MATHEMATICS
MIDDLE SCHOOL

Answer: The answer is 330mm3

HIGH SCHOOL

Pamela drove her car 99 kilometers and used 9 liters of fuel. She wants to know how many kilometers shee can drive with 12 liters of fuel. How many kilometers can Pamela drive with 12 liters of fuel?

Answer:

132 km

Step-by-step explanation:

1. she can drive 99 km (kilometers) with 9 liters of fuel, 99/9 is 11

2. if she wants to find out how many kilometers she can drive with 12 liters of fuel, then just multiply 12x11 which is 132

121 kilometers. The ratio of kilometers to liters of gas is 11:1. Then you substitute the 1 for twelve and multiply 11 by 12. The answer is 121 kilometers.

HIGH SCHOOL

Two planes intersect in exactly one _____.

line

plane

point

prism

Two planes (not the same two) can intersect in a line, or

in a plane, or not at all. It depends on their orientation.

Two planes can never intersect in a single point.

Answer:

one plane

Step-by-step explanation:

MIDDLE SCHOOL

How can you use subtraction to complete an addition patern?

Subtract to find the difference between the numbers.

Example: Since 46-39=7 and 39-32=7, so the rule is to add 7.

Example: Since 46-39=7 and 39-32=7, so the rule is to add 7.

Add two numbers then check it to see if you get one of the numbers you added by

MIDDLE SCHOOL

Why is cos(nt) = (-1)^n true, when n could be any integer?

It's not true for any , but it is for .

Start with (which is even). Then

The cosine function is we have

Now, , so

This is the basis for an argument via induction to show that whenever is even. Also, when is even we have .

In a similar way, starting with the fact that

and that is periodic, we have

and so for odd we have .