Answer:
All the expressions other than option E, is equivalent to the expression 18m - 12.
Step-by-step explanation:
A. 6m - 4 + 6m -4 + 6m - 4
or 6m+6m+6m -4 -4 -4
or 18m -12
B. 12m + 6 - 6m -6
or 12m - 6m + 6 - 6
or 6m
C.6(3m - 2)
or 18m - 12
D.3(6m - 4)
or 18m - 12
E. 24n - 4² + 8 -6m
This option can not satisfy the given expression as it contains another variable as n.
Answer:
Student A and Student B both answered 2 questions correctly.
See explanation below
Step-by-step explanation:
Note: that answers in the form:
ARE ALL EQUIVALENT.
First of all, 4/5 is equivalent to 0.8 if we do long division.
and 19/20 is 0.95 if we do long division.
Now, <u>Student A:</u>
Both of the fractions are correct and the negative sign is equivalent and makes the answer correct, so both are correct.
For <u>Student B:</u>
Similarly, both answers are correct for this student as well, looking at the equivalence we showed first.
Also, "-" (negative) in front of the parenthesis and inside parenthesis here doesn't matter.
Hence,
Student A and Student B both answered 2 questions correctly.
Answer:
Option D
Step-by-step explanation:
The questions which involve calculating the angles and the sides of a triangle either require the sine rule or the cosine rule. In this question, the two sides that are given are adjacent to each other the given angle is the included angle. This means that the angle B is formed by the intersection of the lines a and c. Therefore, cosine rule will be used to calculate the length of b. The cosine rule is:
b^2 = a^2 + c^2 - 2*a*c*cos(B).
The question specifies that c=71, B=123°, and a=65. Plugging in the values:
b^2 = 65^2 + 71^2 - 2(65)(71)*cos(123°).
Simplifying gives:
b^2 = 14293.0182932.
Taking square root on the both sides gives b = 119.6 (rounded to the one decimal place).
This means that the Option D is the correct choice!!!
If the budget is $200 and he have 15 members then we have divide the two. 200 / 15 = $13.33 per shorts. 15x =< $200. x represents 13.33. So the solution represents the coach may spend up to $13.33 per pair of shorts. If it was even 1 cent more than $13.33 than he wouldn't have enough.So he can spend up to $13.33 or less per pair of shorts.
