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3 years ago

Are the expressions below equivalent? 3(4x + 8) 12x + 24

Mathematics

1 answer:

pantera1 [17]3 years ago

3 0

Answer:

they are both equal 12x+8 is equal to 12x+24

Step-by-step explanation:

distribute:

3 x 4x = 12x 3 x 4 = 24

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Which of these statements is true for f(x)=(1/10)^x

lana66690 [7]

Step-by-step explanation:

Considering the function

$f\left(x\right)=\:\left(\frac{1}{10}\right)^x$

Analyzing option A)

Considering the function

$f\left(x\right)=\:\left(\frac{1}{10}\right)^x$

Putting $x = 1$ in the function

$f\left(1\right)=\:\left(\frac{1}{10}\right)^1$

$f\left(1\right)=\:\left\frac{1}{10}\right$

So, it is TRUE that when $x = 1$ then the out put will be $f\left(1\right)=\:\left\frac{1}{10}\right$

Therefore, the statement that '' The graph contains $\left(1,\:\frac{1}{10}\right)$ '' is TRUE.

Analyzing option B)

Considering the function

$f\left(x\right)=\:\left(\frac{1}{10}\right)^x$

The range of the function is the set of values of the dependent variable for which a function is defined.

$\mathrm{The\:range\:of\:an\:exponential\:function\:of\:the\:form}\:c\cdot \:n^{ax+b}+k\:\mathrm{is}\:\:f\left(x\right)>k$

$k=0$

$f\left(x\right)>0$

Thus,

$\mathrm{Range\:of\:}\left(\frac{1}{10}\right)^x:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)>0\:\\ \:\mathrm{Interval\:Notation:}&\:\left(0,\:\infty \:\right)\end{bmatrix}$

Therefore, the statement that ''The range of $f(x)$ is $y > \frac{1}{10}$ " is FALSE

Analyzing option C)

Considering the function

$f\left(x\right)=\:\left(\frac{1}{10}\right)^x$

The domain of the function is the set of input values which the function is real and defined.

As the function has no undefined points nor domain constraints.

So, the domain is $-\infty \:$

Thus,

$\mathrm{Domain\:of\:}\:\left(\frac{1}{10}\right)^x\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:$

Therefore, the statement that ''The domain of $f(x)$ is $x>0$ '' is FALSE.

Analyzing option D)

Considering the function

$f\left(x\right)=\:\left(\frac{1}{10}\right)^x$

As the base of the exponential function is less then 1.

i.e. 0 < b < 1

Thus, the function is decreasing

Also check the graph of the function below, which shows that the function is decreasing.

Therefore, the statement '' It is always increasing '' is FALSE.

Keywords: function, exponential function, increasing function, decreasing function, domain, range

Learn more about exponential function from brainly.com/question/13657083

#learnwithBrainly

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3 years ago

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John jogs 2 7/10 miles to the park. Marsha jogs 4/5 miles to the park. How much farther does John jog?

Elden [556K]

Answer:

1.9 miles.

Step-by-step explanation:

John jogs 2 7/10 miles to the park. Marsha jogs 4/5 miles to the park.

Convert the fractions into decimals:

2 7/10 = 2.7

4/5 = 0.8

Subtract '0.8' from '2.7':

$2.7-0.8=1.9$

John should jog 1.9 miles farther than Marsha.

Hope this helps.

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natima [27]

Answer:

Step-by-step explanation:

4037 in standard form

4037=4.037*10^3

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What is the quotient of the following division problem?

Whitepunk [10]

Answer:

D. 10r7

Explaination:

9 goes into 97 10 times, and has a remainder of 7

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A cylinder has a diameter of 14 ft and a height of 10 ft.

enyata [817]

The answer is 140 feet because 10×14 is 140

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