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soldier1979 [14.2K]

2 years ago

13

Louis plans to buy a new washing machine. The washing machine costs $560 and has an estimated annual operating cost of $48. Whic

h rational function models the average annual cost in dollars of owning the washing machine for x years?

1 answer:

IrinaK [193]2 years ago

5 0

Answer:

The answer is D

Step-by-step explanation:

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Nita earns $20 per week walking her neighbor's dog. She also makes $2 per rose that she sells from her rose garden. Nita wants h

lyudmila [28]

Answer:

20+2<u>></u>50

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Given the following three points, find by the hand the quadratic function they represent (0,6, (2,16, (3,33)

Lisa [10]

Answer:

$f(x) = 4x^2 - 3x + 6$

Step-by-step explanation:

Quadratic function is given as $f(x) = ax^2 + bx + c$

Let's find a, b and c:

Substituting (0, 6):

$6 = a(0)^2 + b(0) + c$

$6 = 0 + 0 + c$

$c = 6$

Now that we know the value of c, let's derive 2 system of equations we would use to solve for a and b simultaneously as follows.

Substituting (2, 16), and c = 6

$f(x) = ax^2 + bx + c$

$16 = a(2)^2 + b(2) + 6$

$16 = 4a + 2b + 6$

$16 - 6 = 4a + 2b + 6 - 6$

$10 = 4a + 2b$

$10 = 2(2a + b)$

$\frac{10}{2} = \frac{2(2a + b)}{2}$

$5 = 2a + b$

$2a + b = 5$ => (Equation 1)

Substituting (3, 33), and c = 6

$f(x) = ax^2 + bx + x$

$33 = a(3)^2 + b(3) + 6$

$33 = 9a + 3b + 6$

$33 - 6 = 9a + 3b + 6 - 6$

$27 = 9a + 3b$

$27 = 3(3a + b)$

$\frac{27}{3} = \frac{3(3a + b)}{3}$

$9 = 3a + b$

$3a + b = 9$ => (Equation 2)

Subtract equation 1 from equation 2 to solve simultaneously for a and b.

$3a + b = 9$

$2a + b = 5$

$a = 4$

Replace a with 4 in equation 2.

$2a + b = 5$

$2(4) + b = 5$

$8 + b = 5$

$8 + b - 8 = 5 - 8$

$b = -3$

The quadratic function that represents the given 3 points would be as follows:

$f(x) = ax^2 + bx + c$

$f(x) = (4)x^2 + (-3)x + 6$

$f(x) = 4x^2 - 3x + 6$

6 0

3 years ago

Lionfish are considered an invasive species, with an annual growth rate of 67%. A scientist estimates there are 8,000 lionfish i

natita [175]

<em>Answer:</em>

<em>There would be 173,535 lionfish after 6 years.</em>

<em>Step-by-step explanation:</em>

<em>Since lionfish are considered an invasive species, with an annual growth rate of 67%, ya scientist estimates there are 8,000 lionfish in a certain bay after the first year, A) to write the explicit equation for f (n) that represents the number of lionfish in the bay after n years; B) determine how many lionfish will be in the bay after 6 years; and C) if scientists remove 1,200 fish per year from the bay after the first year, determine what is the recursive equation for f (n); the following calculations must be performed:</em>

<em></em>

<em>A)</em>

<em>8000 x 1.67 ^ n = f </em>

<em>B)</em>

<em>8000 x 1.67 ^ 6 = X</em>

<em>8000 x 21.691961596369 = X</em>

<em>173,535.692770952 = X </em>

<em>C)</em>

<em>(8000 - 1200 x 1 ^ n) x 1.67 ^ n = f</em>

<em>Therefore, there would be 173,535 lionfish after 6 years.</em>

5 0

2 years ago

Clara scored a 79 on her history test what grade does she have to get on her next test so she will have a average of a 83

Airida [17]

79 is 4 below 83 so her next grade needs to be 4 above in order to get an average of 83. The answer is 87.

6 0

3 years ago

Dan draws a circle with a radius of 8 inches. Question 1 Part A: What is the circumference of Dan's circle, inches? If needed, r

geniusboy [140]

Answer:

The circumference of Dan's circle is approximately 50.27 inches.

Step-by-step explanation:

The length of the circumference ( $s$ ), measured in inches, is determined by the formula:

$s = 2\pi\cdot r$ (1)

Where $r$ is the radius, measured in inches.

If we know that $r = 8\,in$ , then the length of the circumference is:

$s = 2\pi\cdot (8\,in)$

$s \approx 50.27\,in$

The circumference of Dan's circle is approximately 50.27 inches.

8 0

3 years ago