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Answer:
Hardy has 470 more tennis balls than Kerns.
Step-by-step explanation:
Given that:
Total number of tennis balls = 940
Let,
x represents the number of tennis balls Hardy has.
y represents the number of tennis balls Kerns has.
According to given statement,
x+y=940 Eqn 1
x = 3y Eqn 2
Putting x = 3y in Eqn 1
3y+y=940
4y=940
Dividing both sides by 4
Putting y=235 in Eqn 2
x = 3(235)
x = 705
Difference = Hardy's tennis balls - Kerns' tennis balls
Difference = 705 - 235 = 470
Hence,
Hardy has 470 more tennis balls than Kerns.
The x-intercept is the point at which the function intersects the x-axis.
For any point on the x-axis, y = 0. Thus we can plug in 0 for y and solve for x.
Let's split the middle on this quadratic.
To do this we need to find two numbers that add to equal -6 and multiply to equal -72. (-3 times 24)
Consider ways to multiply to get 72.
72 = 36 ×2...that's not going to work.
72 = 24 × 3
72 = 18 × 4
72 = 12 × 6...and 12 minus 6 is 6!
Let's add our signs; our numbers are -12 and 6.
Now, split the middle and factor.
Now you should know that anything multiplied by zero is zero.
So any value that makes one of those factors equal zero is an x-intercept.
Solve each of these equations.
-3x+6 = 0
-3x = -6
x = 2
x+4 = 0
x = -4
Oh, and since all parabolas (graphs of quadratics) are symmetrical, our axis of symmetry will be the average between the two, which is x=-1.
Now for our y-intercepts. For any points on the y-axis, x=0, so if we plug in 0 for x and solve for y we'll get our y-intercept.
y = -3×0² - 6×0 + 24
y = 0 - 0 + 24
y = 24
What about our vertex? Well, we know it's going to line up with the axis of symmetry, so let's just plug in -1 for x.
y = -3×-1² - 6×-1 + 24
y = -3×1 -6×-1 + 24
y = -3 + 6 + 24
y = 27
Thus the vertex is (-1, 27)
The y value is not going to exceed 27, as this is a decreasing quadratic, (we already know y=24 is a possibilty) and this equation goes downwards infinitely, so our range is (-∞, 27)
As for x, well, it's sort of the input for our equation, meaning it can be whatever we want it to be. Thus the domain is (-∞, ∞)
For any point on the x-axis, y = 0. Thus we can plug in 0 for y and solve for x.
Let's split the middle on this quadratic.
To do this we need to find two numbers that add to equal -6 and multiply to equal -72. (-3 times 24)
Consider ways to multiply to get 72.
72 = 36 ×2...that's not going to work.
72 = 24 × 3
72 = 18 × 4
72 = 12 × 6...and 12 minus 6 is 6!
Let's add our signs; our numbers are -12 and 6.
Now, split the middle and factor.
Now you should know that anything multiplied by zero is zero.
So any value that makes one of those factors equal zero is an x-intercept.
Solve each of these equations.
-3x+6 = 0
-3x = -6
x = 2
x+4 = 0
x = -4
Oh, and since all parabolas (graphs of quadratics) are symmetrical, our axis of symmetry will be the average between the two, which is x=-1.
Now for our y-intercepts. For any points on the y-axis, x=0, so if we plug in 0 for x and solve for y we'll get our y-intercept.
y = -3×0² - 6×0 + 24
y = 0 - 0 + 24
y = 24
What about our vertex? Well, we know it's going to line up with the axis of symmetry, so let's just plug in -1 for x.
y = -3×-1² - 6×-1 + 24
y = -3×1 -6×-1 + 24
y = -3 + 6 + 24
y = 27
Thus the vertex is (-1, 27)
The y value is not going to exceed 27, as this is a decreasing quadratic, (we already know y=24 is a possibilty) and this equation goes downwards infinitely, so our range is (-∞, 27)
As for x, well, it's sort of the input for our equation, meaning it can be whatever we want it to be. Thus the domain is (-∞, ∞)