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diamong [38]
3 years ago
10

Let f(x)=1/2x2+4. The function g(x) is a vertical stretch of f(x) by a factor of 4. What is the equation of g(x)?

Mathematics
1 answer:
andrey2020 [161]3 years ago
6 0

The equation of g(x) is g(x)=2 x^{2}+16

Explanation:

Given that the function f(x) is f(x)=\frac{1}{2} x^{2}+4

Also, given that the function g(x) is a vertical stretch of f(x) by a factor of 4.

We need to determine the equation of g(x)

<u>Equation of g(x):</u>

The vertical stretch of the function can be determined by multiplying the factor 4 with the function f(x).

Thus, we have,

g(x)=4 f(x)

Substituting the values,we have,

g(x)=4\left(\frac{1}{2} x^{2}+4\right)

Simplifying the values, we get,

g(x)=2 x^{2}+16

Hence, the equation of g(x) is g(x)=2 x^{2}+16

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% Decrease = \frac{-3}{12} = -0.25 × 100 = -25

Your answer = -25
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Victor borrowed money at 5.25 percent simple annual interest. At the end of the year, the interest on the loan is $255.94. What
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There is a 12-ft fence on one side of a rectangular garden. The gardener has 44 ft of fencing to the enclose the other three sid
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Step-by-step explanation:

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7 0
3 years ago
Can u guys PLEASE answer this question ASAP.
Andrej [43]

Answer:

  • 1. Interest: $166.67

           Principal: $6,166.67

  • 2. Interest: $200.00

            Principal: $5,200.00

Explanation:

<u><em>1. $6000 for 50 days at 20% p.a</em></u>

<u><em></em></u>

In 20% pa, pa means "per annum", i.e. "per year".

Assume simple interest:

  • Principal: $6,000
  • interest: 20% pa
  • time = 50 days

Interest:

  • Interest = Principal × number of days × annual rate / 360

  • Interest = $6,000 × 50 × 20% / 360 = $166.67

Principal = principal + interest = $6,000 + $166.67 = $6,166.67

<u><em></em></u>

<u><em>2. $5000 for 5 months at 0.8% per month</em></u>

Assume, again, simple interest.

  • Principal: $5,000
  • interest: 0.80% per month
  • time = 5 months

Interest:

  • Interest = Principal × number of months × montly rate

  • Interest = $5,000 × 5 × 0.80%  = $200.00

Principal = principal + interest = $5,000 + $200.00 = $5,200

You can see that the accrued interests depend on the principal, the interest rate, and the time.

8 0
3 years ago
Help please need those answers
icang [17]

We know: The sum of the measures of the angles of a triangle is equal 180°.

We have: m∠A =65°, m∠B =  (3x - 10)° and m∠C = (2x)°.

The equation:

65 + (3x - 10) + 2x = 180

(3x + 2x) + (65 - 10) = 180

5x + 55 = 180        <em>subtract 55 from both sides</em>

5x = 125          <em>divide both sides by 5</em>

x = 25

m∠B =  (3x - 10)° → m∠B =  (3 · 25 - 10)° = (75 - 10)° = 65°

m∠C = (2x)° → m∠C = (2 · 25)° = 50°

<h3>Answer: x = 25, m∠B = 65°, m∠C = 50°</h3>
8 0
3 years ago
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