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konstantin123 [22]
4 years ago
13

Solve

Mathematics
1 answer:
denis-greek [22]4 years ago
3 0

Answer:

\large1.\ x=8\\\\2.\ y=-\dfrac{1}{3}x+7\\\\3.\ y=5x-18\\\\4.\ y=\dfrac{5x+w}{3}

Step-by-step explanation:

1.\\5x+9=3x+25\qquad\text{subtract 9 from both sides}\\\\5x=3x+16\qquad\text{subtract 3x from both sides}\\\\2x=16\qquad\text{divide both sides by 2}\\\\\boxed{x=8}

2.\\\text{The slope-intercept form:}\\y=mx+b\\\\m-slope\\b-y-intercept\\\\\text{Let}\ k:y=m_1x+b_1,\ l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\\text{Given}\\\\y=3x-2\to m_1=3\\\\m_2=-\dfrac{1}{3}\\\\\text{Therefore we have}\ y=-\dfrac{1}{3}x+b.\\\\\text{Substitute the coordinates of the point (-9, 4) to the equation of a line:}\\\\4=-\dfrac{1}{3}(9)+b\\\\4=-3+b\qquad\text{add 3 to both sides}\\\\7=b\to b=7\\\\\text{Finally}\\\\y=-\dfrac{1}{3}x+7

3.\\y=mx+b\\\\\text{We have the slope}\ m=5\ \text{and the point}\ (2,\ -8).\\\\\text{Therefore}\ y=5x+b.\ \text{Substitute the coordinates of the point to the equation:}\\\\-8=5(2)+b\\\\-8=10+b\qquad\text{subtract 10 from both sides}\\\\-18=b\to b=-18\\\\\text{Finally}\\\\y=5x-18

4.\\3y-w=5x\qquad\text{add}\ w\ \text{to both sides}\\\\3y=5x+w\qquad\text{divide both sides by 3}\\\\y=\dfrac{5x+w}{3}

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14x+8=18x-4

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If f(x)=7x what is the inverse of f(x)
Brums [2.3K]

Answer:

f(x)=x/7

Step-by-step explanation:

f(x)=7x

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The inverse of f(x)=7x is f(x)=x/7

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4 years ago
The height of a triangle is 4 inches. Greater than twice it's base. The area of the triangle is no more than 168 in.². Which any
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Step-by-step explanation:

this problem seeks to test our knowledge on word problems and algebra

<u>Solution</u>

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the height h = 2x+4

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substituting our given values we have

168= \frac{1}{2} x*(2x+4)\\\\168= \frac{2x^2+4x}{2} \\\\168= x^2+2x\\\\

re-arranging we have

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we can now find two factors that will add up to give 2 and multiply to give -168

they are 14 and -12

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and the height is

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7 0
3 years ago
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