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2 years ago

15. Which expression shows the sum of 72 and 96 as the product of the GCF

1 answer:

3 0

Here, we are required to determine which expression shows the sum of 72 and 96 as the product of the GCF and a sum of two numbers with no common factor?

The answer is Choice B: 24(3 + 4)

Factors of 72 are;

2 × 2 × 2 × 3 × 3

Factors of 96 are;

2 × 2 × 2 × 2 × 2 × 3

The factors in bold above are common to 72 and 96 and therefore gives a total of 24 which is the GCF of 72 and 96.

The remaining factor of 72 and 96 are 3 and 4 respectively.

And, since 3 and 4 have no common factor,

Therefore, the expression which shows the sum of 72 and 96 as the product of the GCF

and a sum of two numbers with no common factor is:

24(3 + 4)

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Please help. Write the equation of the graph. (Do not use spaces. Use ^ to represent exponents. Example 2^3 is 23.)

lana66690 [7]

This graph has a horizontal asymptote so it is an exponential graph. It also passes through two points (0,-2) and (1,3). The horizontal asymptote is at y=-3.
The unchanged exponential equation is y=a(b)^x +k
For exponential equations, k is always equal to the horizontal asymptote, so k=-3.
You can check this with the ordered pair (0,-2). After that plug in the other ordered pair, (1,3).
This gives you 3=a(b)^1 or 3=ab. If you know the base the answer is simple as you just solve for a.
If you don't know the base at this point you have to sort of guess. For example, let's say both a and b are whole numbers. In that case b would have to be 3, as it can't be 1 since then the answer never changes, and a is 1. Then choose an x-value and not exact corresponding y-value. In this case x=-1 and y= a bit less than -2.75. Plug in the values to your "final" equation of y=(3)^x -3.
So -2.75=(3^-1)-3.
3^-1 is 1/3, 1/3-3 is -8/3 or -2.6667 which is pretty close to -2.75. So we can say the final equation is y=3^x -3.
Hope this helps! It's a lot easier to solve problems like these given either more points which you can use system of equations with, or with a given base or slope.

7 0

3 years ago

The original price of a bicycle was marked down $20 to a sale price of $85. What was the original price ⁉️

vovikov84 [41]

The price was marked down. If the price was reduced, we have to sum with the other value to find the original price:

$85 + 20 = \boxed {105}$

The original price was $105.

4 0

3 years ago

The zeroes of f(x) = x3 + 3x2 + 2x are .

Vaselesa [24]

The zeros of the function f(x) = x^3 + 3x^2 + 2x are x = 0, x = -1 and x = -2

<h3>How to determine the zeros of the function?</h3>

The function is given as:

f(x) = x^3 + 3x^2 + 2x

Factor out x in the above function

f(x) = x(x^2 + 3x + 2)

Set the function to 0

x(x^2 + 3x + 2) = 0

Factorize the expression in the bracket

x(x + 1)(x + 2) = 0

Split the expression

x = 0, x + 1 = 0 and x + 2 = 0

Solve for x

x = 0, x = -1 and x = -2

Hence, the zeros of the function f(x) = x^3 + 3x^2 + 2x are x = 0, x = -1 and x = -2

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1 year ago

Read 2 more answers

The pep club and honor society are joining forces to raise money for school improvements.

Fittoniya [83]

Answer:

Part a) The graph in the attached figure

Part b) see the explanation

Part c) see the explanation

Step-by-step explanation:

Let

x ----> represent pep club donations

y ---> represent donations raised by the honor society

we have

$x+y\geq 500$ ----> inequality A

The solution of the inequality A is the shaded area above the solid line $x+y=500$

$x\geq 100$ ----> inequality B

The solution of the inequality B is the shaded area at right of the solid line $x=100$

Part a) Graph the system of inequalities

using a graphing tool

The solution of the system of inequalities is the shaded area

Remember that the variables x and y cannot be a negative number

see the attached figure

Part b) What does the point (300,100) represent? Is it a viable solution?

The point (300,100) means that the donations raised for pep club was $300 and the donations raised by the honor society was $100

The point (300,100) is not a viable solution, because the point not belong to the shaded area of the solution of the system of inequalities

Verify

If the ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequality

For x=300, y=100

Inequality A

$300+100\geq 500$

$400\geq 500$ ----> is not true

The ordered pair not satisfy the inequality A

therefore

The point (300,100) is not a viable solution

Part c) What does the point (500,200) represent? Is it a viable solution?

The point (500,200) means that the donations raised for pep club was $500 and the donations raised by the honor society was $200

The point (500,200) is a viable solution, because the point belong to the shaded area of the solution of the system of inequalities

Verify

If the ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequality

For x=500, y=200

Inequality A

$500+200\geq 500$

$700\geq 500$ ----> is true

The ordered pair satisfy the inequality A

Inequality B

$500\geq 100$ ---> is true

The ordered pair satisfy the inequality B

therefore

The point (500,200) is a viable solution

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3 years ago

Jorge hiked 15.4 miles on Monday. He hiked 20.6 miles on Tuesday, and the rest of the 50-mile trail on Wednesday. If m represent

sergeinik [125]

Equation: 50-(20.6+15.4)
50-36
14 miles

8 0

2 years ago