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Alekssandra [29.7K]
3 years ago
15

7. Which of the following can be determined from the graph below?

Mathematics
1 answer:
tatyana61 [14]3 years ago
7 0

Answer:

The ordered pair (6,25) is a solution to both

y=-\frac{5}{2}x+40  and  y=\frac{5}{3}x+15

Step-by-step explanation:

Part 7)

<em>step 1</em>

Find the equation of the line with positive slope

take the points (0,15) and (9,30)

<em>Find the slope</em>

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

substitute the given values

m=\frac{30-15}{9-0}

m=\frac{15}{9}

simplify

m=\frac{5}{3}

Find the equation of the line in slope intercept form

y=mx+b

we have

m=\frac{5}{3}

b=15

substitute

y=\frac{5}{3}x+15

<em>step 2</em>

Find the equation of the line with negative slope

take the points (0,40) and (8,20)

<em>Find the slope</em>

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

substitute the given values

m=\frac{20-40}{8-0}

m=-\frac{20}{8}

simplify

m=-\frac{5}{2}

Find the equation of the line in slope intercept form

y=mx+b

we have

m=-\frac{5}{2}

b=40

substitute

y=-\frac{5}{2}x+40

step 3

Find the solution of the system

we know that

The solution of the system of equations is the intersection point both graphs

The intersection point is (6,25) ----> see the graph

therefore

The ordered pair (6,25) is a solution to both y=-\frac{5}{2}x+40  and  

y=\frac{5}{3}x+15

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Answer  :

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x_{1}=\frac{-b-\sqrt{\Delta }}{2a} =\frac{10- 6\sqrt{2}}{2}=\frac{2(5-3\sqrt{2})}{2}= 5-3\sqrt{2}\\ \\x_{2}=\frac{-b+\sqrt{\Delta }}{2a} =\frac{10+ 6\sqrt{2}}{2}=\frac{2(5+3\sqrt{2})}{2}= 5+3\sqrt{2}


Answer : \ x= 5-3\sqrt{2} \ \ or \ \ x = 5+3\sqrt{2}


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<h3><em><u>Thanks for joining brainly community!</u></em></h3>
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