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If the problem is:       √x  =  0.9,

square both sides:  (√x)²  =  (0.9)²

                                  x  =  0.81

Rewrite them from ighest exponent to lowest:

    -g³ +3g² + 4g - 2

If  y  =  ln(3x) - 1.

There are two steps to find the inverse:

1)  Exchange x and y:

     x  =  ln(3y) - 1

2)  Solve for y:

     x + 1  =  ln(3y)

     e^(x + 1)  =  e^(ln(3y))

     e^(x + 1)  =  3y

     y  =  (1/3)e^(x + 1)

the answer is

10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376

or

1.071508607186271 × 10³⁰¹

Speed is the distance divided by the time.

To get velocity, first find the speed and then also attach the direction. 

What is the question?

Since  2² = 4  and  3² = 9, the √8 lies between 2 and 3.

3x³ - 12x² + 27x

=  3x(x² - 4x + 9)

Any further factoring would require radicals.

sin(45)  =  √2/2

30/sin(45)  =  30/(√2/2)  =  60/√2  =  30√2

sqrt( 30√2 )²  =  30√2

30√2 - 30²  =  30√2 - 900

Answer is 30.

The answer is not exactly 0, but it is so small that the calculator can no longer print it.

For example by the time it calculates 0.4444444 ^ 300, the answer has more than 100 zeros right after the decimal point. The calculator isn't programmed to have numbers that small, even when written in scientific notation. Instead, it rounds off the answer, as best it can, to zero.

This equation can simplify to $${{\mathtt{y}}}^{{\mathtt{2}}} = {\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{x}}$$

First, get y by itself: $${\mathtt{y}} = {\sqrt{{\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{x}}}}$$

Now set y to 0 and solve 

$${\mathtt{0}} = {\sqrt{{\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{x}}}}$$

$${\mathtt{x}} = {\mathtt{0}}$$

Let x be the gallons of premium. This means the regular gallons will be x + 420. Add these together to the total profit.

$${\mathtt{2.3}}{\mathtt{\,\times\,}}\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{420}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{2.55}}{\mathtt{\,\times\,}}{\mathtt{x}} = {\mathtt{10\,957}}$$

$${\mathtt{2.3}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{966}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2.55}}{\mathtt{\,\times\,}}{\mathtt{x}} = {\mathtt{10\,957}}$$

Now factor out the x

$${\mathtt{x}}{\mathtt{\,\times\,}}\left({\mathtt{2.3}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2.55}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{966}} = {\mathtt{10\,957}}$$

Now solve for x.

$${\mathtt{4.85}}{\mathtt{\,\times\,}}{\mathtt{x}} = {\mathtt{9\,991}}$$

$${\mathtt{x}} = {\mathtt{2\,060}}$$

a)
2060 gallons of premium,
2480 gallons of regular.

b)
Profit for premium: .20 * 2060 = $412
Profit for regular: .18 * 2480 = $446.40
Total profit: $412 + $446.40 = $858.40

Let the total sales equal x. The sales in New England are $${\frac{{\mathtt{1}}}{{\mathtt{9}}}}{\mathtt{\,\times\,}}{\mathtt{x}}$$. Set this equation equal to the amount made in New England, and solve.

$${\mathtt{600\,000}} = {\frac{{\mathtt{1}}}{{\mathtt{9}}}}{\mathtt{\,\times\,}}{\mathtt{x}}$$     Multiply by 9

x = $5,400,000

$${\mathtt{45}}{\mathtt{\,\times\,}}{\mathtt{3}} = {\mathtt{135}}$$

Remember that we need to take both roots of 16.....so we have

(x - 2)^2 = 16

x - 2 = ±√16

x - 2 = ± 4

So

x - 2 = 4        and       x - 2 = -4         add 2 to both sides of both of these

x = 6             and       x = -2

And those are the two solutions.....

-5*(-6) -3*(-5-3*(-4)+6)

[-5*(-6)] - [3*(-5 - 3(-4) + 6)]                              

[30] - [3*(-5 - 3(-4) + 6)]              (Multiplied -5 x -6.)

[30] - [3*(-5 - [3*(-4)] + 6)]          (Work from the innermost set of parentheses.)

[30] - [3*(-5 + 12 + 6)]                 (Multiplied 3 x -4)

[30] - [3*(13)]                              (Combined -5 + 12 + 6)

30 - 39                                         (MUltiplied 3 x 13)

= -9

Let x be the number of wireless keyboards sold. So the number of regular keyboards sold is three times this = 3x

So we have.....Quantity x Price = Revenue

x(105) +3x(84) = 4998       simplify

105x + 252x = 4998

357x  = 4998     divide both sides by 357

x = 14 = wireless keyboards sold

And 3x = 3(14) = 42 = regular keyboards sold

To solve for x:

     (x - 2)^2 = 16

     x - 2 = sqrt(16)

     x - 2 = 4

     x = 4 - 2

     x = 2

Let  P  =  number of dozen peanut butter cookies sold.

Let  C  =  number of dozens chocolate chip cookies sold.

Number equation:  P  =  85 + C

Value equation:     6.50P + 9.00C  =  4055.50

Substituting the first equation into the second:

                           6.50(85 + C) + 9.00C  =  4055.50

                           552.50 + 6.50C + 9.00C  =  4055.50

                           552.50 + 15.50C  =  4055.50

                                         15.50C  =  3503.00

                                                 C  =  226

                                                 P = 85 + 226  =  311

Let C be the total cost...so we have

C = 3(39.95) + 460(.68) = $432.65....so $400 won't be enough....

The daily sales for any given day (S) are equal to $6.50 per dozen PB cookies sold (P) plus $9.00 per dozen CC cookies sold (C).

S = 6.50P + 9.00C

The sales of this day (S) were $4055.50, so we can write that

4055.50 = 6.50P + 9.00C

Today, Cookie Inc. sold 85 more dozens of PB cookies (P) than dozens of CC cookies, so we can write that

P = C + 85

We have two unknown variables, "P" and "C." We also have two equations with these variables, meaning that we can solve for them by plugging "C + 85" for "P" into the first equation:

4055.50 = 6.50P + 9.00C

4055.50 = 6.50(C + 85) + 9.00C

Now we solve for "C"

4055.50 = 6.50(C + 85) + 9.00C

4055.50 = 6.50C + 85 * 6.5 + 9.00C

4055.50 = 15.5C + 552.5

3503 = 15.5C

226 = C

226 Dozens of Chocolate Chip Cookies were sold.

(1/4)C - 6

Let  P  stand for the amount of money made on selling paperback books.

Let  H  stand for the amount of money made on selling hardcover books.

Then:  P + H  =  124,300

But, since they make four times on paperback books as on hardcover books:  P  =  4H

         4H + H = 124,300

               5H  =  124,300

                 H  =  24,860

    P  =  4H  =  4(24,860)  =  99,440

Key words:  "times"  <--->  x

"divided by"  <--->  /       (or  ÷)

5 times G divided by R

5 x G / R

To emphasize in what order they should be done:

(5 x G) / R