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Mashcka [7]
2 years ago
6

Write an equation of a line (in standard form) that has the same slope as the line 3x-5y=7 and the same y-intercept as the line

2y-9x=8
Mathematics
1 answer:
Vanyuwa [196]2 years ago
3 0

Answer:

3x-5y=-20

Step-by-step explanation:

We can write the equation of a line in 3 different forms including slope intercept, point-slope, and standard depending on the information we have. We have two standard form equations which we will get a slope and a y-intercept from. We will convert each to slope intercept form to get the information. We will then write a new slope-intercept equation and convert to standard form.

3x-5y=7 has the same slope as the line. Let's convert.

3x-5y=7\\3x-3x-5y=7-3x\\-5y=7-3x\\\frac{-5y}{-5}=\frac{7-3x}{-5} \\

y=\frac{3}{5}x -\frac{7}{5}

The slope is m=\frac{3}{5}.

2y-9x=8 has the same y-intercept as the line. Let's convert.

2y-9x=8\\2y-9x+9x=8+9x\\2y=8+9x\\\frac{2y}{2}=\frac{8+9x}{2}

y=\frac{8}{2}+\frac{9x}{2}  \\y=4+\frac{9}{2}x

The y-intercept is 4.

We take m=\frac{3}{5} and b=4 and substitute into y=mx+b.

y=\frac{3}{5}x+4

We now convert to standard form.

-\frac{3}{5}x+y=\frac{3}{5}x-\frac{3}{5}x+4\\-\frac{3}{5}x+y=4

For standard form we need the coefficients of x and y to be not zero or fractions. We need integers but the coefficient of x cannot be negative. So we multiply the entire equation by -5 to clear the denominators.

-5(-\frac{3}{5}x+y=4)\\3x-5y=-20



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x = 5/2

Step-by-step explanation:

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Part A) The potato hit the ground at t=5.70 seconds (see the explanation)

Part B) The potato is 40 feet off the ground at the time t=5.28 seconds (see the explanation)

Step-by-step explanation:

we have

h(t)=-16t^2+80t+64

where

h(t) is the height of a potato in feet

t is the time in seconds

Part A)  Write an equation that can be solved to find when the potato hits the ground. Then solve the equation

we know that

When the potato hit the ground, the value of h(t) must be equal to zero

so

For h(t)=0

-16t^2+80t+64=0

Solve the quadratic equation

The formula to solve a quadratic equation of the form

ax^{2} +bx+c=0

is equal to

x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}

in this problem we have

-16t^2+80t+64=0

so

a=-16\\b=80\\c=64

substitute in the formula

t=\frac{-80\pm\sqrt{80^{2}-4(-16)(64)}} {2(-16)}

t=\frac{-80\pm\sqrt{10,496}} {-32}

t=\frac{-80+\sqrt{10,496}} {-32}=-0.70

t=\frac{-80-\sqrt{10,496}} {-32}=5.70

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The potato hit the ground at t=5.70 seconds

Part B) Write an equation that can be solved to find when the potato is 40 feet off the ground. Then solve the equation

For h(t)=40 ft

substitute in the quadratic equation

-16t^2+80t+64=40

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Solve the quadratic equation

we have

a=-16\\b=80\\c=24

substitute in the formula

t=\frac{-80\pm\sqrt{80^{2}-4(-16)(24)}} {2(-16)}

t=\frac{-80\pm\sqrt{7,936}} {-32}

t=\frac{-80+\sqrt{7,936}} {-32}=-0.28

t=\frac{-80-\sqrt{7,936}} {-32}=5.28

therefore

The potato is 40 feet off the ground at the time t=5.28 seconds

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