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alisha [4.7K]
3 years ago
9

What is the greatest common factor of 96 and 72

Mathematics
1 answer:
Marianna [84]3 years ago
8 0

First, do the prime factorization.

96 = 2 x 2 x 2 x 2 x 2 x 3

72 = 2 x 2 x 2 x 3 x 3

The GCF is the product of their shared factors.

They share 2, 2, 2, and 3.

2 x 2 x 2 x 3 = 24.

Their GCF is 24.

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A 13- ounce package of pistachios costs $5.99. What is the unit rate?
statuscvo [17]
The unit rate is 2.17
5 0
3 years ago
Which represents the inverse of the function f(x) = 4x? h(x) = x + 4 h(x) = x – 4 h(x) = three-quartersx h(x) = one-quarterx
aalyn [17]

Answer:

\large\boxed{f^{-1}(x)=h(x)=\dfrac{1}{4}x}

Step-by-step explanation:

f(x)=4x\to y=4x\\\\\text{exchange}\ x\ \text{to}\ y\to x=4y\\\\\text{solve for}\ y:\\\\4y=x\qquad\text{divide both sides by 4}\\\\\dfrac{4y}{4}=\dfrac{x}{4}\\\\y=\dfrac{1}{4}x

8 0
3 years ago
Read 2 more answers
For what value of c is the function defined below continuous on (-\infty,\infty)?
kozerog [31]
f(x)= \left \{ {{x^2-c^2,x \ \textless \  4} \atop {cx+20},x \geq 4} \right


It's clear that for x not equal to 4 this function is continuous. So the only question is what happens at 4.
<span>A function, f, is continuous at x = 4 if 
</span><span>\lim_{x \rightarrow 4} \  f(x) = f(4)

</span><span>In notation we write respectively
</span>\lim_{x \rightarrow 4-} f(x) \ \ \ \text{ and } \ \ \ \lim_{x \rightarrow 4+} f(x)

Now the second of these is easy, because for x > 4, f(x) = cx + 20. Hence limit as x --> 4+ (i.e., from above, from the right) of f(x) is just <span>4c + 20.
</span>
On the other hand, for x < 4, f(x) = x^2 - c^2. Hence 
\lim_{x \rightarrow 4-} f(x) = \lim_{x \rightarrow 4-} (x^2 - c^2) = 16 - c^2

Thus these two limits, the one from above and below are equal if and only if
 4c + 20 = 16 - c²<span> 
 Or in other words, the limit as x --> 4 of f(x) exists if and only if
 4c + 20 = 16 - c</span>²

c^2+4c+4=0&#10;\\(c+2)^2=0&#10;\\c=-2

That is to say, if c = -2, f(x) is continuous at x = 4. 

Because f is continuous for all over values of x, it now follows that f is continuous for all real nubmers (-\infty, +\infty)

4 0
3 years ago
Here’s another one I don’t understand, please give me the answer and explain how you got it
Alexandra [31]

Answer:

39 degrees

Step-by-step explanation:

The angle of a straight line is 180 degrees. This is constant and will never change. You will add 57 and 84 to get 141 degrees for <LMP.  Take 180-141 to get 39 degrees for <PMN

7 0
3 years ago
What is the solution to 3 + 4e^x+1 = 11?
Alexandra [31]

What is the solution to 3 + 4e^x+1 = 11?

Solution:

3+4e^{x+1}=11

To solve for x, Let us subtract 3 from both sides

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0+4e^{x+1}=8

4e^{x+1}=8

Let us divide by 4 on both sides

\frac{4e^{x+1}}{4} =\frac{8}{4}

\frac{1e^{x+1}}{1} =\frac{2}{1}

e^{x+1} =2

Let us take ln on both sides

ln (e^{x+1}) =ln(2)

So, x+1=ln(2)

To solve for x, Let us subtract 1 from both sides

x+1-1=ln(2) -1

x+0=ln(2)-1

x= ln(2) -1

Answer: Option (A)

x=ln(2)-1

8 0
3 years ago
Read 2 more answers
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