Answer: x
Step-by-step explanation:
The inverse undos any changes to x, reversing those changes will leave x. Ex: f(x)=x+2. The inverse (from replacing x with y and y with x and solving for y) is h(x)=x-2. Plugging x+2 into h(x) (composition of functions) results in x. 2 and -2 cancel out.
Answer:
400 + 6x
Step-by-step explanation:
$400 cabin cost is fixed and doesn't change.
Food cost changes as there are more people so we can write it as 6x
Total cost is 400 + 6x
Answer:
x = -3 or x = 5
Step-by-step explanation:
Solve: x^2 -2x = 15
x^2 - 2x - 15 = 0
Use the Diamond method of factoring
-15 = 3* -5 and 3 - 5 = -2 so...
x^2 - 2x - 15 = x^2 - 5x + 3x - 15
x^2 - 2x - 15 = x *(x - 5) + 3*(x - 5)
x^2 - 2x - 15 = (x + 3)*(x - 5)
x^2 - 2x - 15 = (x + 3)*(x - 5) = 0
solve (x + 3 ) = 0 and (x - 5) = 0
x = -3 or x = 5
Answer:
<u>The equations system is:</u>
<u>x + y = 10</u>
<u>0.5x + 0.9y = 6</u>
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Liters of 60% acid solution needed = 10
x = Number of liters of the 50% solution
y = Number of liters of the 90% solution
2. Which equation represents the total liters of acid that are needed?
There are two equations needed:
The first one related to the total liters needed, 10 in this case:
x + y = 10
The second one related to the acid concentration of the 10 liters:
0.5x + 0.9y = 10 * 0.6
0.5x + 0.9y = 6
<u>The equations system is:</u>
<u>x + y = 10</u>
<u>0.5x + 0.9y = 6</u>
Solving for x and y in the 2nd equation, we have:
0.5 (10 - y) + 0.9y = 6
5 - 0.5y + 0.9y = 6
0.4y = 6 - 5
0.4y = 1
y = 1/0.4 = 2.5 ⇒ x = 7.5 (10 - 2.5)
The scientist can mix 7.5 liters of the 50% acid solution and 2.5 liters of the 90% acid solution to get the 10 liters of the 60% acid solution.
