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3 years ago

Solve the equation 4/x=8

Mathematics

1 answer:

Veseljchak [2.6K]3 years ago

7 0

Answer:

x = .5

Step-by-step explanation:

4 / x = 8

4 / .5 = 8

x = .5

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Match each whole number with a rational, exponential expression 1) (8^4)^3/42) 4 square root 81^33)1,296^3/44)16^3/45) (4 square

natulia [17]

$\displaystyle\left(8^{4}\right)^{\frac{3}{4}}=8^3=512$

$\displaystyle\left(\sqrt[4]{81}\right)^{3}=3^3=27$

$\displaystyle 1296^{\frac{3}{4}}=6^3=216$

$\displaystyle 16^{\frac{3}{4}}=2^3=8$

$\displaystyle\left(\sqrt[4]{2401}\right)^{3}=7^3=343$

$\displaystyle \left(6561^{\frac{1}{4}}\right)^{3}=9^3=729$

8 0

4 years ago

use the graph that shows the averge number of the heartbeats for an active adult brown bear and hibernating brown bear

julia-pushkina [17]

<span>Given the graph that shows the average number of the heartbeats for an active adult brown bear and hibernating brown bear

Part a</span>.
What does the point (2, 120) represent on the graph?

From the graph the x axis represent the time in minutes while the y axis represent the number of heartbeats.

Therefore, point (2, 120) means that it takes an active adult brown bear an average of 2 minutes to have 120 heartbeat.

Part b.
What does the ratio of the y-coordinate to the x-coordinate for each pair of points on the graph represent?

From the graph the x axis represent the time in minutes while the y axis represent the number of heartbeats.

Therefore, the ratio of the y-coordinate to the x-coordinate for each pair of points on the graph represents the average number of heatbeats of an active brown dear and a hibernating brown dear per minute.

Part c.
Use the graph to find the bear’s average heart rate when it is active and when it is hibernating.

The bear's average heart rate is given by the ratio of the y-coordinate to the x-coordinate for each pair of points on the graph.

This can be obtained by taking any two points from the graph and taking the slope.

Recall that the slope of a line is given by
$m= \frac{y_2-y_1}{x_2-x_1}$

For the average hearbeat of an active brown bear, using the points (1.5, 90) and (2, 120), we calculate the average heat rate as follows:
Average heart rate = $\frac{120-90}{2-1.5} = \frac{30}{0.5} =60 \ beats \ per \ minute$

Also, for the average hearbeat of a hibernating brown bear, using the points (1.5, 18) and (2, 24), we calculate the average heat rate as follows:
Average heart rate = $\frac{24-18}{2-1.5} = \frac{6}{0.5} =12 \ beats \ per \ minute$

4 0

4 years ago

Convert the decimal to a fraction in simplest form. 0.25 =

Karo-lina-s [1.5K]

It would be: 0.25 = 25/100 = 1/4

so, your answer is 1/4

5 0

3 years ago

Read 2 more answers

If x is added to 4 and then multiplied by 2, then the function is f(x) = 2(x +4)

romanna [79]

Answer:

Step-by-step explanation:

To find inverse:

replace f(x) with y: y = 2(x + 4)

Then switch y and x: x = 2(y + 4)

Finally make y the subject:

x = 2(y + 4)

x/2 = y + 4 (divide by 2)

x/2 - 4 = y (subtract 4)

So, the inverse is y = x/2 - 4

7 0

3 years ago

Find cot and cos <br> If sec = -3 and sin 0 > 0

Natali5045456 [20]

Answer:

Second answer

Step-by-step explanation:

We are given $\displaystyle \large{\sec \theta = -3}$ and $\displaystyle \large{\sin \theta > 0}$ . What we have to find are $\displaystyle \large{\cot \theta}$ and $\displaystyle \large{\cos \theta}$ .

First, convert $\displaystyle \large{\sec \theta}$ to $\displaystyle \large{\frac{1}{\cos \theta}}$ via trigonometric identity. That gives us a new equation in form of $\displaystyle \large{\cos \theta}$ :

$\displaystyle \large{\frac{1}{\cos \theta} = -3}$

Multiply $\displaystyle \large{\cos \theta}$ both sides to get rid of the denominator.

