Students at Westbrook middle school hold green team meetings

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

1 year ago

Please help! :( ive been stuck on this for about 30 minutes

kondaur [170]

Answer:

dimensions: 4x5x3

volume: 60 cube inches

Step-by-step explanation:

assuming each cube is a one inch cube:

the dimensions of the prism are length 5 -inches, width 4 -inches and height 3 -inches. So, 4x5x3

the volume of a prism is the length x width x height, so the volume is 4x5x3 = 60 inches cubed.

7 0

3 years ago

Read 2 more answers

The line that contains the point Q( 1, -2) and is parallel to the line whose equation is

Triss [41]

Let's call this line y=mx+C, whereby 'm' will be its gradient and 'C' will be its constant.

If this line is parallel to the line you've just mentioned, it will have a gradient 2/3. We know this, because when we re-arrange the equation you've given us, we get...

$y-4=\frac { 2 }{ 3 } \left( x-3 \right) \\ \\ y-4=\frac { 2 }{ 3 } x-2\\ \\ y=\frac { 2 }{ 3 } x-2+4\\ \\ y=\frac { 2 }{ 3 } x+2$

So, at the moment, our parallel line looks like this...

y=(2/3)*x + C

However, you mentioned that this line passes through the point Q(1, -2). If this is the case, for the line (almost complete) above, when x=1, y=-2. With this information, we can figure out the constant of the line we want to find.

-2=(2/3)*(1) + C

Therefore:

C = - 2 - (2/3)

C = - 6/3 - 2/3

C = - 8/3

This means that the line you are looking for is:

y=(2/3)*x - (8/3)

Let's find out if this is truly the case with a handy graphing app... Well, it turns out that I'm correct.

3 0

2 years ago

One angle measures nine more than six times a number. A sequence of rigid motions maps the angle onto another angle that describ

prisoha [69]

Answer:

Step-by-step explanation: one angle is 6x + 9 also equals to 9x -30

9x - 30 = 6x + 9

3x = 39, x = 13

Angle is 6×13+9 = 87

3 0

3 years ago

A 25 gram sample of a sample that's used for drug research has a k value of 0.1205

ra1l [238]

N=12.5(at time t=t) Here half life
No=25
K=12.05
Simple exponential equation where you need to calculate
Your answer should be 5.75225876

4 0

2 years ago