Solve for x:
5 - sqrt(x) + sqrt(3 x - 11) = 6
Subtract 5 from both sides:
sqrt(3 x - 11) - sqrt(x) = 1
(sqrt(3 x - 11) - sqrt(x))^2 = -11 + 4 x - 2 sqrt(x) sqrt(3 x - 11) = -11 + 4 x - 2 sqrt(x (3 x - 11)) = 1:
-11 + 4 x - 2 sqrt(x (3 x - 11)) = 1
Subtract 4 x - 11 from both sides:
-2 sqrt(x (3 x - 11)) = 12 - 4 x
Raise both sides to the power of two:
4 x (3 x - 11) = (12 - 4 x)^2
Expand out terms of the left hand side:
12 x^2 - 44 x = (12 - 4 x)^2
Expand out terms of the right hand side:
12 x^2 - 44 x = 16 x^2 - 96 x + 144
Subtract 16 x^2 - 96 x + 144 from both sides:
-4 x^2 + 52 x - 144 = 0
The left hand side factors into a product with three terms:
-4 (x - 9) (x - 4) = 0
Divide both sides by -4:
(x - 9) (x - 4) = 0
Split into two equations:
x - 9 = 0 or x - 4 = 0
Add 9 to both sides:
x = 9 or x - 4 = 0
Add 4 to both sides:
x = 9 or x = 4
5 - sqrt(x) + sqrt(3 x - 11) ⇒ 5 - sqrt(4) + sqrt(3×4 - 11) = 4:
So this solution is incorrect
5 - sqrt(x) + sqrt(3 x - 11) ⇒ 5 - sqrt(9) + sqrt(3×9 - 11) = 6:
So this solution is correct
The solution is:
Answer: x = 9
Answer:
a. yes
b. no
c. no
d. no
e. yes
Step-by-step explanation:
Here, we want to answer yes or no for each of the numbers
a) Yes
If we compare with the general form
y = mx + b
m
is slope and b is y-intercept
so, 2 is slope and 3 is y intercept; so 3 in y-intercept is (0,3)
b. No
This is the point-slope form we are trying to
get
Evaluating this, we have that
y-3 = 2x - 6
y = 2x-6 + 3
y = 2x-3
c) NO
Just insert the values and check here
-1 = 2(5) + 3
it does not work
d) No
Substitute
-4 = 2(-5) + 3
e) Yes
This is the point-slope form
y + 3 = 2x + 6
y = 2x + 6-3 = 2x + 3
Answer:
it is a :) hope this helped :)
Step-by-step explanation:
Answer:
$6.72
Step-by-step explanation:
The store is selling lemons at $0.56 each. Each lemon yields about 2 tablespoons of juice.How much will it cost to buy enough lemons to make three 9-inch lemon pies, each requiring half a cup of lemon juice?
1 cup = 16 table spoon of juice
half a cup = 8 table spoon of juice
1 pie require half a cup of lemon juice. so 1 pie requires 8 tablespoon of lemon juice
Each lemon yields about 2 tablespoons of juice
2 times 4 = 8
So 4 lemon needed to make a pie
cost of 1 lemon = 0.56
cost of 4 lemons = 
cost of lemon for making 3 pie= 
