What is the volume of the following rectangular prism?

Answer:

The surface area of a rectangular box is the sum of the areas of the flat rectangular faces of the box. The height is the vertical side of the box.  So the other sides are the length and width.  Try to picture a box in your head, or you can draw it on paper.

Let x = length

Let y = width

Let h = height

Using these variables, we can write an equation that represents the surface formula.

A = 2(area of bottom face) + 2(area of front face) + 2(area of side face)

A = 2xy + 2xh + 2yh

This is general equation for surface area.  All we need to do is plug in the known values into it and solve for h.

496 = 2(18)(8) + 2(18)h + 2(8)h

496 = 288 + 36h + 16h

Now it comes down to simple algebra.  Isolate the h terms and solve for h from there.

208 = 52h

Divide both sides of the equation by 52 to get your height.  I let you finish up here.

Step-by-step explanation:

Answer:

Slope intercept: y = -3/2x + 1

Point slope: y + 2 = -3/2 * (x - 2) [Forgot to add the work for this, I will add it if you need it, feel free to ask.]

Step-by-step explanation:

m = (change in y)/change in x)

But also

m = y_2 - y_1/x_2 - x_1

So lets substitute

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

Lets find the slope

m = 3/0 - (2)

m = 3/-2

m = -3/2 (Moved the negative)

Now we find the value of b using the equation of a line.

y = mx + b

y = (-3/2) * x + b

y = (-3/2) * (2) + b

-2 = (-3/2) * (2) + b

Now we find the value of b

Lets rewrite

-3/2 * 2 + b = -2

Cancel the CF of 2

-3 + b = -2

Move the terms without b to the right

b = -2 + 3

b = 1

Now we substitute our values of the slope and y-int into y = mx + b to find the equation.

y = -3/2x + 1

Answer:

[tex]y=\frac{-3}{2}x-1[/tex]

Step-by-step explanation:

Given the two points, we can use the slope formula to get the slope of our equation.

[tex]\frac{y_2-y_1}{x_2-x_1}=m[/tex]

Plug in what we know

[tex]\frac{(1)-(-2)}{0-2}=m[/tex]

[tex]m=\frac{-3}{2}[/tex]

[tex]y=\frac{-3}{2}x-b[/tex]

Plug in one of the points given and solve to find our y-intercept [b]

[tex]-2=\frac{-3}{2}(2)-b[/tex]

[tex]b=1[/tex]

(we already know our y-intercept since we're given what y is when x is 0 [hence (0,1)], but this is how it is done if we did not know it initially)

Final equation

[tex]y=\frac{-3}{2}x-1[/tex]

The marginal cost that can be deduced from the information given about the company is 40e^-t.

Marginal cost simply means the change in production cost due to an additional unit produced.

From the complete question, the cost function is given as 60 - 40e^-t. Therefore, the marginal cost will be:

C'(t) = d/dt (60 - 40e^-t)

= d/dt (60) - 40 d/dt (etc)

= 0 - 40(-1)e^-t

= 40 e^-t.

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Answer:

 7/10

Step-by-step explanation:

1 yard = 3 feet

Then the given ratio is ..

21 feet : 10 yards = 7 yards : 10 yards = 7 : 10

As a fraction, the ratio is 7/10.

Answer:

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

Step-by-step explanation:

Let [tex](x_1,y_1)\rightarrow(-6,5)[/tex] and [tex](x_2,y_2)\rightarrow(6,7)[/tex]

Determine slope

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\ \\m=\frac{7-5}{6-(-6)}\\ \\m=\frac{2}{6+6}\\ \\m=\frac{2}{12}\\ \\m=\frac{1}{6}[/tex]

Use either ordered pair to find the y-intercept

[tex]y=mx+b\\\\7=\frac{1}{6}(6)+b\\\\7=1+b\\\\6=b[/tex]

Final equation

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

Answer:

1. FH, 2. GH,  3.IH  4. GI,  5. FG

Step-by-step explanation:

According to a certain geometric theorem, the smallest angle is always opposite to the smallest side of a triangle. Likewise, the largest angle is always opposite to the largest side. Using this theorem we can properly order the angles and sides.

