geno3141

There are four equal sides to a square.

If the base has a perimeter of 916 meters, then each side is 1/4th that length.

To get the length of one side, find 1/4 of 916.

A is not correct because the left-hand portion (2x + 5) has a slope of 2, but the graph for this part has a slope of 1/2.

B is not correct because the right-hand portion (2x - 10) starts with a y-value of 10 whn x = 10 but the graph has a y-value of -5.

D is not correct because the left-hand portion (2x + 5) has a slope of 2, but the graph for this part has a slope of 5. The right-hand portion isn't correct, either.

The asterick (*) is used as a times sign.

-10 + 4  =  -6

This type of equation is called an "identity".

You are looking for the x-value of the vertex.

An easy way to find this point is to graph it.

If you do not want to graph it, then memorize the formula for finding the x-value of the vertex:  x  =  -b/(2a).

Because your expression is written correctly,  a = -25,  b = 75,  and  c = 24.

Therefore, the x-value of the vertex is  -(75) / (2·-25)  =  -75 / -50  =  1.5   <--- the time.

To find the height, replace x wby 1.5 in the original expression.

1² - 2²  =  1 - 4  =  -3

3² - 4²  =  9 - 16  =  -7

5² - 6²  =  25 - 36  =  -11

7² - 8²  =  49 - 64  =  -15

This is an arithmetic series with a common diference of -4.

The last term:    (this is the 50th term)

99² - 100²  =  9801 - 10000  =  -199  

The formula for the sum of an arithmetic series is:  Sum  = n(f + l) / 2

where         n  =  number of terms (50)         f = first term (-3)          l = last term (-199)

Sum  =  (50)(-3 + -199) / 2  =  -5050

x² + y² - 6x + 4y + 18

Rearrange:

x² - 6x + y² + 4y + 18

Complete the squares:

(x² - 6x   ) + (y² + 4y   ) + 18

(x² - 6x + 9) + (y² + 4y + 4) + 18 - 9 - 4

(x - 3)² + (y + 2)² + 5

Since (x - 3)² can never be less than 0, and neither can (y + 2)², the complete expression must always be at least 5, but can be larger than 5.

The rate of change is the amount of change in one measurement divided by the amount of change in another measurement.

For example, speed is a rate of change:  the change of distance divided by the change of time; or, how far you went divided by how long it took you.

For example, if you are on an interstate and you pass mile marker 100 at 2:00 and you pass mile marker 240 at 4:00, you traveled 140 miles (240 - 100) in 2 hours (4:00 - 2:00), so your speed (rate of change) is 140 miles / 2 hours or 70 miles per hour.

Another example is slope: slope is the change in y-values divided by the change in x-values. It's the rate of change of y (rise) as x changes (run).

(4 1/9) ÷ (1/9)

First, write 4 1/9 as a common fraction  =  37/9:

(37/9) ÷ (1/9)

When dividing by a fraction multiply by the reciprocal:

(37/9) x (9/1)  =  37    (the nines cancel)

Another way to think of this problem:  How man ninths are there in 4 and 1/9?

There are 9 ninths in each 1, so there are 4 x 9 ninths in 4 (which is 36),

so in 4 1/9 there are 36 + 1 ninths.

If you know two sides (sides a and b) and the included angle (∠C), use this formula:  

          Area  =  ½·a·b·sin(C).

If you know the three sides (sides a, b, and c),

first find the semiperimeter (s) by using this formula:  s  =  (a + b + c) / 2

then use Heron's formula:

          Area  =  √[ s·(s - a)·(s - b)·(s - c) ]