Answer:
d.
Step-by-step explanation:
Since it's an isosceles triangle, WX=WZ= 2n-5
Perimeter = n + (2n-5) + (2n-5)
= 5n - 10
The Perimeter is given to be 20
5n - 10 = 20
5n = 30
n = 6
3x + y = -3
-2x + y = 7
Use elimination method
Subtract both equations
5x = -10, x = -2
Plug in -2 for x (any equation)
3(-2) + y = -3
-6 + y = -3
y = 3
Solution: x = -2, y = 3
Or as a coordinate: (-2, 3)
Answer: A. (-8,-3)
Step-by-step explanation:
Original formula is f(x)=|x-h|+k, the vertex is (h,k), so a positive h in the formula would turn out negative in the vertex.
Since
, we can rewrite the integral as

Now there is no ambiguity about the definition of f(t), because in each integral we are integrating a single part of its piecewise definition:

Both integrals are quite immediate: you only need to use the power rule

to get
![\displaystyle \int_0^11-3t^2\;dt = \left[t-t^3\right]_0^1,\quad \int_1^4 2t\; dt = \left[t^2\right]_1^4](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_0%5E11-3t%5E2%5C%3Bdt%20%3D%20%5Cleft%5Bt-t%5E3%5Cright%5D_0%5E1%2C%5Cquad%20%5Cint_1%5E4%202t%5C%3B%20dt%20%3D%20%5Cleft%5Bt%5E2%5Cright%5D_1%5E4)
Now we only need to evaluate the antiderivatives:
![\left[t-t^3\right]_0^1 = 1-1^3=0,\quad \left[t^2\right]_1^4 = 4^2-1^2=15](https://tex.z-dn.net/?f=%5Cleft%5Bt-t%5E3%5Cright%5D_0%5E1%20%3D%201-1%5E3%3D0%2C%5Cquad%20%5Cleft%5Bt%5E2%5Cright%5D_1%5E4%20%3D%204%5E2-1%5E2%3D15)
So, the final answer is 15.
Answer:
x ≈ 33.1°
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan x =
=
, then
x =
(
) ≈ 33.1° ( to the nearest tenth )