Answer:
(-♾,♾)
Step-by-step explanation:
Any value of x makes this equation true
That's of course the sum angle formula for sine
sin(a+b) = sin a cos b + cos a sin b
We have a=20° b=40°
sin 20° cos 40° + cos 20° sin 40°
= sin(20°+40°)
= sin(60°)
= √3/2
Answer: √3/2
The total scores of the x students from class A can be calculated by multiplying x and the average which is equal to 85. That is 85x.
In similar manner, we are able to find for the total scores of the students from Class B. That would be, 90y.
Combining the scores, the new average then becomes 88. This is equal to,
(85x + 90y) / (x + y ) = 88
Cross-multiplying,
85x + 90y = 88x + 88y
Combine all the x's and y's in each side of the equation.
85x - 88x = 88y - 90y
Combining terms,
-3x = -2y
The ratio is obtained through the step below,
-3x/-3y = -2y/-3y
x/y = 2/3
Thus, the ratio is 2/3.
Answer:
$11,500 was invested at 13%.
$17,500 was invested at 4%
Step-by-step explanation:
This is a simple interest problem.
The simple interest formula is given by:

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.
After t years, the total amount of money is:

In this question:
Loans totaling 29,000.
P was invested at 13%
29000 - P was invested at 4%.
First investment:
Principal P.
Interest 13% = 0.13.
One year, so t = 1.
So


Second investment:
Principal 29000 - P.
Interest 4% = 0.04.
One year, so t = 1.
So

The total interest earned for both loans was $2,195.00.
This means that 
So

So we solve the following system:







$11,500 was invested at 13%.
29000 - 11500 = 17500
$17,500 was invested at 4%