Given:
A(3,0)
B(1,-2)
C(3,-5)
D(7,-1)
1) reflect across x=-4
essentially calculate the difference between the x=-4 line and Px and "add" it in the other direction to x=-4
A(-4-(3-(-4)),0)=A(-11,0)
B(-4-(1-(-4)),-2)=B(-9,-2)
C(-4-(3-(-4),-5))=C(11,-5)
D(-4-(7-(-4)),-1)=D(-15,-1)
2) translate (x,y)->(x-6,y+8)
A(-3,8)
B(-5,6)
C(-3,3)
D(1,7)
3) clockwise 90° rotation around (0,0), flip the x&y coordinates and then decide the signs they should have based on the quadrant they should be in
A(0,-3)
B(-2,-1)
C(-5,-3)
D(-1,-7)
D) Dilation at (0,0) with scale 2/3, essentially multiply all coordinates with the scale, the simple case of dilation, because the center point is at the origin (0,0)
A((2/3)*3,(2/3)*0)=A(2,0)
B((2/3)*1,(2/3)*-2)=B(2/3,-4/3)
C((2/3)*3,(2/3)*-5)=C(2,-10/3)
D((2/3)*7,(2/3)*-1)=D(14/3,-2/3)
Answer:
-55/78 OR. -0.7
Step-by-step explanation:
Answer:
34.44 miles
Step-by-step explanation:
Distance covered bty the two trains :
Distance = speed * time
Time = 30 minutes = 0.5hr
Distance of train 1 = 64 * 0.5 = 32 miles
Distance of train 2 = 52 * 0.5 = 26 miles
Included Angle = 72°
Using cosine rule :
a² = b² + c² - 2bcCosA
Let Distance between the trains after 30 minutes = a
a^2 = 32^2 + 26^2 - 2(32)(26) * Cos(72)
a^2 = 1700 - 514.20427
a^2 = 1185.7957
a = sqrt(1185.7957)
a = 34.435
a = 34.44 miles
Answer:
Step-by-step explanation: 4a³ + 24ab² - 25b³
(In other words B)
0.78 ÷ 106 = 39/5300
= 0.007358490566037
Explanation: Convert 0.78 into a fraction
0.78 = 39/50. Next you do, 39/50 ÷ 106.