Additionally, the interior degrees of a triangle will always be 180, and the interior of this quadrilateral is 360 degrees. Using this we can determine the missing angles.

180 - 75 - 55 = 50 (first missing angle)

180 - 59 - 63 = 58 (second missing angle)

The smallest angle would be 50 degrees and the largest 75.

The second smallest is 55 degrees, the third smallest is 58 degrees, the fourth smallest is 59 degrees, and the fifth is 63 degrees.

Now, one thing that seems a bit confusing is the fact that GH is opposite to 2 different angles, so how do we know WHICH angle to use to find its length. From what I understand, we should be able to find the average of the two angles across from this side to see what its place would be in terms of length.

63 + 50 = 56.5

This would make side  GH larger than FH but less than HI

This is how I would solve the problem, and I think this is the correct order. Please let me know whether it turns out right.

Mark the formula/theorem below

Here

So the order is

Answer:

0.025

Step-by-step explanation:

The solution is in the attached file

Answer:

None of them are correct as the correct one is 0.345 (maybe you made a typo when typing the options)

Step-by-step explanation:

We can make:

[tex]\frac{345}{1000}[/tex] which equals 0.345 km

Answer:

Step-by-step explanation:

Both are essentially same questions, considering 30 = 25 + 5.

Solving c)

Solution:

Part-C)

Part-D)

Hoped this helped!

Answer:

-2, 0, d

refer the image attached

Answer:

d > -2

Graph :

Answer:

x²

Step-by-step explanation:

4x²-14x+6

x²-7x²+12x

=2×2×x×x-2×7×x+2×3

x×x×x-7×x×x+2×2×3

= -2+2

x×x

the 2s cancle each other

= x²

Answer:

  sin(x) = ±(√357)/29 ≈ ±0.651533

Step-by-step explanation:

The relation between sine and cosine is ...

  sin(x) = ±√(1 -cos(x)^2)

  sin(x) = ±√(1 -(-22/29)^2) = √(1 -484/841) = √(357/841)

  sin(x) = ±(√357)/29

_____

Additional comment

The sign of the cosine is negative, which places the angle in quadrant II or III. In quadrant II, the sine is positive; in quadrant III, the sine is negative. That is, we cannot tell which sign to apply from the information given.

(20, 21, 29) is a Pythagorean triple. We suspect a typo in the question: 22 is used where 20 or 21 is likely intended.

Answer

125,000 tons of garbage per landfill

Step-by-step explanation:

250 million total tons of garbage was sent to 2,000 landfills. Since it is assumed each landfill gets an equal amount of garbage, we can easily divide.

250,000,000 / 2,000 = 125,000 tons of garbage per landfill

henceforth, each landfill received 125,000 tons of garbage

Answer: The new number is 1.44% smaller than the original.

=========================================================

Explanation:

To increase by 12%, we involve the multiplier 1.12

Think of 1.12 as 100% + 12% = 1 + 0.12 = 1.12

We go from x to 1.12x

To decrease by 12%, we will use the multiplier 0.88 because 1 - 0.12 = 0.88

Think of it like a discount. If you save 12%, then you pay the remaining 88%

So 0.88*1.12x = 0.9856x

The value 0.9856 is smaller than 1, meaning that overall we have a net discount going on.

The discount rate is 1 - 0.9856 = 0.0144 = 1.44%

In other words, x ultimately goes down by exactly 1.44%

----------------

If you want to use an actual number to see an example, let's go for x = 100

Increasing 100 by 12% means we increase by 0.12*100 = 12

We go from 100 to 112

Then decreasing by 12% means the value goes down by 0.12*112 = 13.44 and drops to 112-13.44 = 98.56

The original value 100 becomes the final value 98.56

This is a percent decrease of (100-98.56)/100 = 0.0144 = 1.44%

Answer:

12.22 would be her total cost after including 8% of tax.

