proyaop

Given ad > bc, and we also know all the variables are positive (so when dividing/multiplying you don't have to switch the inequality), you can use the division property and divide both sides by d that still makes the inequality true: a > bc/d.

Then by the same property, you can keep the inequality true by dividing both sides by b, and you obtain a/b > c/d.

Same way to think of it as the example 5/19 > 6/23, because multiplying 23 to both sides won't change the fact that 5 * 23 / 19 > 6, logically speaking, if you fairly multiply each side by the same number, then it's obvious that the bigger side will be even bigger now. After you fiddle around with the division property, you can obtain a/b > c/d.

6 packs of 15 tickets each has the key word "of". Of means multiply, so 2 packs of 2 pokemon cards each is 2 x 2 = 4.

6 packs of 15 tickets each means 15 + 15 + 15 + 15 + 15 + 15 = 15 x 6 = 90 tickets in total. If she has used 38 already, use subtraction.

90 - 38 = 52. Amy has 52 tickets left.

Let the blank be a variable x.

13(5*13*x*3) = 13(17)

Divide both sides by 13. 5*13*3*x = 17              =>          195x = 17

x = 17/195, so the blank is 17/195.

44 feet in height is y value at 44. So 44 = -16t^2 + 60t will help you obtain the time. 

16t^2 - 60t + 44 = 0

4t^2 - 15t + 11 = 0

(4t - 11)(t - 1) = 0

t = 1 and 2.75

If we are looking for the time where it reaches the height of 44 first, then we pick the smaller time, so the answer is 1 second.

If the original price was x, then today's price is 0.62x (38% off is 0.38 times off the original amount). 0.62x = 341. x = 550.

The price of the suit yesterday was 550$.

You can use complimentary counting, first let S = total number of possible subsets.

Let N = the number of subsets with no prime number, then the answer we are looking for is S - N.

S = 2^18 since there are 18 items.

N is any set with 4, 6, 8, 9, 10, 12, 14, 15, 16, 18.

There are a total of 10 items.

So S - N = 2^18 - 2^10

261120 subsets

(3x + 12)(x + 4) = 4x(3x + 2)/2x

6x + 4 = 3x^2 + 24x + 48

3x^2 + 18x + 44 = 0

By quadratic formula, 

\(x = {-9{\pm}i\sqrt{51}\over3}\)

2x + 3y = 15 can be written as 3y = -2x + 15     =>    y = -2x/3 + 5

The slope of this line is -2/3, and if a line is parallel to it, it must also have a slope of -2/3. So the new line is y = -2x/3 + b, where b is the y-intercept.

Plug in (-3, -5): -5 = -2(-3)/3 + b, b = -7

Equation of line: y = -2x/3 - 7 or in standard form: 2x + 3y = -21

PS: smarter solution is to know that new line would be 2x + 3y = c, and plug in -3, -5 to obtain -21. That's if you know the rule about parallel lines + slopes.

Combine like terms: -4t^2 + 8t - 15

Use vertex form: -4(t^2 - 2t + 1) - 11

-4(t - 1)^2 - 11      => (h, k) = (1, -11)

Maximum possible value is -11

The range is what makes the domain the domain, and as you can see x/(1 - x) cannot be undefined, or 1 - x cannot be = to 0. Thus the range is:
(-inf, 1) U (1, inf)

You can use the quadratic formula:

\(x = {16 \pm \sqrt{256 - 12}\over2}\)

\(x = {16\pm2\sqrt{61}\over2}\)

\(x = 8\pm\sqrt{61}\)

Number line has length \(2\sqrt{61}\)

A = 2/3

B = some big number above the thousands

C = 8/25

D = some negative number

E = 3*1.414

DCAEB

13 is prime, so we know we can write it as (13x _ _)(x _ _)

17 is also prime so we can guess put it into either one as (13x - 17)(x + 1) or (13x + 1)(x - 17) or (13x - 1)(x + 17) or (13x + 17)(x - 1).

FOILing it out:

(13x - 17)(x + 1) = 13x^2 - 4x - 17

(13x + 1)(x - 17) = 13x^2 - 220x - 17

(13x - 1)(x + 17) = 13x^2 + 220x - 17

(13x + 17)(x - 1) = 13x^2 + 4x - 17

Values of n: -220, -4, 4, 220

You can use vertex form a(x - h)^2 + k, so that the vertex of the parabola is at (h, k) = (12, -4).

a(x - 12)^2 - 4 = y

Plug in 18

a(18 - 12)^2 - 4 = 0

36a = 4

a = 1/9

(x - 12)^2 - 36 = 9y

If y = 0

x - 12 = +-6

The other x - intercept is (6, 0)

Note how AB is vertical on the line x = 3, and CD is also vertical on the line x = -3. What does this mean? It means that ABCD is a trapzoid, with a height of 3 - (-3) = 6. The base AB has length 4, and the base CD has length 3. The area of a trapzoid is (b1 + b2) * h * 1/2. (4 + 3)*6*1/2 = 21

Combine like terms: x^2 + 10x - 20

Manipulate: r^2 + s^2 = (r + s)^2 - 2rs

Vietas formula: r + s = -10, rs = -20

Substitution: (-10)^2 - 2(-20) = 100 + 40 = 140

Assuming that p is not equal to 0 and q is not equal to 0, simplify p*q*3*3*4*2p*q*2*p*q*q^3

Do the variables: p^3 * q^6

The constants: 3*3*4*2*2 = 144

\(144p^3q^3\)

Combine like terms: x^2 + 10x - 20 = 0

r^2 + s^2 = (r + s)^2 - 2rs

Vietas formula: r + s = -10, rs = -20

Plug it in: (-10)^2 - 2(-20) = 100 + 40 = 140