Is vuw similar to vxy? if yes, explain how you know. if no, explain why not.
1 answer:
Answer:
Yes, because m<UVW is congruent to m<XVY and m<VUW is congruent to m<VXY
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is equal and its corresponding angles are congruent
so
In this problem
we know that
the measure of angle VXY is equal to
-----> by supplementary angles
therefore
Remember that
m<UVW=m<XVY -----> is the same vertex
therefore
Triangles VUW and VXY are similar by AAA Similarity Theorem ( the three angles are congruent)
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Answer: Marvin needs approximately 19 days to rent the car.
Step-by-step explanation:
Since we have given that
Amount Marvin get on a discount coupon = $25
She decided to buy insurance for each day.
Let the number of days be x
cost of insurance = $465
According to question, it becomes,
Hence, Marvin needs approximately 19 days to rent the car.
Refer to the diagram below.
Because ray NP bisects ∠MNQ, therefore
∠MNP = ∠PNQ = 2x + 1.
Therefore
∠MNQ = 2*∠PNQ = 2(2x + 1) = 4x + 2.
Because ∠MNQ is given as x² - 10, therefore
x² - 10 = 4x + 2
x² - 4x - 12 = 0
(x + 2 )(x - 6) = 0
x = -2, or x = 6
When x = -2,
∠MNQ = 4*(-2) + 2 = -6°
This answer is not acceptablle, therefore x = -2 should be rejected.
When x = 6,
∠MNQ = 4*6 + 2 = 26°
Answer: x = 6, and ∠MNQ = 26°
Because ray NP bisects ∠MNQ, therefore
∠MNP = ∠PNQ = 2x + 1.
Therefore
∠MNQ = 2*∠PNQ = 2(2x + 1) = 4x + 2.
Because ∠MNQ is given as x² - 10, therefore
x² - 10 = 4x + 2
x² - 4x - 12 = 0
(x + 2 )(x - 6) = 0
x = -2, or x = 6
When x = -2,
∠MNQ = 4*(-2) + 2 = -6°
This answer is not acceptablle, therefore x = -2 should be rejected.
When x = 6,
∠MNQ = 4*6 + 2 = 26°
Answer: x = 6, and ∠MNQ = 26°