Answer: These Lines are <em>Parallel</em>
Step-by-step explanation: For two lines to be parallel, they must have the same slope with different y-intercepts. Both of the lines above have a slope of 3 and differing y-intercepts of 4 and -5. Therefore, these lines must be parallel to one another.
Answers:
- C) x = plus/minus 11
- B) No real solutions
- C) Two solutions
- A) One solution
- The value <u> 18 </u> goes in the first blank. The value <u> 17 </u> goes in the second blank.
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Explanations:
- Note how (11)^2 = (11)*(11) = 121 and also (-11)^2 = (-11)*(-11) = 121. The two negatives multiply to a positive. So that's why the solution is x = plus/minus 11. The plus minus breaks down into the two equations x = 11 or x = -11.
- There are no real solutions here because the left hand side can never be negative, no matter what real number you pick for x. As mentioned in problem 1, squaring -11 leads to a positive number 121. The same idea applies here as well.
- The two solutions are x = 0 and x = -2. We set each factor equal to zero through the zero product property. Then we solve each equation for x. The x+2 = 0 leads to x = -2.
- We use the zero product property here as well. We have a repeated factor, so we're only solving one equation and that is x-3 = 0 which leads to x = 3. The only root is x = 3.
- Apply the FOIL rule on (x+1)(x+17) to end up with x^2+17x+1x+17 which simplifies fully to x^2+18x+17. The middle x coefficient is 18, while the constant term is 17.
Answer:
4:24 p.m.
Step-by-step explanation:
Figure out how often the buses leave at the same time. This is the same as the least common multiple (LCM) of how often they leave the stadium.
The LCM is found by multiplying the maximum number of each prime factor found in any of the numbers.
The prime factors of a number are found by dividing it by whole numbers until the factors are all prime. Prime numbers only have the factors 1 and itself.
6 = 2 X 3
8 = 2 X 2 X 2
The greatest times 2 repeats is three times.
The greatest times 3 repeats is one time.
2 X 2 X 2 X 3 = 24
The LCM is 24, and the buses have the same leaving times every 24 minutes.
Find 24 minutes after 4:00 p.m. Change the minutes only, which are the numbers right of the colon : .
The buses will next leave together at 4:24 p.m.
Alright.
So let's say the number of adults is x.
Therefore, the number of boys is 7x + 1.
And then the total amount of girls is 3.5x + 0.5
So then:
x + 7x + 1 + 3.5x + 0.5 = 82
11.5x + 1.5 = 82
11.5x = 80.5
x = 7
So now we can figure out the number of male and female students.
Male students = 7x + 1
7*7 + 1
49 + 1
50
Male Students = 50
Female students = half of 50
50/2 = 25
Female Students = 25
4,000 Well If you are rounding to the nearest thousand, If it is 4,500 + It goes tp 5,000 but in this case it goes to 4,000 :)
