Answer:
The answer to your question is x = 3; y = 3
Step-by-step explanation:
Data
angle = 45°
Opposite side = x
Adjacent side = y
hypotenuse = 3√2
To solve this problem, use trigonometric functions.
1) To find x, use the trigonometric function sine.
sin Ф = Opposite side / hypotenuse
-Solve for Opposite side (x)
Opposite side = hypotenuse x sin Ф
-Substitution
Opposite side = 3√2 sin 45
-Simplification
Opposite side = 3√2 (1 / √2)
Opposite side = 3(1)
-Result
x = 3
2) To find y use the trigonometric function cosine
cos Ф = Adjacent side / hypotenuse
-Solve for Adjacent side
Adjacent side = hypotenuse x cos Ф
-Substitution
Adjacent side = 3√2 x cos 45
-Simplification
Adjacent side = 3√2 x (1/√2)
Adjacent side = 3(1)
-Result
y = 3
Answer:
x=-5
Step-by-step explanation:
3(x + 1)=2(x - 1)
3x + 3 = 2x - 2
3x - 2x = -2 - 3
x = -5
Hope this helps!
Answer:
(10, 3)
Step-by-step explanation:
Solve by Substitution
2x − 4y = 8 and 7x − 3y = 61
Solve for x in the first equation.
x = 4 + 2y 7x − 3y = 61
Replace all occurrences of x with 4 + 2y in each e quation.
Replace all occurrences of x in 7x − 3y = 61 with 4 + 2y. 7 (4 + 2y) − 3y = 61
x = 4 + 2y
Simplify 7 (4 + 2y) − 3y.
28 + 11y = 61
x = 4 + 2y
Solve for y in the first equation.
Move all terms not containing y to the right side of the equation.
11y = 33
x = 4 + 2y
Divide each term by 11 and simplify.
y = 3
x = 4 + 2y
Replace all occurrences of y with 3 in each equation.
Replace all occurrences of y in x = 4 + 2y with 3. x = 4 + 2 (3)
y = 3
Simplify 4 + 2 (3).
x = 10
y = 3
The solution to the system is the complete set of ordered pairs that are valid solutions.
(10, 3)
The result can be shown in multiple forms.
Point Form:
(10, 3)
Equation Form:
x = 10, y = 3
The two angles are 45 degrees.
Step-by-step explanation:
You are just halfing the 90 degree angle, so all you have to do is divide 90 by two, and you have 45.
