What is the equation of the following line? Be sure to scroll down first to see

Please don't answer wrong.

Tamiku [17]

Answer:

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<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

5.2412<br> 2x+3y=-5<br> 5x-y=-12

cupoosta [38]

Answer: 5.2412 = 5.2412 = 2x + 3y = −5 = 2x + 3y = -5 = 5x − y= -12

4 0

3 years ago

Zohar is using scissors to cut a rectangle with a length of 5x – 2 and a width of 3x + 1 out of a larger piece of paper. The per

Softa [21]

Answer:

62 cm

Step-by-step explanation:

Given the expressions for width (3x + 1) and length (5x - 2) as well as the formula for the perimeter of a rectangle: 2(5x - 2) + 2(3x +10), we can first solve for the simplified expression of 'x' and then substitute the given value of x = 4cm to find the total distance:

Distribute: 2(5x - 2) + 2(3x +1) = 10x - 4 + 6x + 2

Combine like terms: 16x - 2

Plug in '4' for 'x': 16(4) - 2 = 64 -2 = 62 cm

7 0

3 years ago

Plz help toofree your the best plz help me

goldfiish [28.3K]

------------------------------
Find Radius
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Radius = Diameter ÷ 2
Radius = 32 ÷ 2
Radius = 16

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Find Area
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Area = πr²
Area = π x 16²
Area = 256π mm²

------------------------------
Answer: 256π mm²
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4 0

4 years ago

Which of the angles in the figure are supplementary to Ð5?

Paraphin [41]

Answer:

Option C) Angle 6 and 7 only

Step-by-step explanation:

Two angles are called supplementary when their measures add up to 180 degrees.

So here the angle supplementary to Angle 5 would be 6, since adding both would get us 180 degrees. Then there's angle 7 which would also give us 180 degrees when added to angle 5.

6 0

2 years ago