First you subtract 9x from y and you get 45 - 9x = -y and you don't want negatives so you switch all the signs to get y = -45 + 9x
The correct answer is ∠Y = 75°
because
45°∠A ∼ ∠X
∠B ∼ ∠Y = 75°
60°∠C ∼ ∠Z
45 + 60 = 105
180 -105 = 75
-------------------------------------------------------------------------------------------------
Assumptions
-------------------------------------------------------------------------------------------------
Let x be the amount of 25% orange juice
Let y be the amount of 10% orange juice
-------------------------------------------------------------------------------------------------
There are 15 litres of 13% orange juice
-------------------------------------------------------------------------------------------------
x + y = 15
-------------------------------------------------------------------------------------------------
The 15 litres of juice is 13% orange juice
-------------------------------------------------------------------------------------------------
0.25x + 0.1y = 15 x 0.13
0.25x + 0.1y = 1.95
-------------------------------------------------------------------------------------------------
Rewrite the equations and solve for x and y
-------------------------------------------------------------------------------------------------
x + y = 15 ----------------------- (Equation 1)
0.25x + 0.1y = 1.95 ----------- (Equation 2)
(Equation 1):
x + y = 15
x = 15 - y ----------- (Substitute into Equation 2)
0.25 (15 - y) + 0.1y = 1.95
3.75 - 0.25y + 0.1y = 1.95
0.15y = 1.8
y = 18 ÷ 0.15
y = 12 ------------- (substitute into Equation 1)
x + y = 15
x + 12 = 15
x = 15 - 12
x = 3
x = 3 and y = 12
-------------------------------------------------------------------------------------------------
Answer: 3 liters of 25% of orange juice with 12 liters of 10% orange juice
-------------------------------------------------------------------------------------------------
You must multiply the all the numerators first. This is 8 x 6 x 1 = 48. Therefore you know 48 will be the top number. Now you multiply the denominators 15 x 5 x 3 = 225. Therefore the answer will be 48/225. However you can simply this fraction. Now you must think of a number that both 48 and 225 are divisible by, in this case it is 3. Therefore the answer is 16/75.
<h3>
Answer: (-1, 11)</h3>
This means x = -1 and y = 11 pair up together.
================================================
Work Shown:
Set the two functions equal to one another. Solve for x.
f(x) = g(x)
-4x+7 = 2x+13
7 = 2x+13+4x ... adding 4x to both sides
7 = 6x+13
7-13 = 6x .... subtract 13 from both sides
-6 = 6x
6x = -6
x = -6/6 ... divide both sides by 6
x = -1
Use this x value in either function
f(x) = -4x+7
f(-1) = -4(-1)+7
f(-1) = 11
or
g(x) = 2x+13
g(-1) = 2(-1)+13
g(-1) = 11
Whichever function you pick, the input x = -1 leads to the output y = 11.
The point of intersection is (x,y) = (-1, 11)
Visual confirmation is shown below.
