geno3141

Are you thinking of a particular problem?

Dividing by 5 is the same as multiplying by 10 and dividing by 2. Multiplying by 10 just moves the decimal point over one place. Dividing by 2 

7^1 = 7 ÷ 5 = 1.4                7^5 = 16807 ÷ 3361.4

7^2 = 49 ÷ 5 = 9.8              7^6 = 117649 = 23529.8

7^3 = 343 ÷ 5 = 68.6           etc.

7^4 = 2401 ÷ 5 = 480.2

This pattern cycles every 4 numbers. Which row will 7^2014 be in?

Working with the exponents: 1 ÷ 4 = .25           5 ÷ 4 = 1.25

                                        2 ÷ 4 = .50           6 ÷ 4 = 1.50

                                        3 ÷ 4 = .75           7 ÷ 4 =  1.75

                                        4 ÷ 4 =  1.00         8 ÷ 4 = 2.00

2014 ÷ 4 = 503.5   --->   second row 

Therefore, from the top grouping, the decimal is .8 --->  remainder is 5 x .8  = 4

4(3x - 5) - 6x < 6x + 1

Distributive Property:

12x - 20 - 6x < 6x + 1

Simplifying the left side:

6x - 20 < 6x + 1

Subtract 6x from both sides:

    -20 < 1

This is a true statement; no matter what value you replace for x in the original inequality, the inequality can never be made false.

Answer:  All numbers work.

-96  =  -3x + 2(-2x - 13)

Distributive property:

-96  =  -3x - 4x - 26

Simplifying:

-96  =  -7x - 26

Adding 26 to both sides:

-70  =  -7x

Dividing both sides by -7

10  =  x

In the second quadrant, if the cos(θ) = -1/4, then a right triangle can be drawn with adjacent side = -1 and hypotenuse = 4.

To find the opposite side:  c² = a² + b²   ---> 4² = 1² + b²    --->   b = √15  (this is positive because it is a y-value in the second quadrant.

The value of sin(θ) = √15/4     and the value of tan(θ) = -√15

csc(θ) = 1/sin(θ)  =  1/(√15/4)  =  4/√15  =  4√15/15

cot(θ) = 1/tan(θ)  =  1/(1/-√15)  =  -√15

I'm assuming that you meant "takes the third dose".

Formula for half-life:  F  =  I·(½)^(t/h)

F = final amount          I = initial amount         t = time         h = half-life 

The second dose will be taken 3 hours after the first dose and the third dose will be taken 6 hours after the first dose.

For the initial 300 mg dose after 6 hours (360 minutes):  F  =  300·(½)^(360/188.4)  =  79.78 mg

For the second 300 mg dose after 3 hours (180 mins):    F  =  300·(½)^(180/188.4)  =  154.71 mg

For the third dose (just taken):  F  =  300 mg.

Total:  79.78 mg + 154.71 mg + 300 mg  =  534.49 mg

Use a calculator to find 16/25.

Look at the digit in the third position after the decimal point; if it is 4 or smaller, leave the digit in the second position the same; if it is 5 or larger, increase the digit in the second decimal position by 1.

(2x - 11) + 15  = 3x + 12

Removing parentheses:

2x - 11 + 15  =  3x + 12

Simplifying:

2x + 4  =  3x + 12

Subtacting 2x from both sides:

4  =  x + 12

Subtracting 12 from both sides:

-8  =  x

There are two angles that have a cosine of -1/2 between 0° and 360°.

One is 120° and it has a sin value of √3/2 ≈ 0.8660.

The other is 240° and it has a sin value of -√3/2 ≈ -0.8660.

A 5/3 power means to raise the number to the fifth power and to find the cube root.

These can be done in either order.

The cube root of 27 is 3 and 3 to the fifth power is 243.

The fifth power of 27 is 14348907 and the cube root of 14348907 is 243.