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8_murik_8 [283]
3 years ago
8

Please help me! Write the slope intercept form of an equation for the line that passes through (0,3) and is perpendicular to 9x-

4y=-8
Mathematics
1 answer:
lesya692 [45]3 years ago
6 0

Answer:

y = -4/9x + 3

Step-by-step explanation:

Keep in mind:

- the equation for slope-intercept form is y = mx + b.

- "y" means output, "x" means input, "m" means slope, and "b" means y intercept

The first step in this equation is to turn 9x - 4y = -8 into slope intercept form.

Step 1: subtract 9x from both sides to begin to isolate y.

9x - 4y = -8

-4y = -9x - 8

Step 2: divide both sides by -4 to further isolate y.

y = 9/4x + 2

Now, we have the equation for the perpendicular line. Remember, the slope of a line is the opposite reciprocal of the slope of the line perpendicular to it.

This means that the slope of the line we are trying to find the equation for is -4/9.

Now that we have a slope and a point the line passes through, (0, 3), we can find the equation. Plug the coordinates of the point and the slope into the equation for slope-intercept form.

3 = -4/9(0) + b

To find the equation, solve for b.

Step 1: Simplify -4/9(0)

3 = 0 + b

Step 2: Simplify 0 + b

3 = b

Now that we know b and m, we have our equation.

The final answer is y = -4/9x + 3.

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Step-by-step explanation:

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GJ is a midsegment of triangle DEF, and HK is a midsegment of triangle GFJ. What is the length of HK?
loris [4]

Answer:

Option B) 4 centimeters

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the value of n

we know that

a) GJ is a midsegment of triangle DEF

then

G is the midpoint segment DF and J is the midpoint segment EF

DG=GF and EJ=JF

b) HK is a midsegment of triangle GFJ

then

H is the midpoint segment GF and K is the midpoint segment JF

GH=HF and JK=KF

In this problem we have

HF=7 cm

so

GH=7 cm

GF=GH+HF ----> by addition segment postulate

GF=7+7=14 cm

Remember that

DG=GF

substitute the given values

2n-1=14

solve for n

2n=14+1

2n=15

n=7.5\ cm

step 2

Find the length of GJ

we know that

The <u><em>Midpoint Theorem</em></u> states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side

so

GJ=\frac{1}{2}DE

we have

GE=2n+1=2(7.5)+1=16\ cm

substitute

GJ=\frac{1}{2}16=8\ cm

step 3

Find the length of HK

we have that

HK=\frac{1}{2}GJ ----> by the midpoint theorem

we have

GJ=8\ cm

substitute

HK=\frac{1}{2}8=4\ cm

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stellarik [79]

Responder:

c. x menos 25 menos estilo en línea fracción 4 entre 19 fin estilo paréntesis izquierdo x menos 25 paréntesis derecho igual 3

Explicación paso a paso:

Dado lo siguiente:

Cantidad original de gasolina en el tanque de combustible = x

Gasolina consumida en el primer viaje = 25 litros

Gasolina restante después del primer viaje = (x - 25) litros

Gasolina consumida en el segundo viaje = 4/19 de lo que queda, es decir;

(4/19) * (x - 25)

Gasolina restante después del segundo viaje = 3 litros

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La gasolina que queda después del segundo viaje se puede modelar mediante la ecuación:

x - 25 - 4/19 (x - 25) = 3

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