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andre [41]
2 years ago
6

Find the values of a and b such that x^2-4x+9=(x+a)^2+b

Mathematics
1 answer:
m_a_m_a [10]2 years ago
6 0

Answer:

a = -2

b = 5

Step-by-step explanation:

We can identify the right side of the equation as completing the square. So, we simply complete the square for x² - 4x + 9 to find our answer,

Step 1: Isolate xs

x² - 4x = -9

Step 2: Complete the square

x² - 4x + 4 = -9 + 4

(x - 2)² = -5

Step 3: Move -5 over

(x - 2)² + 5

And we have our answer!

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Will give brainliest to correct answer.
Kobotan [32]
Note that c is the hypotenuse of the blue triangle, and that the Pyth. Thm. states that (length of one leg)^2 + (length of the other leg)^2 = (hyp)^2.

Therefore, (hyp)^2 = c^2 = [2sqrt(x^2+3x)]^2 + 3^2, or
                                        = 4(x^2+3x) + 9, or
                                        = 4x^2 + 12x + 9  = (2x+3)^2
Taking the sqrt of both sides, c = plus or minus (2x+3).  Eliminate -(2x+3) because the middle term of the square of this would be negative, in conflict with the given +12x.

c=2x+3 is the correct answer.

8 0
3 years ago
Answer needed -3x + 9 = 18
Aloiza [94]

Answer:

X=-3

Step-by-step explanation:

Is that what you need?

8 0
3 years ago
Z^m-n (z^m+ z^m+n + z^n)
rusak2 [61]

Answer:Your left hand side evaluates to:

m+(−1)mn+(−1)m+(−1)mnp

and your right hand side evaluates to:

m+(−1)mn+(−1)m+np

After eliminating the common terms:

m+(−1)mn from both sides, we are left with showing:

(−1)m+(−1)mnp=(−1)m+np

If p=0, both sides are clearly equal, so assume p≠0, and we can (by cancellation) simply prove:

(−1)(−1)mn=(−1)n.

It should be clear that if m is even, we have equality (both sides are (−1)n), so we are down to the case where m is odd. In this case:

(−1)(−1)mn=(−1)−n=1(−1)n

Multiplying both sides by (−1)n then yields:

1=(−1)2n=[(−1)n]2 which is always true, no matter what n is

8 0
3 years ago
What should you do first to write 5.871 x 10‐⁷ in standard form?​
notka56 [123]

Answer:

0.000005871

thats just what it is cuz yeah

8 0
3 years ago
Read 2 more answers
Solve the equality for z z+8>12 Simplfy your answer as much as possible
irina [24]
You would subtract 8 from both sides making it Z is greater than 4
8 0
2 years ago
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