All categories

3 years ago

Solve: (1/x)+6 = 5/sqrt(x)

1 answer:

4 0

<em>Solve: </em> $\frac{1}{x} + 6 = \frac{5}{\sqrt{x}}$

Start by squaring both sides to eliminate the square root.
$(\frac{1}{x} + 6)^{2} = \frac{25}{x}$

Expand the left hand side.
$\frac{1}{x^{2}} + \frac{12}{x} + 36 = \frac{25}{x}$

Simplify.
$\frac{1}{x^{2}} - \frac{13}{x} + 36 = 0$
$\frac{1 - 13x + 36x^{2}}{x^{2}} = 0$

Solve for x.
$36x^{2} - 13x + 1 = 0$
$36x^{2} - 9x - 4x + 1 = 0$
$9x(4x - 1) - (4x - 1) = 0$

$(9x - 1)(4x - 1) = 0$
$\therefore x = \frac{1}{9}, \frac{1}{4}$

You might be interested in

What doubles fact can I write to solve 4+5

GenaCL600 [577]

5+4❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤

5 0

3 years ago

Find the Z score of 78 with a mean of 75 and standard deviation of 4

kompoz [17]

Meld,elellelee,lee,”d,d

6 0

3 years ago

Two points in the Cartesian plane are A(2.00 m, −4.00 m) and B(−3.00 m, 3.00 m). Find the distance between them and their polar

Brrunno [24]

The distance between the two points is $d=8.6m$

The polar coordinate of A is $\left(4.47,296.57\right)$

The polar coordinate of B is $\left(4.24,135\right)$

Explanation:

The two points are $A(2,-4)$ and $B(-3,3)$

The distance between two points is given by,

$d=\sqrt{(2+3)^{2}+(-4-3)^{2}}\\d=\sqrt{(5)^{2}+(-7)^{2}}\\d=\sqrt{25+49}\\d=8.6$

Thus, the distance between the two points is $d=8.6m$

The polar coordinates of A can be written as $(Distance, tan^{-1} \frac{y}{x} )$

Distance = $\sqrt{x^{2} +y^{2} }$

Substituting $A(2,-4)$ , we get,

Distance = $\sqrt{2^{2} +(-4)^{2} }=\sqrt{4+16 }=4.47$

$tan^{-1} \frac{y}{x} =tan^{-1} \frac{-4}{2}=-63.43$

To make the angle positive, let us add 360,

$\theta=360-63.43=296.57$

The polar coordinate of A is $\left(4.47,296.57\right)$

Similarly, The polar coordinate of B can be written as $(Distance, tan^{-1} \frac{y}{x} )$

Distance = $\sqrt{x^{2} +y^{2} }$

Substituting $B(-3,3)$ , we get,

Distance = $\sqrt{(3)^{2}+(3)^{2}}=4.24$

$tan^{-1} \frac{y}{x} =tan^{-1} \frac{3}{-3}=-45$

To make the angle positive, let us add 360,

$\theta=180-45=135^{\circ}$

The polar coordinate of B is $\left(4.24,135\right)$

5 0

3 years ago

Solve: -(1/4)m + 5 = 16

liq [111]

Answer:

m=-44

Explanation: distribute the negative and add -1/4 to m and then take the 5 away from 16 and then multiply both sides

3 0

3 years ago

Read 2 more answers

A score that is three standard deviations above the mean would have a z score of

tia_tia [17]

The value of z-score for a score that is three standard deviations above the mean is 3.

In this question,

A z-score measures exactly how many standard deviations a data point is above or below the mean. It allows us to calculate the probability of a score occurring within our normal distribution and enables us to compare two scores that are from different normal distributions.

Let x be the score

let μ be the mean and

let σ be the standard deviations

Now, x = μ + 3σ

The formula of z-score is

$z_{score} = \frac{x-\mu}{\sigma}$