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Stolb23 [73]
2 years ago
13

Question 1 (Essay Worth 10 points)

Mathematics
1 answer:
FromTheMoon [43]2 years ago
8 0

The equation 7x + 3x - 18 = 6(x+3) is 9

<h3>What is equation?</h3>

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

given:

7x + 3x - 18 = 6(x+3)

7x + 3x - 18 = 6x+18      [Distributive Property]

10x-18= 6x+18               [Addition Property of Equality]

10x-6x= 18+18               [Combine Like Terms ]

4x=36                            [Subtraction Property of Equality]

4*x=36                            [Multiplication Property of Equality]

x=36/4                           [Division Property of Equality]

x=9

Learn more about equation here:

brainly.com/question/10413253

#SPJ1

   

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A parabola can be drawn given a focus of ( - 8,0) and a directrix of y= - 2 What can be said about the parabola?
Tcecarenko [31]

Answer:

The equation of the parabola is:

y

=

1

32

x

2

Explanation:

Please notice that we know that the parabola opens upward or downward, because the directrix is a horizontal line:

y

=

−

8

This tells use that the equation of the parabola of the form:

y

=

f

(

x

)

Not

x

=

f

(

y

)

.

Furthermore, we can see that it must open upward, because the y coordinate of the focus is above the directrix.

The vertex has the same x coordinate as the focus:

x

=

0

And its y coordinate is halfway between the focus and the directrix:

y

=

8

−

8

2

=

0

Therefore the vertex is

(

0

,

0

)

Use the vertex form of the equation of a parabola that opens upward or downward:

y

=

a

(

x

−

h

)

2

+

k

where the vertex is the point

(

h

,

k

)

.

Substitute the vertex into the equation:

y

=

a

(

x

−

0

)

2

+

0

Simplify:

y

=

a

x

2

The distance, f, from the vertex to the focus is,

f

=

8

; this allows use to find the value of

a

, using the equation:

a

=

1

4

f

a

=

1

32

The equation of the parabola is:

y

=

1

32

x

2

Step-by-step explanation:

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Makovka662 [10]

Using the image given, the angles that are Alternate Exterior Angles are: 1, 2, 3, 4,13,14, 18, 19.

<h3>What are Alternate Exterior Angles?</h3>

These are known to be the Alternate exterior angles that are regarded as the pair of angles found on the outer side of the two parallel lines but they are seen on the opposite side of the transversal.

Note that in the image given, there are two parallel lines and two transversal lines.

Note also that to get the Alternate exterior angles, it has to be the angles seen on the seen on the opposite side of the transversal that has crossed the parallels lines and from the image given, only angle 1, 2, 3, 4,13,14, 18, 19 fit into the description.

Therefore, Using the image given, the angles that are Alternate Exterior Angles are: 1, 2, 3, 4,13,14, 18 19.

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