Answer:
h = -9
Step-by-step explanation:
Distribute the 2 to the parentheses:
5h + 2(11 - h) = -5
5h + 22 - 2h = -5
Add like terms:
3h + 22 = -5
3h = -27
h = -9
2y=10x-14
5x-y=7
Divide both sides by 2 in the 1st equation
y=5x-7
Now substitute is to 2nd equation
5x-5x+7=7
0=0
Therefore there is no solution or it is inconsistent
A. left 2 units
the vertex form of a parabola is
y = a(x-h)^2 + k
(h,k) is the point of the vertex
since h is -2 in (x+2)^2
the function is shifted 2 units left
Angles JKH and IHK are alternate interior angles
Answer:
Step-by-step explanation:
Q1)
Use Phythogoras theorem:
![(AC)^2=(BC)^2+(AB)^2\\BC^2=AC^2-AB^2\\BC^2=6^2-4^2\\BC^2=36-16\\BC^2=20\\\\Apply\ square\ on\ both\ sides\\\\\sqrt{BC^2}=\sqrt{20} \\BC=\sqrt{20} \\BC=\sqrt{10(2)} \\BC=\sqrt{5(2)(2)} \\BC=2\sqrt{5}](https://tex.z-dn.net/?f=%28AC%29%5E2%3D%28BC%29%5E2%2B%28AB%29%5E2%5C%5CBC%5E2%3DAC%5E2-AB%5E2%5C%5CBC%5E2%3D6%5E2-4%5E2%5C%5CBC%5E2%3D36-16%5C%5CBC%5E2%3D20%5C%5C%5C%5CApply%5C%20square%5C%20on%5C%20both%5C%20sides%5C%5C%5C%5C%5Csqrt%7BBC%5E2%7D%3D%5Csqrt%7B20%7D%20%20%5C%5CBC%3D%5Csqrt%7B20%7D%20%5C%5CBC%3D%5Csqrt%7B10%282%29%7D%20%5C%5CBC%3D%5Csqrt%7B5%282%29%282%29%7D%20%5C%5CBC%3D2%5Csqrt%7B5%7D)
Q2)
Apply phythogoras theorem:
![CD^2=CE^2+DE^2\\CD^2=7^2+9^2\\CD^2=49+81\\CD^2=130\\\\Apply\ square\ root\ on\ both\ sides\\\\\\sqrt{CD^2} = \sqrt{130} \\\\CD=\sqrt{130} \\\\CD=11.4](https://tex.z-dn.net/?f=CD%5E2%3DCE%5E2%2BDE%5E2%5C%5CCD%5E2%3D7%5E2%2B9%5E2%5C%5CCD%5E2%3D49%2B81%5C%5CCD%5E2%3D130%5C%5C%5C%5CApply%5C%20square%5C%20root%5C%20on%5C%20both%5C%20sides%5C%5C%5C%5C%5C%5Csqrt%7BCD%5E2%7D%20%3D%20%5Csqrt%7B130%7D%20%5C%5C%5C%5CCD%3D%5Csqrt%7B130%7D%20%5C%5C%5C%5CCD%3D11.4)
Q3)
Apply phythogoras theorem again:
![BC^2=BD^2+CD^2\\BC^2=7^2+13^2\\BC^2=49+169\\BC^2=218\\\\Apply\ square\ root\ on\ both\ sides\\\\\\sqrt{BC^2} =\sqrt{218} \\\\BC=\sqrt{218} \\\\BC=14.76](https://tex.z-dn.net/?f=BC%5E2%3DBD%5E2%2BCD%5E2%5C%5CBC%5E2%3D7%5E2%2B13%5E2%5C%5CBC%5E2%3D49%2B169%5C%5CBC%5E2%3D218%5C%5C%5C%5CApply%5C%20square%5C%20root%5C%20on%5C%20both%5C%20sides%5C%5C%5C%5C%5C%5Csqrt%7BBC%5E2%7D%20%3D%5Csqrt%7B218%7D%20%20%5C%5C%5C%5CBC%3D%5Csqrt%7B218%7D%20%5C%5C%5C%5CBC%3D14.76)
I have an attached an image for Question 2 for better understanding the length of DE in question equals 15 - 6 = 9