geno3141

An hour is 60 minutes. If you ran for 20 minutes, you ran for 20/60 = 1/3 of an hour.

If you ran 1/3 of an hour, you also ran 1/3 of the distance:  (1/3) x (15)  =  5 km.

First, calculate how much  Seth will save every time that he goes to the movie:  $3.50 - $1.00  =  $2.50.

Now we need to calculate how many times $2.50 goes into $40.00.

$40.00 ÷ $2.50  =  <the answer>

Get it into the form so that you can use the quadratic formula.

x² + 14x = 33     --->     x² + 14x - 33  =  0

a = 1   b = 14   c = -33     Quadratic formula:  x  =  [ -b ± √(b² -4·a·c) ] / (2·a)

Positive solution:  x  =  [ -14 + √(14² -4·1·-33) ] / (2·1)  =  [-14 + √328]/2

     =     [-14 + 2√82]/2     =     -7 + √82     =     √82 - 7

(Notice that the problem has a to be the value under the square root sign and b is the number after the minus sign.)

--->  a  =  82     and  b = 7

So, how much is  a + b ?

3(x/4)  =  -6(2x - 17)

Simplify the lef-hand side:

3x/4  =  -6(2x - 17)

Distribute the right-hand side:

3x/4  =  -12x + 102

Multiply each term by 4:

3x  =  -48x + 408

Get all the x-terms to one side; add 48x to both sides:

51x  =  408

Divide by 51:

x  =  8

the time is 1.5  (probably seconds, but that isn't specified).

The total weight is 37.5 ounces. There are 15 markers, each weighing the same amount.

To find out how much each one weighs, divide the 37.5 ounces by 15.

37.5 ÷ 15  =       <---   your answer.

You need to know the location of the vertex, which is the highest point.

Your expression, -25t² + 75t + 24  has the form  at² + bt + c,  so  a = -25,  b = 75,  and  c = 24.

The x-vaue of the vertex can be found by using this little formula:  x-value  =  -b/(2a).

For this problem, the x-value of the vertex is  -75/(2·-25)  =  -75/-50  =  1.5

This represents the time of the maximum height; time = 1.5.

There are two parts, the number and the variable.

First, the number:  √18  =  √9·√2  =  3√2 

Now, the variable:  √x²  =  |x|    (You need absolute value bars because √(-3)²   isn't  -3,  it's  +3.

Putting these together:   3√2|x|    <---   answer

(5/a) ÷ 3

When dividing, you can multiply by the reciprocal:

=  (5/a) x (1/3)

Multiply the numerator times the numerator and the denominator times the denominator:

  =  5 / (3a)

I'm assuming that you want the answer to 4.1 x 10^-3

10^-1 = 0.1

10^-2 = 0.01

10^-3 = 0.001

4.1 x 10^-3  =  4.1 x 0.001  =  0.0041