Solve x2 − 8x − 20 = 0. (1 point) x = 4, x = −5 x = −4, x = 5 x = 2, x = −10 x = −2, x = 10
2 answers:
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Answer:
The solutions are (-2 , 0) and (1 , 3)
Step-by-step explanation:
∵ -x² + 4 = x + 2
* y = -x² + 4 ⇒ is quadratic represented by parabola
The parabola open downward because coefficient of x² is negative
The x-coordinate of its vertex = -b/2a, where b is the
coefficient of x and a is the coefficient of x²
∴ x = 0/2(-1) = 0
∴ The y-coordinate of the vertex = (0)² + 4 = 4
∴ The maximum point of the parabola is (0 , 4)
∵ -x² + 4 intersects x-axis at y = 0
∴ -x² + 4 = 0 ⇒ -x² = -4 ⇒ x² = 4
∵ x² = 4
∴ x = ±√4 = ± 2
∴ the parabola intersects x-axis at -2 , 2
∵ y = x + 2 represented by a line its slope = 1
It intersects y-axis at 2
∵ x + 2 intersects x-axis at y = 0
∴ x + 2 = 0
∴ x = -2
∴ The parabola and the line intersect each other at
x = -2 and y = 0
To find all the point of intersection between the 2 equations we will solve them as a system of equations
∵ y= -x² + 4 and y = x + 2
∴ -x² + 4 = x + 2
∴ -x² + 4 - x - 2 = 0
∴ -x² - x + 2 = 0 ⇒ × -1
∴ x² + x - 2 = 0 ⇒ factorize
∴ (x + 2)(x - 1) = 0
∴ x + 2 = 0 ⇒ x = -2
∴ x - 1 = 0 ⇒ x = 1
* when x = -2 ⇒ y = -2 + 2 = 0 ⇒ (-2 , 0)
* when x = 1 ⇒ y = 1 + 2 = 3 ⇒ (1 , 3)
The solution graphically
Answer:
I can not solve it in the system of the image, but i will give you the graph so you can copy it, or at least see how it is done.
First, we have the lines:
y = (1/3)*x + 6
y = (-5/3)*x - 6
To graph these lines, you must find two points for the lines and then draw a line that connects the points.
To do it, you can evaluate each line in two different values of x, for example for the first line we can have:
y(0) = (1/3)*0 + 6 = 6 (then we have the point (0, 6))
y(3) = (1/3)*3 + 6 = 7 (then we have the point (3, 7))
And for the second line, we will have:
y(0) = (-5/3)*0 - 6 = -6 (then we have the point (0, -6))
y(3) = -(5/3)*3 - 6 = -11 (then we have the point (-3, -11))
Now with those points we can graph the lines, and the solution of the system of equation will be the point where the two lines intersect.
The graphs of the lines are shown below:
Where the grey line is the first one, and the green is the second.
In the graph, you can see that the lines intersect in the point (-6, 4)
Then the solution for the system is x = -6, and y = 4.
Answer:
x = -24
Step-by-step explanation:
Calculated Steps in IMAGE Attached
