If the hypotenuse of a 30°-60°-90° Triangle is 10√2, find the length of the other two sides.

Answer:

3 feet in a yard, so the answer is 6

Step-by-step explanation:

2 yards x 3 feet in a yard = 6 feet

Answer:

6

Step-by-step explanation:

There are 3 feet in 1 yard, so in 2 yards there would be 6 feet.

Hope that helps!

The equation of the line in slope-intercept form and standard form that passes through the line are  y = -5 / 6x - 43 / 6 and  5x + 6y = -43 respectively.

The Slope intercept equation is use to represent a linear table or graph. Therefore, the formula is represented as follows

y = mx + b

where

m = slope

b = y-intercept

Hence,

(-5, -3)(1, -8)

m = -8 + 3 / 1 + 5 = - 5 / 6

Using (1, -8) let's find b

-8 = -5 / 6 (1) + b

-8 + 5 / 6 = b

-48 + 5/6 = b

b = -43 / 6

Therefore, the slope intercept equation is y = -5 / 6x - 43 / 6

The equation in standard form is represented as Ax + By = C. Therefore,

y + 5 / 6 x = - 43/6

5x + 6y = -43

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Answer:

○ [tex]\displaystyle \pi[/tex]

Step-by-step explanation:

[tex]\displaystyle \boxed{y = 3sin\:(2x + \frac{\pi}{2})} \\ y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{4}} \hookrightarrow \frac{-\frac{\pi}{2}}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 3[/tex]

OR

[tex]\displaystyle \boxed{y = 3cos\:2x} \\ y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 3[/tex]

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 3sin\:2x,[/tex]in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the sine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{4}\:unit[/tex]to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD [tex]\displaystyle \frac{\pi}{4}\:unit,[/tex]which means the C-term will be negative, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{\pi}{4}} = \frac{-\frac{\pi}{2}}{2}.[/tex]So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 3sin\:(2x + \frac{\pi}{2}).[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit [tex]\displaystyle [-1\frac{3}{4}\pi, 0],[/tex]from there to [tex]\displaystyle [-\frac{3}{4}\pi, 0],[/tex]they are obviously [tex]\displaystyle \pi\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle \pi.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex]in which each crest is extended three units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

Answer:

[tex]\pi[/tex]

Step-by-step explanation:

The trigonometric function shown on the graph is a continuous function, and so its period is the length of one wave of the function (i.e. the horizontal distance between a peak and the next peak, or a trough and the next trough).

From inspection of the graph, the horizontal distance between one peak and the next of the given function is [tex]\pi[/tex].  

Therefore, the period of this trigonometric function is [tex]\pi[/tex]

Answer:

x = 10.8

Explanation:

[tex]\sf \sf cos(x)= \dfrac{adjacent}{hypotensue}[/tex]

using cosine rule:

[tex]\rightarrow \sf cos(26)= \dfrac{x}{12}[/tex]

[tex]\rightarrow \sf x = cos(26) *12[/tex]

[tex]\rightarrow \sf x =10.8[/tex]

Answer:

The answer is rounded 10.8

Step-by-step explanation:

Cosine is the adjacent side over the hypotenuse, or a/h. So, cos 26=x/12. To solve for x, isolation of the variable is necessary. If both sides are multiplied by 12, the equation becomes 12 (cos 26)=x. The cosine of 26 is 0.8988, which multiplied by 12 is 10.8.

Hope this helps!

Answer:

Multiply the numbers then Add on both sides then simplify

Step-by-step explanation:

Answer

102.1

Step-by-step explanation:

area of the shaded region is the area of the the whole circle subtract area area of the unshaded minor segment.

Answer:

x=-9

y=4

Step-by-step explanation:

x + 3y = 3

x - 5y = -29

Multiply the second equation by -1

-x + 5y = 29

Add the two equations together to eliminate x

x + 3y = 3

-x + 5y = 29

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

0x +8y = 32

Divide each side by 8

8y/8 = 32/8

y = 4

Now solve for x

x+3y =3

x+3(4) = 3

x+12 = 3

Subtract 12 from each side

x+12-12 = 3-12

x = -9

Answer:

He did not put the numbers in order.

Explanation:

The numbers need to be in order from smallest to largest before you find the median.

Answer:

10

Step-by-step explanation:

Using the formula

d=2r

Solving for r

r=d

2=10

2=5

Answer:

27/5

Step-by-step explanation:

because If you do 5 2/5 = ? you get 27/5

Answer:

The smallest number by which 256 must be divided so that the quotient is a perfect cube is 4.

Step-by-step explanation:

Answer:Experimental probability = 0.297

Step-by-step explanation: experimental probability = number of times event occurs/total number of trials
Probability = 22 divided by 74 = 0.297

Therefore the experimental probability of choosing green marble is 0.297.

The answer for this equation funtion would be The first one because it is the correct answer.

Answer:

Step-by-step explanation:

The height of the tree can be found by establishing a proportional relationship between the heights and the shadows of the tree and Cameron and the height of the tree to the nearest hundredth of a meter is 2.40 m.

Proportional relationships are relationships between two variables where their ratios are equivalent.

Therefore, we will establish a proportion to find the height of the tree.

Cameron height = 1.85 m

Tree shadow = 21.55 m

Cameron shadow length = 16.6 m

height of the tree = x

Therefore,

1.85 / x = 16.6 / 21.55

16.6x = 21.55 × 1.85

x = 39.8675 / 16.6

x = 2.40165662651

x = 2.40 m

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<-------------------288km---------->

x=48 km 5x=240km

⊙__________⊙___________⊙

jonesville smitville cityville

6x=288

x=48

=48km

Answer:

Each box of two inch nails contained 67 nails

Step-by-step explanation:

Givens

291 one inch nails

5 boxes of 2 inch nails

Total number of nails = 626 nails

Formula

291 + 5*two = 626      Two is the number of 2" nails in one box

Solution

291 + 5*two = 626              Subtract 291 from both sides.

