Answer:
There are plenty of numbers that can multiply with 28 to create a perfect square.
The smallest perfect square could be created as following:
We have: 28 = 4 x 7 = 2^2 x 7 (2 and 7 are prime numbers).
=> Another 7 is left to create a perfect square.
=> The smallest one among possible solutions is 7
Check:
28 x 7 = 196 = 16^2 (valid)
Hope this helps!
:)
Answer:
Step-by-step explanation:
Here y = -x^2 + 36.
We can choose x values pretty much at random and then calculate the associated y values:
x y = -x^2 + 36
---- --------------------
0 36
2 -2^2 + 36 = 32
-2 -4 + 36 = 32
3 -9 + 36 = 27
You did not share the equation of the slanted line. Let's assume that the equation of this line is y = mx + b. The first two points in the table above are (0, 36) and (2, 32). We could find the equation of this line as follows:
Slope: as we move from (0, 36) to (2, 32), x increases by 2 and y decreases by 4. Thus, the slope is m = rise / run = -4/2, or -2. Using info from the point (0, 36), we find the y-intercept of this straight line:
y = mx + b becomes 36 = m(0) + b, so b = 36, and the line is y = -2x + 36.
We need to find the points of intersection of y = -2x + 36 and y = -x^2 + 36. We can equate these equations to eliminate y: -2x + 36 = -x^2 + 36, or
-2x = -x^2. Equivalently, 2x - x^2 = 0, or (x)(2 - x) = 0. Then x = 0 and x = 2.
This says that the line and the parabola intersect in at least two places:
(0, 36) and (2, 32).
Answer:
A
Step-by-step explanation:
point H is the point of intersection of the perpendicular bisectors of the triangle's sides and is the circumcentre.
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The equation of a elipse:
The length of the major axis is equal 2a if a > b or 2b if b > a.
We have
therefore the length of the major axis is equal 2 · 7 = 14.