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Slope is defined as   rise/run    if run = 0 (as a vertical line)  then the  slope is UNDEFINED .(zero in the denominator)

Look up information regarding the binomial theorem for further information.

\(\binom{6}{4}(2x)^4 (2)^2 = \boxed{960x^4}\)

The coefficient is 960.

V = a³

V = 5³ cm

V = 5 cm * 5 cm * 5 cm

V = 125 cm³

The coefficient of x^4 is 960x^4.

C. Negative

5 cm * 5 cm * 5 cm = 125 cm³

Note the vertex at    3, 8

  vertex form       y = a(x-3)^2 + 8     sub in a point to solve for 'a'      I'll use 5,4

                           4 = a ( 5-3)^2 + 8

                             a = -1

y = -(x-3)^2 + 8      expand to  y =    -x^2 + 6x -1      <======== take it from here !

\(30 \times 1.4 = \color{brown}\boxed{42}\)

\(30\) is the original price, and \(1.4\) is the markup.

210?

Add (1) + (2) (both equations) together and you get 2x + 2y + 2z = 42 (3).
Multiply the equation (3) by 5 and you get 10x + 10y + 10z = 42 * 5 = ............... (diy).

There are many, many of them such as:

 
33  = 3 * 11  
34  = 2 * 17  
35  = 5 * 7  
  
85  = 5 * 17  
86  = 2 * 43  
87  = 3 * 29  
  
  
93  = 3 * 31  
94  = 2 * 47  
95  = 5 *19  

Wellllll..... round it to two decimal places.....you SHOULD know how to do THAT!!!

By complementary counting, there are 792 - 142 = 650 ways.

Wait... Never mind, my hint is wrong, sorry. 

Hint: The consecutive series of positive integers should be numbers that have divisors, e.g. 9 and 10 are consecutive, where 9 = 3 * 3 and 10 = 2 * 5.
 

There are infinite solutions for x and y, when \(x \in \mathbb{P}\) and \(y = 1\), or \(x = 1\) and \(y \in \mathbb{P}\) .

Simply plug in the expression into the function.

a. f(1) = 3(1) - 2 = 1

b. f(t) = 3t - 2

c. f(x^2) = 3x^2 - 2

d. f(f(x)) = f(3x - 2) = 3(3x - 2) - 2 = 9x - 8

Let x be the number of apples Nicole has and y be the number of apples that Hannah has.

x/y = 1/3

(x + 4)/(y + 3) = 1/2

Rewrite the first equation to get y = 3x, then substitute into the second equation.

(x + 4)/(3x + 3) = 1/2

2(x + 4) = 3x + 3

2x + 8 = 3x + 3

5 = x

Nicole had 5 apples in the beginning, so Hannah had 15 apples in the beginning. In the end, Hannah had 15 + 3 = 18 apples.

1584 = 2^4 * 3^2 * 11

To be a perfect cube, a number's prime factors' exponents must all be multiples of 3. So, the smallest value of x is:

\(\frac{2^6 \cdot 3^3 \cdot 11^3}{2^4 \cdot 3^2 \cdot 11} = \boxed{1452}\)

In other terms, x = 1452 = 2^2 * 3 * 11^2. The product xy must be a multiple of 1584, so,

xy = 2^2 * 3 * 11^2 * y = 2^4 * 3^2 * 11 * n

y must have 2^2 * 3 as a factor, so the smallest value of y is 12.

Use the following algebraic identity:

(x + y + z)^2 = x^2 + y^2 + z^2 + 2(xy + xz + yz) = 9 + 2(18) = 45

i need the answer in two decimal places

\(\frac{1}{x} + \frac{1}{y} = \frac{1}{17}\)

\(\frac{x + y}{xy} = \frac{1}{17}\)

\(17(x + y) = xy\)

\(0 = xy - 17x - 17y\)

\(289 = (x - 17)(y - 17)\)

The possible values of x are 18, 34, and 306.

Thanx for finding my mistake !

Yah.....I manged to mix weekly and MONTHLY payments ....here is my corrected:

Present value of ordinary annuity

PV = C * ( 1-(1+i)^-n ) /i         i = .0279 / 52      n = 8 yr * 52 wks = 416       PV = 28250       find 'C'

C = payments = $ 75.787

Total payments = 416 * 75.787 =  $ 31527.43         interest =   31527.4 - 28250 = $ 3277.43