What is the slope and the y-intercept of the equation y = -x + 8?

A page should have perimeter of 42 inches. The printing area within the page

Tamiku [17]

Overall dimensions of the page in order to maximize the printing area is page should be 11 inches wide and 10 inches long .

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

We have , A page should have perimeter of 42 inches. The printing area within the page would be determined by top and bottom margins of 1 inch from each side, and the left and right margins of 1.5 inches from each side. let's assume width of the page be x inches and its length be y inches So,

Perimeter = 42 inches

⇒ $2(x+y) = 42\\x+y = 21\\y = 21-x$

width of printed area = x-3 & length of printed area = y-2:

area = $length(width)$

$area = (x-3)(y-2)\\area = (x-3)(21-x-2)\\area = (x-3)(19-x)\\area = -x^{2} + 22x -57$

Let's find $\frac{d(area)}{dx}$ :

$\frac{d(area)}{dx}$ = $\frac{d(-x^{2}+22x-57)}{dx} = -2x +22$ , for area to be maximum $\frac{d(area)}{dx}$ = 0

⇒ $-2x+22 = 0\\2x =22\\x=11 inches$

And ,

$y = 21-x\\y = 21-11\\y = 10 inches$

∴ Overall dimensions of the page in order to maximize the printing area is page should be 11 inches wide and 10 inches long .

7 0

3 years ago

Multiply.<br><br> 132.71 × 10²

Darya [45]

10*10=100
100*132.71=13271

5 0

4 years ago

Read 2 more answers

Examine the following table, which represents some points on a line

Lady bird [3.3K]

Answer:

Option (b)

Step-by-step explanation:

Let the points represented by the given table lie on a line.

And the equation of the line is,

y = mx + b

Where m = slope of the line

b = y-intercept

Let the points lying on the line are (0, -2) and (3, -3)

Slope of the line 'm' = $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

m = $\frac{-2-(-3)}{0-3}$

m = $\frac{-2+3}{0-3}$

m = - $\frac{1}{3}$

y-intercept 'b' = (-2)

Equation of the line is,

y = $-\frac{1}{3}x-2$

This equation matches with equation given in option (b).

Option (b) will be the answer.

7 0

4 years ago

A ceiling fan with 16-in. blades rotates at 45 rpm.

Kobotan [32]

A. We're told the fan completes 45 full revolutions every minute. One full revolution is $2\pi\,\mathrm{rad}$ , so the fan has an angular speed of

$\dfrac{2\pi\,\mathrm{rad}}{1\,\mathrm{rev}}\cdot\dfrac{45\,\mathrm{rev}}{\mathrm{min}}=90\pi\dfrac{\rm{rad}}{\rm{min}}$

B. Throughout one full revolution of the fan, a point at the tip of one of the fan's blades travels the circumference of a circle with radius 16 in. The circumference is then $2\pi(16\,\mathrm{in})=32\pi\,\mathrm{in}$ . This means the linear speed is

$\dfrac{32\pi\,\mathrm{in}}{1\,\mathrm{rev}}\cdot\dfrac{45\,\mathrm{rev}}{\mathrm{min}}=1440\pi\,\dfrac{\rm{in}}{\rm{min}}$

8 0

3 years ago

Given the parabola equation: y=(x-2)^2+3

sp2606 [1]

y=2x-4+3 okayyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy

5 0

3 years ago