Answer:
![Length = 5x + 3](https://tex.z-dn.net/?f=Length%20%3D%205x%20%2B%203)
![Width = x +1](https://tex.z-dn.net/?f=Width%20%3D%20x%20%20%2B1)
Step-by-step explanation:
Given
![Area = 5x^2 + 8x + 3](https://tex.z-dn.net/?f=Area%20%3D%205x%5E2%20%2B%208x%20%2B%203)
Required
Determine the dimensions
To do this, we simply factorize the given expression.
![Area = 5x^2 + 8x + 3](https://tex.z-dn.net/?f=Area%20%3D%205x%5E2%20%2B%208x%20%2B%203)
Expand
![Area = 5x^2 + 5x +3x+ 3](https://tex.z-dn.net/?f=Area%20%3D%205x%5E2%20%2B%205x%20%2B3x%2B%203)
Factorize
![Area = 5x(x + 1) +3(x+ 1)](https://tex.z-dn.net/?f=Area%20%3D%205x%28x%20%2B%201%29%20%2B3%28x%2B%201%29)
Factor out x + 1
![Area = (5x +3) (x+ 1)](https://tex.z-dn.net/?f=Area%20%3D%20%285x%20%2B3%29%20%28x%2B%201%29)
Area is calculated as:
![Area = Length * Width](https://tex.z-dn.net/?f=Area%20%3D%20Length%20%2A%20Width)
So:
![Length = 5x + 3](https://tex.z-dn.net/?f=Length%20%3D%205x%20%2B%203)
![Width = x +1](https://tex.z-dn.net/?f=Width%20%3D%20x%20%20%2B1)
Frank = F
Sue = S
John = J
F=3*S
F = J+15
S = J-1
If you want to find Frank's age, then his age would be equivalent to John's plus 15 years.
A.-Would not work because Frank is three times Sue's age, not John's (left hand side of the equation).
B.-Notice that the right hand side of the equation is equivalent to Sue's age, which we know is John-1, however it is currently written to be "three times Sue's age minus one" which would give us John's age, plus two more years than his actual age on the left hand side.
C.-Frank's age is equal to John's plus fifteen (right side of the equation) and Frank is equal to Sue's age times 3. But, if Sue is in terms of Johns, then Sue's age is John's minus one. Therefore, Frank's age is equal to three times Sue's age of John minus one, which is the left-hand side of our equation.
Therefore C is the answer. C:
<h2>
Hello!</h2>
The answer is:
![3x^{2} -14x+7](https://tex.z-dn.net/?f=3x%5E%7B2%7D%20-14x%2B7)
<h2>
Why?</h2>
To solve the problem we need to add/subtract like terms. We need to remember that like terms are the terms that share the same variable and the same exponent.
For example, we have:
![x^{2} +2x+3x=x^{2} +(2x+3x)=x^{2}+5x](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B2x%2B3x%3Dx%5E%7B2%7D%20%2B%282x%2B3x%29%3Dx%5E%7B2%7D%2B5x)
We have that we were able to add just the terms that were sharing the same variable and exponenr (x for this case).
So, we are given the expression:
![5x^2-5x+1-(2x^2+9x-6)=5x^{2}-2x^{2}-5x-9x+1-(-6)\\\\(5x^{2}-2x^{2})+(-5x-9x)+(1-(-6))=3x^{2}-14x+7](https://tex.z-dn.net/?f=5x%5E2-5x%2B1-%282x%5E2%2B9x-6%29%3D5x%5E%7B2%7D-2x%5E%7B2%7D-5x-9x%2B1-%28-6%29%5C%5C%5C%5C%285x%5E%7B2%7D-2x%5E%7B2%7D%29%2B%28-5x-9x%29%2B%281-%28-6%29%29%3D3x%5E%7B2%7D-14x%2B7)
Hence, the answer is:
![3x^{2} -14x+7](https://tex.z-dn.net/?f=3x%5E%7B2%7D%20-14x%2B7)
Have a nice day!
Total coins in the jar = 50. Number of coins with a value less than $0.05 = 20 (the pennies). ... Probability of picking a penny = 20/50 = 40%. ... 'Odds' = 3 to 2 against it.
The probability of 150 flips and 84 tails would be 84/66 or 56 percent