Step-by-step explanation:

$2.29x3=$6.87

$6.87+1.89x2=$10.65

$10.65+$1.49=$12.14

$12.14+¢.08= $12.22

This is what I think is the answer from my work.

Answer:

32

Step-by-step explanation:

let both sides of equation be squared

((x+4)^½)² = 6²

x+4 = 36

x = 36-4

x = 32

Answer:

Option A

Step-by-step explanation:

Given the following question:
Mrs. Hernandez earns $35.60 an hour
One week she earned $854.40

To find the answer we divide 8,544 by 356

[tex]8544\div356=24[/tex]
[tex]854.40\div35.60=24[/tex]

Mrs. Hernandez worked "24 hours last week" by using the first options equation, we can find that answer.

Hope this helps.

Answer:

[tex]2x+3y-45=0[/tex]

Step-by-step explanation:

The slope of the line that goes through (18, 3) and (21, 1) is

[tex]\frac{1-3}{{21-18}}=\frac{-2}{3}\\[/tex]

The slope of the line that goes through (18, 3) and (x, y) is

[tex]\frac{y-3}{{x-18}}[/tex]

So

[tex]\frac{y-3}{{x-18}} = \frac{-2}{3}\\-2(x-18)=3(y-3)\\-2x+36=3y-9\\2x+3y-45=0[/tex]

Answer:

Step-by-step explanation:

Let's replace Ram with r and Sudha with s.

(r = 3s) + 3 = (r = 2s)

(r = 2x) = ( r = 3s - 3)

3s - 3 = 2x

3s - 1x = 2x

s = 3

If r = 3s and s = 3, then r = 3 x 3 = 9.

Ram is 9 years old and Sudha is 3 years old.

Answer:

age of ram = 9 years

and the age of sudha is 3 years

Step-by-step explanation:

let the present age of ram be x

and his sister sudha's present age be y

Ram is three times as old as his sister Sudha

so, x = 3y ----i)

After three years, he will be twice as old as Sudha.

so , x+3 =(y+3)2

=> x+3 = 2y+6 ----ii)

now putting the value of x in equation ii)

=> 3y+3 = 2y+6

=> 3y-2y = 6-3

=> y = 3 { the present age of sudha is 3 year}

now the age of ram = x = 3y

=> x = 3(3)

=> x = 9

Answer:

30

Step-by-step explanation:

(3+3³)

3+27

30

Answer:

[tex]30[/tex]

Step-by-step explanation:

[tex]3\cdot(1+3^2)\\\\3\cdot(1+9)\\\\3\cdot(10)\\\\30[/tex]

Remember to follow PEMDAS

The cost per friend is $6.84.

The first step is to determine the total cost of the vegetables the two friends bought.

Total cost of the vegetables = ( 1 x $2.82) + 4.19 X 2 + (1.24 x 2) = $13.60

In order to determine the cost per friend, divide the total cost of the vegetables by the number of friends that purchased the items.

$13.6 / 2 = $6.84

To learn more about division, please check: https://brainly.com/question/194007

Answer:

Step-by-step explanation:

→ y² -16y +64

→ y²-8y-8y+64

→ y(y-8) -8(y-8)

→ (y-8) (y-8)

Answer:

26400

Step-by-step explanation:

1 mi=1760 yd

5mi=8800yd

1yd=3ft

8800yd=26400ft

If Heather jogged 5 miles in terms of feet he jogged 26400 feet.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Heather jogged 5 miles.

Also given that 1 mi = 1760 yd and 1 yd = 3 ft.

Therefore, If Heather jogged 5 miles then he jogged 5×1760 yards and

5×1760×3 feet which is,

= 26400 feet.

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#SPJ2

Answer:

Step-by-step explanation:

An exponent is a number that makes another number multiply itself.

If it's on a fraction, then we need to do this:

It can be confusing.

Remember,

We are not adding.

Answer:

it was 200

Step-by-step explanation:

srry if its wrong

Answer:

1 5/8

Step-by-step explanation: