Help me with this please

Answer:

1. Express the width of the rectangle in terms of the length X.

width = 500 - X

2. Express the surface area of the rectangle in terms of X.

area = -X² + 500X

3. What value of X gives the maximum surface area?

maximum surface area results from the rectangle being a square, so 1,000 ÷ 4 = 250

X = 250 ft

4. What is the maximum surface area?

maximum surface area = X² = 250² = 62,500 ft²

Step-by-step explanation:

since the perimeter = 1,000

1,000 = 2X + 2W

500 = X + W

W = 500 - X

area = X · W = X · (500 - X) = 500X - X² or -X² + 500X

The area of a shape is the amount of space it occupies.

The length is represented as x.

Let the width be y.

So, we have:

[tex]\mathbf{Perimeter =2(x + y)}[/tex]

This gives

[tex]\mathbf{2(x + y) = 1000}[/tex]

Divide both sides by 2

[tex]\mathbf{x + y = 500}[/tex]

Make y the subject

[tex]\mathbf{y = 500 -x}[/tex]

So, the width in terms of x is 500 - x

The surface area is calculated as:

[tex]\mathbf{A = xy}[/tex]

Substitute [tex]\mathbf{y = 500 -x}[/tex]

[tex]\mathbf{A = x(500 - x)}[/tex]

So, the surface area in terms of x is x(500 - x)

Expand [tex]\mathbf{A = x(500 - x)}[/tex]

[tex]\mathbf{A = 500x - x^2}[/tex]

Differentiate

[tex]\mathbf{A' = 500- 2x}[/tex]

Equate to 0

[tex]\mathbf{500- 2x = 0}[/tex]

Rewrite as:

[tex]\mathbf{2x = 500}[/tex]

Divide both sides by 2

[tex]\mathbf{x = 250}[/tex]

So, the value of x that gives maximum surface area is 250

Substitute 250 for x in [tex]\mathbf{A = x(500 - x)}[/tex]

[tex]\mathbf{A = 250 \times (500 - 250)}[/tex]

[tex]\mathbf{A = 250 \times 250}[/tex]

[tex]\mathbf{A = 62500}[/tex]

Hence, the maximum area is 62500

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Answer:

$2,639.19

Step-by-step explanation:

Her balance at the end of the month is

$2358.19 - $80.00 + $99.50 = $2537.69

So the finance charge is 2537.69 * 0.04% = $101.50

and her new balance is $101.50 + $2537.69 = $2639.19

Answer:

The first one

Answer: a) 62.591 lb  b) 7.5

Step-by-step explanation:

Answer:

a) 62.625 lb

b) 8.35

Step-by-step explanation:

a) Use a proportion.

4 gal is to 33.4 lb as 7.5 gal is to x lb.

4/33.4 = 7.5/x

4x = 33.4 * 7.5

4x = 250.5

x = 62.625

Answer: 62.625 lb

b) 33.4/4 = 8.35

Tada!!!!!

Answer:

10 apples

Step-by-step explanation:

if Person a bought twice as many apples as person b then it would be ten considering 10 x 2 = 20

eqaution: 10 divided by 2

Answer:

9

Step-by-step explanation:

Answer:

There are 64 trucks!

Step-by-step explanation:

Answer: x=6/5

Step-by-step explanation:

Answer:

6/5

Step-by-step explanation:

Answer:

53.3 degrees

Step-by-step explanation:

∆DEF and ∆RSQ are similar. We know this, because the ratio of their corresponding sides are equal. That is:

DE corresponds to RS

EF corresponds to SQ

DF corresponds to RQ.

Also <D corresponds to <R, <E corresponds to <S, and <F corresponds to <Q.

The ratio of their corresponding sides = DE/RS = 6/3 = 2

EG/SQ = 8/4 = 2

DF/RQ = 4/2 = 2.

Since the ratio of their corresponding sides are equal, it means ∆DEF and ∆RSQ are similar.

Therefore, their corresponding angles would be equal.

Thus, m<Q = m<F

Let's find angle F

m<F = 180 - (98 + 28.7)

m<F = 53.3°

Since <F corresponds to <Q, therefore,

m<Q = 53.3°

Answer:

D divide both the numerator and denominator by cos(x)cos(y)

Step-by-step explanation:

just took the test

your answer should be 1/3 if I did my math right

Answer:

the answer is 4

Step-by-step explanation:

Answer:

3 to the 4th power is 81.

