A three-dimensional model of Arthur’s apartment is shown below.

A rectangular prism is shown. The base of the prism has dimensions of 13 feet by 25 feet. A rectangular prism is cut out of the side of the larger prism. The smaller prism has base dimensions of 5 feet by 11 feet.

Complete the statements to determine the amount of BTUs needed to properly cool Arthur's apartment.

The total volume of the apartment is
ft3.

An hourly rating of 2.5 BTUs per cubic foot is required, so
.

Arthur needs an air conditioner that will provide
BTUs to properly cool his apartment.

Answer:

4 ≥ x

Step-by-step explanation:

14 ≥ 3x + 2

14 - 2 ≥ 3x

12 ≥ 3x

4 ≥ x

Solving the inequality 14 ≥ 3x+2 we get x ≥ 4.

In mathematics, an assertion of an order connection greater than, greater than, or equal to, less than, or less than or equal to between two numbers or algebraic expressions.

Given:

14 ≥ 3x+2

Switch sides

3x+2 ≥ 14

Subtract 2 from both sides of the equation, we get

3x + 2 - 2 ≥ 14 - 2

Simplifying the above equation

3x ≥ 12

Divide both sides by 3, we get

3x/3 ≥ 12/3

x ≥ 4

Therefore, the value of x ≥ 4.

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Answer:

y = 8x+6

Step-by-step explanation:

First find the slope since it is a linear function

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

    = (18-2)/(1 1/2 -  -1/2)

    =16 /  (1 1/2 +1/2)

    = 16/2

  = 8

The linear function is in the form

y = mx+b where m is the slope

y = 8x+b

Substitute the other point into the equation to determine b

10 = 8(1/2) +b

10 = 4+b

10-4 = b

6 = b

y = 8x+6

Answer:

D

Step-by-step explanation:

"x" represents the hours.

so 8 is the fee for the hours, rather than insurance.

6 is the insurance fee.

if the cost per hours is doubled, it'll now be 16.

the answer is "6 + 16x" (D)

Answer:

3,6,12,24.48,96,192

Step-by-step explanation:

Part (a)

x and y are nonnegative whole numbers.

3x represents the total weight of all the bass, since one bass weighs 3 pounds. Similarly, 2y is the total weight of the trout with each one being 2 pounds.  Adding up all the weight of all the fish, we get 3x+2y. This is set equal to 34 pounds which is the total stated weight caught.

In short, we end up with the equation 3x+2y = 34

Now onto the second equation. The expression 5x represents how many points Pat gets from catching x bass, because he gets 5 points per bass. Then we subtract off 2y to represent Pat losing 2 points per trout he catches. Overall, his point total is 5x-2y. This is set equal to his point total of 14.

The second equation is 5x-2y = 14

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

Answer:

3x+2y = 34

5x-2y = 14

Both equations are needed to form this particular system.

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

Part (b)

We could use a number of methods to solve for (x,y). Possibly the most efficient is elimination. Why? Because note how we have 2y up top and -2y down below. They add to 0y which is just 0. The y terms go away, and are eliminated. Afterward, all we're left with is x in which we can solve for just like any other single variable equation. More info is in part (c).

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

Part (c)

Refer to the answer in part (a). We'll add straight down. So that means we have these three sets of addition operations.

After those three sets of addition operations, we're left with the much simpler equation 8x = 48. To solve this, we divide both sides by 8 and we get x = 6. This says Pat caught 6 bass.

Use this value of x to find y. So we'll plug x = 6 into either equation involving x,y and solve for y

3x+2y = 34

3(6)+2y = 34

18+2y = 34

2y = 34-18

2y = 16

y = 16/2

y = 8

So we can see that Pat caught 8 trout as well.

The check portion is shown in the attached image below. Effectively, all we're doing is replacing x and y with 6 and 8 respectively. Then we're simplifying both sides. Getting the same number on both sides results in a true equation, and therefore verifies we have the correct (x,y) solution.

Solution: (x,y) = (6,8)

Interpretation: Pat caught 6 bass and 8 trout

Answer:

109 days and 9 hours

Step-by-step explanation:

Answer:

About 110 days

Step-by-step explanation:

Round up

2,197 would round up to 200

Divide 2,200 by 20, and there is your answer

Answer:

should be 48

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

Apply rule- a * (-b) = -a * b

4 * (-6)

= -24(-2)

= 48

Hope this helps:)

Answer:

63/50 or 1 13/50

Step-by-step explanation:

Answer:

Step-by-step explanation:

the first one

A = ( - 3 , 2 ) ..**&**.. B = ( 4 , 5 )

_________________________________

Slope = [ y(B) - y(A) ] ÷ [ x(B) - x(A) ]

Slope = [ 5 - 2 ] ÷ [ 4 - ( - 3 ) ]

Slope = [ 3 ] ÷ [ 4 + 3 ]

Slope = 3 ÷ 7

Slope = 3/7

_________________________________

y - y(A) = Slope × ( x - x(A) )

y - 2 = 3/7 × ( x - ( - 3 ) )

y - 2 = 3/7 ( x + 3 )

y - 2 = 3/7 x + 9/7

y = 3/7 x + 9/7 + 2

y = 3/7 x + 9/7 + 14/7

y = 3/7 x + 23/7

Answer:

X=5/2 , y=2

Step-by-step explanation:

Sorry if I'm not correct

F4 ke?

