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2 years ago

Two parallel lines are crossed by a transversal. What is the value of x ?

Mathematics

2 answers:

Salsk061 [2.6K]2 years ago

8 0

Answer:

Step-by-step explanation:

olga nikolaevna [1]2 years ago

4 0

Answer:

Angle x = angle 115°.

Step-by-step explanation:

Given : Two parallel lines are crossed by a transversal.

To find : What is the value of x.

Solution : We have given Two parallel lines are crossed by a transversal.

Corresponding angles : A pair of angle that lies on the same side of the transversal line one lies on interior angle and other lies on exterior.

Corresponding angle are equal.

Then , angle x = angle 115 are corresponding.

Therefore, angle x = angle 115.

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Write the equation in vertex form and then find the vertex, focus, and directrix of a parabola with equation x=y^2+18y-2

kakasveta [241]

Answer:

Part 1) The vertex is the point (-83,-9)

Part 2) The focus is the point (-82.75,-9)

Part 3) The directrix is $x=-83.25$

Step-by-step explanation:

step 1

Find the vertex

we know that

The equation of a horizontal parabola in the standard form is equal to

$(y - k)^{2}=4p(x - h)$

where

p≠ 0.

(h,k) is the vertex

(h + p, k) is the focus

x=h-p is the directrix

In this problem we have

$x=y^{2} +18y-2$

Convert to standard form

$x+2=y^{2} +18y$

$x+2+81=y^{2} +18y+81$

$x+83=(y+9)^{2}$

This is a horizontal parabola open to the right

(h,k) is the point (-83,-9)

The vertex is the point (-83,-9)

step 2

we have

$x+83=(y+9)^{2}$

Find the value of p

$4p=1$

$p=1/4$

Find the focus

(h + p, k) is the focus

substitute

(-83+1/4,-9)

The focus is the point (-82.75,-9)

step 3

Find the directrix

The directrix of a horizontal parabola is

$x=h-p$

substitute

$x=-83-1/4$

$x=-83.25$

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Answer:

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Step-by-step explanation:

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