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3 years ago

Find the equation of the line with slope = -2 and passing through (3,2). Write your equation in the form

Mathematics

1 answer:

horrorfan [7]3 years ago

3 0

Answer:

Step-by-step explanation:

y - 2 = -2(x - 3)

y - 2 = -2x + 6

y = -2x + 8

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Please don't answer wrong.

Tamiku [17]

Answer:

<u />

<u>Equation of a circle</u>

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

where:

(a, b) is the center
r is the radius

Given equation: $x^2+y^2=6.25$

Comparing the given equation with the general equation of a circle, the given equation is a <u>circle</u> with:

center = (0, 0)
radius = $\sqrt{6.25}=2.5$

To draw the circle, place the point of a compass on the origin. Make the width of the compass 2.5 units, then draw a circle about the origin.

Given equation: $x+y=1.5$

Rearrange the given equation to make y the subject: $y=-x+1.5$

Find two points on the line:

$x=-2 \implies -(-2)+1.5=3.5\implies (-2,3.5)$

$x=2 \implies -(2)+1.5\implies-0.5\implies (2,-0.5)$

Plot the found points and draw a straight line through them.

The <u>points of intersection</u> of the circle and the straight line are the solutions to the equation.

To solve this algebraically, substitute $y=-x+1.5$ into the equation of the circle to create a quadratic:

$\implies x^2+(-x+1.5)^2=6.25$

$\implies x^2+x^2-3x+2.25=6.25$

$\implies 2x^2-3x-4=0$

Now use the quadratic formula to solve for x:

$x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0$

$\implies x=\dfrac{-(-3) \pm \sqrt{(-3)^2-4(2)(-4)}}{2(2)}$

$\implies x=\dfrac{3 \pm \sqrt{41}}{4}$

To find the coordinates of the points of intersection, substitute the found values of x into $y=-x+1.5$

$\implies y=-\left(\dfrac{3 + \sqrt{41}}{4}\right)+1.5=\dfrac{3-\sqrt{41}}{4}$

$\implies y=-\left(\dfrac{3 - \sqrt{41}}{4}\right)+1.5=\dfrac{3+\sqrt{41}}{4}$

Therefore, the two points of intersection are:

$\left(\dfrac{3 + \sqrt{41}}{4},\dfrac{3-\sqrt{41}}{4}\right) \textsf{ and }\left(\dfrac{3 - \sqrt{41}}{4},\dfrac{3+\sqrt{41}}{4}\right)$

Or as decimals to 2 d.p.:

(2.35, -0.85) and (-0.85, 2.35)

6 0

2 years ago

Mr.kowolishi ordered 35 boxes of granola bars

meriva

Umm isn’t there more context to this question? I rlly can’t help if you don’t add more detail

3 0

3 years ago

What is the perimeter of a regular octagon in which all sides have a length of 5 feet.

sineoko [7]

Octagons have 8 sides. If each side is 5 feet then the perimeter is 40 feet. You add up the sides.

5 0

2 years ago

Read 2 more answers

The quotient of two numbers is 3 their product is 3 what are the two numbers

ruslelena [56]

Answer:

3 and 1

Step-by-step explanation:

They are the only numbers that could give the right answer.

3 0

3 years ago

2.75j + 2.25 - 1.5j + 3 simplified

sergiy2304 [10]

You can say 2.75j - 1.5j = 1.25j and 2.25+3 = 5.25 so now you have :
1.25j + 5.25 and thats simplify :)))
i hope this is helpful
have a nice day

4 0

3 years ago

Read 2 more answers