Multiples of 3 between 81 and 110

Y = 0.95X 7.95<br> Write and solve a linear equation to find how many songs he downloaded

Dmitry [639]

0.95 x 7.95 = 7.5525

5 0

3 years ago

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

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3 0

3 years ago

Read 2 more answers

Antar is flying a triangular-shaped kite. It has a height of 4 1/2 feet and a base of 5 3/4 feet. What is the area of Antar's ki

kotykmax [81]

$Area\ of\ triangle: \\ \frac{1}{2}bh \\ \\ \frac{1}{2}(4.5\ feet)(5.75\ feet) \\ \\ \boxed{12.9375\ feet^{2}}$

8 0

3 years ago

Read 2 more answers

Two mechanics worked on a car. The first mechanic charged $65 per hour, and the second mechanic charged $90 per hour. The mechan

Katena32 [7]

Answer:

First mechanic worked 20 hours and second mechanic worked 5 hours

Step-by-step explanation:

Let the number of hours the first mechanic worked = $a$

Let the number of hours the second mechanic worked = $b$

Therefore, we can write 2 equations and then solve them simultaneously:

$a+b=25$

$65a+90b=1750$

Rearranging the first equation: $a=25-b$

and substituting into the second equation to find $b$ :

$65(25-b)+90b=1750$

$1625-65b+90b=1750\\
25b=125\\
b=5$

Now sub $b=5$ into the first equation to find $a$

$a+5=25\\
a=20$

Therefore, first mechanic (a) worked 20 hours and second mechanic (b) worked 5 hours

4 0

2 years ago

I am half way between two consecutive numbers. The product of the two numbers is 650. what number am I ?

elena-14-01-66 [18.8K]

Answer: 325

650/2=325

6 0

3 years ago