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3 years ago

What is the slope of the line that’s parallel to the line whose equation is 2x+y=4

Mathematics

1 answer:

Gelneren [198K]3 years ago

6 0

$\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2,\ \text{then}\\\\l\ \parallel\ k\iff m_1=m_2\\\\\text{Convert the equation to the slope-intercept form}\ y=mx+b.\\\\2x+y=4\qquad\text{subtract 2x from both sides}\\\\y=-2x+4\to m_1=-2\\\\Amswer:\ \boxed{slope=-2}$

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A circle has a diameter with endpoints at (6, 5) and (8, 5). Write the equation for the circle.

mario62 [17]

Answer:

$(x-7)^2+(y-5)^2=1$

Step-by-step explanation:

The two things that are required to formulate the equation of the circle is the center coordinate and the radius of the circle!

Center of the circle:

The center of the circle always lies at the midpoint of the endpoints of its diameter: Let's call the endpoints A(6,5) and B(8,5).

Using the midpoint formula we'll get:

$(x_m, y_m) = \left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

$(x_m, y_m) = \left(\dfrac{6+8}{2},\dfrac{5+5}{2}\right)$

$(x_m, y_m) = (7,5)$

This is the center coordinate of our circle.

Radius:

The radius of the circle is the distance from the center of the circle to any of the endpoints of the diameter (A or B)

We can use the distance formula:

$r = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

$r = \sqrt{(x_1-x_m)^2+(y_1-y_m)^2}$

$r = \sqrt{(6-7)^2+(5-5)^2}$

$r = \sqrt{1^2}$

$r = 1$

Equation of the circle:

The equation is written as:

$(x-a)^2+(y-b)^2=r^2$

here, (a,b) are the center points of the circle

in our case this is $(a,b)=(x_m,y_m)=(7,5)$

and r = 1

$(x-7)^2+(y-5)^2=1^2$

$(x-7)^2+(y-5)^2=1$

This is the equation of the circle!

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2 years ago

Kelly earns 15% more than her sister, and together they earn $999.75. How much does Kelly earn per week?

valina [46]

Answer:

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Step-by-step explanation:

let the income of kellys sister be x

kellys income=x+15% of x

=23x over 20

x+23x/20=999. 75

or, x=465

kellys income=23×465/20

=534. 75

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kykrilka [37]

He has 2.3 packs left. So he has 2 packs and 2 stickers so it would be 2 2/6

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A function g is defined by g:x→3−2sinx,for 0◦ ≤x≤A◦,where A is a constant.

Crank

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Sloan [31]

Answer:

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