X2+16 is the prime <span>polynomial.
x2+16 is the only </span><span>polynomial that couldn't be factored out anymore
x2-36 --> (x-6)(x+6)
x2-7x+12 --> (x-3)(x-4)
x2-x-20 --> (x+5)(x-4)</span>
f(x) = (x - 4)^2 - 1
g(x) = -(1/4) ( x - 4)^2 + 4
both the x and y values have to be the same. Start with the y values
f(x) = g(x)
(x - 4)^2 - 1 = -(1/4) (x - 4)^2 + 4 Add 1 to both sides.
(x - 4)^2 = -(1/4) (x - 4)^2 + 5 Add 1/4(x - 4)^2 to both sides.
(5/4) (x - 4)^2 = 5 Divide by 5/4 on both sides.
(x - 4)^2 = 5//(5/4)
(x - 4)^2 = (5/1)//5/4 Invert the second fraction and multiply
(x - 4)^2 = 5/1 * 4/5
(x - 4)^2 = 4 The 5s cancel
(x - 4)^2 = 4 Take the square root of both sides.
(x - 4) = +/- 2 Add 4 to each answer. Start with +2 on the right.
x - 4 + 4 = 2 + 4
x = 4 + 2 = 6
The x value that makes f(x)- g(x) = 0 is x = 6 The point is (6,3) answer.
Answer C.
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You do not need this next part. It is just for completeness.
x - 4 = - 2
x = 4 -2
x = 2
What are the y values for these 2 x values?
y = (x - 4)^2 - 1
y = (6 - 4)^2 - 1
y = 4 - 1
y = 3
The point where f(x) - g(x) = 0 is (6,3) <<<<<< Answer 1
The second point is
y = (x - 4)^2 - 1
y = (2 - 4)^2 - 1
y = (-2)^2 - 1
y = 4 - 1
y = 3
The second point is (2,3). Answer 2
Note the y values are the same. You might expect that.
A tilted or slanted cylinder has the same volume as its equivalent right cylinder, provided that
(a) the two bases of the tilted cylinder are parallel,
(b) the base areas of the tilted and right cylinders are equal,
(c) the vertical height of the right and tilted cylinders are equal.
This fact can be verified by slicing the tilted cylinder into thin, flat washers, as in integral calculus.
Because all 3 conditions are satisfied, the volume of the tilted cylinder is 450 cm³.
Answer: 430 cm³
Answer:
x + y = 4
Step-by-step explanation:
Given that, (x + iy)(1 - 3i) = 10, then we have to calculate x + y.
Now, (x + iy)(1 - 3i) = 10
⇒ x(1 - 3i) + iy(1 - 3i) = 10
⇒ x - 3xi + iy - 3yi² = 10
⇒ (x + 3y) + i(y - 3x) = 10
Now, comparing the real and imaginary part of both sides we get,
(x + 3y) = 10 ............. (1) and
y - 3x = 0
⇒ y = 3x ............... (2)
Solving equations (1) and (2) we get
x + 3(3x) = 10
⇒ x = 1
So, y = 3x = 3
Therefore, x + y = 1 + 3 = 4 (Answer)
Answer:
$333
Step-by-step explanation:
4,000 / 12 is about 333.34
Rounding the .34 down to the nearest whole number (0), we end up with about $333.
