Answer:
When six guests choose cheesecake and eight choose apple pie, the ratio is 6:8. If we use the same prompt but change 6 to 3 and change 8 to 4, the ratio becomes 3:4 with the pie graph looking exactly the same.
6:8 comes out to a total of 14 people
and 3:4 comes out to a total of 7 people
The two ratios are equivalent due to the graphs looking exactly the same as well as that 14 is double of 7.
Step-by-step explanation:
X = -17/8
Do you need explanation?
A) The signs of the first derivative (g') tell you the graph increases as you go left from x=4 and as you go right from x=-2. Since g(4) < g(-2), one absolute extreme is (4, g(4)) = (4, 1).
The sign of the first derivative changes at x=0, at which point the slope is undefined (the curve is vertical). The curve approaches +∞ at x=0 both from the left and from the right, so the other absolute extreme is (0, +∞).
b) The second derivative (g'') changes sign at x=2, so there is a point of inflection there.
c) There is a vertical asymptote at x=0 and a flat spot at x=2. The curve goes through the points (-2, 5) and (4, 1), is increasing to the left of x=0 and non-increasing to the right of x=0. The curve is concave upward on [-2, 0) and (0, 2) and concave downward on (2, 4]. A possible graph is shown, along with the first and second derivatives.
Answer:
A. 2
Step-by-step explanation:
Count the steps to get to the both points.
From (-3, -2) to (-1, 2), it gets up by 4 and move to the right by 2.
Rise ÷ Run = 4 ÷ 2 = 2
Given:
Triangle QRS has coordinates Q(-2, -2), R(0, 3), and S(4, -2) and is dilated by a scale factor of 2.
To find:
The new coordinates of point S', and state whether the dilation is an enlargement or a reduction.
Solution:
If a figure is dilated by factor k with origin as center of dilation, then
Where, 0<k<1 is reduction and k>1 is enlargement.
The figure is dilated by scale factor 2 which is greater than 1, so the dilation is an enlargement. The rule of dilation is:
Using this rule, we get
Therefore, the new coordinates of point S' are (8,-4).
