Mathematics, 20.12.2019 05:31 lin550

How to solve slope intercept form for a line parallel to y=x+4 passing through (2,2)

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Answer from: honeytolentino08

The slope intercept form for a line parallel to y = x + 4 passing through (2,2) is y = x

Solution:

Given that line parallel to y = x + 4 passing through (2, 2)

To find: slope intercept form of line

The slope intercept form is given as:

y = mx + c

Where "m" is the slope of line and "c" is the y intercept

Let us first find slope of line

On comparing the given equation y = x + 4 with slope intercept form, we get

m = 1

Thus slope of line is 1

We know that slopes of parallel lines are equal

So slope of line parallel to given line is also 1

Now we have to find the equation of line in slope intercept form with slope m = 1 and passing through (2, 2)

Substitute m = 1 and (x, y) = (2, 2) in slope intercept form

2 = 1(2) + c

c = 0

Thus the required equation is:

Substitute m = 1 and c = 0 in slope intercept form

y = 1x + 0

y = x

Thus the required equation of line is found

Answer from: Quest

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2 polynomial long division

dividing : x4+5x3-4x2-8x+6

("dividend")

by : x-1 ("divisor")

dividend x4 + 5x3 - 4x2 - 8x + 6

- divisor * x3 x4 - x3

remainder 6x3 - 4x2 - 8x + 6

- divisor * 6x2 6x3 - 6x2

remainder 2x2 - 8x + 6

- divisor * 2x1 2x2 - 2x

remainder - 6x + 6

- divisor * -6x0 - 6x + 6

remainder 0

quotient : x3+6x2+2x-6 remainder: 0

Answer from: Quest

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

$ab^2+ac^2=bc^2$

$ab^2+ac^2=x^2$ )

triangle abd and cba are similar,

$\frac{ab}{bc}=\frac{bd}{ab}$

$ab^2=bc\cdot bd$

$25=bc\cdot bd$ (2)

triangle cad and cba are similar,

$\frac{ac}{bc}=\frac{cd}{ac}$

$ac^2=bc\cdot dc$

$7\times 7=bc\cdot dc$

$49=bc\cdot dc$ )

using (1), (2) and (3), we get

$25+49=x^2$

$74=x^2$

hence proved.

therefore option 2 is correct.

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