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.
Answer:
30 are girls, and 20 are boys because every 3 out of five students are girls, and every 2 out of 5 students are boys.
Answer:
He made approximately 32 free throws.
Step-by-step explanation:
Assuming that there's a typo in the question and that he made 57% of his attempted free throws, then we can solve it as shown below:
We can apply a rule of three in order to calculate the number of free throws he made. This is done as follows:
56 free throws -> 100%
x free throws -> 57%
56/x = 100/57
100*x = 57*56
x = 57*56/100 = 31.92
It can also be solved by transforming the percentage in a fraction such as 57% = 57/100 and then multiplying it by the total attempts.
free throws made = 56*57/100 = 31.92
He made approximately 32 free throws.
Around 14 weeks
45*14=630
675-630=45
So around 14 weeks
So what I did for this problem I added as a comment. check it out.
