The triangles are similar. If QR = 9, QP = 6, and TU = 19, find TS. Round to the nearest tenth.

Answers

Answer 1

Answer: QR=9
QP=6
TU=19
TS=?
Okay so the triangles are kindred, now the equation can be made
9/16=6/x
So now we are going to cross multiply
9x=114
Now divide both sides by
912 2/3
Your answer is:
TS=12.6

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factor completely:

4x^3 - 36x

Answers

You would take out a 4x out of both terms because this is a common factor
4x^3-36x
4x(x^2-9)
and then you would notice that (x^2-9) is a difference of squares, so that factors out too
4x(x-3)(x+3)
that is all you can factor! hope this helps

the factor of this is 4x(x^2-9)
then x^2-9 can be factored using sum and difference.
4x(x+3)(x-3)

Ms. Howard wrote a test. Part A had true/false questions, each worth points. Part B had multiple choice questions, each worth points. She made the number of points for Part A equal the number of points for Part B. It was the least number of points for which this was possible.

Answers

Full question attached

Answer and explanation:

Since x = number of true or false questions correct

And y = number of multiple choice questions correct

And each question for x =2 points

each question for y=3 points

since she then needs a total score of more than 93 to pass, we add up total correct questions and

Inequality equation = 2x +3y >93

Final answer:

To find the least number of points for which the number of points for Part A is equal to the number of points for Part B, we need to find the least common multiple (LCM) of the values of points for true/false questions and multiple choice questions.

Explanation:

To find the least number of points for which the number of points for Part A is equal to the number of points for Part B, we need to find a common multiple of the values of points for true/false questions and multiple choice questions. Let's assume the number of points for true/false questions is x and the number of points for multiple choice questions is y. We need to find the least common multiple (LCM) of x and y. Once we find the LCM, that will be the minimum number of points for which the number of points in Part A is equal to the number of points in Part B.

For example, if the number of points for true/false questions is 4 and the number of points for multiple choice questions is 6, we can find the LCM as follows:

List the multiples of 4: 4, 8, 12, 16, 20, 24, ...
List the multiples of 6: 6, 12, 18, 24, 30, ...
Find the smallest number that appears in both lists: 12

Therefore, the least number of points for which the number of points in Part A is equal to the number of points in Part B is 12.