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Aliun [14]
3 years ago
14

Willie changes the quadratic function f(x)=x2?6x+14 to vertex form f(x)=a(x?h)2+k. If Willie does this correctly, what is the va

lue of k?
Mathematics
1 answer:
andrew11 [14]3 years ago
8 0

Answer:

The value of k is 5.

Step-by-step explanation:

Since we know we can convert function's quadratic form to vertex form by completing the square.

f(x)=x2?6x+14

We will add and subtract 9 to our equation in order to complete the square.

1(x^{2} ?6x+9)-9+14

Upon completing the square and combining like terms we will get,

1(x?3)^{2} +5

Upon comparing Willie's vertex form with our expression we can see that k is 5.

Therefore, the value of k is 5.

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Samuel has an ant farm with a volume of 375 cubic inches. The width of the ant farm is 2.5 inches and the length is 15 inches. W
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Answer:

Step-by-step explanation:

From the given information, it is clear that the shape of ant form is rectangular prism.

Let us write formula for volume of rectangular prism (ant form)

V = l x w x h

Use the formula to write an equation.

Plug V = 375, w = 2.5 and l = 15

375 = 15 x 2.5 x h

375 = 37.5 x h

Divide both sides of the equation by 37.5

375/37.5 = (37.5 x h)/37.5

10 = h

Hence, the height of the form is 10 inches.

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There are 9 students in a class: 7 boys and 2girls.
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Answer:

The probability is either 2 but mostly 3 boys.

Step-by-step explanation:

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Trent is 25 years old and works for a company that matches his 401(k) contribution up to 5%. the interest rate for his 401(k) is
weqwewe [10]

If he puts away 10% of his $32,000 salary every year, The total of his 401(k) be in 10 years is: a. $67,266.16.

<h3>401(k) in 10 years</h3>

First step

Contribution=(10% ×$32,000)+ 50% from employer

Contribution=$3,200+ ($3,200×50%)

Contribution=$3,200+$1,600

Contribution=$4,800

Second step

Future value= 4800 (1 + 0.073)^10 – 1/ 0.073

Future value= 4800 (1 .073)^10 – 1/ 0.073

Future value= 4800 (2.0230062274104 – 1) / 0.073

Future value= 4800 (1.0230062274104) / 0.073

Future value=$4,910.42989157/0.073

Future value=$67,226.16

Therefore the total of his 401(k) be in 10 years is: a. $67,266.16.

Learn more about 401(k) here:brainly.com/question/3516994

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