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marishachu [46]
3 years ago
11

Find the missing lengths of the sides

Mathematics
2 answers:
SCORPION-xisa [38]3 years ago
8 0
That's a 30-60-90 triangle, so the hypotenuse will always be 2x, the shorter leg will be x and the longer leg will be x√3. In this case, we are given the longer leg and we can deduce that x = 9. So, a = x = 9 and c = 2x = 18. Your answer is A, a = 9 yd, c = 18 yd.
Mandarinka [93]3 years ago
8 0

Answer:

a) a = 9d, c = 18 yd

Step-by-step explanation:

The given triangle is a 30-60-90 triangle. The ratio of the sides of the triangle is 1x: 2x: √3x.

Here the hypotenuse is 2x, the shorter leg is x and the longer leg is √3x.

In given figure, we are given the longer leg.

√3x = 9√3

From this we can find the value of x, which is the shorter leg.

Dividing both sides by √3, we get

x = 9

The shorter side, a = 9 yd

Now let's find the hypotenuse.

Plug in x = 9, in 2x, we get

= 2*9

= 18 yd

The hypotenuse "c" = 18 yd.

So the answer is a) a = 9d, c = 18 yd

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6 0
3 years ago
The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognition. He wants to first deter
VMariaS [17]

Answer:

He must survey 123 adults.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the z-score that has a p-value of 1 - \frac{\alpha}{2}.

The margin of error is:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

Assume that a recent survey suggests that about 87​% of adults have heard of the brand.

This means that \pi = 0.87

90% confidence level

So \alpha = 0.1, z is the value of Z that has a p-value of 1 - \frac{0.1}{2} = 0.95, so Z = 1.645.

How many adults must he survey in order to be 90​% confident that his estimate is within five percentage points of the true population​ percentage?

This is n for which M = 0.05. So

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.05 = 1.645\sqrt{\frac{0.87*0.13}{n}}

0.05\sqrt{n} = 1.645\sqrt{0.87*0.13}

\sqrt{n} = \frac{1.645\sqrt{0.87*0.13}}{0.05}

(\sqrt{n})^2 = (\frac{1.645\sqrt{0.87*0.13}}{0.05})^2

n = 122.4

Rounding up:

He must survey 123 adults.

6 0
2 years ago
Is it true that the planes x + 2y − 2z = 7 and x + 2y − 2z = −5 are two units away from the plane x + 2y − 2z = 1?
zhuklara [117]

Lets Find It Out..

First we'll find the equation of ALL planes parallel to the original one.

As a model consider this lesson:

Equation of a plane parallel to other

The normal vector is:
<span><span>→n</span>=<1,2−2></span>

The equation of the plane parallel to the original one passing through <span>P<span>(<span>x0</span>,<span>y0</span>,<span>z0</span>)</span></span>is:

<span><span>→n</span>⋅< x−<span>x0</span>,y−<span>y0</span>,z−<span>z0</span>>=0</span>
<span><1,2,−2>⋅<x−<span>x0</span>,y−<span>y0</span>,z−<span>z0</span>>=0</span>
<span>x−<span>x0</span>+2y−2<span>y0</span>−2z+2<span>z0</span>=0</span>
<span>x+2y−2z−<span>x0</span>−2<span>y0</span>+2<span>z0</span>=0</span>

Or

<span>x+2y−2z+d=0</span> [1]
where <span>a=1</span>, <span>b=2</span>, <span>c=−2</span> and <span>d=−<span>x0</span>−2<span>y0</span>+2<span>z0</span></span>

Now we'll find planes that obey the previous formula and at a distance of 2 units from a point in the original plane. (We should expect 2 results, one for each half-space delimited by the original plane.)
As a model consider this lesson:

Distance between 2 parallel planes

In the original plane let's choose a point.
For instance, when <span>x=0</span> and <span>y=0</span>:
<span>x+2y−2z=1</span> => <span>0+2⋅0−2z=1</span> => <span>z=−<span>12</span></span>
<span>→<span>P1</span><span>(0,0,−<span>12</span>)</span></span>

In the formula of the distance between a point and a plane (not any plane but a plane parallel to the original one, equation [1] ), keeping <span>D=2</span>, and d as d itself, we get:

<span><span>D=<span><span>|a<span>x1</span>+b<span>y1</span>+c<span>z1</span>+d|</span><span>√<span><span>a2</span>+<span>b2</span>+<span>c2</span></span></span></span></span>
<span>2=<span><span><span>∣∣</span>1⋅0+2⋅0+<span>(−2)</span>⋅<span>(−<span>12</span>)</span>+d<span>∣∣</span></span><span>√<span>1+4+4</span></span></span></span>
<span><span>|d+1|</span>=2⋅3</span> => <span><span>|d+1|</span>=6</span>First solution:
<span>d+1=6</span> => <span>d=5</span>
<span>→x+2y−2z+5=0</span>Second solution:
<span>d+1=−6</span> => <span>d=−7</span>
<span>→x+2y−2z−7=<span>0</span></span></span>
8 0
3 years ago
John ,Rick , and Molli are painting a room together. It takes all of them 16 hours to paint the room to perfection. It takes Joh
CaHeK987 [17]
John's hourly rate is 1/8 of the room per hour.
Rick's hourly rate is 1/2 of the room per hour.
Molli's hourly rate would be 3/8 of the room per hour.

It takes Molli 2 2/3 hours to paint the room alone.

Explanation
Since John paints the entire room (100%=1) in 8 hours, he would paint 1/8 of the room in 1 hour.
Since Rick paints the entire room (100%=1) in 2 hours, he would paint 1/2 of it in 2 hour.

We do not yet know Molli's rate, so we will call it x.

We know that 1/8+1/2+x = 1 hour.

We will use 8 as a common denominator:
1/8+4/8+8x/8 = 1

Adding the numerators, 
(1+4+8x)/8 = 1

Multiply both sides by 8:
1+4+8x = 8

Add like terms:
5+8x = 8

Subtract 5 from both sides:
5+8x-5=8-5
8x=3

Divide both sides by 8:
8x/8 = 3/8
x = 3/8

Molli's rate is 3/8.

Since she can paint 3/8 of the room in 1 hour, we can set up the equation
3/8x = 1

Divide both sides by 3/8:
3/8x ÷ 3/8 = 1 ÷ 3/8
x = 1/1 ÷ 3/8 = 1/1 × 8/3 = 8/3
x = 2 2/3

This is the amount of time it takes Molli to paint the entire room.
5 0
3 years ago
Part A name the asymptote for the graphed function
jasenka [17]

Answer:

The horizontal line  y=2  is the asymptote


Step-by-step explanation:

This is an exponential function.

An asymptote is the line a function approaches but never touches.

Here, y=2 is the horizontal line that is asymptote of the function.


<u>Note:</u> <em>Normally, y=0 is the asymptote of a parent exponential function, since this graph is parent function shifted 2 units up, the asymptote becomes y=2</em>

8 0
3 years ago
Read 2 more answers
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