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A triangle in a circle that way, always must be a right triangle, so b  must be 90. 

The sum of angles in a triangle are 180. 

C = 54

B = 90

A + B + C = 180

A + 90 + 54 = 180

Can you solve for A?

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S A H   C A H  T O A

SINE = OPPOSITE/ HYPOTENUSE

SINE A = 3/5

Cylinder volume =  pi r^2 h

     653.12          = 3.14  (4²)  h

h = 653.12 / (3.14 * 4² ) = .......... ft

Triangle

base = 8, height = 6.

8*6/2 = 24

Rectangle

width = 8, length = 10

8*10 = 80

Now we just have to add them together. :))

What's 80 + 24?

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Since the traingles are similar, y should be equal to 40 degrees too. 

And since the ratio of sides are 1:2, 2(5x) = 8x+10. 

Can you solve for x?

I hope this helped. :))

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18 now, 20 before, meaning it decreased by 2cm. 

2/20 = 10%

10% decrease

I hope this helped. :))

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I'm so sorry I made a typo. What I meant to write was: show that (sin(a))^7+(cos(a))^7 <1 if  0

They caught 1/5 of the tagged parrots    and that amounts to 75 parrots

   5 * 75 = 375 parrots

By the wording of this problem, I am unsure if a=0

If so, sin(0) = 0 and cos(0) = 1. You can find these solutions using the unit circle. 

Basically, 0^7 + 1^7 <1

1 is not less than 1 so it is false unless you don't know how to do a less or equal to sign. The latex form for it is \leq. \(\leq\)

adage

Just plug in 2 for the first f(x).

f(2)= 3(2^2)-5

f(2)=3(4)-5

f(2)=12-5

f(2)=7

Then plug in 7 for the second f(x)

f(7)=3(7^2)-5

f(7)=3(49)-5

f(7)=147-5

f(7)=142

f(f(2)=142

The first probability problem is quite easy since the numbers are percentages.

Quick refresher: 1% is 1/100

Since 45% of customers want their plate sets to be moved, you would think its 45/100, but actually you also need to add the people that need both of their sets moved, which includes plate sets. It would be 50/100 ( ill let you simplify)

Second question

Since the knife sets have been moved, a 25% probability, we know that 50% of customers want their plates moved. However, it is no longer 50/100 but 50/75 (simplify). This is because there are only 75% of customers remaining. 

I may have made a mistake, but hopefully this makes it clearer. :)

You can see the jump between each number is 4.

To find the 21st term, do 4 x 20 = 80 and add it to the first term

80+3=83

Why do we have to do this?

I really don't know but here is a guess.

75 parrots = 10 tags

times both by 5

375 parrots = 50 tags

375 parrots.   

It is likely to be wrong though.

\(a^2b+b^2c+c^2a-ab^2-bc^2-ca^2 = 0\\ a^2b+b^2c+c^2a=ab^2+bc^2+ca^2 \\ \text{factor out b}\\ b(a^2+bc)+ac^2=b(c^2+ab)+ca^2\\ \)

Now, no matter what integer b is,   a =b

Convince yourself of that.....

Factor out c instead of b and what do you find?

Factor out a instead of b and what do you find?

Now you have all of your answer sets.

Student tickets = 180

General admission tickets = 270

(180 * 4) + (270 * 6) = 2340

(2x + 5)(2x + 7) = 80

x = 1.5

\(1. \) Write the equation:

\((65+115)\)\(\div \)\(5\)

\(2.\) Do the PEMDAS(parenthesis, exponents, multiplication, division, addition, subtraction) which you do the parenthesis first

\(180\div \:5\)

\(3.\) Follow the multiplcation rule for \(5\) which means the ones digit is \(5\) or \(0\)

180

The remainder is \(0\) because \(5\) can perfectly fit \(180\)

Hey there!

For the left triangle, we can gather that the bottom left unknown = 75 and the top unnkown = 45. From this, and knowing that the flat portions add up to 180, you should be able to find the value of x. Give it a crack and let me know how you go :)

Hope this helped :)

Here we want to multiply the fraction by its conjugate, thus:

\(\frac{10\sqrt{7}}{-1+\sqrt{10}} \times \frac{1+\sqrt{10}}{1+\sqrt{10}}=\frac{10\sqrt{7}(1+\sqrt{10}}{(-1+\sqrt{10})(1+\sqrt{10})}\)

expanding the denomenator comes out as 9. after expanding we get the following

\(\frac{10\sqrt{7}+10\sqrt{70}}{9}=\frac{-10\sqrt{7}-10\sqrt{70}}{-9}\)

I hope this helped :)

Hey there!

Is any of this question cut off? I am not getting any of these 4 answer?

EDIT: nevermind, i'm dumb, give me minute...

Hey there!

Here we know that the angles along A and C will add up to a total of 180. Due to what i know as the Z rule (I don't actually know the correct term for this is), we know that angle 2 will be equal to the unknown inner angle of the triangle near C. Using this, you should be able to find all the angles that you are looking for! Give it a go and let me know how you go.

Hope this helped :)

Hey there!

We know that near H, G, D and C that these angles will add to give 180, we also know that the two angles at the tops of the triangles near F will be equal to eachother. Finally we know that the sum of angles in a triangle is equal to 180. Using this you can find all the angles needed to find angle B. Give it a crack and let me know how you go!

Hope this helped :)