Answer:
![x\approx 50^\circ](https://tex.z-dn.net/?f=x%5Capprox%2050%5E%5Ccirc)
Step-by-step explanation:
![c^2 = a^2 + b^2 - 2ab(cos(C))](https://tex.z-dn.net/?f=c%5E2%20%3D%20a%5E2%20%2B%20b%5E2%20-%202ab%28cos%28C%29%29)
See the figure below to get the values as:
![7^2=7^2+9^2-2\left(7\right)\left(9\right)cos\left(x\right)\\\\cos(x)=\frac{7^2+9^2-7^2}{2\cdot \:7\cdot \:9}\\\\x\approx 50^\circ](https://tex.z-dn.net/?f=7%5E2%3D7%5E2%2B9%5E2-2%5Cleft%287%5Cright%29%5Cleft%289%5Cright%29cos%5Cleft%28x%5Cright%29%5C%5C%5C%5Ccos%28x%29%3D%5Cfrac%7B7%5E2%2B9%5E2-7%5E2%7D%7B2%5Ccdot%20%5C%3A7%5Ccdot%20%5C%3A9%7D%5C%5C%5C%5Cx%5Capprox%2050%5E%5Ccirc)
There are multiple concepts to solve this problem. This is one of the concept used in high school. Other concept to solve this problem is to use the concept of isosceles triangle. An isosceles triangle is a triangle with (at least) two equal sides. The angles shared by the two equal sides are also equal. So that the sum of all the three angles will add up to 180.
![x+x+80=180\\\\2x=100\\\\x=50^{\circ}](https://tex.z-dn.net/?f=x%2Bx%2B80%3D180%5C%5C%5C%5C2x%3D100%5C%5C%5C%5Cx%3D50%5E%7B%5Ccirc%7D)
Best Regards!
Answer:
C. 604
Step-by-step explanation:
Karana returned the items so you are adding the money back to the credit card which would be 604. 369 + 235 = 604
Answer:
![(\frac{1}{2},0),(\frac{3}{2},0)](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B2%7D%2C0%29%2C%28%5Cfrac%7B3%7D%7B2%7D%2C0%29)
Step-by-step explanation:
The vertex form of a parabola is given by:
, where V(h,k) is the vertex of the parabola.
The given parabola has vertex (1,1).
This implies that:
.
Put these values into the vertex form equation.
![\implies y=a(x-1)^2+1](https://tex.z-dn.net/?f=%5Cimplies%20y%3Da%28x-1%29%5E2%2B1)
The y-intercept of this parabola is: (0,-3).
This point lies on the parabola hence it must satisfy its equation.
![\implies -3=a(0-1)^2+1](https://tex.z-dn.net/?f=%5Cimplies%20-3%3Da%280-1%29%5E2%2B1)
![\implies -3=a(-1)^2+1](https://tex.z-dn.net/?f=%5Cimplies%20-3%3Da%28-1%29%5E2%2B1)
![\implies -3=a(1)+1](https://tex.z-dn.net/?f=%5Cimplies%20-3%3Da%281%29%2B1)
![\implies -3=a+1](https://tex.z-dn.net/?f=%5Cimplies%20-3%3Da%2B1)
![\implies -3-1=a](https://tex.z-dn.net/?f=%5Cimplies%20-3-1%3Da)
![\implies -4=a](https://tex.z-dn.net/?f=%5Cimplies%20-4%3Da)
The equation now becomes
![\implies y=-4(x-1)^2+1](https://tex.z-dn.net/?f=%5Cimplies%20y%3D-4%28x-1%29%5E2%2B1)
To find the x-intercept, put y=0 into the equation:
![\implies -4(x-1)^2+1=0](https://tex.z-dn.net/?f=%5Cimplies%20-4%28x-1%29%5E2%2B1%3D0)
![\implies -4(x-1)^2=-1](https://tex.z-dn.net/?f=%5Cimplies%20-4%28x-1%29%5E2%3D-1)
Divide through by -4.
![\implies \frac{-4(x-1)^2}{-4}=\frac{-1}{-4}](https://tex.z-dn.net/?f=%5Cimplies%20%5Cfrac%7B-4%28x-1%29%5E2%7D%7B-4%7D%3D%5Cfrac%7B-1%7D%7B-4%7D)
![\implies (x-1)^2=\frac{-1}{-4}](https://tex.z-dn.net/?f=%5Cimplies%20%28x-1%29%5E2%3D%5Cfrac%7B-1%7D%7B-4%7D)
![\implies (x-1)^2=\frac{1}{4}](https://tex.z-dn.net/?f=%5Cimplies%20%28x-1%29%5E2%3D%5Cfrac%7B1%7D%7B4%7D)
Take plus or minus square root of both sides.
![\implies x-1=\pm \sqrt{\frac{1}{4}}](https://tex.z-dn.net/?f=%5Cimplies%20x-1%3D%5Cpm%20%5Csqrt%7B%5Cfrac%7B1%7D%7B4%7D%7D)
![\implies x-1=\pm \frac{1}{2}](https://tex.z-dn.net/?f=%5Cimplies%20x-1%3D%5Cpm%20%5Cfrac%7B1%7D%7B2%7D)
![\implies x=1\pm \frac{1}{2}](https://tex.z-dn.net/?f=%5Cimplies%20x%3D1%5Cpm%20%5Cfrac%7B1%7D%7B2%7D)
or ![\implies x=1+ \frac{1}{2}](https://tex.z-dn.net/?f=%5Cimplies%20x%3D1%2B%20%5Cfrac%7B1%7D%7B2%7D)
or ![\implies x=1 \frac{1}{2}](https://tex.z-dn.net/?f=%5Cimplies%20x%3D1%20%5Cfrac%7B1%7D%7B2%7D)
Therefore the x-intercepts are:
![(\frac{1}{2},0),(\frac{3}{2},0)](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B2%7D%2C0%29%2C%28%5Cfrac%7B3%7D%7B2%7D%2C0%29)
To the nearest hundredth, we have ![0.50,0),(1.50,0)](https://tex.z-dn.net/?f=0.50%2C0%29%2C%281.50%2C0%29)
To check the answer, sub in 67 for x and 25 for y in both equations...because for it to be a solution, it has to satisfy both of the equations.
(67,25)...x = 67 and y = 25
x + y = 92
67 + 25 = 92
92 = 92 (correct)
y = 3x - 4
25 = 3(67) - 4
25 = 201 - 4
25 = 197 (incorrect)
so (67,25) is NOT a solution to this system of equations because it does not satisfy both of the equations