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3 years ago

Find g(x), where g(x) is the translation 8 units up of f(x)=x2.

1 answer:

7 0

Find g(x), where g(x) is the translation 8 units up of f(x)=x2.
Write your answer in the form m(x+a)2+b, where m, a, and b are integers.
g(x)=

there for the answer is ...

x^2+8

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The price of products may increase due to inflation and decrease due to depreciation. Marco is studying the change in the price

likoan [24]

Answer:

A) 3%

B) Product A

Step-by-step explanation:

Exponential Function

General form of an exponential function: $y=ab^x$

where:

a is the initial value (y-intercept)
b is the base (growth/decay factor) in decimal form
x is the independent variable
y is the dependent variable

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

Part A

Product A

Assuming the function for Product A is exponential:

$f(x) = 0.69(1.03)^x$

The base (b) is 1.03. As b > 1 then it is an increasing function.

To calculate the percentage increase/decrease, subtract 1 from the base:

⇒ 1.03 - 1 = 0.03 = 3%

Therefore, product A is increasing by 3% each year.

Part B

$\sf percentage\:change=\dfrac{final\:value-initial\:value}{initial\:value} \times 100$

To calculate the percentage change in Product B, use the percentage change formula with two consecutive values of f(t) from the given table:

$\implies \sf percentage\:change=\dfrac{10201-10100}{10100}\times 100=1\%$

Check using different two consecutive values of f(t):

$\implies \sf percentage\:change=\dfrac{10303.01-10201}{10201}\times 100=1\%$

Therefore, as 3% > 1%, Product A recorded a greater percentage change in price over the previous year.

Although the question has not asked, we can use the given information to easily create an exponential function for Product B.

Given:

a = 10,100
b = 1.01
n = t - 1 (as the initial value is for t = 1 not t = 0)

$\implies f(t) = 10100(1.01)^{t-1}$

To check this, substitute the values of t for 1 through 4 into the found function:

$\implies f(1) = 10100(1.01)^{1-1}=10100$

$\implies f(2) = 10100(1.01)^{2-1}=10201$

$\implies f(3) = 10100(1.01)^{3-1}=10303.01$

$\implies f(4) = 10100(1.01)^{4-1}=10406.04$

As these values match the values in the given table, this confirms that the found function for Product B is correct and that Product B increases by 1% per year.

4 0

2 years ago

PROBLEM 2 What is the greatest common factor of 15 and 30?

seropon [69]

Answer: 15

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

PQRS has vertices P(0, 0), Q(4, 2), and S(4, ␣2). Its diagonals intersect at H(4, 0). What are the possible coordinates of R for

True [87]

Any point on the x-axis beyond the point (4, 0) is a possible cordinate of R.

8 0

3 years ago

Solve for x. 5(x – 10) = 30 – 15x

SIZIF [17.4K]

Hey!

The first step to solving this problem would be to distribute the parenthesis. We do this so that we can get rid of the parenthesis.

Original Equation :
5 ( x - 10 ) = 30 - 15x

New Equation {Changed by Distribution} :
5x - 50 = 30 - 15x

The next step would be to 50 to both sides. The reason we do that is to get rid of the 50 that is on the left side of the equation.

Old Equation :
5x - 50 = 30 - 15x

New Equation {Changed by Adding 50 to Both Sides} :
5x = 80 - 15x

And now we would add 15x to both sides to get rid of the -15x on the right side of the equation.

Old Equation :
5x = 80 - 15x

New Equation {Changed by Adding 15x to Both Sides} :
20x = 80

Now we divide both sides by 20 to get x on it's own.

Old Equation :
20x = 80

New Equation {Changed by Dividing Both Sides by 20} :
$\frac{20x}{20}$ = $\frac{80}{20}$

Finally, all we have to do is solve to find x.

Old Equation :
$\frac{20x}{20}$ = $\frac{80}{20}$

Solution {Old Equation Solved} :
x = 4

So, in the equation 5 ( x – 10 ) = 30 – 15x, x = 4.

Hope this helps!

- Lindsey Frazier ♥

3 0

3 years ago

Read 2 more answers

Help please and thanks will mark as brainliest

Paraphin [41]

11)

3x = 180
x = 60

12)
6x + 18 = 180
6x = 162
x = 27

8 0

3 years ago