The final balance is $23,970.67
Step-by-step explanation:
Answer:
x ≈ 43.3°
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos x = 
= 
, then
x = 
( ) ≈ 43.3° ( to 1 dec. place )
Answer:
0
Step-by-step explanation:
<h3>Given</h3>
- (x +
)(y + 
) = 1 - (x+y)² = ?
<h3>Solution</h3>
<u>Let's make substitution as:</u>
- (x + ) = m
then
- (y + ) = 1/m
<u>Solving the first equation for x and the second one for y:</u>
- (x + ) = m
- = m - x
- 1 + x² = (m - x)²
- 1 + x² = m² - 2mx + x²
- 2mx = m² - 1
- x = (m² - 1)/2m
And
- (y + ) = 1/m
- = 1/m - y
- 1 + y² = 1/m² -2y/m + y²
- 1 = 1/m² - 2y/m
- m² = 1 - 2my
- 2my = 1 - m²
- y = (1 - m²)/2m
- y = - (m² - 1)/2m
<u>Now, sum of x and y:</u>
- x + y = (m² - 1)/2m - (m² - 1)/2m = 0
<u>Therefore:</u>
Answer is zero
Kendall and Sophia swam (2n - 12) laps together
<em><u>Solution:</u></em>
Given that, Kendall Swam (n) laps in the pool
To find: Number of laps swam together
From given statement,
Number of laps by Kendall = n
Also, Sophia swam 12 less than Kendall
Therefore, number of laps swam by Sophia is 12 less than the number of laps by Kendall
Number of laps by Sophia = Number of laps by Kendall - 12
Number of laps by Sophia = n - 12
<em><u>How many laps did they swim altogether ?</u></em>
Number of laps swam together = Number of laps by Kendall + Number of laps by Sophia
Number of laps swam together = n + n - 12 = 2n - 12
Thus they swam (2n - 12) laps together
Answer:
a. 1/4
Step-by-step explanation:
3r=12p
<em>Divide the left side by 12 to get 1 cup of pineapple juice.</em>
3r=12p
---- = p
12
<em>So now you have</em>
3r=p
<em>BUT you have to divide BOTH sides by 12 so</em>
3r=p
---
12
<em>NOW you have</em>
3/12 r = p
<em>Simplify.</em>
1/4r = p
So 1 cup of pineapple juice is equivalent to a quarter cup of orange juice!
