Answer:
g(x) = |x/5|
Step-by-step explanation:
A function is stretched horizontally by a factor of k when x is replaced by x/k.
g(x) = f(x/5)
g(x) = |x/5| . . . . . stretch of absolute value by a factor of 5
Given:
The vertex of a quadratic function is (4,-7).
To find:
The equation of the quadratic function.
Solution:
The vertex form of a quadratic function is:
...(i)
Where a is a constant and (h,k) is vertex.
The vertex is at point (4,-7).
Putting h=4 and k=-7 in (i), we get


The required equation of the quadratic function is
where, a is a constant.
Putting a=1, we get

![[\because (a-b)^2=a^2-2ab+b^2]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%28a-b%29%5E2%3Da%5E2-2ab%2Bb%5E2%5D)
Therefore, the required quadratic function is
.
Answer:
<h2>y = 3.5x - 2</h2>
Step-by-step explanation:
The slope-intercept form of an equation of a line:
<h3>y = mx + b</h3>
m - slope
b - y-intercept
We have y-intercept b = -2. Substitute:
<h3>y = mx - 2</h3>
We have the point (4, 12) → x = 4, y = 12. Put them in the equation:
12 = 4m - 2 <em>add 2 to both sides</em>
14 = 4m <em>divide both sides by 4</em>
14/4 = m → m = 3.5
Answer:
h = 1.74
t = 1.19
Step-by-step explanation:
15.4t + 11.6h = 38.51
10.2t + 7.3h = 24.84
15.4•t + 11.6•h = 38.51
10.2•t + 7.3•h = 24.84
11.6h+15.4t = 38.51
7.3h+10.2t = 24.84
h = 87
50
= 1.74
t = 119
100
= 1.19