Answer:
Step-by-step explanation:
(-4,0) ; (-7, -14)
![d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\\\\ =\sqrt{(-7-[-4])^{2}+(-14-0)^{2}}\\\\ =\sqrt{(-7+4)^{2}+(-14)^{2}}\\\\=\sqrt{(-3)^{2}+(-14)^{2}}\\\\=\sqrt{9+196} \\\\=\sqrt{205} \\\\=14.3178](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_%7B2%7D-x_%7B1%7D%29%5E%7B2%7D%2B%28y_%7B2%7D-y_%7B1%7D%29%5E%7B2%7D%7D%5C%5C%5C%5C%20%3D%5Csqrt%7B%28-7-%5B-4%5D%29%5E%7B2%7D%2B%28-14-0%29%5E%7B2%7D%7D%5C%5C%5C%5C%20%3D%5Csqrt%7B%28-7%2B4%29%5E%7B2%7D%2B%28-14%29%5E%7B2%7D%7D%5C%5C%5C%5C%3D%5Csqrt%7B%28-3%29%5E%7B2%7D%2B%28-14%29%5E%7B2%7D%7D%5C%5C%5C%5C%3D%5Csqrt%7B9%2B196%7D%20%5C%5C%5C%5C%3D%5Csqrt%7B205%7D%20%5C%5C%5C%5C%3D14.3178)
Split the second term 7x^2 - 8x - 12 into two terms
7x^2 + 6x - 14x - 12
Factor out common terms in the first two terms, then in the last two terms
x(7x + 6) - 2(7x + 6)
Factor out the common term; 7x + 6
<u>(7x + 6)(x - 2) </u>
Answer:
(a) Domain: x > 4
(b) Range: y < -2
Step-by-step explanation:
Domain is the set of x-values that can be inputted into function f(x).
Range is the set of y-values that can be outputted by function f(x).
We see that our x-values span from 4 to infinity. Since it is an open dot, we cannot include it in our domain:
(-4, ∞)
We also see that our y-values span from -2 to negative infinity. Since it is an open dot, we cannot include it in our range:
(-∞, -2)
She worked 2 1/2 hrs yesterday and 4 1/4 hrs today...
2 1/2 + 4 1/4 =
2 + 4 = 6
1/2 + 1/4 = 2/4 + 1/4 = 3/4
so she worked a total of 6 3/4 hrs....or 6.75 hrs
she is paid $ 54
54 / 6.75 = $ 8 per hr <=== what she earned per hr
