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3 years ago

Find the equation of a line that is parallel to y = x + 1 and passes through the point (3,-4).

Mathematics

1 answer:

White raven [17]3 years ago

4 0

Given:

The equation of a line is:

$y=x+1$

A line is parallel to the given line and passes through the point (3,-4).

To find:

The equation of the line in the slope intercept form.

Solution:

The slope intercept form of a line is:

$y=mx+b$ ...(i)

Where, m is the slope and b is the y-intercept of the line.

We have,

$y=x+1$ ...(ii)

On comparing (i) and (ii), we get

$m=1$

Slope of the given line is 1.

We know that the slopes of parallel lines are equal. So, the slope of the required line is 1.

The required line passes through the point (3,-4) with slope 1. So, the equation of the required line is:

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

$y-(-4)=1(x-3)$

$y+4=x-3$

Subtracting 4 from both sides, we get

$y=x-3-4$

$y=x-7$

Therefore, the equation of the required line is $y=x-7$ .

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The area of rectangle ABCD is 72. If point A and the midpoints of BC and CD are joined to form triangle, the area of that triang

vredina [299]

Answer:

Step-by-step explanation:

Name the midpoint of BC point M and the midpoint of CD point N.

Triangle ABM has the 1/4 the area of the rectangle, 18. Triangle ADN also has 1/4 the area of the rectangle, 18. Triangle CMN has 1/8 the area of the rectangle, 9. That is, of the rectangle area, ...

18 + 18 + 9 = 45

are not included in triangle AMN. So, the area of that triangle is ...

72 -45 = 27 . . . . units²

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<em>Comment on the triangle area</em>

The triangle created by joining the midpoint of the side of a rectangle with an opposite vertex will have the same dimension as the rectangle in one direction (L), and half the dimension of the rectangle in the other direction (W). Thus, where the rectangle area is LW, the triangle area is (1/2)(L)(1/2W) = (1/4)LW, 1/4 the area of the rectangle.

Similarly, if the midpoints of adjacent sides are joined to form a triangle, the area of that is (1/2)(1/2L)(1/2W) = (1/8)LW, or 1/8 the area of the rectangle.

3 0

3 years ago

Sharon is jumping from an 18-foot diving board with an initial upward velocity of 4 ft/s. when sharon jumps, megan throws a beac

Alinara [238K]

It will take 1.08 seconds for the ball to reach Sharon after she jumps if the upward velocity of the ball is 16 ft/s from a height of 5 feet option third is correct.

<h3>What is the equation of motion?</h3>

It is defined as the equation by which we can find the motion of a physical particle with respect to time. It is the representation of physical entity movement in a mathematical function.

We have:

The height of the Sharon from the diving board = 18 feet

The initial upward velocity of the Sharon = 4 ft/s

The height of the Megan from the ground = 5 feet

The initial upward velocity of the beach ball = 16 ft/s

We know the equation of motion is given by:

$\rm h(t) = x + ut+\frac{1}{2} gt^2$

Put x = 18 feet and u = 4 ft/s in the above equation, we get:

$\rm h(t) = 18 + 4t+\frac{1}{2} \times9.8t^2$ ....(1) [g = 9.8 m/s²]

Put x = 5 feet and u = 16 ft/s in the equation of motion, we get:

$\rm h(t) = 5 + 16t+\frac{1}{2} \times9.8t^2$ ....(2)

Equate the equation (1) and equation (2), we get

$\rm 18 + 4t+\frac{1}{2} \times9.8t^2= 5 + 16t+\frac{1}{2} \times9.8t^2\\$

18 + 4t = 5 + 16t

12t = 13

t = 1.08 seconds

Thus, it will take 1.08 seconds for the ball to reach Sharon after she jumps if the upward velocity of the ball is 16 ft/s from a height of 5 feet.

Learn more about the equation of the motion here:

brainly.com/question/13514745

6 0

3 years ago

In the equation x+44=136, what is x?

ad-work [718]

The answer is 92. subtract 44 from 136 and you get x = 92

6 0

3 years ago

How is a debit card like a check?

madam [21]

Erm I would say it comes from the same money pot (account) but not 100% sure what your tryin to ask