Step-by-step explanation:
x2 - 6x + 8 = 0
x2 - 4x - 2x + 8 = 0
x(x - 4) - 2(x - 4) = 0
(x-4)(x-2) =0
x-4 = 0. x-2 = 0
x = 4. x = 2
Option C is the correct answer
Answer:
y > -3x + 6
Step-by-step explanation:
First, find the equation of the dashed line. We can use y = mx + b, where m is the slope and b is the y-intercept.
Here, the y-intercept is (0, 6). To find the slope, we need a second point on the line. Let's choose (2, 0).
m = Δy / Δx
m = (6 − 0) / (0 − 2)
m = -3
So the equation of the dashed line is y = -3x + 6.
Now look which side of the line is shaded. In this case, the area <em>above</em> the line is shaded. So the inequality is:
y > -3x + 6
The number of feet in the length of the handrail is 17.3 ft.
The easiest way to see this is to imagine that we can "unfold" the spiral to create a rectangle
The bottom side of the rectangle is just the arc length of a circle with a radius of 3 ft turned through 270°= (3/4) of a whole revolution
(3/4) (2pi) (3) = (9/2)pi ft = 4.5 pi ft
The side of the rectangle will be the rise of the staircase = 10ft
And the diagonal of the rectangle will be the length of the handrail
We can use the Pythagorean Theorem to solve this
Handrail length = √ [ (4.5 pi)^2 + 10^2 ] ≈ 17.3 ft
Pythagorean theorem is the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
Learn more about the Pythagorean theorem here: brainly.com/question/343682
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Step-by-step explanation:
-2a + x
Putting values of a = - 2 and x = 7
-2(-2) + 7
4 + 7
= 11
