Melissa baked 84 cookies. After giving some cookies to Molly

A painter charges an initial fee of $50 and $30 for each hour of labor. Write a linear function to determine the total cost. How

il63 [147K]

The initial fee of $50 is essentially the y intercept because this is the value when x = 0 (x is the number of labor-hours). So b = 50.

The slope is m = 30 because each increase of 1 hour leads to the cost bumping up by 30 dollars. In other words, slope = rise/run = (change in cost)/(change in hours) = 30/1

So we plug m = 30 and b = 50 into the y = mx+b formula to get y = 30x+50

Replace y with f(x) to get f(x) = 30x+50

The linear function for the cost is f(x) = 30x+50

Note: Some books may use other letters (instead of x and f(x)), but the idea is still the same

Once you know the cost function, you replace x with 4.5 to find the amount it will cost to have a painter work for 4.5 hours.

f(x) = 30x+50
f(4.5) = 30*4.5+50
f(4.5) = 135+50
f(4.5) = 185

It will cost 185 dollars to have the painter work for 4.5 hours

7 0

3 years ago

Selma uses a jogging trail that runs through a park near her home. The trail is a loop that is of a mile long. On Monday, Selma

deff fn [24]

Answer:

4.5 miles per hour

Step-by-step explanation:

Selma uses a jogging trail that runs through a park near her home. The trail is a loop that is 3/4 of a mile long. On Monday, Selma ran the loop in 1/6 of an hour. What is Selma's unit rate in miles per hour for Monday's run?

Distance = 3/4 of a mile

Time taken on Monday = 1/6 of an hour.

What is Selma's unit rate in miles per hour for Monday's run?

Unit rate in miles per hour for Monday's run = distance ÷ time taken

= 3/4 ÷ 1/6

= 3/4 × 6/1

= (3 * 6) / (4 * 1)

= 18/4

= 4.5 miles per hour

Unit rate in miles per hour for Monday's run = 4.5 miles per hour

3 0

3 years ago

Find the monthly payment for the loan. Finance $500,000 for an apartment complex with a 12.3% 10-year loan.

Marina86 [1]

Using it's formula, it is found that the monthly payments for the loan of the apartment is of $7,260.50.

<h3>What is the monthly payment formula?</h3>

It is given by:

$A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}$

In which:

P is the initial amount.

r is the interest rate.

n is the number of payments.

In this problem, the parameters are given as follows:

P = 500000, r = 0.123, n = 12 x 10 = 120.

Hence:

r/12 = 0.123/12 = 0.01025.

Then, the monthly payments will be of:

$A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}$

$A = 500000\frac{0.01025(1+0.01025)^{120}}{(1+0.01025)^{120} - 1}$

A = 7260.50.

More can be learned about the monthly payment formula at brainly.com/question/26267630

#SPJ1

6 0

2 years ago

a hiking path is represented by the equation y=3/8x on a coordinate map. The county would like to create a parallel path for bik

stepladder [879]

Answer:

The equation of the bike path on a coordinate map is represented by $y = \frac{3}{8}\cdot x +1$ .

Step-by-step explanation:

From Analytical Geometry, we know that resultant parallel line is a translated version of parent line. Two lines are parallel to each other when they share the same slope. The resultant line can be construted from slope-point form:

$y-y_{o} = m_{\parallel}\cdot (x-x_{o})$

Where:

$x_{o}$ , $y_{o}$ - Components of known point, dimensionless.

$m_{\parallel}$ - Slope of the parallel line, dimensionless.

In addition, a line has also this form:

$y = m\cdot x + b$

Where:

$x$ - Independent variable, dimensionless.

$y$ - Dependent variable, dimensionless.

$m$ - Slope, dimensionless.

$b$ - y-Intercept, dimensionless.

Given that parent function is $y = \frac{3}{8}\cdot x$ , the slope of the resulting line is $m_{\parallel} = \frac{3}{8}$ . Now, if $x_{o} = 16$ and $y_{o} = 7$ , we obtain the equation of the line:

$y-7 = \frac{3}{8}\cdot (x-16)$

$y = \frac{3}{8}\cdot x +1$

The equation of the bike path on a coordinate map is represented by $y = \frac{3}{8}\cdot x +1$ .

3 0

3 years ago

What are the zeros of the polynomial function? f(x)=x2−12x+20 Enter your answers in the boxes. The zeros of f(x) are and

Schach [20]

$f(x)=x^{2} -12x+20$
$f(x)=0$
x $x^{2} -12x+20=0$
Factoring:
$(x-2)(x-10)=0$
Two possible soolutions:

$x-2=0 [tex]x=2$

$x-10=0$
$x=10$

The zeros of the polynomial function are x=2 and x=10

5 0

3 years ago

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