Answer:
(x + 1)² = 7
Step-by-step explanation:
Given:
-2x = x² - 6
We'll start by rearranging it to solve for zero:
x² + 2x - 6 = 0
The first term is already a perfect square so that's fine. Normally, if that term had a non-square coefficient, you would need to multiply all terms a value that would change that constant to a perfect square.
Because it's already square (1), we can simply move to the next step, separating the -6 into a value that can be doubled to give us the 2, the coefficient of the second term. That value will of course be 1, giving us:
x² + 2x + 1 - 1 - 6 = 0
Now can group our perfect square on the left and our constants on the right:
x² + 2x + 1 - 7= 0
x² + 2x + 1 = 7
(x + 1)² = 7
To check our answer, we can solve for x:
x + 1 = ± √7
x = -1 ± √7
x ≈ 1.65, -3.65
Let's try one of those in the original equation:
-2x = x² - 6
-2(1.65) = 1.65² - 6
- 3.3 = 2.72 - 6
-3.3 = -3.28
Good. Given our rounding that difference of 2/100 is acceptable, so the answer is correct.
Answer:
Step-by-step explanation:
Hello, please consider the following.
So this is divisible by 3.
Now, to prove that this is divisible by 9 = 3*3 we need to prove that
is divisible by 3. We will prove it by induction.
Step 1 - for n = 1
4+17=21= 3*7 this is true
Step 2 - we assume this is true for k so 
is divisible by 3
and we check what happens for k+1
is divisible by 3 and
is divisible by 3, by induction hypothesis
So, the sum is divisible by 3.
Step 3 - Conclusion
We just prove that is divisible by 3 for all positive integers n.
Thanks
<h3>Answer: Choice D</h3>
Divide both sides of the first equation by 7, then add the result to the second equation
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Explanation:
We can multiply both sides of an equation by the same number and the equation will be equivalent to the original.
For example, if we had x = 5, then we could get 2x = 10 after multiplying both sides by 2. The reason they are equivalent equations is because the same x value is the solution for both equations.
We can also divide both sides of an equation by the same number and the two equations would be equivalent. We can go from 2x = 10 back to x = 5 when we divide both sides by 2.
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If we divide both sides of 7x - 21y = 14 by 7, then we end up with x - 3y = 2. Simply divide each term (7x, -21y, and 14) by 7.
Because 7x-21y=14 and x-3y=2 are equivalent, this means we can replace the "7x-21y=14" with "x-3y=2"
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The new system would be
x-3y = 2
2x+3y = 11
From here you add straight down. Doing so will have the y terms add to -3y+3y = 0y = 0. After this point the y terms are eliminated and you can solve for x just like with any other equation of one variable.
Yes. Absolute values are always positive, so for example:
the absolute value of 1 is 1, and the absolute value of -1 is also 1
or the absolute value of 7 is 7, and the absolute value of -7 is also 7
and so on!
Answer:
1 Pen cost $2.25
Step-by-step explanation:
Assume:
Cost of Pen = a
Cost of pencil = b
Cost of notebook = c
a = 3b -------------------(1)
c = 4a -------------------(2)
2a + 6b + c = $18 -----(3)
From equation (1), b = a ÷ 3 ---------(4)
Substitute equations (2) and (4) in equation (3)
2a + 6 * (a ÷ 3) + 4a = $18
2a + 2a + 4a = $18
8a = $18
a = $2.25
Therefore, 1 Pen cost $2.25
