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KonstantinChe [14]
3 years ago
12

Rewrite the function by completing the square. f(x)=x^2-9x+14​

Mathematics
1 answer:
salantis [7]3 years ago
7 0

Answer:

f(x)=(x-9/2)²-25/4

Step-by-step explanation:

f(x)=x²-9x+14

f(x)=x²-9x+(-9/2)²-(-9/2)²+14

f(x)=(x-9/2)²-81/4+14

f(x)=(x-9/2)²+(-81+56)/4

f(x)=(x-9/2)²-25/4

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Mhanifa please help! Find the coordinates of the circumcenter of the triangle with the vertices A(4, 12), B(14, 6), and C(-6, 2)
melamori03 [73]

Answer:

  • (4.5, 1.5)

Step-by-step explanation:

<u>Given vertices of a triangle:</u>

  • A(4, 12), B(14, 6), and C(-6, 2)

Let the circumcenter is point M(x, y)

We know that the circumcenter is equidistant from each of the vertices.

<u>Use distance formula:</u>

  • AM = √(x - 4)² + (y - 12)²
  • BM = √(x - 14)² + (y - 6)²
  • CM = √(x + 6)² + (y - 2)²

<u>All three distances are equal:</u>

  • AM = BM = CM ⇒ AM² = BM² = CM² ⇒
  • (x - 4)² + (y - 12)² = (x - 14)² + (y - 6)² = (x + 6)² + (y - 2)²

<u>Square of each:</u>

  • AM² = x² - 8x + 16 + y² - 24y + 144 = x² + y² - 8x - 24y + 160
  • BM² = x² - 28x + 196 + y² - 12y + 36 = x² + y² - 28x - 12y + 232
  • CM² = x² + 12x + 36 + y² - 4y + 4 = x² + y² + 12x - 4y + 40

<u>Comparing the squares, we get following system:</u>

  • -8x- 24y + 160 = -28x - 12y + 232 ⇒ 20x - 12y = 72 ⇒ 5x - 3y = 18
  • - 8x - 24y + 160 = 12x - 4y + 40 ⇒ 20x + 20y = 120 ⇒ x + y = 6

<u>Solve by substitution, x = 6 - y:</u>

  • 5(6 - y) - 3y = 18
  • 30 - 8y = 18
  • 8y = 12
  • y = 1.5

<u>Find x:</u>

  • x = 6 - 1.5 = 4.5

So the circumcenter is M(4.5, 1.5)

7 0
3 years ago
A peregrine falcon can fly 332 kilometers per hour.How many meters per hour can the falcon fly.
devlian [24]
1 kilo = 1000 meters
So, 332 kilo =  332000 meters
8 0
3 years ago
Select the three number bonds that represent factor pairs of the number 56. CLEAR CHECK Number bond: 1 times 56 = 56. Number bon
Ray Of Light [21]

Answer:

The answer is -

Number bond: 1 times 56 = 56.

Number bond: 4 times 14 = 56.

Number bond: 7 times 8 = 56.

Step-by-step explanation:

We can define a factor pair as a set of two factors, which, when multiplied together, give a particular product.

For example -

5 and 6 are factors of 30 because 5×6 = 30

Now,

Given -

Number bond: 1 times 56 = 56.                         ...................(1)

Number bond: 4 times 14 = 56.                         ...................(2)

Number bond: 5 times 6 = 56.                         ...................(3)

Number bond: 7 times 8 = 56.                         ...................(4)

In equation (1)

1 times 56 = 1×56 = 56

⇒1 and 56 are the factor pairs of 56

Satisfies

In equation (2)

4 times 14 = 4×14 = 56

⇒4 and 14 are factor pairs of 56

Satisfies

In equation (3)

5 times 6 = 5×6 = 30 ≠ 56

⇒5 and 6 are not factor pairs of 56

Not Satisfies

In equation (4)

7 times 8 = 7×8 = 56

⇒7 and 8 are factor pairs of 56

Satisfies

∴ we get

The answer is -

Number bond: 1 times 56 = 56.

Number bond: 4 times 14 = 56.

Number bond: 7 times 8 = 56.

6 0
3 years ago
Simplify (-3ab^2)^3
koban [17]

(-3ab^2)^3

(-3)^3 a^3 (b^2)^3

-27 a^3 b^(2*3)

-27 a^3  b^6

7 0
4 years ago
Read 2 more answers
Solve this equation. Does this equation have one solution, no solution, or infinitely many solution. use the drop down menus to
WINSTONCH [101]

Answer: no solution

Step-by-step explanation:

24x + 72 = 24x +12

-24x -24x

———————————

72=12

72 doesn’t equal 12 so the answer is no solution

3 0
4 years ago
Read 2 more answers
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