You will need to use the Pythagorean Theorem and plug in the varibles. The rope is the hypotenuse of the right triangle formed, and the 40ft water is the vertical leg, which leaves the ocean floor to be the horizontal leg.[a^{2}+b^{2}=c^{2}\] \[a^{2}+40^{2}=140^{2}\] Then solve for a. \[a^{2}=18000\] \[a=134.164\]
Answer: x = 5, y = 2; Solution = (5, 2)
Step-by-step explanation:
Substitution
2x + y = 12
x + 2y = 9
x + 2y = 9
Subtract 2y from both sides
x = 9 - 2y
Now, substitute x for (9 - 2y) in the first equation
2x + y = 12
2 (9 - 2y) + y = 12
Distribute 2
18 - 4y + y = 12
18 - 3y = 12
Subtract 18 from both sides
-3y = -6
Divide both sides by -3
<em>y = 2</em>
Now to find x, substitute 2 for y in (x = 9 - 2y)
x = 9 - 2y
x = 9 - 2(2)
x = 9 - 4
<em>x = 5</em>
Solution: (5, 2)
Elimination
2x + y = 12
x + 2y = 9
Multiply the second equation by -2 to find y
2x + y = 12
(x + 2y = 9) -2
2x + y = 12
-2x - 4y = -18
Add both equations
2x and -2x are cancelled out
You get:
-3y = -6
Divide both sides by -3
<em>y = 2</em>
Substitute 2 for y in any of the equations to find x
I chose x + 2y = 9
x + 2y = 9
x + 2 (2) = 9
x + 4 = 9
Subtract both sides by 4
<em>x = 5</em>
Solution = (5, 2)
Btw you can use any of these methods, I used both so you could know that you get the same answer no matter the method.
Hope I helped!
When an angle lies along an axis, the values of the trigonometric functions are either 0, 1, -1, or undefined. When the value of a trigonometric function is undefined, it means that the ratio for that given function involved division by zero.
Answer: d
Step-by-step explanation: because every x has 1 y
Answer:
y = 4(x - 2)² + 48
Step-by-step explanation:
Given
y = 4x² - 16x + 64
Using the method of competing the square
Factor out 4 from 4x² - 16x
y = 4(x² - 4x) + 64
add/ subtract ( half the coefficient of the x- term)² to x² - 4x
y = 4(x² + 2(- 2)x + 4 - 4 ) + 64
= 4(x - 2)² - 16 + 64
= 4(x - 2)² + 48
