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\(sin\;3\theta = cos\; 17\theta\\ sin\;3\theta = sin\; (90-17\theta)\\ \)

you can take it from there.

5 trays + 20 cups = (5 + 20/3) trays

                             = 35/3 trays

35/3 trays ---> 7/9 of her money

1 tray ---> 1/15 of her money

9/10 of her remaining money (2/9) = 9/10 * 2/9

                                                       = 1/5 of her money

1/5 / 1/15 = 3

She bought 3 more trays with her remaining money.

I don't think there are any 4 digit₃ that translate to 2 digit₅

Smallest 4 digit base 3 is 1000  which is 27₁₀

Largest base 5  two digit is 44₅ = 24₁₀

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🥳🥳🥳🥳🥳

Can you be more specififc please? Like are you trying to find the derivative, root, integral???

Find 4y

2x+4y=180 (1) and   

x+2y=4y     (2)and

3x+2y=180  (3)

rearrange 1  

4y=180-2x

2y=90-x

rearrange2

x=2y

sub

2y=90-2y

4y=90 degrees

6y + x = 180

4y = 2y + x

4x = 180

8y = 180

Angle R = xº

2x + 4y = 180

4y = 90º

x⁴ - 5x³ + 5x² + 17x - 42 - x⁴ + 5x³ - 4x² - 16x + 20

= x⁴ - x⁴ - 5x³ + 5x³ + 5x² - 4x² + 17x - 16x - 42 + 20

= x² + x - 22

\(x = \frac{-1 + \sqrt{89}}{2}\)

\(x = \frac{-1 - \sqrt{89}}{2} \)

Your answer is more intelligent than mine. 

(sin R)² + (sin T)² = 1

sin(T) = 0.916515139    or   809995 / 883777

sinθ = opposite/hypotenuse

hence because sinR = 2/5,

opposite = 2 units

hypotenuse = 5 units

using the pythagorean theorem, the adjacent side to angle R would be:

\(=\sqrt{5^2 - 2^2}\)

\(= \sqrt{21}\)

therefore sinT = \(\frac{\sqrt{21}}{5}\)

All these satisfy your equation. Remove any duplicates:

1  = (1, 1, 1)
2  = (2, 2, 1)
3  = (3, 3, 1)
4  = (4, 4, 1)
5  = (5, 5, 1)
6  = (1, 1, 2)
7  = (2, 2, 2)
8  = (3, 3, 2)
9  = (4, 4, 2)
10  = (5, 5, 2)
11  = (1, 1, 3)
12  = (2, 2, 3)
13  = (3, 3, 3)
14  = (4, 4, 3)
15  = (5, 5, 3)
16  = (1, 1, 4)
17  = (2, 2, 4)
18  = (3, 3, 4)
19  = (4, 4, 4)
20  = (5, 5, 4)
21  = (1, 1, 5)
22  = (2, 2, 5)
23  = (3, 3, 5)
24  = (4, 4, 5)
25  = (5, 5, 5)

Dr. Zaius invests $10,000 in a CD with an annual interest rate of 4% that compounds semi-annually (twice a year). After six months, he rolls over the CD into another CD with an annual interest rate of 6% that also compounds semi-annually. After six months in the second CD, how much does Dr. Zaius have, in dollars?

10,000  x  1.02 ==10,200 - principal + interest for the first 6 months.

10,200  x  1.03 ==$10,506 - principal + interest after the second 6-month period.

The human resource manager of a large USA based IT company has derived a linear regression model to predict the current salary of an employee based on the employee's starting salary (in $), previous experience (in months) and years in education. The model's output is shown below:  

By looking at the model's output what is an employee’s current salary if the employee started working with a salary of 20500$, has 2 years of previous experience and has been studying for 8 years? (Give your answer in 2 decimal points).

RQ = 5

The endpoints of a diameter of a circle are (7,−4) and (−3,2).

What is the equation of the circle in standard form?

Hello Guest!

\((x-x_0)^2+(y-y_0)^2=r^2\)

\(\color{blue}P_0(2,-1)\\ d^2=10^2+6^2\\ r=\frac{d}{2}=5.831\\ \color{blue}r^2=34\)

\((x-2)^2+(y+1)^2=34\)

  !

11! + 12! + 13!

=11!(1+12+12*13)

=11!*169

=11! * 13 *13

so yes the largest prime is 13

AG, your answer is absurd!

You need to learn to read the question and understand what it is asking. Blindly throwing random equations at the problem rarely results in a correct solution.

The answer to this question is three (3) arrangements.

The books are identical, so the only distinguishable difference is the number of books.

Of the six books, at least two (2) books are checked-out and at least two (2) books are in the library. So the library can have a set of two, or a set of three, or a set of four books. 

The quantity is the only distinguishable arrangement characteristic of the sets. 

GA

--. .-

11!  +  12!  +13! ==6,745,939,200

6745939200 = 2^8 * 3^4 * 5^2 * 7 * 11 * 13^2

The largest prime divisor ==13

7x^2 + x - 5 = 0

a+b = -1/7, ab = -5/7

(a+4)(b+4) = 4(a+b) + ab + 16 = 4(-1/7)+(-5/7)+16 = 16 - 9/7 = 103/7

(a + 4)(b + 4)/(ab) = (103/7)/(-5/7) = -103/5

7x^2 + x - 5 = 0

a+b = -1/7, ab = -5/7

(a+4)(b+4) = 4(a+b) + ab + 16 = 4(-1/7)+(-5/7)+16 = 16 - 9/7 = 103/7

(a + 4)(b + 4)/(ab) = (103/7)/(-5/7) = -103/5

The polygon ABCDE is an irregular pentagon. 

[ABCDE] = 5√3

A fruit company delivers its in two types of boxes: large and small. Delivery of 3 large boxes has a total weight of 153 kilograms. A Delivery of 5 large boxes and 2 small boxes has total weight of 102 kilograms. How much does each type of box weigh?