1. Mr. Lui wrote 15 - 5x/x^2 - 9x + 18.
a. Explain what kind of expression it is.
b. Simplify the expression. Show your work.
c. Identify any excluded values.
A:
a. It is a rational expression.
b. 5/x - 6
c. Excluded value: x = 6
2. Lynne can paint a wall in 40 minutes. Jeff can paint the same wall in 60 minutes. How long will it take Lynne and Jeff to paint the wall if they work together?
A: ?
3. What are 2 values of b that will make 2x^2 - bx - 20 factorable? Explain your answer.
A: ?
1.(15-5x)/(x^2-9x+18).
-5(x-3)/(x-3)(x-6) = -5/(x-6).
2. T=T1*T2/(T1+T2)
T = 40*60/(40+60)=24 min.
3. A*C = 2*(-20)-40 = 4*(-10) = 5*(-8)
B = The sum of the pair of factors that
are divisible by 2:
B = 2+(-20) = -18
B = 4+(-10) = -6
Eq1: 2x^2-18x-20 = 0
Divide by 2:
x^2-9x-10 = 0
(x+1)(x-10) = 0
Eq2: 2x^2-6x-20 = 0
Divide by 2 and factor.
9
Henry is right the way he explained it
2. To find out how long it will take Lynne and Jeff to paint the wall together, we can use the concept of rates.
First, let's find the rate at which each person paints the wall. Lynne can paint the wall in 40 minutes, so her rate is 1 wall per 40 minutes (1 wall/40 minutes). Jeff, on the other hand, can paint the same wall in 60 minutes, so his rate is 1 wall per 60 minutes (1 wall/60 minutes).
Now, to find out how long it will take them to paint the wall together, we can add up their rates. When they work together, their rates will sum up.
So, the combined rate of Lynne and Jeff is (1/40 + 1/60) walls per minute. To simplify this expression, we need to find a common denominator, which in this case is 120.
(1/40 + 1/60) = (3/120 + 2/120) = 5/120
Therefore, their combined rate is 5/120 walls per minute.
To find out how long it will take them to paint the wall together, we can divide the total number of walls (1) by their combined rate (5/120):
Time = 1 / (5/120)
To divide by a fraction, you can multiply by its reciprocal, so we can write:
Time = 1 / (5/120) = 1 * (120/5) = 120/5
Simplifying this expression:
Time = 24 minutes
Therefore, it will take Lynne and Jeff 24 minutes to paint the wall together.
3. To find values of b that will make the quadratic expression 2x^2 - bx - 20 factorable, we need to consider the factors of the quadratic expression.
The quadratic expression 2x^2 - bx - 20 can be factored into (2x - a)(x - b), where a and b are the factors that multiply to give the constant term (-20) and add up to give the coefficient of the middle term (-b).
In this case, we are looking for two values of b. So, let's factorize the quadratic expression:
2x^2 - bx - 20 = (2x - a)(x - b)
Now, we look for two numbers that multiply to give -20. Some possible pairs are (1, -20), (2, -10), (4, -5), and (-1, 20), (-2, 10), (-4, 5).
However, we also need these two numbers to add up to give the value of -b. Without the specific value of b, we cannot find the exact pair.
Therefore, there are multiple values of b that will make the expression 2x^2 - bx - 20 factorable but without further information, we cannot determine the exact values of b.