9 chairs because 2 to 4 is equal to 1/2 and half of 18 chairs is 9
Answer:
Step-by-step explanation:
The first parabola has vertex (-1, 0) and y-intercept (0, 1).
We plug these values into the given vertex form equation of a parabola:
y - k = a(x - h)^2 becomes
y - 0 = a(x + 1)^2
Next, we subst. the coordinates of the y-intercept (0, 1) into the above, obtaining:
1 = a(0 + 1)^2, and from this we know that a = 1. Thus, the equation of the first parabola is
y = (x + 1)^2
Second parabola: We follow essentially the same approach. Identify the vertex and the two horizontal intercepts. They are:
vertex: (1, 4)
x-intercepts: (-1, 0) and (3, 0)
Subbing these values into y - k = a(x - h)^2, we obtain:
0 - 4 = a(3 - 1)^2, or
-4 = a(2)². This yields a = -1.
Then the desired equation of the parabola is
y - 4 = -(x - 1)^2
Answer:
2:3
Step-by-step explanation:
Just divide each by 6
Answer:
h = p - l - w
Step-by-step explanation:
p = 4l + 4w + 4h Divide l, w, and h by 4
p = l + w + h Set the equation equal to h
h = p - l - w
Answer:
1. x = 15 in
2. x = 8 m
Step-by-step explanation:
1. Given:
length = 10 in
width = 3 in
height = x in
surface area of the rectangular prism = its volume
Required:
Value of x
Area = 2(wl + hl + hw)
Volume = l*w*h
Therefore:
2(3*10 + x*10 + x*3) = 10*3*x
2(30 + 10x + 3x) = 30x
2(30 + 13x) = 30x
60 + 26x = 30x
Subtract 26x from both sides
60 + 26x - 26x = 30x - 26x
60 = 4x
Divide both sides by 4
60/4 = 4x/4
15 = x
x = 15 in
2. Given:
length = 8 m
width = 4 m
height = x m
surface area of the rectangular prism = its volume
Required:
Value of x
Area = 2(wl + hl + hw)
Volume = l*w*h
Therefore:
2(4*8 + x*8 + x*4) = 8*4*x
2(32 + 8x + 4x) = 32x
2(32 + 12x) = 32x
64 + 24x = 32x
Subtract 24x from both sides
64 + 24x - 24x = 32x - 24x
64 = 8x
Divide both sides by 8
64/8 = 8x/8
8 = x
x = 8 m
