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The two smaller sides, when added together, cannot be longer than the longest side.

100 + 65 > 160    <--- OK

100 + 65 = 165    <--- Not OK, the sum must be larger ...

100 + 65 < 170    <--- Not OK, the sum must be larger ...

100 + 65 < 175    <---  Not OK, the sum must be larger ...

You can find the perimeter of a triangle by using this formula:  P  =  2L + 2W

If the length is 5 cm more than twice the width, you have the equation:  L = 5 + 2W

Substituting 5 + 2W for L into the first equation:  P  = 2(5 + 2W) + 2W

Since P = 34                                                    34  =  2(5 + 2W) + 2W

                                                                      34  =  10 + 4W + 2W

                                                                      34  =  10 + 6W

                                                                      24  =  6W

                                                                        4  =  W

If W = 4, the L = 5 + 2W   --->   L  =  5 + 2(4)  =  13 

An excellent answer hamilton.  Thank you.  

The only triangle that you can make from side DE, angle E, and side EF is the triangle shown.

The modulo is the remainder when you have whole number division.

Read Melody's answer ....

jLara, what does frequency mean?  It is the height of the columns but what does it mean?

Also what does the first column mean? The one that goes from 5 to 10 and up to 1?

Now, you are asking alot of questions.  This is fine but we want you to learn from our answers.

If we just tell you exactly what the answer is then there is no evidence that you have learned anything and we get disheartened.   

If the equation is in the form:  y  =  mx + b  then  m is the slope  and  b is the y-intercept.

Let's take  4x + y  =  -5  and get the y-term alone on the left side by subtracting 4x from both sides:

--->                 y  =  -4x - 5

--->     slope = -4  and  y-intercept is -5

3y + 2  =  -13

Subtract 2 from both sides:

3y  =  -15

Divide both sides by 3:

y  =  -5

Let A be the beginning point. After 85.5 m, it comes to point B. 

Then it makes a 150° angle (180° - 30° = 150°) and procedes 45.0 m to point C.

You wish to find the distance from point A to point C.

Side AB = c, side BC = a, and side AC = b.

Use the Law of Cosines: b²  =  a² + c² - 2a·b·cos(B)

--->   b²  =  45.0² + 85.5² - 2· 45.0 · 85.5 · cos(150)

Can you finish this?

The median is the number in the middle of the data set. Which number is the middle number?

Range is largest minus smallest:  is largest minus smallest equal to 95?

Is the lowest grade 95?

The median is the middle number, when the data is sorted from smallest to largest. (In the case of an even number of numbers, the median is halfway between the two middle numbers.) Is 95 the median score?

The mode is the number found most often in the data set? Is 95 the number found most often?

To create a triangle, the lengths of the two shorter sides, when added together, must be more than the longest side.

In which of the cases is the sum of the two smaller numbers greater than the largest number? 

Must be greater, equal to is not good enough...

Since the order in which these persons are chosen, it is a combinations problem.

To choose 1 instructor from 4:  ₄C₁  =  4

To choose 2 asst profs from 9:  ₉C₂  =  36

To choose 2 assoc profs from 5:  ₅C₂  =  10

To find the final answer, multiply these together:   ₄C₁ · ₉C₂ · ₅C₂  =  4 x 36 x 10 =  ...

1+1=2

In a number sentence it would be:one plus one equals two

3¹ = 3 mod 8 = 3     3³ = 27 mod 8 = 3     3⁵ = 243 mod 8 = 3

3² = 9 mod 8 = 1     3⁴ = 81 mod 8 = 1     3⁶ = 729 mod 8 = 1

So, if the exponent is even, its mod 8 value is 8 ...

and, if the exponent is add, its mode 8 value is 1 ...

Find the mean of the test scores. This will be the answer ...

Go online:     https://stuff.mit.edu/afs/sipb/contrib/pi/

Let   F = number of female flies

and  M = number of male flies.

Then 8F + 3M = total number of legs.

If  8F + 3M  =  140,

we can have  F = 1   --->   8(1) + 3M  =  140  --->   3M = 132  --->   M = 44

we can have  F = 4   --->   8(4) + 3M  =  140   --->   32 + 3M  =  140   --->   3M  =  108   --->  M = 36

So, two answers so far:  1 female and 44 males; 4 females and 36 males; and there will be more ...

Try interpreting the questions as a formula.

Let x = Female Mega-flies

Let y = Male Mega-flies

8x + 3y = 140

*There are multiple solutions for this problem.

Meaning of "sin", "cos", "tan"
The ratio of two sides of any right triangle with the same interior angles is always the same number independent of the size of the triangle, the triangle's orientation, or the units used to measure the sides of the triangles. See similar right triangles for some specific example.

There are three ways to form a ratio of the three sides of a triangle (six if you count the inverse ratios also). The symbols "sin", "cos", and "tan" are the tags/labels we use to identify which ratio is which.

.

Source: http://faculty.wwu.edu/vawter/PhysicsNet/Topics/Vectors/MeaningOfSine.html

If they are hung in a line, from left to right:

There are 8 ways to choose the first picture

   are 7 ways to choose the second picture

     are 6 ways to choose the third picture

         etc.

To find the total number of ways, multiply these together:  8 x 7 x 6 x ... x 1  =     <--- answer

What is the smallest number in the table? What is the largest number in the table?

To find the range subtract the smallest number from the largest number ...

[Do you know how to read a step-and-leaf table?]

1. magnitude; quantity; number represented by a figure, symbol, orthe like:
   the value of an angle; the value ofx; the value of a sum.
2. a point in the range of a function; a point in the range correspondingto a given point in the domain of a function:
   The value of x 2 at 2 is 4.

Source: http://dictionary.reference.com/browse/value?s=t

An example of Scientific Notation would be:

$${\mathtt{1.02}}{\mathtt{\,\times\,}}\left({{\mathtt{10}}}^{{\mathtt{6}}}\right) = {\mathtt{1\,020\,000}}$$

   ^This number must be between 1 and ~10.

                     ^This number is how many zeros are to be added/subtracted to the number(moving the decimal)

Hint:

Some measurements of average are mean, median, and mode.

Largest, smallest, and range are not measurements of the average.

After you eliminate the three that aren't correct, you are left with the one that is.