A teacher is making a history test composed of the same number of multiple-choice questions as short-answer questions. She estim
1 answer:
Answer:
The inequality is
Step-by-step explanation:
Total time:
The total time to complete the test is the sum of the number of multiple-choice questions multiplied by the time it takes to solve each and the number of short-answer questions multiply by the time it takes to solve each.
In this question:
Same number(n) of both.
Multiple-choice takes 2 minutes, short-answer takes 3.5 minutes. The total time is given by:
Write an inequality to determine how many questions, n, the teacher can include if the test must take students less than 45 minutes to complete.?
This means that:
So
The inequality is
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Answer:
h(x) = 4·log₃(x) +2
Step-by-step explanation:
<h3>Part A:</h3>h(x) = f(x) +g(x)
h(x) = (log₃(x) +3) +(log₃(x³) -1)
h(x) = log₃(x) +3·log₃(x) +2
h(x) = 4·log₃(x) +2 . . . . . "simplest" form
h(x) = log₃(9x⁴) . . . . . . . as a single logarithm
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<h3>Part B:</h3>No system of equations is given. Perhaps you want to find x for f(x) = g(x).
log₃(x) +3 = log₃(x³) -1
log₃(x) +3 = 3·log₃(x) -1
4 = 2·log₃(x) . . . . . . . . . . . add 1-log₃(x)
2 = log₃(x) . . . . . . . . . . . . divide by 2
3² = x = 9 . . . . . . . . . . . . . take the antilog
The solution to f(x) = g(x) is x = 9.
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<em>Additional comment</em>
The relevant rules of logarithms are ...
a = log₃(b) ⇔ 3^a = b
log(a^b) = b·log(a)
log(ab) = log(a) +log(b)
Answer: 300 yards
Step-by-step explanation:
Since b1 is equal to 14 yds and b2 is equal to 26 yds we can plug that into the equation below (in the image).
b1 + b2 = 14 + 26 = 40 yards
Now that we have found (b1 + b2), you can multiply that by h (the height of the trapezoid) which is 15, so we get 40 x 15 = 600.
In a lot of area equations, you will have to divide by two like in the trapezoid equation. Divide our number (600) by 2, so we get 600 ÷ 2 = 300.
300 yds is your final answer.
Hope this helps!
