Which of the following is equivalent to “the quotient of 30 and the difference of 12 and 6”?
2 answers:
Answer:
Option D,
Step-by-step explanation:
<u>Step 1: Determine the correct expression</u>
So we know for sure that we will be doing 12 - 6 because we have the part where it says the difference of 12 and 6. That leaves us with Options A and D. Looking back at the statement we can see that the quotient of 30 and the rest which means that 30 would be the numerator and located at the top. This gives us option D.
Answer: Option D,
Answer:
D.
Step-by-step explanation:
We can immediately eliminate choices B and C because B shows "the difference of 6 and 12", not "of 12 and 6", and C shows "the quotient of 30 and 12 minus 6." 12 and 6 are not being subtracted properly.
30 is being stated before the difference of 12 and 6, so the difference will be the divisor, and 30 will be the dividend, therefore it will go in the <u>numerator</u>.
The only option that fits this criteria is D, so that is the answer.
hope this helps :)
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Slope of the line = .
y-intercept of the line = -7.
Solution:
General form of equation of a line:
y = mx + c
where m is the slope and c is the y-intercept of the line.
Equation of a line:
To compare this with general equation.
Slope of the line = .
y-intercept of the line = -7.
9514 1404 393
Answer:
1. asymptotes: x=-6, x=6, y=0; zero: x=0
2. 20 blue fish
Step-by-step explanation:
1. The vertical asymptotes are where the denominator is zero. It factors as (x-6)(x+6), so will have zeros at x=-6 and x=6.
The horizontal asymptote is at the limit when x goes to infinity. Here, the ratio of highest-degree terms is 6/x, so the value goes to zero as x gets large.
The zero is where the numerator is zero, at x=0.
In summary:
- vertical asymptotes: x = ±6
- horizontal asymptote: y = 0
- zero: (0, 0)
__
2. 60% are red, so 40% are blue. The difference in percentages is 60%-40% = 20%. The percentage of blue fish (40%) is twice the difference (=2×20%), so the number of blue fish is twice the difference in numbers.
blue fish = 2×10 = 20 fish
<em><u>Check</u></em>
There are then 20+10=30 red fish, so 20+30=50 fish total. Reds are 30/50 = 60% of the total.
<u><em>Additional comment</em></u>
I find it often works well to work with ratios, which I can often do in my head. Other folks like to see equations. Here, we could write equations like ...
r = 60%(r + b) . . . . reds are 60% of the total
r - b = 10 . . . . . . . . 10 more reds than blues
We want the value of b, so we can eliminate r by substituting for it:
r = 10 + b . . . . from the second equation above
(10 +b) = 0.60((10 +b) + b) . . . . substitute for r
10 +b = 6 + 1.2b . . . simplify
4 = 0.2b . . . . subtract b+6
20 = b . . . . . . multiply by 5 (there are 20 blue fish)
