Answer:
1.5 seconds
Step-by-step explanation:
Since f(x) represents the distance from the ground to the rock (in feet), we just need to find the values of x for which f(x) = 340. Substituting f(x) = 340 into f(x) = -16x² - 4x + 382 gives us:
340 = -16x² - 4x + 382
0 = -16x² - 4x + 42 (Subtract 340 from both sides)
16x² + 4x - 42 = 0 (Multiply entire equation by -1, "flip" equation)
8x² + 2x - 21 = 0 (Divide entire equation by 2)
(4x + 7)(2x - 3) = 0 (Factor LHS)
4x + 7 = 0 or 2x - 3 = 0 (Zero Product Property)
4x = -7 or 2x = 3 (Subtract -7 and add 3 from/to both sides, respectively)
or 
x = -1.75 is an extraneous solution because in the context of the question, you can't have negative seconds so therefore, the final answer is 1.5 seconds.
Hope this helps!
To make this new triangle I am going to pretend that the original triangle was at the points (4,4) (-4,4) and (0,8). So if this was dilated down by 1/2 then the triangles points would be (2,2) (-2,2) and (0,4). Then if it is reflected over the x-axis the new points would be (2,-2) (-2,-2) and (0,-4) and if it was translated left by 2 units then the points would be (0,-2) (-4,-2) and (-2, -4), then if the triangle was translated up by 4 units the points and the new triangle would be (0,2) (-4,2) and (-2,0). And that would be what the new triangle would be.
The triangle went from (4,4) (-4,4) and (0,8) to (0,2) (-4,2) and (-2,0).
Answer:
7/3 is constant of proportionality and, 3/7 of a cup of red paint should be added to 1 cup of white paint.
Step-by-step explanation:
Constant of proportionality is the constant value of the ratio of two proportional quantities x and y; usually written y = kx, where k is the factor of proportionality.
To make color pink,
for every 3 cups of red , we need 7 cups of white.
Let 'r' be the cups of red required
let 'w' be the cups of white required
so , as per the question
for 3 r we need = 7 w
r = 7/3 w
so, 7/3 is constant of proportionality and, 3/7 of a cup of red paint should be added to 1 cup of white paint.
You already have the answer! ;)
