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Andrej [43]
3 years ago
11

Please answer asap!!!!!!!!!!!!!!!!!!1

Mathematics
2 answers:
Vlad [161]3 years ago
8 0

Answer:

x= 145 degrees

Step-by-step explanation:

I'm going to assume that the 2 lines are parallel only because if they weren't, the problem would be impossible to solve.

If 2 parallel lines are cut by a transversal, then:

1. Corresponding angles are congruent

2. Alternate interior angles are congruent

3. Alternate exterior angles are congruent

4. Consecutive interior angles are supplementary

So, how do you solve this?

There are many ways.

1. All vertical angles are congruent. In this case, x and a 145 degree angle is congruent. This is one way to show x=145

2. x and another 35 degree angle are consecutive interior angles. They should add up to 180 degrees, 180-35-145. Therefore x=145 degrees.

Mkey [24]3 years ago
6 0

Answer:

x=145° (vertically opposite angles)

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The equation of a parabola with a directrix at y = -3 and a focus at (5 , 3) is y = one twelfth (x - 5)² ⇒ 1st answer

Step-by-step explanation:

The form of the equation of the parabola is  (x - h)² = 4p(y - k), where

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- Compare it with the 2nd rule above

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∴ k + p = 3 ⇒ (1)

∵ The directrix is at y = -3

- By using the 3rd rule above

∴ k - p = -3 ⇒ (2)

Solve the system of equations to find k and p

Add equations (1) and (2) to eliminate p

∴ 2k = 0

- Divide both sides by 2

∴ k = 0

- Substitute the value of k in equation (1) to find p

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∴ p = 3

Substitute the values of h , k , and p in the form of the equation above

∵ (x - 5)² = 4(3)(y - 0)

∴ (x - 5)² = 12 y

- Divide both sides by 12

∴ \frac{1}{12} (x - 5)² = y

- Switch the two sides

∴ y =  \frac{1}{12} (x - 5)²

The equation of a parabola with a directrix at y = -3 and a focus at (5 , 3) is y =  \frac{1}{12} (x - 5)²

Learn more:

you can learn more about the quadratic equations in brainly.com/question/8054589

#LearnwithBrainly

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