The trick to solving this problem is to realize that the independent variable is x, which represents the number of people who can attend the party without the total party cost exceeding $80.
This is the form of the inequality:
(total cost) [less than or equal to] $80
(rent) + (cost per guest)(number of guests) [less than or equal to] $80
$45 + $5.50 x [less than or equal to] $80
Simplify. To do this, subtract $45 from both sides of this inequality.
Divide both sides of the resulting inequality by $5.50.
What is the restriction on x?
Answer:
undefined. No one knows the answer. ¯\_(ツ)_/¯¯
There would be 25 people in the line.
There are 6 people between jane and ken
k - - - - - - j
there are 18 people ahead of jane including ken
- - - - - - - - - - -k - - - - - - j
and 13 people behind ken including jane
- - - - - - - - - - -k - - - - - - j - - - - - -
if you add all of the dashes up from the row above, you will get your answer of 25 people in the line
Answer:
1. 18 (sqrt21 - sqrt2a)
2. 3
3. x^m/n
4. (5x^4√10)/(√2x)
5. x = -2 or -6
6. x = 30
Step-by-step explanation:
Number 1
3^3sqrt21 - 6^3sqrt2a
3 * 6 * sqrt21 - sqrt2a
18 (sqrt21 - sqrt2a)
Number 2
3^1/2 * 3^1/2 =
3^1/2+1/2 =
3^1 =
3
Number 3
^nsqrtx^m =
x^m/n
Number 4
(√250x^16)/(√2x) =
(√25 * 10 * x^16)/√(2x )=
(5x^4√10)/(√2x)
Number 5
√2x + 13 - 5 = x
√2x + 13 = x + 5
square both side to take away the sqrt sign
(√2x + 13)^2 = (x + 5)^2
expand the equation on the RHS
2x + 13 = x(x+5) + 5(x+5)
2x+13 = x^2 + 10x +25
substract 13 from both sides
2x = x^s + 10x +12
subtract 2x from both sides
0 = x^2 +8x + 12
Factorize equation
x^2 + 6x +2x + 12 = 0
x(x+6) + 2(x+6) = 0
(x+2)(x+6) = 0
x = -2 or -6
Number 6
3 ^5sqrt(x+2)^3 + 3 = 27
subtract 3 from both sides
3 ^5sqrt(x+2)^3 = 27 - 3
3 ^5sqrt(x+2)^3 = 24
divide through by 3
^5sqrt(x+2)^3 = 8
square both sides by 5 to take away the 5th root sign
(x+2)^3 = (8)^5
(x+2)^3 = 32,768
take the cube root of both sides to take away the ^3
x+2 = ^3sqrt 32,768
x+2 = 32
x = 32 - 2
x = 30
9/6 = 1.5
24/1.5 = 16
triangle DEF has a primeter of 16 inches
