All categories

3 years ago

The geometric mean of a number and four times the number is 22. What is the number?

Mathematics

1 answer:

Misha Larkins [42]3 years ago

8 0

2 square root x • 4x= 22

2x=22

x=11

Answer is 11

You might be interested in

How can you<br> change the equation y = mx + b to<br> shift the graph down?

IrinaK [193]

Step-by-step explanation: To shift the graphs up and down on the coordinate system, you need to manipulate or change the y-intercepts.

The y-intercept is just the constant term in the equation.

As long as the slopes remain the same, the graphs can be

translated up or down by changing the constant value.

Take a look at these lines graphed below.

Notice that y = x + 11 is the same as y = x + 4 but

y = x + 11 is translated 7 units down to get y = x + 4.

8 0

3 years ago

Kevin plans to watch 3 movies each month. Write an equation to represent the total number of movies n that he will watch in m mo

GREYUIT [131]

Answer:

Step-by-step explanation:

n = 3m

6 0

3 years ago

Given the function f(x) = 4x - 2, explain and show how to find the average rate of change between x = 2 and x = 4.

zalisa [80]

Answer:

The average rate of change between x = 2 and x = 4 is of 4.

Step-by-step explanation:

Average rate of change:

The average rate of change of a function f(x) in an interval [a,b] is given by:

$A = \frac{f(b)-f(a)}{b-a}$

In this question:

$f(x) = 4x - 2, b = 4, a = 2$

Thus:

$f(b) = f(4) = 4(4) - 2 = 16 - 2 = 14$

$f(a) = f(2) = 4(2) - 2 = 8 - 2 = 6$

Average rate of change:

$A = \frac{f(b)-f(a)}{b-a}$

$A = \frac{14-6}{4-2}$

$A = \frac{8}{2}$

$A = 4$

The average rate of change between x = 2 and x = 4 is of 4.

7 0

3 years ago

Solve the given equation by completing the square.

Dmitriy789 [7]

Answer:

a = -4, b = 3 and c = 6 (OR)

a = -4, b = -3 and c = 6

Step-by-step explanation:

$x^{2} +8x = 38$

Add 16 to both sides.

$x^{2} +8x+16 = 38 + 16$

$(x+4)^{2} =54$

$x + 4 = \sqrt{54}$ or $x + 4 = -\sqrt{54}$

$x+4=3\sqrt{6}$ or $x+4=-3\sqrt{6}$

$x=-4+3\sqrt{6}$ or $x=-4-3\sqrt{6}$

Therefore, a = -4, b = 3 and c = 6 (OR)

a = -4, b = -3 and c = 6

6 0

3 years ago

Read 2 more answers

At the beginning of each year for 14 years, Sherry Kardell invested $400 that earns 10% annually. What is the future value of Sh

Naddik [55]

Hmm if I'm not mistaken, is just an "ordinary" annuity, thus

$\bf \qquad \qquad \textit{Future Value of an ordinary annuity}
\\\\
A=pymnt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]
\\\\\\$

$\bf \begin{cases}
A=
\begin{array}{llll}
\textit{original amount}\\
\textit{already compounded}
\end{array} &
\begin{array}{llll}

\end{array}\\
pymnt=\textit{periodic payments}\to &400\\
r=rate\to 10\%\to \frac{10}{100}\to &0.1\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{annually, so once}
\end{array}\to &1\\

t=years\to &14
\end{cases}
\\\\\\
A=400\left[ \cfrac{\left( 1+\frac{0.1}{1} \right)^{1\cdot 14}-1}{\frac{0.1}{1}} \right]
$

3 0

3 years ago

Read 2 more answers