Answer:
Graph D (look in the attached picture)
The way you do this is use the quadratic formula to solve for the x intercepts which are and
Answer:
C. ⇒ 2 : 4. This is because 2 may be a multiple of 1, however, 3 is not a direct multiple of 4.
<u>Answer-</u>
The missing length to the nearest tenth is 20.2 ft.
<u>Solution-</u>
As given in the question, that the given triangle is a right angle triangle.
Pythagoras Theorem-
Here,
Hypotenuse = x ft
Base = 17 ft
Perpendicular = 11 ft
Putting the values,
Therefore, the missing length to the nearest tenth is 20.2 ft.
<h3>
Answer: x = 3 and x = -3</h3>
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Explanation:
We could add 9 to both sides, and then apply the square root to both sides. Don't forget about the plus minus
x^2 - 9 = 0
x^2 = 9
x = sqrt(9) or x = -sqrt(9)
x = 3 or x = -3
To check these answers, you replace x with those values we found. I'll show you how to check x = 3
x^2 - 9 = 0
(3)^2 - 9 = 0
9 - 9 = 0
0 = 0
So that confirms x = 3. The confirmation for x = -3 is nearly the same. Keep in mind that (-3)^2 = (-3)(-3) = 9. You'll be squaring the negative as well.
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Another method you could do is to use the difference of squares rule
x^2 - 9 = 0
x^2 - 3^2 = 0
(x - 3)(x + 3) = 0
Now apply the zero product property. This effectively means you set each factor equal to zero and solve for x
x-3 = 0 or x+3 = 0
x = 3 or x = -3
We end up with the same solution set.
Yet another method you could use is the quadratic formula, but that may be overkill. It's still good practice to do.
Graphing is a visual way to find the answers. You'll graph y = x^2 - 9 and look to see where the curve crosses or touches the horizontal x axis.
The volume of the remaining solid can be calculated by subtracting the volume of the cylindrical hole from the volume of the original box.
1- getting volume of original box:
We have:
length of box = 24 cm
width of box = 16 cm
height of box = 16 cm
Since the box has a rectangular shape, therefore:
volume of box = length * width * height
volume of box = 24 * 16 * 16 = 6144 cm^3
2- getting the volume of cylindrical hole:
We have:
radius of hole = 4 cm
height of hole = 24 cm (as it goes along the hole length of the original box)
Volume pf cylinder = pi * r^2 * h
volume of cylinder = pi * (4)^2 * 24 = 1206.371579 cm^3
3- getting volume of remaining solid:
volume of remaining solid = volume of box - volume of cylinder
volume of remaining solid = 6144 - 1206.371579 = 4937.628421 cm^3