Answer:

4 9/10

Step-by-step explanation:

The rates of population growth are not the same, of course, in all parts of the world. Among the industrialized countries, Japan and most of the countries of Europe are now growing relatively slowly—doubling their populations in 50 to 100 years. Another group of industrialized countries—the United States, the Soviet Union, Australia, New Zealand, Canada, and Argentina—are doubling their populations in 30 to 40 years, approximately the world average. The pre-industrial, low-income, and less-developed areas of the world, with two thirds of the world’s population—including Asia (except Japan and the Asiatic part of the Soviet Union), the southwestern Pacific islands (principally the Philippines and Indonesia), Africa (with the exception of European minorities), the Caribbean Islands, and Latin America (with the exception of Argentina and Uruguay)—are growing at rates ranging from moderate to very fast. Annual growth rates in all these areas range from one and one-half to three and one-half per cent, doubling in 20 to 40 years.

The rates of population growth of the various countries of the world are, with few exceptions, simply the differences between their birth rates and death rates. International migration is a negligible factor in rates of growth today. Thus, one can understand the varying rates of population growth of different parts of the world by understanding what underlies their respective birth and death rates

Answer:

so what should I do

Step-by-step explanation:

hope it helps

Answer:

tan2θ = 4√2/7

Step-by-step explanation:

Given sin theta=1/3 and 0 < theta< π/+

Required

tan 2 theta

tan2 theta = 2tanθ/1-tan²θ

Get tan θ

sinθ = opp/hyp

adj = √3²-1²²

adj = √9-1

adj = √8

tanθ = opp/adj = 1/2√2

tan2 theta = 2(1/2√2/1-(1/2√2)²

tan2θ = 1/√2/1-1/8

tan2θ = 1/√2/7/8

tan2θ =  8/7√2

Rationalize

tan2θ = 8√2/14

tan2θ = 4√2/7

Answer:

12

Step-by-step explanation:

Hi there!

[tex]\large\boxed{\text{ C. Rectangle}}[/tex]

If cross sections were made perpendicular to the base, they would assume the shape of the lateral sides.

Thus, the cross sections would be rectangles. The correction answer is C.

Answer:

you have to add all the angles of a triangle so the value of m is 6

Answer:

1 picnic table : 9 benches

Step-by-step explanation:

You just simplify the equation down to its simplest form, so since they both have the gcf of 6, you divided both sides by 6, which results in the answer above.

Answer:

your answer is B

Step-by-step explanation:

Answer:

24/ 10

Step-by-step explanation:

We know,

tan θ = opposite/adjacent

∴ tan Z =  24/ 10

Answer:

30 ft²

Step-by-step explanation:

Area of a paralleogram formula:

A = bh

A = (6)(2)

A = 12

Area of a rectangle:

A = bh

A = 6(3)

A = 18

Combined:

12 + 18

30

Answer:

40

60% of 40 is 24

so the answer would be 40

Step-by-step explanation:

5 = 5(-4)+c

5 = -20 + c

5+20= 25

25= c

so

y = 5x + 25

Answer:

m= 5

Points=(-4,5)

y-y'= m(x-x')

y-5 = 5(x-(-4)

y-5=5(x+4)

y-5=5x + 20

y - 5x -25 = 0

Or

y= 5x + 25.

Answer:

formula of slope if angle is given:

Tan (angle given)

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

Answer:

The answer is below

Step-by-step explanation:

Let x represent the number of slides ridden and y represent the total cost. Hence:

1) For option 1, the table is shown. It passes through (2,10) and (6, 20). The equation is:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-10=\frac{20-10}{6-2} (x-2)\\\\y=2.5x+5[/tex]

2) For option 2, the equation is given by y = 5x + 7.5

3) For option 3, the graph passes through (30, 100) and (10, 40). Hence the equation is:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-40=\frac{100-40}{30-10} (x-10)\\\\y=3x+10[/tex]

Option 2 has the highest rate

Her unit cost per shirt is,

= $9.10

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that;

Jenna's unit cost per shirt is, $9.10

Here, We have;

Cost for each shirt = $7

Cost for ink per shirt = $2

Cost of a bag = $0.10

Hence, Cost of T-shirt is,

= Cost for each shirt + Cost for ink per shirt + Cost for bag

= $7 + $2 + $0.10

= $9.10

Thus, Her unit cost per shirt is,

= $9.10

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Step-by-step explanation:

Hey there!

Given;

a1 = 6

and r = 3

Then;

Let's see, we have a1 "first term" and r "common ratio". So, firstly use the formula.

[tex]nth \: term \: of \: geometric \: sries = {a}^{} . {r}^{n - 1} [/tex]

Now, keep all values.

[tex]nth = 6 \times {3}^{n - 1} [/tex]

So, it becomes like this.

Therefore, the rule is nth= 6*3^n-1.

Hope it helps!

Answer:

2m/s²

Step-by-step explanation:

acceleration = change in velocity/time taken

a  = v-u/t

Given

v = 15m/s

u = 5m/s

time t = 5secs

Substitute

a = 15 - 5/5

a = 10/5

a = 2m/s²

Hence Ellie’s acceleration is 2m/s²

Answer:

[tex] {7}^{3} = 7 \times 7 \times 7 = 147 {m}^{3} \\ to \: calculate \: the \: volume \: of \: a \: cube \: we \: need \: to \: use \: this \: formula \\ {x}^{3} \\ x = side \: length[/tex]