First we have to combine like terms. 4x² is one term. -8x is another term. -7 is another term. poly = "many" ⇒ polynomial = many terms
(4x² - 8x - 7) + (-5x + 16)
4x² - 8x - 7 - 5x + 16
Combine like terms.
Step 1: 4x² has no other terms with x² so it stays by itself.
Step 2: -8x and -5x are like terms because they both have x.
So -8x -5x = -13x (You put two negatives together)
Step 3: -7 and 16 don't have any x with them. -7 + 16 = 16 - 7 = 9
Now we put all the answers of the steps together.
Step 1: 4x²
Step 2: -13x
Step 3: 9
So the answer is 4x² - 13x +9
And it's a polynomial because there are three terms = "more than one term"
Answer:
x = 2
Step-by-step explanation:
Given
- 7x - 3x + 2 = - 8x - 2 ← simplify left side
- 10x + 2 = - 8x - 2 ( add 8x to both sides )
- 2x + 2 = - 2 ( subtract 2 from both sides )
- 2x = - 4 ( divide both sides by - 2 )
x = 2
Answer:
0
Step-by-step explanation:
First we need to find the value of constant k in equation. To find k we use the formula:
![\int\limits^{100}_0 {ke^{-0.01x}} \, dx =1\\Integrating:\\k\int\limits^{100}_0 {e^{-0.01x}} \, dx =1\\\frac{k}{-0.01}[e^{-0.01x}]_0^{100}=1\\-100k [e^{-0.01x}]_0^{100}=1\\-100k[e^{-0.01*100}-e^{-100*0}]=1\\-100k[e^{-1}-e^0]=1\\-100k(-0.632)=1\\63.2k = 1\\k=0.0158](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%7B100%7D_0%20%7Bke%5E%7B-0.01x%7D%7D%20%5C%2C%20dx%20%3D1%5C%5CIntegrating%3A%5C%5Ck%5Cint%5Climits%5E%7B100%7D_0%20%7Be%5E%7B-0.01x%7D%7D%20%5C%2C%20dx%20%3D1%5C%5C%5Cfrac%7Bk%7D%7B-0.01%7D%5Be%5E%7B-0.01x%7D%5D_0%5E%7B100%7D%3D1%5C%5C-100k%20%5Be%5E%7B-0.01x%7D%5D_0%5E%7B100%7D%3D1%5C%5C-100k%5Be%5E%7B-0.01%2A100%7D-e%5E%7B-100%2A0%7D%5D%3D1%5C%5C-100k%5Be%5E%7B-1%7D-e%5E0%5D%3D1%5C%5C-100k%28-0.632%29%3D1%5C%5C63.2k%20%3D%201%5C%5Ck%3D0.0158)
the probability that a person age 20 will live for at least 20 more years = P(40 ≤ x <∞).
The person would live for at least 40 years
Therefore:
P(40 ≤ x <∞) =
![\int\limits^{\infty}_{40} 0.0158e^{-0.01x}} \, dx \\Integrating:\\0.0158\int\limits^{\infty}_{40} {e^{-0.01x}} \, dx =\frac{0.0158}{-0.01}[e^{-0.01x}]_{40}^{\infty}\\=-1.58 [e^{-0.01x}]_{40}^{\infty}=-1.58[e^{-\infty}-e^{-100*40}]\\=-1.58[e^{-\infty}-e^{-4000}]=-1.58(0-0)=0](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%7B%5Cinfty%7D_%7B40%7D%200.0158e%5E%7B-0.01x%7D%7D%20%5C%2C%20dx%20%5C%5CIntegrating%3A%5C%5C0.0158%5Cint%5Climits%5E%7B%5Cinfty%7D_%7B40%7D%20%7Be%5E%7B-0.01x%7D%7D%20%5C%2C%20dx%20%3D%5Cfrac%7B0.0158%7D%7B-0.01%7D%5Be%5E%7B-0.01x%7D%5D_%7B40%7D%5E%7B%5Cinfty%7D%5C%5C%3D-1.58%20%5Be%5E%7B-0.01x%7D%5D_%7B40%7D%5E%7B%5Cinfty%7D%3D-1.58%5Be%5E%7B-%5Cinfty%7D-e%5E%7B-100%2A40%7D%5D%5C%5C%3D-1.58%5Be%5E%7B-%5Cinfty%7D-e%5E%7B-4000%7D%5D%3D-1.58%280-0%29%3D0)
Answer:
Need more information. What do you mean "Sixty people are invited to a party" ?
Step-by-step explanation:
4^3 = 64
log4 64 = 3
The exponent always comes to the other side.
