MATHEMATICS MIDDLE SCHOOL

X – y ≥ -4.
2x – y ≤ 5.
2y + x > 1

Answers

Answer 1
Answer: I took a picture of the work instead ^^

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A can of juice has a radius of 7 inches and a height of 8 inches. What is the volume of the can?

Answers

Answer:

V = 392 pi in^3 or approximately 1230.88 in^3

Step-by-step explanation:

The volume of a can, which is a cylinder, is given by

V = pi r^2 h

   = pi (7)^2 * 8

   = pi *392

We can approximate pi by 3.14

V = 392 * 3.14

   =1230.88 in^3

What is the answer of 30% of $40.00 please tell with the steps

Answers

1.First you multiply $40.00 by .30 (since to make a percent a decimal you move the decimal or percent to the left 2 times)
2.Then you'll get 120000 so when you multiplied  $40.00 by .30 you have 4 decimals so you move the decimal 4 times in the answer starting from the right.
3. The answer will be 12 

Give an example of an irrational number that is less than -5.

Answers

For example, Pi, which is 3.14159265359...

What is 7/15 and 5/14 written as a decimal

Answers

First of all, to change non mixed fractions into a decimal, you divide the numerator (top) by the denominator (bottom)

(7)/(15)⇒7÷15= .467

(5)/(14)⇒5÷14= .357

Need help ASAP1) A new truck that sells for $42,000 depreciates 11% each year. write a function that models the value of the truck. Find the value of the truck after 8 years. Round to the nearest dollar.

2) Earl mows lawns one weekend. He earns $15 for each lawn that he mows. He spends $50 on gas and other supplies. What function equation represents Earl's profit from mowing x lawns?

A)f(x)=50x-15
B)f(x)=50x+15
C)f(x)=15x-50
D)f(x)=15+50

3) find the common geometric series.
-2,-4,-8,-16.....

Answers

Answer:

\boxed{1) V = 40 000(0.89)^(n), \text{\$15 746; }\text{2) C) f(x) = 15x - 50 ; 3) }a_(n) = -2^(n)}

Step-by-step explanation:

1) Depreciation

The formula for the value V of an asset after depreciation by an annual percentage rate is  

V = P(1 - r)ⁿ

where

P = present value

r = annual percentage rate

n = number of years

Data:

V = 40 000

r = 11 % = 0.11

n = 8 yr

Calculations:

(a) Function model

V= 40 000(1 - 0.11)ⁿ = 40 000(0.89)ⁿ

The function model is \boxed{ V= 40 000(0.89)^(n) }

(b) Future value

V = 40 000(0.89)ⁿ = 40 000 × 0.393 659 = $15 746

In eight years, the truck will be worth \boxed{ \text{\$15 476}}.

2) Profit function

Income from 1 lawn = $15

  Income from x lawns =  15x

Less gas and supplies =         -50        

                 Net income = 15x – 50

The function is \boxed{f(x) = 15x - 50}.

3) Geometric series

(a) Calculate the common ratio

a₁ = -2

a₂ = -4

a₃ = -8

a₄ = =16

The ratios of consecutive pairs are

a₄/a₃ = -16/(-8)  = 2

a₃/a₂ =   -8/(-4)  = 2

a₂/a₁ =   -4/(-2)  = 2

All adjacent pairs have the same common ratio r = 2.

(b) Write the formula for the series

The formula for the nth term of a geometric series is

aₙ = a₁rⁿ⁻¹

If a₁ = -2, the formula for the series is

aₙ = -2(2)ⁿ⁻¹ = -2ⁿ

The formula for the series is \boxed{a_(n) = -2^(n)}.

Solve v = 1/3bh for b

Answers

Answer:

Step-by-step explanation:
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