All categories

3 years ago

Please help me with this. (show work.)

Mathematics

1 answer:

BlackZzzverrR [31]3 years ago

5 0

GCF: greatest common factor of any two (or more) numbers

Top left:

GCF of 24 and 60: 12

Top right:

GCF of 12 and 18: 6

Bottom left:

GCF of 18 and 42: 6

Right left:

GCF of 30 and 72: 6

You might be interested in

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

The width of a rectangle is 22 inches and the perimeter is at least 165 inches. what inequality could be used to find the minimu

Lera25 [3.4K]

The answer is D.

We know that a rectangle has two widths that are equal and two lengths that are equal. One width is 22, so the other one is also 22.

If you wanted to find the lengths, you would add both widths together (same as multiplying a width by two) and add that to the two lengths equaled to the perimeter.

So, 22 * 2 + 2x = perimeter of rectangle. We added all four sides together.

We know that the perimeter is at least 165, so 22 * 2 + 2x = 165. Here's the twist. They want the most minimum possible length. So, what answer choice gives you 165 or less for the most minimum or smallest length while still getting to 165?
That is D.
22 * 2 + 2x < = 165.
Hope this helped!

6 0

4 years ago

Read 2 more answers

Consider the following equations: f(x) = 2x – 2 and g(x) = 5 - x

zysi [14]

Answer:

The difference in slopes of $f(x)\ and\ g(x)$ is = 3