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3 years ago

A line contains the point (8, –5). If the slope of the line is 5/7 write the equation of the line using point-slope form.

1 answer:

7 0

Point slope form
y – y1 = m(x – x1)

so equation
y + 5 = 5/7(x - 8)

hope that helps

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A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of t

Makovka662 [10]

Answer:

132.233 ft2

Step-by-step explanation:

Let's call the width of the rectangle 'w' and the length 'x'. So the area of the semicircle is:

$A_1 = \pi*radius^2/2$

$A_1 = \pi*(w/2)^2/2$

$A_1 = \pi/8*w^2$

And the area of the rectangle is:

$A_2 = w*x$

If the perimeter of the window is 41 feet, we have:

$Perimeter = length + 2*width + \pi*radius$

$41 = x + 2*w + \pi*w/2$

$x = 41 - w(2 + \pi/2)$

Now, the equation for the total area of the window is:

$A = A_1 + A_2 = \pi/8*w^2 + w*x$

$A = \pi/8*w^2 + w*(41 - w(2 + \pi/2))$

$A = (\pi/8-2 - \pi/2)*w^2 + 41w = -3.1781w^2 + 41w$

To find the maximum area, we can find the x-coordinate of the vertex of the quadratic equation:

$x\_vertex = -b / 2a = -41 / (-3.1781*2) = 6.45$

So the width that gives us the maximum area of the window is 6.45 feet, and the area will be:

$A = -3.1781w^2 + 41w = -3.1781*(6.45)^2 + 41*6.45 = 132.233\ ft^2$

3 0

3 years ago

Simplify the fraction 40 and 24

Ganezh [65]

I hope this helps you

40=8.5=5.2^3

24=8.3=3.2^3

6 0

3 years ago

PLEASE HELP ME OUT I DONT UNDERSTAND!!

liberstina [14]

Answer:

1.) Rate of Change (can't create a table sorry)

2.) Equation

Step-by-step explanation:

7 0

2 years ago

Write the quadratic equation whose roots are -2 and 3, and whose leading coefficient is 3

KIM [24]

Now, if the roots are -2 and 3, that simply means $\bf \begin{cases}
x=-2\implies &x+2=0\\
x=3\implies &x-3=0
\end{cases}$

now, as far as the leading term's coefficient having a 3, we can simply make it a "common factor" of both terms.

$\bf \begin{cases}
x=-2\implies &x+2=0\\
x=3\implies &x-3=0
\end{cases}\implies (x+2)(x-3)=0
\\\\\\
\stackrel{\textit{common factor}}{3}(x+2)(x-3)=\textit{original polynomial}
\\\\\\
3(x^2-x-6)=y\implies 3x^2-3x-18=y$

5 0

3 years ago

Which expression represents the phrase: “3 fewer than a number, p”?

Artyom0805 [142]

Answer:

p - 3

Step-by-step explanation:

"fewer than" means subtract from, in this case 3, from an unknown number represented by p

3 0

3 years ago