5*two = 626 -291                Combine

5*two = 335                        Divide both sides by 5

5*two/5 = 335/5

two = 67

The volume of the container is the amount of can in it

The contents weigh 1047.1 ounces

The given parameters are:

Volume = 28.3 cubic feet

Average weight of can = 37 ounces per cubic foot

So, the weight of the container would be:

Weight = Volume * Average weight of can

Substitute known values

Weight = 28.3 cubic feet * 37 ounces per cubic foot

Evaluate the product

Weight = 1047.1 ounces

Hence, the contents weigh 1047.1 ounces

Read more about volumes at:

https://brainly.com/question/1972490

Answer:

20

Step-by-step explanation:

I'm not too sure why 22 is there. Triangle = (bh) / 2

90 x 2 = 180. 180 / 9 = 20, therefore, base is 20.

Answer:

First, we must know the formula for the area of a triangle.

A = BH x 1/2

Where 'b' represents the base, and 'h' represents the height.

Multiplying by 1/2 basically means dividing the result of (base x height) by 2.

Now we plug in what we know, given the dimensions shown.

We know that the area is 90 square units.

We also know that the height is 9, so;

A = BH x 1/2

90 = B(9) x 1/2

Solve for B:-

90 = 9b(we reverse b9 because they both serve as the same thing) x 1/2

90 = 9b x 1/2

Dividing by 1/2 also means multiplying by 2, so we multiply 2 to both sides to get rid of 1/2;

*2         *2

180 = 9b

To isolate b(base) we divide by 9 from both sides because the inverse operation of multiplication is division.

÷ 9    ÷ 9

20 = b, our base is 20 square units.

Answer:

240 Minutes

Step-by-step explanation:

0.6 per minute × 2 = 1.2 gallons .

120 balloons × 2 mins= 240 mins

Answer: 40.82

Step-by-step explanation: You have to multiply pi and 13 to get the answer

Answer:

3 feet by 7 feet

Step-by-step explanation:

perimeter = 20 feet

area = 21 feet²

If the desk is a rectangle:

perimeter = 2l + 2w = 2 (l+w) = 20

                                    2 (l+w) = 20 , divide both sides by 2

                                          l+w = 10

area = l · w = 21

What numbers we know that have sum as 10 and their product as 21?

l + w = 10

l · w = 21

factors of 21 are 1,3,7

3+7 = 10

3 ·7 = 21

The dimensions of the desk could be 3 feet by 7 feet.

Answer:

y=ax, y»a

Step-by-step explanation:

that means that gradually the lines going up instead of going down and the step by step function will give you two set of points in the graph that will be your your center point

Answer:

standard form:   y = x² - 2x - 8

vertex form:  y = (x − 1)² - 9

factorized form:  y = (x + 2)(x - 4)

Step-by-step explanation:

From inspection of the graph:

Standard quadratic form:   y = ax² + b x + c

Vertex form of a quadratic equation:   y = a(x − h)² + k

If a > 0 then the parabola opens upwards

If a < 0 then the parabola opens downwards

(h, k) is the vertex

c is the y-intercept

Inputting the vertex into the vertex form gives:

y = a(x − 1)² - 9

  = a(x² - 2x + 1) - 9

  = ax² - 2ax - 8

Using the x-intercepts to create a quadratic equation:

y = a(x + 2)(x - 4)

  = a(x² - 2x - 8)

  = ax² - 2ax - 8a

Comparing the y-intercepts:

-8 = -8a  ⇒  a = 1

Therefore,   y = x² - 2x - 8

Answer:

5.5 hours

Step-by-step explanation:

dibide by 2 one is 5 and one is 6, middle. is 5.5,

Answer:

B

C/15=3

Step-by-step explanation:

They devided the coconuts among 15 children

3x15 =45

45÷3 =15

So the number of coconut the kids gathered is 45

C/15=3 multiply by 15 on both side

15/1 ×c/15=3×15

C=3×15

C=45

Answer:

$321.75

Step-by-step explanation:

k = y/x

514.80/18= 28.6  

28.6 * 11.25 =321.75

Thus, Ashley will earn 321.75 in 11.25 Hours

~Lenvy~

Answer:

$321.75

Step-by-step explanation:

Formula ⇒ k = y/x

Dollar = y

x = Hour

Hence,

514.80/18= 28.6  

28.6 × 11.25 =321.75

Therefore, Ashley will make $321.75 in 11.25 Hour

[RevyBreeze]

Answer:

30.84 cm

Step-by-step explanation:

Formula for perimeter of semi-circle = πr + 2r

Radius (r) = 6 cm

π = 3.14

Perimeter

= πr + 2r

= 3.14(6) + 2(6)

= 3.14(6) + 12

= 18.84 + 12

= 30.84 cm

_________

Hope it helps ⚜

Answer:

30.85 cm to 2 d.p.

Step-by-step explanation:

The perimeter is made up of the diameter ( = 2*radius) and half a full circle

= 6*2 + 1/2 * π* 6

= 12 + 3π

= 30.849

Answer: h + 97 = 240

Step-by-step explanation:

Total hours worked per year: 240 hours

Current hours worked so far: 97 hours.

The variable h represents hours

Therefore, h + 97 = 240

Answer:

There are 18 choices for first place, 17 for second, and 16 for third.

Therefore, there are 18 x 17 x 16=4896

So there are 4,896 ways possible

Step-by-step explanation:

Hope this helps:)...if not then sorry for wasting your time and may God bless you:)

Answer:

Answer is C

Step-by-step explanation:

Because you divide each side by 2 because that is the scale factor