Answer:
Step-by-step explanation:
f(x) = x^2 + 4x + 4
f(x + a) = (x + a)^2 + 4(x + a) + 4
f(x + a) = x^2 + 2ax + a^2 + 4x + 4a + 4 Now combine like terms and use the distributive property.
f(x + a) = x^2 + (2a + 4)x + a^2 + 4a + 4
We are told that f(x + a) = x^2 - 6x + 9
So that means that
2a + 4 = - 6 Subtract 4 from both sides.
2a = - 6 - 4
2a = - 10 Divide by 2
a = - 10/2
a = - 5.
But you are not finished. You have to check the last part.
a^2 + 4x + 4 = 9
(a + 2)^2 = 9
Take the square root of both sides
sqrt(a+ 2)^2 = +/- 3
a+2 = 3
a = 1.
Does this work or is it extraneous? It is extraneous because it will not work for 2(a) + 4 = - 6
You get 6 = - 6 which is not correct. But you did give the second best answer.
a + 2 = - 3
a = - 3 - 2
a = - 5 which agrees with your previous answer.
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This is an extremely hard or tricky or sneaky problem. It takes a lot of conniving to get the right answer and 1 is not a left field answer. It just does not happen to be correct.
The perimeter because the fence goes AROUND the yard, not in it.
P = 2w + 2l
P = 2(60) + 2(20)
P = 120 + 40
P = 160
Charlene needs 160 meters of fencing material.
Answer:
-5.2, -4.75, -9/2
Step-by-step explanation:
Answer:
16.2 m
Step-by-step explanation:
First, we can draw a picture. The cable goes from the top of the pole to the ground (with the pole on the right in my drawing), and the point on the ground is 10 m away from the base of the pole. This forms a right triangle, with the right angle being between the 10 m distance and the pole itself. We can then apply the Pythagorean Theorem, so
a²+b²=c², with c being the side opposite the right angle (the cable), getting us
10²+(length of pole)² = 19²
19²-10²=(length of pole)²
= 261
square root both sides to isolate the length of the pole
length of pole ≈ 16.2 m
To simplest form of a fraction you find the lowest common factor, usually I use this trick: if both numbers are even I keep dividing by 2 to the numerator and denominator till I can't anymore
In this case:
6 divided by 2= 3
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8 divided by 2= 4
now I can't simplify an further because 3 isn't an even number, therefore its the simplest form
remember= my trick only works if both number are even, if not you'll have to find the lowest common factor and divide them by that
