I need helpppp with this plssssssssssss

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

An artist wishes to make a sign in the shape of an isosceles triangle as shown. find the area

Katarina [22]

Answer:

Step-by-step explanation:

Drop an angle bisector from angle C until it intersects AB. Because of the symmetry of the triangles created, you will form two small right angle congruent triangles. Call the point of intersection with AB = D. In other words the bisector of <C is CD.

CB = AC Isosceles triangle

CD / CB = Sin(38.5)

CD=?

CB = 35

CD / 35 = Sin(38.5) Multiply both sides by 35

CD = 35 * sin(38.5)

CD = 21.79

BD/CB = Cos(38.5)

BD = CB* Cos(38.5)

BD = 35 * Cos (38.5)

BD = 27.39

Area = CD * BA/2

BA/2 = DB

Area = CD * BD

Area = 21.79 * 27.39

Area = 596.9

3 0

3 years ago

Solve the volume of the box! Help ASAP also you get extra points <3.

olga2289 [7]

Answer:

22½ in³ or 22.5 in³

Step-by-step explanation:

V=bwh

V=5(3)(1.5)

V=15(1.5)

V=22.5

8 0

3 years ago

Solve the quadratic equation 3x² + 2x - = 0

tatyana61 [14]

Answer:

first try taking the common

Step-by-step explanation:

x(3x+2)=0

3x=-2

x=-2/3

7 0

3 years ago

Read 2 more answers

The nursing department of a college surveyed two hundred graduates from their programs about their current

lukranit [14]

Answer:

8/9

Step-by-step explanation:

3 0

3 years ago