The expressions in which the numbers, or variables, or both, are connected by operational signs (+, - etc.) are called algebraic expressions. For example 5, 4x, a+b, x−y.
Answer:
The value of x is about 2.206.
Step-by-step explanation:
Consider the given equation is
We need to find the value of x.
Using the properties of logarithm we get
![[\because \ln a^b=b\ln a]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Cln%20a%5Eb%3Db%5Cln%20a%5D)
![[\because \ln (ab)=\ln a+\ln b]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Cln%20%28ab%29%3D%5Cln%20a%2B%5Cln%20b%5D)
![[\because \ln 1=0]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Cln%201%3D0%5D)
On comparing both sides we get
Using graphing calculator, the real solution of the above equation is
Therefore, the value of x is about 2.206.
Answer:
Solution
p = {-3, 1}
Step-by-step explanation:
Simplifying
p2 + 2p + -3 = 0
Reorder the terms:
-3 + 2p + p2 = 0
Solving
-3 + 2p + p2 = 0
Solving for variable 'p'.
Factor a trinomial.
(-3 + -1p)(1 + -1p) = 0
Subproblem 1
Set the factor '(-3 + -1p)' equal to zero and attempt to solve:
Simplifying
-3 + -1p = 0
Solving
-3 + -1p = 0
Move all terms containing p to the left, all other terms to the right.
Add '3' to each side of the equation.
-3 + 3 + -1p = 0 + 3
Combine like terms: -3 + 3 = 0
0 + -1p = 0 + 3
-1p = 0 + 3
Combine like terms: 0 + 3 = 3
-1p = 3
Divide each side by '-1'.
p = -3
Simplifying
p = -3
Subproblem 2
Set the factor '(1 + -1p)' equal to zero and attempt to solve:
Simplifying
1 + -1p = 0
Solving
1 + -1p = 0
Move all terms containing p to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + -1 + -1p = 0 + -1
Combine like terms: 1 + -1 = 0
0 + -1p = 0 + -1
-1p = 0 + -1
Combine like terms: 0 + -1 = -1
-1p = -1
Divide each side by '-1'.
p = 1
Simplifying
p = 1
Solution
p = {-3, 1}
All together they play 36 games
Six kids each day play each other so six times six
Answer:
p = all real numbers
Step-by-step explanation:
First distribute the numbers to the expressions inside the parenthesis
-11 + 10(p + 1) = -16 + 5(2p + 3)
-11 + 10p + 10 = -16 + 10p + 15
Then, add up the like terms
10p - 1 = 10p - 1
Add one to both sides
10p - 1 = 10p - 1
+ 1 + 1
10p = 10p
Divide both sides by 10
10p/10 = 10p/10
p = p
This means that no matter what you plug in for p, it will always be true.
