Show all steps. Use algebra to find the point at ehich the line h(x)=92x+1135 intersects the line f(x)=−92x−585. Write the values of x and y as reduced fractions or integers.

Step 1 To determine the point of intersection. Step 2 Given: h(x)=92x+1135 f(x)=−92x−585 h(x)=f(x) Step 3 At the point of intersection h(x)=f(x) as, h(x)=f(x) 92x+1135=−92x−585 92x+92x=−585−1135 x(9+92)=−58−1135 9x=−1715 x=−1715×9 x=−195 Step 4 The value of the function at the point of intersection is h(195)=92×(−195)+1135 =−17110+1135 =−171+22610 =5510 =112 Step 5 Thus, the point of intersection is (−195,112).

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Answered question

2021-11-13

Show all steps. Use algebra to find the point at ehich the line

h (x) = \frac{9}{2} x + \frac{113}{5}

intersects the line

f (x) = - \frac{9}{2} x - \frac{58}{5}

.
Write the values of x and y as reduced fractions or integers.

Answer & Explanation

Nancy Johnson

Beginner2021-11-14Added 17 answers

Step 1
To determine the point of intersection.
Step 2
Given:

h (x) = \frac{9}{2} x + \frac{113}{5}

f (x) = - \frac{9}{2} x - \frac{58}{5}

h (x) = f (x)

Step 3
At the point of intersection

h (x) = f (x)

as,

h (x) = f (x)

\frac{9}{2} x + \frac{113}{5} = - \frac{9}{2} x - \frac{58}{5}

\frac{9}{2} x + \frac{9}{2} x = - \frac{58}{5} - \frac{113}{5}

x (\frac{9 + 9}{2}) = \frac{- 58 - 113}{5}

9 x = - \frac{171}{5}

x = - \frac{171}{5 \times 9}

x = - \frac{19}{5}

Step 4
The value of the function at the point of intersection is

h (\frac{19}{5}) = \frac{9}{2} \times (\frac{- 19}{5}) + \frac{113}{5}

= \frac{- 171}{10} + \frac{113}{5}

= \frac{- 171 + 226}{10}

= \frac{55}{10}

= \frac{11}{2}

Step 5
Thus, the point of intersection is

(- \frac{19}{5}, \frac{11}{2})

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