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AnnyKZ [126]
3 years ago
5

Simplify the square root of 180

Mathematics
1 answer:
bonufazy [111]3 years ago
6 0

√180 = √(2 x 2 x 3 x 3 x 5) = 6√5


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A lighthouse operator sights a sailboat at an angle of depression of 12 degrees. If the sailboat is 80m away, how tall is the li
mart [117]
Check out the attached image for the drawing of how this would look. The drawing isn't 100% needed but it helps I think. 

Based on the figure shown in the attachment, we have a right triangle with the adjacent leg of 80 (this leg is closest to the bottom 12 degree angle) and an opposite leg of h

In short,
adjacent = 80
opposite = h

We'll use the tangent rule
tan(angle) = opposite/adjacent
tan(12) = h/80
80*tan(12) = h
h = 80*tan(12)
h = 17.0045249336018  <<-- see note below

So the lighthouse is roughly 17.0045249336018 meters tall

Answer: 17.0045249336018

Note: Make sure you are in degree mode. The value is approximate. Round this answer however you need to

4 0
3 years ago
Mr, Obrien needs to buy 8 television for the school. Each television costs $795. Mr. O'Brien has 120 fifty-dollar bills that he
Nina [5.8K]

Answer:

A. $6360, B. He doesn't have enough money.

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
Please Help Meee!!
Mazyrski [523]
A. There will be 60 ounces of pineapple juice needed. 150 servings divided by 20 servings is 7.5 servings. 7.5 servings times 8 ounces is 60 ounces.

B. You can make 50 servings of punch. 20 servings divided by 8 ounces is 2.5 ounces. 2.5 ounces times 20 ounces equals 50 servings.
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2 years ago
F(x)=x-1/x^2-x-6 which is the graph of
hoa [83]

Answer:

The graph is attached below.

Step-by-step explanation:

<em>As you have not added the graph, so I will be solving the function for a graph.</em>

Given the function

f\left(x\right)=x-\frac{1}{x^2}-x-6

x-\mathrm{axis\:interception\:points\:of\:}-\frac{1}{x^2}-6:

\mathrm{x-intercept\:is\:a\:point\:on\:the\:graph\:where\:}y=0

-\frac{1}{x^2}-6=0

-1-6x^2=0

\mathrm{No\:Solution\:for}\:x\in \mathbb{R}

\mathrm{No\:x-axis\:interception\:points}

y-\mathrm{axis\:interception\:point\:of\:}-\frac{1}{x^2}-6:

y\mathrm{-intercept\:is\:the\:point\:on\:the\:graph\:where\:}x=0

As we know that the domain of a function is the set of input or argument values for which the function is real and defined.

\mathrm{Domain\:of\:}\:-\frac{1}{x^2}-6\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x0\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:0\right)\cup \left(0,\:\infty \:\right)\end{bmatrix}

\mathrm{Since}\:x=0\:\mathrm{is\:not\:in\:domain}

\mathrm{No\:y-axis\:interception\:point}

\mathrm{Asymptotes\:of}\:-\frac{1}{x^2}-6:\quad \mathrm{Vertical}:\:x=0,\:\mathrm{Horizontal}:\:y=-6

\mathrm{Range\:of\:}-\frac{1}{x^2}-6:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)

The graph is attached below.

5 0
3 years ago
Express the ratios as a fraction without reducing.
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6/13
7/40
45/36
37/43

??? To turn them into a fraction you just make the first number the numerator and the second one denominator
5 0
3 years ago
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