is a formula to find area of triangle

[tex]area = \frac{1}{2} \times base \times height \\ 1728 = \frac{1}{2} \times base \times 48 \\ 1728 = 24 \times base \\ \frac{1728}{24} = base \\ 72 \: inches = base[/tex]

Result :-

The base of triangle window of beach house is 72 inches.

What is the greatest common factor of x^6 and x^9

Answers

X^6 because it is really right bc Ik it is
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