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3 years ago

The value of a new $5400 sailboat decreases 10% per year. Find its value after 5 years. Round to the nearest penny.

Mathematics

1 answer:

Furkat [3]3 years ago

5 0

Answer:

FV= $3,352.98

Step-by-step explanation:

Giving the following information:

Initial investment (PV)= $5,400

Number of periods (n)= 5 years

Interest rate (i)= 10%

To calculate the future value (FV), we need to use the following formula:

FV= PV / (1 + i)^n

FV= 5,400 / (1.1^5)

FV= $3,352.98

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Which pairs of points would result in a line with a rate of change of 2:1? select all that apply

Reil [10]

Answer:

A,C,D

Step-by-step explanation:

Complete Question:

"Which pairs of points would result in a line with a rate of change of 2:1? select all that apply"

A.(−4,−11) and (−2−7)

B.(5,6) and (−5, 12)

C.(0,−3)and (−4,−11)

D. (0,−3) and (5, 7)

Rate of change is the slope. 2:1 would mean a slope of simply, 2.

We need to find slope of each of the choices from A - D and see which one has 2. The formula would be:

$m=\frac{y_2-y_1}{x_2-x_1}$

Where m is the slope and

x_1 is first x point

x_2 is second x point

y_1 is first y point

y_2 is second y point

Let's calculate slope of each of the choices.

$m=\frac{y_2-y_1}{x_2-x_1}\\m=\frac{-7+11}{-2+4}\\m=2$

THis one is okay.

$m=\frac{y_2-y_1}{x_2-x_1}\\m=\frac{12-6}{-5-5}\\m=-\frac{3}{5}$

THis one is not 2:1.

$m=\frac{y_2-y_1}{x_2-x_1}\\m=\frac{-11+3}{-4-0}\\m=2$

THis one is okay.

$m=\frac{y_2-y_1}{x_2-x_1}\\m=\frac{7+3}{5-0}\\m=2$

This one is okay.

Hence, A, C, and D all have rate of change of 2:1

4 0

3 years ago

show that thw roots of the equation (x-a)(x_b)=k^2 are always real if a,b and k are real. Please I really need help with this

VLD [36.1K]

Answer:

see explanation

Step-by-step explanation:

Check the value of the discriminant

Δ = b² - 4ac

• If b² - 4ac > 0 then roots are real

• If b² - 4ac = 0 roots are real and equal

• If b² - 4ac < 0 then roots are not real

given (x - a)(x - b) = k² ( expand factors )

x² - bx - ax - k² = 0 ( in standard form )

x² + x(- a - b) - k² = 0

with a = 1, b = (- a - b), c = -k²

b² - 4ac = (- a - b)² + 4k²

For a, b, k ∈ R then (- a - b)² ≥ 0 and 4k² ≥ 0

Hence roots of the equation are always real for a, b, k ∈ R

8 0

3 years ago

Jenn buys 4 balls of yarn for a total of $23.78. She pays with two $20 bills. What is her change?

tamaranim1 [39]

Her change will be $16.22 since 20 +20 is 40 and 40 - 23.78 is 16.22

3 0

3 years ago

Read 2 more answers

A hummingbird can make up to 150 flaps in 4 seconds. How long will it take for it to flap its wings 1000 times?

andreev551 [17]

1000/150 = 6 2/3 * 4 = 26 2/3 seconds

6 0

3 years ago

What is the approximate average rate of change of the function f(x) = -20(1.3)x^

ollegr [7]

Answer:

Step-by-step explanation:

7 0

3 years ago