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kakasveta [241]
3 years ago
12

Jose wants to rewrite 24+9 using the greatest common factor and the distributive property. Which expression should he write?

Mathematics
1 answer:
Reil [10]3 years ago
4 0
First get the factors of 24: 2*2*2*3Then the factors of 9: 3*3 Comparing the factors, the GCF is 3 Then you can rewrite the expression: 3*8 + 3*3 At this point, I'm not sure whether what you mean is really distributive property or not since this case is more of a factoring. 3*(8+3)
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The exponential function f(x) = 3(5)x grows by a factor of 25 between x = 1 and x = 3. What factor does it grow by between x = 5
Delvig [45]

Answer:

B) 25

Step-by-step explanation:

Given exponential function:

f(x)=3(5)^x

The growth factor between x=1 and x=3 is 25.

To find the growth factor between x=5 and x=7

Solution:

The growth factor of an exponential function in the interval x=a and x=b is given by :

G=\frac{f(b)}{f(a)}

We can check this by plugging in the given points.

The growth factor between x=1 and x=3 would be calculated as:

G=\frac{f(3)}{f(1)}

f(3)=3(5)^3

f(1)=3(5)^1

Plugging in values.

G=\frac{3(5)^3}{3(5)^1}

G=\frac{(5)^3}{(5)^1} (On canceling the common terms)

G=(5)^{(3-1)}  (Using quotient property of exponents \frac{a^b}{a^c}=a^{(b-c)} )

G=(5)^{2}

∴ G=25  

Similarly the growth factor between x=5 and x=7 would be:

G=\frac{f(7)}{f(5)}

f(7)=3(5)^7

f(5)=3(5)^5

Plugging in values.

G=\frac{3(5)^7}{3(5)^5}

G=\frac{(5)^7}{(5)^5} (On canceling the common terms)

G=(5)^{(7-5)}  (Using quotient property of exponents \frac{a^b}{a^c}=a^{(b-c)} )

G=(5)^{2}

∴ G=25  

Thus, the growth factor remains the same which is  =25.

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Answer:

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