1. Write the equation in slope-intercept form. Identify the slope and y-intercept. SHOW ALL WORK
2x - 3y = 9
2. Write the equation in slope-intercept form. Identify the slope and y-intercept. SHOW ALL WORK
x - 4y = -20
3. Find the x- and y-intercepts for -x + 4y = 12. Write each intercept as a unique ordered pair. SHOW ALL WORK
4. y = 2/3x + 7 written in standard form using integers is 3x - y = 21.
A) True
B) False
5. Write an equation of a line that has the same slope as 2x – 5y = 12 and the same y-intercept as 4y + 24 = 5x.
A) y= 2/5x−6
B) y=6x−2/5
C) y=5/2x−6
D) y=1/6x−5/2
6. Write the equation of a line that is perpendicular to the given line and that passes through the given point.
x + 8y = 27; (–5, 5)
A) y=-1/8x-45
B) Y=1/8x+45
C) y=8x+45
D) y=-8x+45
7. Are the graphs of the lines in the pair parallel? Explain.
y = 8/3x+ 19
8x – 3y = 17
A) Yes, since the slopes are the same and the y-intercepts are different.
B) No, since the y-intercepts are different.
C) Yes, since the slopes are the same and the y-intercepts are the same.
D) No, since the slopes are different.
8. A line passes through (2, –1) and (8, 4).
a. Write an equation for the line in point-slope form. (2 points)
b. Rewrite the equation in standard form using integers. (2 points)
SHOW ALL WORK
9. Write at least one complete sentence with a capital letter and punctuation describing slope and how to find it.
10. Find the slope of the line passing through the points (-3, -1) and (-1, 5). SHOW ALL WORK
11. Write an equation in point-slope form for the line through the given point with the given slope.
(10, –9); m = - 2
A) y - 10 = -2(x + 9)
B) y - 9 = -2(x - 10)
C) y - 9 = -2(x + 10)
D) y + 9 = -2(x - 10)

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.