I don’t know how to use parallel lines to prove things...

Two mechanics worked on a car. The first mechanic worked for 5 hours, and the second mechanic worked for 15 hours. Together they

Lunna [17]

Answer:

The mechanic who worked 5 hours charged $115 per hour, the one who worked 15 hours charged $120 per hour.

Step-by-step explanation:

x = rate of mechanic who worked 5 hours

y = rate of mechanic who worked 15 hours

Then

x + y = 235

5x + 15y = 2375

Just solve these 2 equations above for x and y.

x + y = 235 ⇒ x = 235 - y

Substitute into second equation to find y.

5(235 - y) + 15y = 2375

1175 - 5y + 15y = 2375

10y = 1200

y = 1200/10 = 120

x = 235 - y = 235 - 120 = 115

5 0

2 years ago

A country's population in 1991 was 136 million. In 2000 it was 141 million. Estimate the population in 2016 using the exponentia

katrin [286]

The answer is 150 million.

Step 1. Calculate the growth rate.
Step 2. Calculate the population number in 2014.

We will use the formula for exponential growth:
A = P * eⁿˣ
where:
A - the final amount (value)
P - the initial amount (value)
e - the mathematical constant (e ≈ 2.72)
n - the growth rate
x - the time

Step 1:
A = 141 million = 141 000 000
P = 136 million = 136 000 000
n = ?
x = 2000 - 1991 = 9
Therefore:
$141 000 000 = 136000 000 * e ^{n*9} \\ e ^{n*9} =141000 000 /136000000 \\ e ^{n*9} =1.04$

Logarithm both sides of the equation:
$ln(e ^{n*9})=ln(1.04) \\ n*9*ln(e) = ln(1.04) \\ 6n=ln(1.04) \\ n = \frac{ln(1.04)}{9} \\ n = \frac{0.04}{9} \\ n = 0.004$

Step 2:
Now when we know the growth rate, it is easy to estimate the population in 2016
A = ?
P = 141 000 000
n = 0.004
t = 2016 - 2000 = 16
$A = 141 000 000 * e ^{0.004*16} \\ A = 141000 000 * e^{0.0640} \\ A = 141000 000 * 1.066\\ A = 150306 000$

Thus, the population will be nearly 150 million in 2016

7 0

4 years ago

I suck at math help ill give brainliest

bija089 [108]

Answer:

3

Step-by-step explanation:

5x + 40 = 55

5x = 55 - 40

5x = 15

x = 15 / 5

x = 3

7 0

3 years ago

20 points!!!<br> volume of a cylinder problems please help

balandron [24]

Answer:

Step-by-step explanation:

Part A

The formula for determining the volume of a cylinder is expressed as

Volume = πr²h

Where

r represents the radius of the cylinder.

h represents the height of the cylinder.

π is a constant whose value is 3.14

1) radius = diameter/2 = 4/2 = 2 inches

Volume = 3.14 × 2² × 10 = 125.6 inches³

2) Volume = 3.14 × 20² × 50 = 62800 cm³

3) radius = 16/2 = 8 mm

Volume = 3.14 × 8² × 10 = 2009.6 mm³

4) Volume = 3.14 × 9² × 9 = 2289.06 ft³

Part B

The formula for determining the volume of a sphere is expressed as

Volume = 4/3πr³

Where

r represents the radius of the sphere.

5) Volume = 4/3 × 3.14 × 5³ = 523.3 cm³

6) radius = 24/2 = 12 inches

Volume = 4/3 × 3.14 × 12³ = 7234.56 inches³

7) Volume = 4/3 × 3.14 × 1³ = 4.2 ft³

8) radius = 42/2 = 21 mm

Volume = 4/3 × 3.14 × 21³ = 38772.72 mm³

6 0

4 years ago

Slope line G(-3,1)H(-2,-2)

Anton [14]

The slope from point G to point H is -3/1 or -3
$m = \frac{y2 - y1}{x2 - x1}$
Plug into points into formula with the corresponding x and y variables.
(x1,y1), (x2,y2)
$m = \frac{ - 2 - 1}{ - 2 - ( - 3)}$
Solve
m=-3/1
m=3

8 0

3 years ago