<h2>
Answer:</h2>
The statement which best describes the effect of replacing the function f(x) with g(x) is:
The graph shifts 7 units up.
<h2>
Step-by-step explanation:</h2>
The function f(x) is given by :
![f(x)=2x-2](https://tex.z-dn.net/?f=f%28x%29%3D2x-2)
The function f(x) is a linear function with positive slope.
and the function g(x) is given by:
![g(x)=2x+5](https://tex.z-dn.net/?f=g%28x%29%3D2x%2B5)
The function g(x) is a linear function with same positive slope.
Also, we know that any transformation of the type:
f(x) → f(x)+k
is a translation transformation such that it if k>0 then it is a shift k units upwards and if k<0 then it is a shift k units downward.
Here we have:
g(x)=2x+5-2+2
i.e.
g(x)=2x-2+7
i.e.
g(x)=f(x)+7
Hence, the function g(x) is a translation of the function f(x) 7 units upward.
Let be A(2,2) and B(4, 4) two points, let be C the point which is on the perpendicular bisector of the segment AB, so the coordinate of C must be
C(2+4 / 2, 2 + 4 /2) = C(3,3)
<span>C is equidistant from the endpoints of the segment.
proof
vect AC= (1, 1), and vect CB= (1, 1), the length of each vect is
CB= sqrt2, and AC=</span>sqrt2, so it is prooved that AC=CB, C is equidistant to the two endpoints
<h2>c=10.35</h2><h2><a=50.87°</h2><h2><b=87.13°</h2>
Step-by-step explanation:
as we know
law of cosine
![c = \sqrt{ {a}^{2} + {b}^{2} - 2ab. \cos(c) }](https://tex.z-dn.net/?f=c%20%3D%20%20%5Csqrt%7B%20%7Ba%7D%5E%7B2%7D%20%2B%20%20%7Bb%7D%5E%7B2%7D%20%20-%202ab.%20%5Ccos%28c%29%20%20%7D%20%20)
![c = \sqrt{ {14}^{2} + {18}^{2} - 2.14.18 - \cos( {35}^{o} ) }](https://tex.z-dn.net/?f=c%20%3D%20%20%5Csqrt%7B%20%7B14%7D%5E%7B2%7D%20%20%2B%20%20%7B18%7D%5E%7B2%7D%20%20-%202.14.18%20-%20%20%5Ccos%28%20%7B35%7D%5E%7Bo%7D%20%29%20%7D%20)
![c = 10.35](https://tex.z-dn.net/?f=c%20%3D%2010.35)
using the law of cosine
![cos(a) = \frac{ {b}^{2} + {c}^{2} - {a}^{2} }{2bc}](https://tex.z-dn.net/?f=cos%28a%29%20%3D%20%20%5Cfrac%7B%20%7Bb%7D%5E%7B2%7D%20%20%2B%20%20%7Bc%7D%5E%7B2%7D%20%20-%20%20%7Ba%7D%5E%7B2%7D%20%7D%7B2bc%7D%20)
![\cos(a) = \frac{ {18}^{2} + {10.35 }^{2} - {14}^{2} }{2.18.(10.35)}](https://tex.z-dn.net/?f=%20%5Ccos%28a%29%20%20%3D%20%20%5Cfrac%7B%20%7B18%7D%5E%7B2%7D%20%20%2B%20%20%7B10.35%20%7D%5E%7B2%7D%20%20-%20%20%7B14%7D%5E%7B2%7D%20%7D%7B2.18.%2810.35%29%7D%20)
![a = {50.87}^{o}](https://tex.z-dn.net/?f=a%20%3D%20%20%7B50.87%7D%5E%7Bo%7D%20)
b=87.13°
Answer:
Perpendicular lines
Step-by-step explanation:
MN: (-4, 8) and (-4, -6), This line parallel to y-axis as as x-value doesn't change
KL: (-8, 2) and (6, 2), This line is parallel to x-axis as y-value doesn't change
The given lines are perpendicular as one is parallel to x, another one is parallel to y
Answer:
x = 21
Step-by-step explanation:
Inscribed angle = (3x - 3)°
Intercepted arc measure = 120°
Thus:
(3x - 3)° = ½(120°) => an inscribed angle of any circle = ½ the measure of its intercepted arc.
Multiply both sides by 2
2(3x - 3) = 120
6x - 6 = 120
6x - 6 + 6 = 120 + 6
6x = 126
6x/6 = 126/6
x = 21