This morning, Kevin's car had 13.8 gallons of fuel. Now, 1.9 gallons are left. How much fuel did Kevin use?
2 answers:
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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 (-∞, ∞)
<span>The standard form of the equation of a circumference is given by the following expression:
</span>
<span>
On the other hand, the general form is given as follows:
</span>
<span>
In this way, we can order the mentioned equations as follows:
Equations in Standard Form:
</span>
Equations in General Form:
So let's match each equation:
Then, its general form is:
<em><u>First. a) matches 5) </u></em>
Then, its general form is:
<em><u>Second. b) matches 1) </u></em>
Then, its general form is:
<em><u>Third. c) matches 3)</u></em>
Then, its general form is:
<em><u>Fourth. d) matches 6)</u></em>
</span>
<span>
On the other hand, the general form is given as follows:
</span>
In this way, we can order the mentioned equations as follows:
Equations in Standard Form:
</span>
Equations in General Form:
So let's match each equation:
Then, its general form is:
<em><u>First. a) matches 5) </u></em>
Then, its general form is:
<em><u>Second. b) matches 1) </u></em>
Then, its general form is:
<em><u>Third. c) matches 3)</u></em>
Then, its general form is:
<em><u>Fourth. d) matches 6)</u></em>
Answer:
D
Step-by-step explanation:
First, find the coordinates of pointD if A(2,-6), B(10,2) and point D divides line segment AB in the ratio of 5:3.
If point D divides the segment AB in the ratio m:n, then
So
Point C has the x-coordinate the same as point A and the y-coordinate the same as point D.
Thus, C(2,-1)