Answer:
f(6) = - 75 , g(- 5) = - 8
Step-by-step explanation:
substitute x = 6 into f(x) , that is
f(6) = - 2(6)² - 3 = - 2(36) - 3 = - 72 - 3 = - 75
substitute x = - 5 into g(x) , that is
g(- 5) = 2(- 5) + 2 = - 10 + 2 = - 8
Answer:
The greatest number of miles that she can travel is 36(2/3) miles
Step-by-step explanation:
m=miles
25+1.50m ≤ 80
1.5 m ≤ 55
m ≤ 36.66666......
m ≤ 36 (6/9)
m ≤ 36(2/3)
Answer:
its kika 700
Step-by-step explanation-
i took the math test and got it right
Answer:
17) 250 km²
18) never
19) sometimes
20) 288 in³
Step-by-step explanation:
17)
this polygon can be seen as the combination of two shapes : a 16×13 rectangle on top, and a right-angled triangle at the bottom.
this triangle has the side lengths
15 km
(16 - 10) = 6 km
(27 - 13) = 14 km
the total area is the area of the rectangle plus the area of the triangle.
the area of the rectangle (length×width)
Ar = 16×13 = 208 km²
the area of the triangle (baseline×height/2)
since it is a right-angled triangle, we use one side of the 90 degree angle as baseline and the other as height
At = 6×14/2 = 3×14 = 42 km²
so the total area of the polygon
Ap = Ar + At = 208 + 42 = 250 km²
18) the first quadrant is the area between the right (positive) side of the x axis and the upper (positive) part of the y axis. all points here have always and only positive x and y values. never any negative ones.
19) when a point is on the x-axis, well, left of point 0 on the x -axis are only negative values of x. and right of point 0 of the x-axis are only positive values of x. so, for some of these points the x value is positive, and for some it is negative. therefore "sometimes".
20) the volume of a box is length×width×height.
V = 8×3×12 = 24×12 = 288 in³
For this case we must simplify the following expression:
![\sqrt {\frac {2160x ^ 8} {60x ^ 2}}](https://tex.z-dn.net/?f=%5Csqrt%20%7B%5Cfrac%20%7B2160x%20%5E%208%7D%20%7B60x%20%5E%202%7D%7D)
We rewrite the expression:
![\sqrt {\frac {60 * 36 * x ^ 8} {60x ^ 2}} =](https://tex.z-dn.net/?f=%5Csqrt%20%7B%5Cfrac%20%7B60%20%2A%2036%20%2A%20x%20%5E%208%7D%20%7B60x%20%5E%202%7D%7D%20%3D)
We eliminate common terms:
![\sqrt {\frac {36 * x ^ 8} {x ^ 2}} =](https://tex.z-dn.net/?f=%5Csqrt%20%7B%5Cfrac%20%7B36%20%2A%20x%20%5E%208%7D%20%7Bx%20%5E%202%7D%7D%20%3D)
For division of powers of the same base, the same base is placed and the exponents are subtracted:
![\sqrt {36x ^ {8-2}} =\\\sqrt {36x ^ {6}} =](https://tex.z-dn.net/?f=%5Csqrt%20%7B36x%20%5E%20%7B8-2%7D%7D%20%3D%5C%5C%5Csqrt%20%7B36x%20%5E%20%7B6%7D%7D%20%3D)
By definition of properties of powers and roots we have:
![\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}](https://tex.z-dn.net/?f=%5Csqrt%20%5Bn%5D%20%7Ba%20%5E%20m%7D%20%3D%20a%20%5E%20%7B%5Cfrac%20%7Bm%7D%20%7Bn%7D%7D)
So:
![6x ^ {\frac {6} {2}} =\\6x ^ 3](https://tex.z-dn.net/?f=6x%20%5E%20%7B%5Cfrac%20%7B6%7D%20%7B2%7D%7D%20%3D%5C%5C6x%20%5E%203)
Answer:
Option C