Answer:
<h3><u>Part (a)</u></h3>
<u />
<u>Equation of a circle</u>

where:
- (a, b) is the center
- r is the radius
Given equation: 
Comparing the given equation with the general equation of a circle, the given equation is a <u>circle</u> with:
- center = (0, 0)
- radius =

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.
<h3><u>Part (b)</u></h3>
Given equation: 
Rearrange the given equation to make y the subject: 
Find two points on the line:


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
into the equation of the circle to create a quadratic:



Now use the quadratic formula to solve for x:



To find the coordinates of the points of intersection, substitute the found values of x into 


Therefore, the two points of intersection are:

Or as decimals to 2 d.p.:
(2.35, -0.85) and (-0.85, 2.35)
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.
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...

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.
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
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