7+3x≤8(3+x) perform indicated multiplication on right side
7+3x≤24+8x subtract 8x from both sides
7-5x≤24 subtract 7 from both sides
-5x≤17 divide both sides by -5 (and reverse direction of inequality sign because of multiplication/division by a negative value)
x≥-17/5
x≥ -3.4
Let's make some variables to represent the cost of the tables and chairs.
Let x be equal to the cost of one chair
Let y be equal to the cost of one table
The total cost for 3 chairs and 2 tables is $17.
3x + 2y = 17
The total cost for 8 chairs and 4 tables is $37.
8x + 4y = 37
Now we have our system of equations.
Let's solve it.
3x + 2y = 17
8x + 4y = 37
We can cancel the y's very easily. Then it would just leave us with the x's.
Multiply the top equation by -2.
3x(-2) + 2y(-2) = 17(-2) =
-6x - 4y = -34
Then add the equations together.
-6x - 4y = -34
8x + 4y = 37
=
2x = 3
Then just divide both sides by 2.
x = 1.5
Substitute 1.5 into one of the equation. I'll pick 3x + 2y = 17
3(1.5) + 2y = 17 ; Start
4.5 + 2y = 17 ; Multiply 3 and 1.5 together
2y = 12.5 ; Subtract 4.5 from each side of the equation
y = 6.25 ; Divide both sides by the coefficient of y. Which 2
So, a chair costs $1.50 and a table costs $6.25.
Y-intercept = (0,2)
x-intercept = (-4,0)
Answer:
5 amperes will produce the maximum power of 300 watts.
Step-by-step explanation:
The general form of a quadratic function presents the function in the form
The vertex of a quadratic function is the highest or lowest point, also known as the maximum or minimum of a quadratic function.
We can define the vertex by doing the following:
- Identify a, b, and c
- Find, the x-coordinate of the vertex, by substituting a and b into
- Find, the y-coordinate of the vertex, by evaluating
We know that the power generated by an electrical circuit is modeled by
This function is a quadratic function.
To find the current that produce the maximum power you must
a = -12 and b = 120
- Find, the maximum current of the vertex, by substituting a and b into
- Find, the maximum-power, by evaluating
5 amperes will produce the maximum power of 300 watts.
We can check our work with the graph of the function and see that the maximum is (5, 300).
