math.not.maths

When you take the square root of a fraction, it's like taking the square root of the numerator over the sqare root of the denominator.

The first one would be sqrt(17)/6.

The second would be sqrt(20)/9, except that sqrt(20) can be simplified to be 2*sqrt(5).

If it were 7x - 4x, you'd have 3x. Similarly, 7x^3/2 - 4x^3/2 = 3x^3/2.

I assume that by 0 you mean theta.

First you'd need to find the cosine of theta (because secant is the reciprocal of cosine). We can do this with right triangle trig. Sine is opposite over hypotenuse, so draw a right triangle, pick an angle and call it theta, and then lable the opposite side 17 and the hypotenuse 37. You can use the pythagorean theorem to get the measure of the third side.

17² + b² = 37²

289 + b² = 1369

b² = 1080

b = 6*sqrt(30)

The cosine of theta is 6*sqrt(30)/37. Therefore, the secant of theta is 37/6*sqrt(30). Apparently you're not supposed to leave radicals in the denominator of a fraction, so you'd multiply by sqrt(30)/sqrt(30) to get 37*sqrt(30)/6*30, which is 37*sqrt(30)/180.

650,000/2 = 325,000 minutes

325,000/60 ≈ 5416.66666... hours

5416.666.../24 ≈ 225.69444444... days.

225.6944444.../365 ≈ 0.618 year.

3(a-b)-a+b

first, distribute (because of PEMDAS, multiplication comes before addition and subtraction [you can't do anything inside of the parentheses])

3a-3b-a+b

then, combine like terms

3a-a-3b+b

2a-2b

Simplify

2(a-b)

I'm not sure what you're asking, but sin(30)=0.5

Well, that isn't enough information to do anything with. I'm going to assume that there's a circle and that you are given a circumference.

formula for circumference:

C = 2πr

We can rearrange it to solve for the radius in terms of the circumference (by dividing both sides by 2π):

r = C / (2π)

And if you're using 3.14 for pi, then you would obviously substitute that in:

r = C / 6.28

They might have given you the area of the circle instead of the circumference.

formula for area of a circle:

A = πr²

Same thing as before; rearrange the equation, solving for r.

r² = A / π

r = sqrt(A / π)

2x*x=12

x*x=x², so 2*x*x=2x²

2x²=12

x²=6

x=sqrt6

I suppose that we're solving for x here.

2 - 3x/8 = 0

-3x/8 = -2

-3x = -16

x = 16/3

If the problem wasn't to solve for x, then I suppose you meant that you wanted this simplified, in which case I believe the following makes a simpler form:

2 - (3x)/8

16/8 - (3x)/8

(16-3x)/8

Remember the order of operations.

(5²*2)-8

(25*2)-8

50-8

42

slope = (y₁-y₂)/(x₁-x₂)

2 = (2-y)/(2-5)

2 = (2-y)/(-3)

-6 = 2-y

-8 = -y

8 = y

x+8=-x

x+8+x=-x+x

2x+8=0

2x+8-8=-8

2x=-8

2x/2=-8/2

x=-4

Using a two-column proof:

Statements (reasons)

<1 and <2 are complementary, <3 and <4 are complementary, m<1 = m<3 (given)

m<1 + m<2 = 90, m<3 + m<4 = 90 (definition of complementary angles)

m<3 + m<2 = 90, m<3 + m<4 = 90 (substitution property of equality)

m<2 = 90 - m<3, m<4 = 90 - m<3 (subtraction property of equality)

m<2 = m<4 (transitive property of equality)