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3 years ago

Heather made a total of $451.78 last month at her part-time job. If she worked 14 hours, how much did she make per hour?

1 answer:

3 0

The amount of money divided by the amount of hours will give you how much money she makes per hour.

451.78/14=32.27.

She earned $32.27 per hour.

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Which equations correctly represent a line that has a slope of -2/3 and passes through the points (–2, 8) and (1, 6)?

OlgaM077 [116]

Answer:

2x + 3y = 20

Step-by-step explanation:

Slope of the line is -2/3 . We can use any of the given points to find the equation of the line. Lets use (1, 6)

The general point-slope form of a line is:

$y-y_{1} =m(x-x_{1} )$

Here m is the slope which is -2/3

x1 and y1 are the coordinates of the point. So x1 = 1 and y1 = 6

Using these values, we get:

$y-6=-\frac{2}{3} (x-1)\\\\ 3(y-6)=-2(x-1)\\\\ 3y-18=-2x+2\\\\ 2x+3y=20$

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4 years ago

Read 2 more answers

Ty knows that 3.15 ÷ 0.25 = 12.6. Use the drop-down menus to explain how

vagabundo [1.1K]

Answer:

The first one is C. 2

The second one is A. Left

The last one is D.0.126

Step-by-step explanation:

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3 years ago

Read 2 more answers

5. The combined perimeter of a circle and a square is 16. Find the dimensions of the circle and square

Tanya [424]

The dimensions of the circle and square that produce a minimum total area are 1.12 and 2.24 respectively

Represent the side length of the square with s, and the radius of the circle with r.

So, the perimeter (P) and the area (A) of the shape are:

$P =4s + 2\pi r$

$A =s^2 + \pi r^2$

The perimeter is 16. So, we have:

$4s + 2\pi r = 16$

Divide through by 4

$s + 0.5\pi r = 4$

Make s the subject

$s = 4 - 0.5\pi r$

Substitute $s = 4 - 0.5\pi r$ in $A =s^2 + \pi r^2$

$A = (4 - 0.5\pi r )^2 + \pi r^2$

Expand

$A = 16 - 4\pi r + 0.25(\pi r)^2 + \pi r^2$

This gives

$A = 16 - 4\pi r + (0.25\pi^2 + \pi )r^2$

Differentiate with respect to r

$A' = 0 - 4\pi + 2(0.25\pi^2 + \pi )r$

$A' = - 4\pi + 2(0.25\pi^2 + \pi )r$

Set to 0

$- 4\pi + 2(0.25\pi^2 + \pi )r =0$

Add 4pi to both sides

$2(0.25\pi^2 + \pi )r =4\pi$

Divide both sides by 2

$(0.25\pi^2 + \pi )r =2\pi$

Make r the subject

$r =\frac{2\pi}{(0.25\pi^2 + \pi )}\\$

Factor out pi

$r =\frac{2\pi}{\pi(0.25\pi + 1 )}$

Cancel out the common factors

$r =\frac{2}{0.25\pi + 1 }$

Express pi as 3.14

$r =\frac{2}{0.25\times 3.14 + 1 }$

$r =\frac{2}{1.785}$

Divide

$r =1.12$

Recall that:

$s = 4 - 0.5\pi r$

This gives

$s =4 -0.5 \times \pi \times 1.12$

This gives

$s =4 -0.5 \times 3.14 \times 1.12$

$s =2.24$

Hence, the dimensions of the circle and square that produce a minimum total area are 1.12 and 2.24 respectively