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Answer:
9. A. (3,-2)
10. B. 43°
11. D. 343 cm²
12. A. 15
Step-by-step explanation:
9.Coordinates for summit/vertex U (2,3) after a rotation of 270 degrees.
Rotating a figure by 270 degrees is exactly like rotating it -90 degrees, crossing down over the X-axis (at least for the two summits that are in the first Quadrant).
Doing so, what we do is invert the coordinate numbers (so 2,3 become 3,2) and we change the sign of the Y-value, since we are now in the 4th quadrant, in a negative Y-value domain.
So, vertex U (2,3) becomes (2,-3) after a 270 degrees rotation.
10. Parallelogram JKLM. Determine angle L real value, using the expressions: ∠J =(6x + 7)° , ∠M =(y + 10)° and ∠L =(4x + 19)° ,
Since it's a parallelogram, we know that ∠J = ∠L, so we create an equation and solve it.
6x + 7 = 4x + 19
2x = 12
x = 6
Then we use that value inside the expression given for L:
∠L =(4x + 19)° = (4 (6) + 19)° = (24 + 19)° = 43°
Answer is 43°
11. 2 similar trapezoidal prisms, 5 and 7 of sides respectively. Surface area of the small one is 175 sq cm, what' the surface area of the larger one?
We know that the two prisms are similar.... so all respective sides will be in the same proportion. We know the scale factor is 1.4 (7/5).
So, to calculate the surface area of any side, we'll have something like that:
SA = 1.4x * 1.4y = 1.96xy (x and y representing the dimensions of the small prism)
So, the surface area of the large one is 1.96 times the one of the small one.
SA = 1.96 * 175 = 343
Answer is then D. 343 cm²
12. For the triangle shown, solve for x.
We know the angle facing the 25 units side is a right angle (90 degrees).
So, we can use the Law of Sines to solve this:
Let's assume c = x, what we're looking for. C is then 37 degrees. A = 90 degres and a = 25.
We isolate c and solve:
The length of x is 15.05 or 15, answer A.