Answer:
b. (1, 3, -2)
Step-by-step explanation:
A graphing calculator or scientific calculator can solve this system of equations for you, or you can use any of the usual methods: elimination, substitution, matrix methods, Cramer's rule.
It can also work well to try the offered choices in the given equations. Sometimes, it can work best to choose an equation other than the first one for this. The last equation here seems a good one for eliminating bad answers:
a: -1 -5(1) +2(-4) = -14 ≠ -18
b: 1 -5(3) +2(-2) = -18 . . . . potential choice
c: 3 -5(8) +2(1) = -35 ≠ -18
d: 2 -5(-3) +2(0) = 17 ≠ -18
This shows choice B as the only viable option. Further checking can be done to make sure that solution works in the other equations:
2(1) +(3) -3(-2) = 11 . . . . choice B works in equation 1
-(1) +2(3) +4(-2) = -3 . . . choice B works in equation 2
Answer:
5 dollars :)
Step-by-step explanation:
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Answer:
The correct option is B.
Step-by-step explanation:
Two triangle are similar if their corresponding sides are in the same proportion or the corresponding angles are same.
It is given that the ΔPQR is similar to ΔPTS. It means all corresponding angles are same.
![\angle R=\angle S](https://tex.z-dn.net/?f=%5Cangle%20R%3D%5Cangle%20S)
![\angle Q=\angle T](https://tex.z-dn.net/?f=%5Cangle%20Q%3D%5Cangle%20T)
![\angle P=\angle P](https://tex.z-dn.net/?f=%5Cangle%20P%3D%5Cangle%20P)
Angle P can be defined as
![\angle QPR=\angle TPS](https://tex.z-dn.net/?f=%5Cangle%20QPR%3D%5Cangle%20TPS)
![\angle RPQ=\angle TPS](https://tex.z-dn.net/?f=%5Cangle%20RPQ%3D%5Cangle%20TPS)
Therefore option B is correct.
![\angle PST\neq\angle QPR](https://tex.z-dn.net/?f=%5Cangle%20PST%5Cneq%5Cangle%20QPR)
![\angle SPT\neq\angle PTS](https://tex.z-dn.net/?f=%5Cangle%20SPT%5Cneq%5Cangle%20PTS)
![\angle PRQ\neq\angle PTS](https://tex.z-dn.net/?f=%5Cangle%20PRQ%5Cneq%5Cangle%20PTS)
Therefore option A, C and D are incorrect.
Answer:
The standard form of the equation for the conic section represented by
is:
![4\left(-\frac{3}{2}\right)\left(y-12\right)=\left(x-\left(-5\right)\right)^2](https://tex.z-dn.net/?f=4%5Cleft%28-%5Cfrac%7B3%7D%7B2%7D%5Cright%29%5Cleft%28y-12%5Cright%29%3D%5Cleft%28x-%5Cleft%28-5%5Cright%29%5Cright%29%5E2)
Step-by-step explanation:
We know that:
is the standard equation for an up-down facing Parabola with vertex at (h, k), and focal length |p|.
Given the equation
![x^2\:+\:10x\:+\:6y\:=\:47](https://tex.z-dn.net/?f=x%5E2%5C%3A%2B%5C%3A10x%5C%3A%2B%5C%3A6y%5C%3A%3D%5C%3A47)
Rewriting the equation in the standard form
![4\left(-\frac{3}{2}\right)\left(y-12\right)=\left(x-\left(-5\right)\right)^2](https://tex.z-dn.net/?f=4%5Cleft%28-%5Cfrac%7B3%7D%7B2%7D%5Cright%29%5Cleft%28y-12%5Cright%29%3D%5Cleft%28x-%5Cleft%28-5%5Cright%29%5Cright%29%5E2)
Thus,
The vertex (h, k) = (-5, 12)
Please also check the attached graph.
Therefore, the standard form of the equation for the conic section represented by
is:
![4\left(-\frac{3}{2}\right)\left(y-12\right)=\left(x-\left(-5\right)\right)^2](https://tex.z-dn.net/?f=4%5Cleft%28-%5Cfrac%7B3%7D%7B2%7D%5Cright%29%5Cleft%28y-12%5Cright%29%3D%5Cleft%28x-%5Cleft%28-5%5Cright%29%5Cright%29%5E2)
where
vertex (h, k) = (-5, 12)
I can’t see the photo could you please make it bigger so I can help I