All categories

2 years ago

Find the missing lengths of the sides.

Mathematics

1 answer:

uranmaximum [27]2 years ago

6 0

Answer:

b = 8√3 and c = 16

Step-by-step explanation:

Points to remember

If the angles of a right angled triangle with angles are 30°, 60, and 90 the their sides are in the ratio 1 : √3 : 2

To find the unknown side lengths

From the given figure we can see a right angled triangle

Angles are 30°, 60° and 90°

sides are in the ratio 1 : √3 : 2

1 : √3 : 2 = 8 : b : c

b = 8√3 and c = 8 * 2 = 16

Therefore b = 8√3 and c = 16

You might be interested in

Keevyn has a bag of Jolly Ranchers. Keevyn gave 3/8 of the bag to Zavion and 1/4 of the bag to Qeisha. Then keeyvn gave 1/2 of t

sergejj [24]

Answer:

1.5/8 of the bag

Step-by-step explanation:

1/4 * 2 = 2/8

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

3/8 + 2/8 = 5/8

1 - 5/8 = 3/8

3/8 divided by 1/2 = 1.5/8

3 0

2 years ago

Read 2 more answers

Seven times the smaller

Taya2010 [7]

Given:

Seven times the smaller of two consecutive even integers is the same as -300 minus 4 times the larger integer.

To find:

The integers .

Solution:

Let the smaller even integer be x.

So, larger even integer is x+2 because they are consecutive even integers.

Seven times the smaller integer = 7x

-300 minus 4 times the larger integer = -300-4(x+2)

Now,

$7x=-300-4(x+2)$

$7x=-300-4x-8$

$7x+4x=-308$

$11x=-308$

Divide both sides by 11.

$x=\dfrac{-308}{11}$

$x=-28$

So, the smaller even integer is -28.

$x+2=-28+2=-26$

So, the larger even integer is -26.

5 0

3 years ago

PLEASE HELP QUICKLY 25 POINTS

Natalija [7]

Answer:

○ $\displaystyle \pi$

Step-by-step explanation:

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

OR

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

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 $\displaystyle y = 3sin\:2x,$ 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 $\displaystyle \frac{\pi}{4}\:unit$ to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD $\displaystyle \frac{\pi}{4}\:unit,$ which means the C-term will be negative, and by perfourming your calculations, you will arrive at $\displaystyle \boxed{-\frac{\pi}{4}} = \frac{-\frac{\pi}{2}}{2}.$ So, the sine graph of the cosine graph, accourding to the horisontal shift, is $\displaystyle y = 3sin\:(2x + \frac{\pi}{2}).$ 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 $\displaystyle [-1\frac{3}{4}\pi, 0],$ from there to $\displaystyle [-\frac{3}{4}\pi, 0],$ they are obviously $\displaystyle \pi\:units$ apart, telling you that the period of the graph is $\displaystyle \pi.$ 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 $\displaystyle y = 0,$ 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.

7 0

2 years ago

Read 2 more answers

Given that the measure of ∠x is 66°, and the measure of ∠y is 66°, find the measure of ∠z

kirza4 [7]

Answer:

Step-by-step explanation:

66*2=132

180-132=48

Hope this helps!

If not, I am sorry.

7 0

2 years ago

YALL PLEASE HELP FRFR

Arturiano [62]

First of all, let's note the sales tax rates in each town. In Washington, we know it's 6%. In the town in Virginia, it's 5%. In the town in Maryland, it's 9%.

Let's figure out the total taxes in every town by applying the sales tax rate for each town.

To add percents to a whole number, we always multiply using 0.XX (example: to add 1% to a the number 100, we would multiply 100*0.01 and get the answer 1. We'd then add the 1 to the original number, 100, and get 101.)

In this case, we need to multiply the $1000 by the sales tax in Washington, 6%.

1000 x 0.06 = 60. Now, we add the 60 to the original number (1000), and get 1060. Now we know the total tax in Washington on the computer will be $60, and the total price we will pay is $1060.00

For Virginia, the sales tax is 5%. Let's add the 5% using the same method we used in the equation above.

1000 x 0.05 = 50. Now, add the 50 to the original 1000, and we get 1050. Now we know that the total tax in Virginia is going to be $50, and the total price that we'll pay in Virginia is $1050.00.

On to the final town, Maryland. In Maryland, the sales tax rate is 9%. Let's use the same formula again.

1000 * 0.09 = 90. Now that we have the 90, we add it to the original 1000, and we get 1090. In Maryland the total sales tax will be $90, and the total price we'll pay is $1090.00.

Now, let's complete the question by answering the 3 parts.

To spend the least amount total Amir should buy the computer in Virginia ($1050.00).

Amir would pay the most sales tax in Maryland ($90.00).

Amir would pay $60 sales tax in Washington, DC.

I hope this answer was in depth enough to help you out so that you can do this on your own in the future. :)

3 0

3 years ago

Read 2 more answers