Answer:
x = 4 or x = 1 or x = -2 or x = -3/2
Step-by-step explanation:
Solve for x over the real numbers:
2 x^4 - 3 x^3 - 21 x^2 - 2 x + 24 = 0
The left hand side factors into a product with four terms:
(x - 4) (x - 1) (x + 2) (2 x + 3) = 0
Split into four equations:
x - 4 = 0 or x - 1 = 0 or x + 2 = 0 or 2 x + 3 = 0
Add 4 to both sides:
x = 4 or x - 1 = 0 or x + 2 = 0 or 2 x + 3 = 0
Add 1 to both sides:
x = 4 or x = 1 or x + 2 = 0 or 2 x + 3 = 0
Subtract 2 from both sides:
x = 4 or x = 1 or x = -2 or 2 x + 3 = 0
Subtract 3 from both sides:
x = 4 or x = 1 or x = -2 or 2 x = -3
Divide both sides by 2:
Answer: x = 4 or x = 1 or x = -2 or x = -3/2
Answer:
<em>First.</em> Let us prove that the sum of three consecutive integers is divisible by 3.
Three consecutive integers can be written as k, k+1, k+2. Then, if we denote their sum as n:
n = k+(k+1)+(k+2) = 3k+3 = 3(k+1).
So, n can be written as 3 times another integer, thus n is divisible by 3.
<em>Second. </em>Let us prove that any number divisible by 3 can be written as the sum of three consecutive integers.
Assume that n is divisible by 3. The above proof suggest that we write it as
n=3(k+1)=3k+3=k + k + k +1+2 = k + (k+1) + (k+2).
As k, k+1, k+2 are three consecutive integers, we have completed our goal.
Step-by-step explanation:
For any sort of pyramid or cone, the volume is 1/3 of the volume of a prism with the same base and height. Since the volume of a prism/cylinder is

, the volume of a pyramid/cone is

.
In this case, our base is a circle, which has a radius of 4 cm.
The area of a circle is

where r is the radius.

We now know that our base is 16π cm.
We also know that our height is 9 cm.
Let's plug these into our volume formula.

Use 3.14 to approximate pi as the question states. 16 × 3.14 = 50.24.

We could punch all of that into our calculator to get the same answer, but since 1/3 of 9 is clearly 3, let's just go with that.

Answer:
-9 = 0.45m
Step-by-step explanation:

- ^ Subtract 0.45m from BOTH sides. so
... etc - Why? So that we can make the equation less complicated. Our goal is to isolate the variable m to be on one side of the "=" sign by itself
- That will equal to:
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