Step-by-step explanation:

You would do 3 × 3, which would get you to 9. Then, you multiply 9 × 9, which gives you 81.

Answer: A) segment AB = segment AD

The diagram below pretty much says it all. The color coding indicates what is given (in blue). The segments in red are congruent because of the reflexive property. If we know the green stuff is true, then we have enough to use SAS.

The fraction of the shape which is shaded in simplest form is 1/3.

The square in the diagram provided has a total of 12 boxes .

The number of shaded part is 4

To calculate the shaded fraction of the shape we have to use the formula:

Number of shaded part/ Total number of boxes present.

= 4/12

We can divide the numerator and denominator by 4 to get the simplest form.

= 1/3

The fraction of the shape which is shaded in simplest form is therefore

= 1/3.

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oooooooooooooooopppppppppppppppppppppppppssssssssssss

Answer:

thankssssssssss cuhhhhhhh

Step-by-step explanation:

lm ao like if they are gonna wait lol

Answer: Elijah would be 42 inches tall

Step-by-step explanation:

We all know that Samuel is 48 inches while Elijah is 6 inches shorter.

You subtract 6 from 48 to get 42.

Hopefully, this helped. :D

Answer:

The answer is A

Step-by-step explanation:

Answer:

multiply it by .12 then it says for 12 months, multiply it by 12 then

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

(3+x)+x=27

2x+3=27

2x=24

x=12

Answer:

its y=-5x

Step-by-step explanation:

Why?

linear functions have only the slope, they dont include the y-intercept

Answer:

A C E

Step-by-step explanation:

Answer: h is 5 and k is 2

Step-by-step explanation:

The equation of the transformed of the parent cube root function is

y = ∛(x-4) - 1.

All the points (and only those points) which lie on the graph of the function satisfy its equation.

Thus, if a point lies on the graph of a function, then it must also satisfy the function.

The given graph represents a transformation of the parent cube root function.

The Parent cube root function is

y = ∛(x -h) - k

where the value of h  and k is equal to 0

h=0, k=0 in parent function

The graph changes direction at (0,0) in parent function.

From the given graph we can see that the graph changes direction at (4,-1) which means the graph is shifted 4 units to the right and 1 unit down

So, the value of h=4  and value of k=1

The equation of the transformed function,

y = ∛(x-4) - 1

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#SPJ5

Answer:

yes

Step-by-step explanation:

I figured this out by determining how many times 3 fits into 7.

7/3 is equal to 2 and 1/3

2 1/3 < 6

Hope this helps <3

please give brainliest

Answer:

14

Step-by-step explanation:

f(2)=4(2)+2

f(2)=10

g(3)=2(3)-2

g(3)=6-2

g(3)=4

10+4=14

Answer:

17

Step-by-step explanation:

f(x) = 4x + 2

g(x) = x² - 2

f(2) = 4(2) + 2 = 10

g(3) = 3² - 2 = 7

10 + 7 = 17

Answer:

d. 48 inches

Step-by-step explanation:

We assume the mirror is a rectangle

We solve for the length of a diagonal using Pythagoras Theorem

a² + b² = c²

c = √a² + b²

Where c = diagonal

a = 30 inches

b = 38 inches

c = √30² + 38²

c = √2344

c = 48.414873748 inches

Approximately = 48 inches

Answer:

10

Step-by-step explanation:

A decagon is a polygon that has 10 sides !

Answer:

c

Step-by-step explanation:

Answer:

Z = -6.3

Step-by-step explanation:

Given that:

[tex]\mathbf{H_o :p= 0.28}[/tex]

[tex]\mathbf{H_o :p < 0.28}[/tex]

Since the alternative hypothesis is less than 0.28, then this is a left-tailed hypothesis.

Sample sixe n = 800

[tex]\hat p[/tex] = 0.217

The standard error [tex]S.E(p) = \sqrt{\dfrac{p(1-p)}{n}}[/tex]

[tex]S.E(p) = \sqrt{\dfrac{0.28(1-0.28)}{800}}[/tex]

[tex]S.E(p) \simeq0.015[/tex]

Since this is a single proportional test, the test statistics can be computed as:

[tex]Z = \dfrac{\hat p - p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]

[tex]Z = \dfrac{0.217- 0.28}{0.01}[/tex]

Z = -6.3