Answer:
see explanation
Step-by-step explanation:
In 13 - 17
Consider the factors of the constant term which sum to give the coefficient of the x- term
13
x² - x - 42 = (x - 7)(x + 6)
15
x² + x - 6 = (x + 3)(x - 2)
17
x² - 27x + 50 = (x - 25)(x - 2)
19
r² - 25 ← is a difference of squares and factors in general as
a² - b² = (a - b)(a + b) , thus
r² - 25
= r² - 5² = (r - 5)(r + 5)
Answer:
The domain will be all real numbers, range will be all real numbers below -3
Step-by-step explanation:
its quadratic so it goes forever left and right. but the vertex has a y value of -3. It is a negative sloped graph, so anything below that is in the range
Area of a parallelogram=base x heigth
Data:
base=(2x+3)
heigth=(ax+5)
area of this parallelogram=8x²+bx+15
Therefore:
8x²+bx+15=(2x+3)(ax+5)
8x²+bx+15=2ax²+10x+3ax+15
8x²+bx+15=2ax²+(10+3a)x+15
Then:
8x²=2ax²
a=(8x²)/(2x²)=4
bx=(10+3(4))x
bx=(10+12)x
b=22x/x=22
Answer: a=4 and b=22.
Answer:
The width of the frame is 0.0746 meters
Step-by-step explanation:
We are told that after the frame has been attached to the solar collector, the area that is left exposed is 
. As we see in the figure, the dimensions of this area are
and 
where 
is the width of the frame.
The product of these dimensions must equal the exposed area:
Now since 
and 
we have:
we expand this and solve for x using the quadratic formula:
we get two solutions:
We take the second solution i.e , because first one gives a width larger than the dimensions of the solar collector which cannot be possible.
Thus the width of the frame is 0.0746 meters.
