hich equation may be used to determine the value of x?

Question

(1 point)
Responses

7x − 9 = 4x + 90
7x − 9 = 4x + 90

7x − 9 − 4x = 90
7x − 9 − 4x = 90

7x − 9 + 4x = 90
7x − 9 + 4x = 90

7x − 9 = 4x
7x − 9 = 4x
Question 2
Consider the figure.

An illustration shows three rays A, D, and C emerging from a point labeled B, forming a right angle at B. The right angle is divided into two parts by ray B D. The angles face leftward. Angle A B C measures 90 degree, angle A B D measures 4 x degrees, and angle D B C measures left parenthesis 7 x minus 9 right parenthesis degrees.

(3 points)
x
=

7x−9
=

4x
=

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Answer 1

To determine the value of \( x \), we can set up an equation based on the angles given in the figure. Since ray \( A \), ray \( D \), and ray \( C \) form a right angle, we know that the sum of the angles \( \angle ABC \), \( \angle ABD \), and \( \angle DBC \) must equal 90 degrees.

Given:

• \( \angle ABC = 90^\circ \)
• \( \angle ABD = 4x \)
• \( \angle DBC = 7x - 9 \)

We can set up the equation:

\[ \angle ABD + \angle DBC = \angle ABC \]

This gives us:

\[ 4x + (7x - 9) = 90 \]

Simplifying this equation:

\[ 4x + 7x - 9 = 90 \]

Combining like terms:

\[ 11x - 9 = 90 \]

Now, we can solve for \( x \):

1. Add 9 to both sides:

\[ 11x = 99 \]

2. Divide by 11:

\[ x = 9 \]

So the value of \( x \) is \( 9 \).

Summary of Responses:

• The equation that can be used is \( 4x + (7x - 9) = 90 \).
• The value of \( x \) is \( 9 \).
• Thus, substituting \( x \) back into the angle equations:
  • \( 7x - 9 = 7(9) - 9 = 63 - 9 = 54 \)
  • \( 4x = 4(9) = 36 \)

This completes the answer.