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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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Answer:

the first option is the right answer.

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2 years ago
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Point R is located at (3, 2) and point S is located at (8, 15) .
Ulleksa [173]

Answer: (4, 4.6)

=======================================

The x coordinates of the points (3,2) and (8,15) are x = 3 and x = 8 respectively. The distance between these x values is 8-3 = 5 units. So we move 5 units to the right to go from the first point to the second point.

Imagine we had 5 blocks. If 1 of them is colored red and the other four are green, then the ratio of red to green is 1:4. We have 1 part red, 4 parts green. So 1+4 = 5 total. The "red block" in the metaphor mentioned basically tells us how far to move over the total distance 5. So we move 1/5th of the way along the horizontal distance of 5.

1/5 of 5 = (1/5)*5 = 1

So we move exactly one unit along the x direction. Therefore, we add 1 to to the x coordinate of (3,2) to end up with (3+1,2) = (4,2). This isn't the final answer, but it helps get us closer.

---------------

For the y coordinates of the given points we see that the y difference is 15-2 = 13. Multiply this by 1/5 to get

(1/5)*13 = 13/5 = 2.6

We follow effectively the same steps as before, but now we're dealing with the y values this time. So we move 2.6 units in the y direction (ie move 2.6 units up)

Add 2.6 onto the y value of that last point we found to get (4,2+2.6) = (4,4.6)

So that explains why the answer is (4, 4.6)

A visual might help so I've posted one below in the attached images. In that image, the location of point T is the final answer.

6 0
3 years ago
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180 degrees. in an equilateral triangle, each angle is 60 degrees
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Answer:

7.5

Step-by-step explanation:

x = 10 \tan \: 37 \degree \\  \\  \therefore \: x = 7.535540501 \\  \\ \therefore \: x  \approx 7.5

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2 years ago
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The function f(x) = 50 Times 0.8^x Models the number of ants in Jonathan's ant farm after it is stricken by a deadly any plague,
KATRIN_1 [288]

Answer:

A, D, H

Step-by-step explanation:

The function models exponential decay because the factor is 0.8 which is < 1

0.8 means 80% of the previous which is a decay of 100 - 80 = 20%

50(0.8^x)

50(0.8²)

= 32

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