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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

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?