Answer:
1
Step-by-step explanation:
1. Convert the mixed number to an improper fraction to match the rest of the problem (this just makes it easier for now, the answer will still be a mixed number)
-1
becomes 
2. Re-write the new equation. When there is a "+" in front of a set of parentheses the expression doesn't change aside from removing the plus signs.
The new equation becomes
3. Calculate. Just work out the new expression.
The answer is 
4. Convert to a simplified mixed decimal.
27 goes into 20 once with seven left over, making the answer 1
That statement would be best express by " x + 25 < 75 ". Since the statement says the sum of x and 25, thus, it will be x + 25. Then it also states that the sum is less than 75, so the best expression would be " < 75".
Answer:
Step-by-step explanation:
Left
When a square = a linear, always expand the squared expression.
x^2 - 2x + 1 = 3x - 5 Subtract 3x from both sides
x^2 - 2x - 3x + 1 = -5
x^2 - 5x +1 = - 5 Add 5 to both sides
x^2 - 5x + 1 + 5 = -5 + 5
x^2 - 5x + 6 = 0
This factors
(x - 2)(x - 3)
So one solution is x = 2 and the other is x = 3
Second from the Left
i = sqrt(-1)
i^2 = - 1
i^4 = (i^2)(i^2)
i^4 = - 1 * -1
i^4 = 1
16(i^4) - 8(i^2) + 4
16(1) - 8(-1) + 4
16 + 8 + 4
28
Second from the Right
This one is rather long. I'll get you the equations, you can solve for a and b. Maybe not as long as I think.
12 = 8a + b
<u>17 = 12a + b Subtract</u>
-5 = - 4a
a = - 5/-4 = 1.25
12 = 8*1.25 + b
12 = 10 + b
b = 12 - 10
b = 2
Now they want a + b
a + b = 1.25 + 2 = 3.25
Right
One of the ways to do this is to take out the common factor. You could also expand the square and remove the brackets of (2x - 2). Both will give you the same answer. I think expansion might be easier for you to understand, but the common factor method is shorter.
(2x - 2)^2 = 4x^2 - 8x + 4
4x^2 - 8x + 4 - 2x + 2
4x^2 - 10x + 6 The problem is factoring since neither of the first two equations work.
(2x - 2)(2x - 3) This is correct.
So the answer is D
Answer:
The first three terms of the series are 8, 10 and 12. The number of terms is 12 to make the sum 228.
Step-by-step explanation:
The series is defined as
Put n=1.
Put n=2.
Put n=3.
The first three terms of the series are 8, 10 and 12.
It is an arithmetic series. The first terms is 8 and the common difference is
The sum of n terms of an arithmetic series is
![S_n=\frac{n}{2}[2a+(n-1)d]](https://tex.z-dn.net/?f=S_n%3D%5Cfrac%7Bn%7D%7B2%7D%5B2a%2B%28n-1%29d%5D)
![288=\frac{n}{2}[2(8)+(n-1)2]](https://tex.z-dn.net/?f=288%3D%5Cfrac%7Bn%7D%7B2%7D%5B2%288%29%2B%28n-1%292%5D)
![288=\frac{2n}{2}[8+n-1]](https://tex.z-dn.net/?f=288%3D%5Cfrac%7B2n%7D%7B2%7D%5B8%2Bn-1%5D)
![288=n[n+7]](https://tex.z-dn.net/?f=288%3Dn%5Bn%2B7%5D)
Equate each factor equal to zero.
The number of terms can not be negative, therefore the value of n must be 12.
