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:
- Maria–Ava: 15.7 feet
- Lucas–Maria: 10.1 feet
- angle at Maria: 50°
Step-by-step explanation:
The cosine and tangent functions are useful here. The relevant relations are ...
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent
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The distance from Maria to Ava (ma) is the hypotenuse of the triangle, so we have ...
cos(40°) = 12/ma
ma = 12/cos(40°) ≈ 12/0.76604 ≈ 15.7 . . . feet
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The distance from Lucas to Maria (ml) is the side opposite the given angle, so we have ...
tan(40°) = ml/12
ml = 12·tan(40°) ≈ 12·0.83910 ≈ 10.1 . . . feet
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The angle formed at Maria's position is the complement of the other acute angle in the right triangle:
M = 90° -40° = 50°
In summary, ...
- Maria–Ava: 15.7 feet
- Lucas–Maria: 10.1 feet
- angle at Maria: 50°
In order to solve the problem what you must do is 5- .99 to get 5.01
Step-by-step explanation:
1 year = 12 months
2yrs = 24 months
F(c) =100+5(24)
= 100+120
= $220