15y+6-4y=2(y-6)
2 answers:
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Answer:
(6, - 4 )
Step-by-step explanation:
Given the 2 equations
-
y = 3 → (1)
x -
= 12 → (2)
Multiply (1) by 8 and (2) by 6 to clear the fractions
2x - 3y = 24 → (3)
10x - 3y = 72 → (4)
Rearrange (3) expressing - 3y in terms of x by subtracting 2x from both sides
- 3y = 24 - 2x
Substitute 3y = 24 - 2x into (4)
10x + 24 - 2x = 72, that is
8x + 24 = 72 ( subtract 24 from both sides )
8x = 48 ( divide both sides by 8 )
x = 6
Substitute x = 6 in either (3) or (4) and solve for y
Substituting in (3)
2(6) - 3y = 24
12 - 3y = 24 ( subtract 12 from both sides )
- 3y = 12 ( divide both sides by - 3 )
y = - 4
Solution is (6, - 4 )
The hole is 8 feet deep at ground level ⇒ 3rd answer
Step-by-step explanation:
The form of the quadratic function is y = ax² + bx + c, where
- a is the coefficient of x²
- b is the coefficient of x
- c is the y-intercept (at x = 0)
The vertex point of the quadratic is (h , k), where
and k is the value of y when x = h
The table:
→ x : -2 , 0 , 2
→ y : -6 , -8 , -6
∵ x represents distance from hole's center in feet
∵ y represents the depth from level ground
∴ The quadratic function is y = ax² + bx + c
∵ c is the value of y at x = 0 ⇒ y-intercept
- From the table at x = 0 ⇒ y = -8
∴ c = -8
- Substitute its value in the function model
∴ y = ax² + bx - 8
- To find the values of a and b substitute x and y in the model by
the coordinates of the point in the table
∵ x = -2 and y = -6
∴ -6 = a(-2)² + b(-2) - 8
∴ -6 = 4a - 2b - 8
- Add 8 to both sides
∴ 2 = 4a - 2b
- Switch the two sides
∴ 4a - 2b = 2 ⇒ (1)
∵ x = 2 and y = -6
∴ -6 = a(2)² + b(2) - 8
∴ -6 = 4a + 2b - 8
- Add 8 to both sides
∴ 2 = 4a + 2b
- Switch the two sides
∴ 4a + 2b = 2 ⇒ (2)
Now we have a system of equation to solve it
Add equations(1) and (2) to eliminate b
∵ 8a = 4
- Divide both sides by 8
∴ a = 0.5
- Substitute value of a in equation (1) or to to find b
∵ 4(0.5) + 2b = 2
∴ 2 + 2b = 2
- Subtract 2 from both sides
∴ 2b = 0
- Divide both sides by 2
∴ b = 0
Substitute the values of a and b in the function model
∴ y = 0.5x² + (0)x - 8
∴ y = 0.5x² - 8
∵ y represents the depth from level ground
∵ The vertex of the function model is (h , k)
∴ The deep of the hole at ground level is the value of k
∵
∴
∴ h = 0
∵ k is the value of y when x = h
- From the table at x = 0 ⇒ y = -8
∴ k = -8
- Ignore the sign (-) because the k represents the depth of the
hole in feet
∴ The deep of the hole at ground level is 8 feet
The hole is 8 feet deep at ground level
Learn more:
You can learn more about the quadratic function in brainly.com/question/1332667
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