SamHenry

You need to use the degree to radian ratio. The ratio is 

$${\frac{{\mathtt{\pi}}}{{\mathtt{180}}}} = {\frac{{\mathtt{radians}}}{{\mathtt{degrees}}}}$$

So just plug in the degree, and solve!

$${\frac{{\mathtt{\pi}}}{{\mathtt{180}}}} = {\frac{{\mathtt{rad}}}{{\mathtt{30}}}}$$

$${\mathtt{rad}} = {\frac{{\mathtt{30}}{\mathtt{\,\times\,}}{\mathtt{\pi}}}{{\mathtt{180}}}}$$

30 degrees in radians is pi/6 radians :)

For this question, you should use the foil method.

(4x + 5y)(3x - 8y)

12x^2 -32xy + 15xy - 40y^2

-40y^2 + 12x^2 - 17xy

And that's it! :)

Divide the numbers, and subtract the exponents.

-6x^2

For this question, you have to factor.

2x^2 - 3x - 2 = 0

2x^2 - 4x + x - 2 = 0

2x(x - 2) + 1(x - 2) = 0

(2x + 1)(x-2) = 0

Now solve both parts.

x = -1/2, 2

Not a bad guess, but that's actually not right. How can you prove that the number line is correct? What if 2 didn't actually represent 2? It's kinda mind boggling ;) Believe it or not, the proof is... 2 + 2 = 4. It's the basis of most math, and it's one of those things that we accept as fact. 

-140/350 divided by 70/70 = -2/5

Just find the biggest number that will go into both numbers, the greatest common factor, and divide by that number to simplify. :)

2/3 + 1/3 = 1

Think of it like three slices of a pie that is cut into 3. Two slices plus one slice makes a whole.

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

To solve this, you must use logarithms.

x = $${{log}}_{{\frac{{\mathtt{1}}}{{\mathtt{2}}}}}{\left({\mathtt{32}}\right)}$$

x = -5

2.54 * 10^-1

Dividing by fraction is the same as multiplying by the reciprocal of that fraction. So it would be the same as 5 * 3/2.

5/1 * 3/2 = 15/2

The first answer is incorrect. You do not divide to find percentages. You multiply the number by the percentage in decimal form. 5% in decimal is .05.

So do 3600 * .05 = 180

8n + 3 = 5

Subtract 3 to get n alone

8n = 2

Now divide by n to get the answer.

n = 1/4

A power to a power is the same as multiplying the two powers. So 10^10^50 is the same as 10^500, which is 10 with 500 zeros after it. That's it :)

You can just add them together with this site: 129211732691

x + 1800 - 2700 = 800

Solve for x: First combine the 2 numbers on the left

x - 900 = 800

Now add 900 to the right to get x

x = 800 + 900

x = 1700

Could you give more information on the problem you're doing this with?

But the easiest way: If you have the exact answer, and the estimate is lower than that answer, it's an underestimate. If it's higher, then it's an overestimate.