Answer:
y = 3x - 6
y = -x+2
To solve the system of equations graphically, graph both equations on a set of axes, then find the intersection point, which is the solution to the system.
To solve the system of equations graphically, we first need to graph each equation on a set of axes.
The first equation, y = 3x - 6, is a straight line with a slope of 3 and a y-intercept (where the line crosses the y-axis) at -6. To graph this, start at point (0, -6) on the y-axis, then move up 3 units and to the right 1 unit to find the next point. Repeat this process to plot several points, then draw a straight line through them.
The second equation, y = -x + 2, is also a line, but with a slope of -1 and a y-intercept at 2. Start at point (0, 2) on the y-axis, then move down 1 unit and to the right 1 unit. Draw a straight line through the points.
The solution to the system of equations is the point where the two lines intersect on the graph. By examining the graph, you can determine this point.
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of its previous height. What height
will it reach after the third bounce?
Answer:
1.7342 m
Step-by-step explanation:
in order to find this, we need to find what 2 thirds of 6 is. The answer to that is 4, because 2/3 can be changed to 4/6, which means the 1st bounce would reach a height of 4m. Now, we need to find 2 thirds of 4, which is mildly harder. In order to find the exact value, we need to find what to multiply 3 by to get to 4. Unfortunately, you cant do that. Fortunately, though, I looked it up. So, On the 2nd bounce, the ball would reach 2.6 m. Now, we need to find 2 thirds of THAT, too, which would equal, on the third bounce, 1.7342 m.
The height of the ball after the third bounce is approximately 1.78 m.
To find the height after the third bounce, we need to calculate the height after each bounce and then determine the height after the third bounce.
Given that the ball rises to 2/3 of its previous height after each bounce, we can start with the initial height of 6 m and calculate the height after the first bounce, which is 6 * 2/3 = 4 m.
Similarly, after the second bounce, the height will be 4 * 2/3 = 8/3 m. Finally, after the third bounce, the height will be (8/3) * (2/3) = 16/9 m, which is approximately 1.78 m. Therefore, after the third bounce, the ball will reach a height of approximately 1.78 m.
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B)The graph of the function is negative on (negative infinity, 0).
C)The graph of the function is positive on (–2, 4).
D)The graph of the function is negative on (4, positive infinity).
Answer:
-6,-2
Step-by-step explanation:
Answer:
The values of "p" and "q" are p = -5 and q = -6
Step-by-step explanation:
Let's start by finding the zeroes of the polynomial 2x² - 5x - 3, and then we'll determine the relationship between these zeroes and the zeroes of x² + px + q.
The zeroes of a quadratic polynomial of the form ax² + bx + c can be found using the quadratic formula:
For the polynomial 2x² - 5x - 3, a = 2, b = -5, and c = -3. So, the quadratic formula becomes:
x = [-b ± √(b² - 4ac)] / (2a)
Substitute the values:
x = [-(-5) ± √((-5)² - 4(2)(-3))] / (2(2))
Simplify:
x = (5 ± √(25 + 24)) / 4
x = (5 ± √49) / 4
x = (5 ± 7) / 4
Now, we have two possible values for x:
x₁ = (5 + 7) / 4 = 12/4 = 3
x₂ = (5 - 7) / 4 = -2/4 = -1/2
So, the zeroes of 2x² - 5x - 3 are x₁ = 3 and x₂ = -1/2.
Now, we need to find the relationship between these zeroes and the zeroes of x² + px + q.
If the zeroes of x² + px + q are double in value to the zeroes of 2x² - 5x - 3, it means that for each zero "x" of 2x² - 5x - 3, there will be a corresponding zero "2x" for x² + px + q.
So, for x² + px + q, the zeroes will be 2 times the zeroes of 2x² - 5x - 3:
For x₁ = 3, the corresponding zero for x² + px + q is 2x₁ = 2(3) = 6.
For x₂ = -1/2, the corresponding zero for x² + px + q is 2x₂ = 2(-1/2) = -1.
Now, we have the zeroes of x² + px + q: 6 and -1.
To find "p" and "q," we can use Vieta's formulas. Vieta's formulas state that for a quadratic polynomial of the form ax² + bx + c with zeroes α and β:
α + β = -b/a
α * β = c/a
In our case, for x² + px + q with zeroes 6 and -1:
α + β = 6 - 1 = 5
α * β = 6 * (-1) = -6
Now, let's match these with the coefficients of x² + px + q:
α + β = 5, which corresponds to -p (since there's an "x" term in the middle)
α * β = -6, which corresponds to q (the constant term)
So, we have the following equations:
-p = 5
q = -6
Solve for "p" and "q":
p = -5
q = -6
So, the values of "p" and "q" are p = -5 and q = -6.
If the zeroes of the polynomial x² + px + q are double in value to the zeroes of 2x² - 5x - 3, find the value of p and q
Answer:
p and q are -5 and -6 respectively.
Step-by-step explanation:
factor
2x²-5x-3=0
(x-3) (2x + 1) = 0
x = 3, -1/2
multiply both by 2 = "double in value to the zeroes"
x = 6, -1
reverse factor them
(x-6)(x+1)
multiply
x2−5x−6
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B.C' (−2, −3)
C.C' (−2, 3)
D.C' (2, 3)