In the function f(x) = 5(x2 − 4x + ____) + 15, what number belongs in the blank to complete the square?

2 answers:

5 0

If you would like to find the number which belongs in the blank to complete the square, you can calculate this using the following steps:

f(x) = 5(x^2 - 4x + a) + 15
a ... the number = ?

x^2 - 4x + a = (x - 2)^2 = x^2 - 4x + 4
a = 4

The correct result would be 4.

gavmur [86]2 years ago

5 0

Hey there!

I took the test, and I can confirm that 4 is the CORRECT answer

xXxGolferGirlxXx

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You have two parents, four grandparents, eight greatgrandparents, and so forth.

Leviafan [203]

A.
In the first generation we have 2 ancestors.
In the second generation we have 4 ancestors or $2^{2}$ ancestors.
In the third generation we have 8 ancestors ot $2^{3}$ ancestors.

We can see that each succesive generation has two times more members. The sum is:
$2+4+8+16+...+ 2^{40}$

To calculate number of ancestors we can use formula for the sum of a geometric sequence. Geometric sequence is sequence of numbers that differ by a certain factor. This factor is called ratio. Formula is:
 $S= a_{1} * \frac{1- r^{n} }{1-r}$
Where:
S -> sum
a1 -> first member of a sequence
r -> ratio
n -> number of elements

For this question:
a1 = 2
r = 2
n = 40
 $S= 2* \frac{1- 2^{40} }{1-2} =2 199 023 255 550$

b.
1 generation = 25 years
40 generations = 40 * 25 = 1000 years

c.
Total number of people who have ever lived = $10^{10}$
Number of ancestors in 40 generations = $2.2*10^{12}$

The number of ancestors is greater than total number of people who have ever lived. This means that not all ancestors were distinct and that in each generation both men and women had children with more than one partner.

8 0

3 years ago

What is the quotient 931/4?

lianna [129]

Answer:

here's a photo of the calculator to that question