1. distribute the parentheses.
-3=12y-10y+35
2. Move the constants to the other side
-3-35=12y-10y
3. Subtract the terms
-38=2y
4. Divide by 2 to get y by itself
y=-19
Answer:
<STP=105°
Step-by-step explanation:
two interior angles equal one opposite exterior angle therefore
7x+6+7x+1=15x
group like terms
6+1=15x-7-7
7=15x-14x
7=x
for 15x
15 will multiply 7 and that is 105
Answer:
33.89
Step-by-step explanation:
the side lengths are the distances between the corner points of the triangle.
P and Q have the same x value, and they therefore create a side parallel to the y-axis. and it is easy to find the length of this side : it is just the difference of the y values.
PQ = 6 - (-6) = 6 + 6 = 12
QR and RP are trickier.
we need Pythagoras to calculate the length of the direct connection between these points as the Hypotenuse of the right triangles with the differences in x and in y values as the other sides.
QR :
QR² = (-3 - 6)² + (-6 - -2)² = (-9)² + (-4)² = 81 + 16 = 97
QR = sqrt(97) ≈ 9.848857802
RP :
RP² = (6 - -3)² + (-2 - 6)² = 9² + (-8)² = 81 + 64 = 145
RP = sqrt(145) ≈ 12.04159458
the perimeter/circumference of the triangle is the sum of all 3 sides
= 12 + sqrt(97) + sqrt(145) ≈ 33.89
Given that AB has been dilated by scale factor 3 to form A'B', and by laws of dilation, the image is congruent to the pre image. This implies that the image will not change in any way whatsoever apart from the size. Hence the slope will remain the same. That means the slope of A'B' will be 3
