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2 years ago

The Hiking Club is on a trip to hike up a mountain. The members increased their elevation 290 feet during their hike

Mathematics

1 answer:

3241004551 [841]2 years ago

4 0

Answer:

Step-by-step explanation:

A. Subtract 290 from 450, 450-290= 160

B. The variable e represents the elevation before they started the hike

C. 450+-290= 450-290

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What is the following quotient?

seropon [69]

Answer: Choice B) $\frac{5\sqrt{11}+5\sqrt{3}}{8}\\\\$

==========================================

Work Shown:

$\frac{5}{\sqrt{11}-\sqrt{3}}\\\\\\\frac{5(\sqrt{11}+\sqrt{3})}{(\sqrt{11}-\sqrt{3})(\sqrt{11}+\sqrt{3})}\\\\\\\frac{5\sqrt{11}+5\sqrt{3}}{(\sqrt{11})^2-(\sqrt{3})^2}\\\\\\\frac{5\sqrt{11}+5\sqrt{3}}{11-3}\\\\\\\frac{5\sqrt{11}+5\sqrt{3}}{8}\\\\\\$

This shows why choice B is the answer.

---------------

Explanation:

In the second step, I multiplied top and bottom by $(\sqrt{11}+\sqrt{3})$
This is so we can apply the difference of squares rule in step 3. The difference of squares rule is (x-y)(x+y) = x^2-y^2.
In step 4, the square roots cancel out with the squaring operation. The two operations are inverses of one another, which is why they cancel.

So in general, if the denominator is $\sqrt{a}-\sqrt{b}$ and you want to rationalize the denominator, then you should multiply top and bottom by $\sqrt{a}+\sqrt{b}$ . The same applies in reverse as well.

This leads to the denominator becoming $(\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b}) = (\sqrt{a})^2-(\sqrt{b})^2 = a-b$

Keep in mind that $a \ge 0$ and $b \ge 0$

4 0

2 years ago

Hello! Please answer this question with all of the info it is asked for. Please be sure to include all of your work and share an

bija089 [108]

Answer:

a) 6.5 seconds
b) 13 seconds
c) 679 ft

Step-by-step explanation:

Given function:

h(t) = -16t^2 + 208t + 3

a) Maximum height is the vertex. The ball reaches the maximum after:

h = -208/2(-16) = 6.5 seconds

b) Time the ball was in the air:

-16t^2 + 208t + 3 = 0

Solving we get approximately t = 13 seconds

c) Maximum height is at vertex, we found t above:

h(6.5) = -16(6.5)^2 + 208*6.5 + 3 = 679 ft

3 0

2 years ago

Identify the domain of a radical function with an odd index.

Sonja [21]

Answer:When n is an odd number, $\sqrt[n]{a}$ is a real number for all values of a. Then, the domain is the real domain.

8 0

3 years ago

1 cat + 20 dogs + 60 men + 5 shark=

Goryan [66]

Answer:

Step-by-step explanation:

1 cat + 20 dogs + 60 men + 5 shark= 86

6 0

3 years ago

Read 2 more answers

A relation is plotted as a linear function on the coordinate plane starting at point C (0,−1)(0,−1) and ending at point D (2,−11

Alika [10]

To find the rate of change, or slope, pick two points. The slope, is change in y coordinates over change in x coordinates.
$slope = \frac{y2-y1}{x2-x1}$ .

In this case, the slope is
$\frac{-11+1}{2-0} = \frac{-10}{2} = -5$ .
Remember that subtracting a negative number equals adding the number without the negative sign.
a-(-b) = a+b

Now for the y-intercept. The y-intercept is where the graph intersects the y-axis, where x = 0.
You have the coordinate (0, -1), where x = 0. So the y-intercept is -1.

Putting these values into the slope-intercept form y = mx+b, the equation is
y = -5x - 1

4 0

2 years ago