Here we are asked to find the smallest number which must be multiplied to 240 to make it a perfect square .
So , lets do prime factorisation of 240 .
Here , 240 = 2 × 120 .
= 2 × 2 × 60.
= 2 × 2 × 2 × 30.
= 2 × 2 × 2 × 2 × 3 × 5 .
Hence we got 240 = 2⁴ × 3¹ × 5¹ .
Now here we can see that , in order to make a perfect square it should be multiplied by 3 × 5 = 15 in order to make power of prime factors even .
Answer:
Step-by-step explanation:
Standard form of a sideways parabola:
Given equation:
Add x to both sides:
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<u>Standard form of circle equation</u>
(where (a,b) is the center and r is the radius)
Given equation:
Group like terms:
Divide by 2:
Factor by completing the square for each variable:
Rearrange into standard form:
Therefore, the circle has a center at (4.5, 2.5) and a radius of √23
Answer:
The third graph.
Step-by-step explanation:
The equations for the lines will be
P(x) = 2x-4
l(x) = -2x-4
When x = 0 both of these functions equal -4. The only graph where this happens is the third one.
You can check this by looking at the slopes and plugging in points.
2x=-y+6
-4x+3y=8
Rewriting the equations;
y+2x=6
3y-4x=8
Multiplying equation I by 3;
3y+6x=18
3y-4x=8
Subtracting equation II from equation I;
10x=10
x=1
Replacing for x in the first equation;
2x=-y+6
2(1)=-y+6
2=-y+6
2-6=-y
-4=-y
y=4