What is his help me please

Find the equation of the line that is parallel to the given line and passes through the given point

Sati [7]

Answer:

$\huge\boxed{y=-\dfrac{1}{4}x-1\to x+4y=-4}$

Step-by-step explanation:

$\text{Let}\ k:y=m_1x+b_1;\ l:y=m_2x+b_2\\\\l\ ||\ k\iff m_1=m_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\==========================\\\\\text{We have}\ x+4y=-6.\\\text{Convert to the slope-intercept form:}\\\\x+4y=-6\qquad\text{subtract}\ x\ \text{from both sides}\\\\4y=-x-6\qquad\text{divide both sides by 4}\\\\y=\dfrac{-x}{4}-\dfrac{6}{4}\\\\y=-\dfrac{1}{4}x-\dfrac{3}{2}\to m_1=-\dfrac{1}{4}$

$\text{Lines are to be parallel. Therefore}\ m_2=-\dfrac{1}{4}.\\\\\text{We initially have the form equation}\ y=-\dfrac{1}{4}x+b.\\\\\text{The line passes through the point}\ (9,\ -3).\\\\\text{Substitute the coordinates of the point to the equation of a line:}\\\\x=9,\ y=-3\\\\-3=-\dfrac{1}{4}(9)+b\\\\-3=-\dfrac{9}{4}+b\qquad\text{add}\ \dfrac{9}{4}\ \text{to both sides}\\\\-\dfrac{12}{4}+\dfrac{9}{4}=b\to b=-\dfrac{3}{4}$

$\text{Lines are to be parallel. Therefore}\ m_2=-\dfrac{1}{4}.\\\\\text{We initially have the form equation}\ y=-\dfrac{1}{4}x+b.\\\\\text{The line passes through the point}\ (8,\ -3).\\\\\text{Substitute the coordinates of the point to the equation of a line:}$

$x=8,\ y=-3\\\\-3=-\dfrac{1}{4}(8)+b\\\\-3=-2+b\qquad\text{add 2 to both sides}\\\\-1=b\to b=-1$

$\text{Therefore the equation is:}\ y=-\dfrac{1}{4}x-1.\\\\\text{Convert to the standard form}\ Ax+By=C:\\\\y=-\dfrac{1}{4}x-1\qquad\text{multiply both sides by 4}\\\\4y=-x-4\qquad\text{add}\ x\ \text{to both sides}\\\\x+4y=-4$

5 0

4 years ago

Explain why you do not have to do any computing to solve 15 by 0 by (13+7)

NARA [144]

We dont have to do any cmputing, because multiplying by 0 is always 0. Its mean that no matter what are the different numbers, if we multiply it by 0, we get 0

The result is 0

6 0

4 years ago

If a couple files a return as married filing jointly how many returns will the irs get

tangare [24]

In 2018, married filing separately taxpayers only receive a standard deduction of $12,000 compared to the $24,000 offered to those who filed jointly. If you file a separate return from your spouse, you are automatically disqualified from several of the tax deductions and credits mentioned earlier.

6 0

3 years ago

Jaqleen can unload a grocery truck twice as fast as Marco. Together, they can unload the truck in 5 hours. How long would it tak

amm1812

Jaqleen unloads a truck in x hours and Marco takes 2x hours.

Working together (x*2x) / (x+2x) = 5 hours

2x^2 / 3x = 5 Multiplying both sides by 3x equals 2x^2 -15x = 0

x = 7.5 hours

So Jaqleen takes 7.5 hours and Marco takes 15 hours

Double-Check (7.5 * 15) / (7.5 + 15) = 112.5 / 22.5 equals

5 hours Correct!!

7 0

3 years ago

Find the relative extrema of the function, if they exist. Also, state the intervals where the function is increasing or decreasi

oksian1 [2.3K]

Answer:

The question is not complete. I will explain relative extrema and how to calculate it.

Step-by-step explanation:

The singular of extrema is extremum and it is simply used to describe a value that is a minimum or a maximum of all function values.

A function will have relative extrema (relative maximum or relative minimum) at points in which it changes from decreasing to increasing, or vice versa.

So if f(y) is a function of y

Function f(d) will be is a relative maximum of f(y),

if there exists an interval (a, b) containing d

such that for all y in (a, b) , f(y) ≤ f(d)

Function f(d) will also be a relative minimum of f(y),

if there exists an interval (a, b) containing d

such that for all y in (a, b) , f(y) ≥ f(d)

Kindly note that If f(d) is a relative extrema of f(y), then the relative extrema occurs at y = d.

For the local extrema of a critical point to be determined, the function must go from increasing, that means positive $f^{'}$ , to decreasing, that means negative $f^{'}$ , or vice versa, around that point.

$f^{'}$ is determined by finding the first derivative of the function f(y). The relative extrema will therefore allows us to check for any sign changes of f′ around the function's critical points.

3 0

3 years ago