Answer:
- C) (x − 3)2 = 25
- C) Factor out 4 from 4x2 + 40x.
Step-by-step explanation:
1. Adding the square of half the x-coefficient to both sides of the equation will "complete the square." That square is 9, so the result on the right is 16+9 = 25. Only selection C matches.
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2. To complete the square, you want to be able to put the quadratic into the form a(x -h)^2 = -k. For the purpose, it is most convenient to first factor "a" from the given quadratic. Then you can determine "-h" to be half the x-coefficient inside the parentheses.
Here, that looks like ...
4(x² +10x) = 80 . . . . . . . . . . step 1: factor out 4
4(x² +10x +25) = 180 . . . . . add 25 inside parentheses and the same number (4·25) on the right side of the equation
4(x +5)² = 180 . . . . . . . . . . . written as a square
Answer:
The sequence is:
10, 30, 50, 70, 90.....................
Step-by-step explanation:
We have,
First term (a) = 10
Common difference (d) = ?
Sum of first 5 terms (
) = 250
or, ![\frac{n}{2} [{2a+(n-1)d}] = 250](https://tex.z-dn.net/?f=%5Cfrac%7Bn%7D%7B2%7D%20%5B%7B2a%2B%28n-1%29d%7D%5D%20%3D%20250)
or, ![\frac{5}{2} [2*10 + 4d]=250](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B2%7D%20%5B2%2A10%20%2B%204d%5D%3D250)
or, ![\frac{5}{2} * 4[5+d]=250](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B2%7D%20%2A%204%5B5%2Bd%5D%3D250)
or, 10(5 + d) =250
or, 5 + d = 25
∴ d = 20
Now,
2nd term = a + d = 10 + 20 = 30
3rd term = a + 2d = 10 + 2*20 = 10 + 40 = 50
4th term = a + 3d = 10 + 3*20 = 10 + 60 = 70
5th term = a + 4d = 10 + 4*20 = 10 + 80 = 90
Answer:
The number of deserters is 34.
Step-by-step explanation:
We have to calculate the number of desertors in a group of 1500 soldiers.
The sergeant divides in groups of different numbers and count the lefts over.
If he divide in groups of 5, he has on left over. The amount of soldiers grouped has to end in 5 or 0, so the total amount of soldiers has to end in 1 or 6.
If he divide in groups of 7, there are three left over. If we take 3, the number of soldiers gruoped in 7 has to end in 8 or 3. The only numbers bigger than 1400 that end in 8 or 3 and have 7 as common divider are 1428 and 1463.
If we add the 3 soldiers left over, we have 1431 and 1466 as the only possible amount of soldiers applying to the two conditions stated until now.
If he divide in groups of 11, there are three left over. We can test with the 2 numbers we stay:

As only 1466 gives a possible result (no decimals), this is the amount of soldiers left.
The deserters are 34:

According to the normal distribution curve:
<span>"the percent of women whose heights are between 64 and 69.5 inches"</span> represents the values within 2 standard deviation ,,,
And that value is 95% of the whole data
Answer:
CBA=MNP
Step-by-step explanation:
Side NP=CB
Side NM=AB
then the angles between those sides are equal