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2 years ago

Write in slope-intercept form an equation of a line that passes through the point (-2, 7) and m= -4.

Mathematics

1 answer:

Vedmedyk [2.9K]2 years ago

3 0

Answer:

y = -4x - 1

Step-by-step explanation:

We are given the slope and a point.

Point Slope is :

$y-y_1=m(x-x_1)$

Replace the variables with the appropriate values:

$y-y_1=m(x-x_1) \rightarrow\boxed{y-7=-4(x+2)}$

Convert to slope-intercept form:

$y-7=-4(x+2)\\\\y-7=-4x-8\\\\y-7+7=-4x-8+7\\\\\boxed{y=-4x-1}$

Hope this helps!

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3 years ago

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3 years ago

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3/4x = 1/5. X=__ A. 3 3/4 B. 11/20 C. 4/15 D. 3/20

gizmo_the_mogwai [7]

Answer:

Step-by-step explanation:

transposition

3x/4=1/5

xc=yc

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1 year ago

Complete the proof given below.

allochka39001 [22]

Given that the opposite sides of a parallelogram are congruent, a diagonal

of the parallelogram forms two congruent triangles.

The correct options to complete the proof are;

Opposite sides of a parallelogram; ABCD is a parallelogram

Reflexive property of congruency

SSS

Reasons:

The completed two column proof is presented as follows;

Statement ${}$ Reason

1. ABCD is a parallelogram ${}$ 1. Given

2. $\overline{AB}$ ≅ $\overline{DC}$ and $\overline{BC}$ ≅ $\overline{DA}$ ${}$ 2. Opposite sides of a parallelogram

3. $\overline{AC}$ ≅ $\overline{CA}$ ${}$ 3. Reflexive property of congruency

4. ΔABC ≅ ΔCDA ${}$ 4. SSS

The correct options are therefore;

Opposite sides of a parallelogram; ABCD is a parallelogram

Reflexive property of congruency

SSS;

Reason 2. Opposite sides of a parallelogram, which is based on the

properties of a parallelogram and that ABCD is a parallelogram.

Reason 3. The reflexive property of congruency, states that a side is

congruent to itself.

Reason 4. SSS is an acronym for Side-Side-Side, which is a congruency

postulate that states that if the three sides of one triangle are equal to the

three sides of another triangle, then the two triangles are congruent.

Learn more about parallelograms here:

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2 years ago

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. Verify y

mariarad [96]

Answer:

the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis is;

$\frac{\pi }{2} [e^2 - 1 ]$ or 10.036

Step-by-step explanation:

Given the data in the question;

y = $y = e^{(x - 1 )$ , y = 0, x = 1, x = 2.

Now, using the integration capabilities of a graphing utility

y = $y = e_2}^{(x - 1 )_$ , y = 0

Volume = $\pi \int\limits^2_1 ( e^{x-1)^2} - (0)^2 dx$

Volume = $\pi \int\limits^2_1 ( e^{x-1)^2 dx$

Volume = $\pi \int\limits^2_1 e^{2x-2}dx$

Volume = $\frac{\pi }{e^2} \int\limits^2_1 e^{2x}dx$

Volume = $\frac{\pi }{e^2} [\frac{e^{2x}}{2}]^2_1$

Volume = $\frac{\pi }{2e^2} [e^4 - e^2 ]$

Volume = $\frac{\pi }{2} [e^2 - 1 ]$ or 10.036

Therefore, the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis is;

$\frac{\pi }{2} [e^2 - 1 ]$ or 10.036

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3 years ago