What are the factors of 2x + 3x - 54? Select two options
2 answers:
Answer:
The answer: The factors are (2x-9) and (x+6).
The Problem:
Factor
Step-by-step explanation:
So I'm going to do trial factors using the choices to aid me.
Factored form for this problem if it exist will be in the form:
.
In general this is what it would look like if we factored any quadratic in terms of (given the quadratic is not prime but technically you could factor even over the complex numbers).
Let's look at:
We want to choose such that when you multiply them you get 2. Well those would have to be 2 and 1.
we want to choose such that when you multiply them you get -54. Based on the choices we want to get with -9 and 6, or 9 and -6. We don't know the order we want to choose it in either.
For example which of these would work:
We are going to consider only the outer and inner of FOIL since we already know the first times the first is and the last times the last is
.
Let's test the first one:
Outer: 2x(9)=18x
Inner: -6(x)=-6x
------------------------ADD!
18x-6x=12x
The first choice did not give us the middle term 3x.
Trying the second one would give us the opposite since they are in the same form as previous just the + and - are switched.
Let's look at the third one:
Outer: 2x(6)=12x
Inner: -9(x)=-9x
--------------------------ADD!
12x-9x=3x
This is the winner.
The answer: The factors are (2x-9) and (x+6).
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Step-by-step explanation:
The equation is given by :
63.25=800r+3.50
Here,
63.25 is the electric company charges
3.5 is an administrative fee
800 is charge per kilowatt hours
r is rate per kilowatt hour
In this proble, we need to tell that what does r represents. Hence, r shows kilowatt per hour.
We can solve it as follows :
63.25-3.5=800r+3.50-3.50 (Subtracting 3.50 to the both sides)
59.75=800r
The values of a and b are a = 33% and b = 43% ⇒ last answer
Step-by-step explanation:
The venn-diagram contains:
- A circle labeled blue 32
- A circle labeled gold 25
- The two circles are overlap with label 12 on the overlap
The table:
→ Band : blue : N.b : total
→ gold : 16% : a : 49%
→ N.g : b : 8% : 51%
→ Total : 59% : 41% : 100%
We need to find the values of a and b
From the table
16% represents the percentage of blue and gold uniforms (2nd row with 2nd column)
From venn-diagram
The common part of blue and gold label with 12 (overlap of two circles)
∴ 16% of the total number of students = 12
∵ 16% × x = 12
∴ × x = 12
∴ 0.16 x = 12
- Divide both sides by 0.16
∴ x = 75
∵ x represents the total number of students
∴ The total number of students were asked is 75
From the table
b represents the percentage of blue but not gold uniforms (3rd row and 2nd column)
From venn-diagram
The part that has blue and not gold labeled with 32 (the part of the blue circle not in the gold circle)
∴ 32 of the total number of students like the blue but not gold
- Divide 32 by the total 75 , then multiply the quotient by 100%
to find the percentage of blue but not gold
∴ b = × 100% = 42.6666%
∴ b ≅ 43%
From the table
a represents the percentage of gold nut not blue uniforms (2nd row and 3rd column)
From venn-diagram
The part that has gold and not blue labeled with 25 (the part of the gold circle not in the blue circle)
∴ 25 of the total number of students like the gold but not blue
- Divide 25 by the total 75 , then multiply the quotient by 100%
to find the percentage of gold but not blue
∴ a = × 100% = 33.3333%
∴ a ≅ 33%
The values of a and b are a = 33% and b = 43%
To check your answer complete the table you will find the total of it is 100% ( for the columns 16% + 43% = 59% , 33% + 8% = 41% , then 59% + 41% = 100%, for the rows 16% + 33% = 49% , 43% + 8% = 51% , then 49% + 51% = 100%)
Learn more:
You can learn more about the probability in brainly.com/question/3756853
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