$\displaystyle \large{\frac{1}{\cos \theta} \cdot \cos \theta = -3 \cos \theta}\\\displaystyle \large{1=-3 \cos \theta}$

Then divide both sides by -3 to get $\displaystyle \large{\cos \theta}$ .

Hence, $\displaystyle \large{\boxed{\cos \theta = - \frac{1}{3}}}$

__________________________________________________________

Next, to find $\displaystyle \large{\cot \theta}$ , convert it to $\displaystyle \large{\frac{1}{\tan \theta}}$ via trigonometric identity. Then we have to convert $\displaystyle \large{\tan \theta}$ to $\displaystyle \large{\frac{\sin \theta}{\cos \theta}}$ via another trigonometric identity. That gives us:

$\displaystyle \large{\frac{1}{\frac{\sin \theta}{\cos \theta}}}\\\displaystyle \large{\frac{\cos \theta}{\sin \theta}$

It seems that we do not know what $\displaystyle \large{\sin \theta}$ is but we can find it by using the identity $\displaystyle \large{\sin \theta = \sqrt{1-\cos ^2 \theta}}$ for $\displaystyle \large{\sin \theta > 0}$ .

From $\displaystyle \large{\cos \theta = -\frac{1}{3}}$ then $\displaystyle \large{\cos ^2 \theta = \frac{1}{9}}$ .

Therefore:

$\displaystyle \large{\sin \theta=\sqrt{1-\frac{1}{9}}}\\\displaystyle \large{\sin \theta = \sqrt{\frac{9}{9}-\frac{1}{9}}}\\\displaystyle \large{\sin \theta = \sqrt{\frac{8}{9}}}$

Then use the surd property to evaluate the square root.

Hence, $\displaystyle \large{\boxed{\sin \theta=\frac{2\sqrt{2}}{3}}}$

Now that we know what $\displaystyle \large{\sin \theta}$ is. We can evaluate $\displaystyle \large{\frac{\cos \theta}{\sin \theta}}$ which is another form or identity of $\displaystyle \large{\cot \theta}$ .

From the boxed values of $\displaystyle \large{\cos \theta}$ and $\displaystyle \large{\sin \theta}$ :-

$\displaystyle \large{\cot \theta = \frac{\cos \theta}{\sin \theta}}\\\displaystyle \large{\cot \theta = \frac{-\frac{1}{3}}{\frac{2\sqrt{2}}{3}}}\\\displaystyle \large{\cot \theta=-\frac{1}{3} \cdot \frac{3}{2\sqrt{2}}}\\\displaystyle \large{\cot \theta=-\frac{1}{2\sqrt{2}}$

Then rationalize the value by multiplying both numerator and denominator with the denominator.

$\displaystyle \large{\cot \theta = -\frac{1 \cdot 2\sqrt{2}}{2\sqrt{2} \cdot 2\sqrt{2}}}\\\displaystyle \large{\cot \theta = -\frac{2\sqrt{2}}{8}}\\\displaystyle \large{\cot \theta = -\frac{\sqrt{2}}{4}}$

Hence, $\displaystyle \large{\boxed{\cot \theta = -\frac{\sqrt{2}}{4}}}$

Therefore, the second choice is the answer.

__________________________________________________________

Summary

Trigonometric Identity

$\displaystyle \large{\sec \theta = \frac{1}{\cos \theta}}\\ \displaystyle \large{\cot \theta = \frac{1}{\tan \theta} = \frac{\cos \theta}{\sin \theta}}\\ \displaystyle \large{\sin \theta = \sqrt{1-\cos ^2 \theta} \ \ \ (\sin \theta > 0)}\\ \displaystyle \large{\tan \theta = \frac{\sin \theta}{\cos \theta}}$

Surd Property

$\displaystyle \large{\sqrt{\frac{x}{y}} = \frac{\sqrt{x}}{\sqrt{y}}}$

Let me know in the comment if you have any questions regarding this question or for clarification! Hope this helps as well.

5 0

2 years ago

Solve the equation 4/x=8​

Solve the equation 4/x=8