Complete the two-column proof using the answers in the bank. Given: V is the midpoint of (SU) ̅ .∠RSV ≅ ∠TUV Prove: ∆VUT ≅∆VSR

Mathematics

1 answer:

ivann1987 [24]3 years ago

8 0

Step-by-step explanation:

1. V is the midpoint of (SU) ̅ 1. Given

2. UV ≅ VS 2. Definition of midpoint

3. ∠RSV ≅ ∠TUV 3. Given

4. ∠SVR ≅∠UVT 4. Vertical Angle Theorem

5. ∆VUT ≅ ∆VSR 5. ASA Congruence

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Which is the equation of a parabola with a directrix at y = −3 and a focus at (5, 3)?

kramer

Answer:

y = 1/12 (x − 5)²

Step-by-step explanation:

We can solve this graphically without doing calculations.

The y component of the focus is y = 3. Since this is above the directrix, we know this is an upward facing parabola, so it must have a positive coefficient. That narrows the possible answers to A and C.

The x component of the focus is x = 5. Since this is above the vertex, we know the x component of the vertex is also x = 5.

So the answer is A. y = 1/12 (x−5)².

But let's say this wasn't a multiple choice question and we needed to do calculations. The equation of a parabola is:

y = 1/(4p) (x − h)² + k

where (h, k) is the vertex and p is the distance from the vertex to the focus.

The vertex is halfway between the focus and the directrix. So p is half the difference of the y components:

p = (3 − (-3)) / 2

p = 3

k, the y component of the vertex, is the average:

k = (3 + (-3)) / 2

k = 0

And h, the x component of the vertex, is the same as the focus:

h = 5

So:

y = 1/(4×3) (x − 5)² + 0

y = 1/12 (x − 5)²

3 0

3 years ago

PLEASE HELP ASAP!!!!!

maw [93]

Answer:

Step-by-step explanation

Since we are reflecting across the x axis, all of the y coordinates will remain the same. You find the distance away from the x = 4, double it, and add that value to x. So,

X' is now (8,3)

Y' is now (6,0)

Z' is now (4,2) because its x was 0, and anything * 0 = 0 so it does not move.

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4 years ago

Joanna set a goal to drink more water daily. The number of ounces of water she drank each of the last seven days is shown below.

hammer [34]

<u>Answer:</u>

The median amount of water is higher when the eighth day's amount is included in the data.

<u>Explanation:</u>

Given the ounces of water drank is 60, 58, 64, 64, 68, 50, 57

Arranging in ascending order: 50, 57, 58, 60, 64, 64, 68