Answer:
The parabola's axis of symmetry is x = -6
Step-by-step explanation:
Parabola general equation:
y = a*(x - r1)*(x - r2)
Equation given:
y = (-1/4)*(x + 2)*(x + 10)
a = -1/4
r1 = -2
r2 = -10
To check if the parabola passes through the point (2, 10) it is necessary to replace x = 2 and check the y-value, as follows:
y = (-1/4)*(2+ 2)*(2 + 10) = -12
Then, point (2, 10) is not included in the parabola.
If a > 0 then the parabola opens upward; if a < 0 then the parabola opens downward. Then, the parabola opens downward
Axis of symmetry:
h = (r1 + r2)/2
h = (-2 + -10)/2 = -6
Then, The parabola's axis of symmetry is x = -6
To find Parabola's vertex, replace with the axis of symmetry:
y = (-1/4)*(-6 + 2)*(-6 + 10) = 4
Therefore, the parabola has a vertex at (-6, 4)
No, not at all.
The general quadratic equation is
Ax² + Bx + C = 0 .
The roots are real only if (B² - 4AC) is not negative.
That means if you graph it, it touches or crosses the x-axis.
If the graph is up in the air and never touches the x-axis,
then it has no real roots.
<h3>
Answer: C) 4/8 = 0.5</h3>
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Explanation:
The sine ratio involves the opposite over hypotenuse.
With respect to reference angle J, the opposite leg is the one furthest from the angle. So the opposite side is KL = 4. The hypotenuse is always the longest side, always opposite the 90 degree angle, so LJ = 8 is the hypotenuse.
sin(angle) = opposite/hypotenuse
sin(J) = KL/LJ
sin(J) = 4/8
sin(J) = 0.5
Answer:
Mean: 65.25
Median: 70.5
Mode: 70
Step-by-step explanation:
Mean is the sum of the set of numbers divided by the number of numbers in the set.
20+68+70+70+71+72+75+76=522
522/8=65.25
The median is the number that is in the middle of the set when put in numerical order.
Since there is an even amount of numbers, the two middle numbers are 70 and 71, so you would take the mean of these two numbers to find the median.
70+71=141
141/2=70.5
The mode is the number that occurs most frequently in the set.
70 appears more times than any other number, therefore it is the mode.
