You get 3x + 4x, +4- -3,and +3 + 4
Answer:
5
Step-by-step explanation:
Given:
Cost to build a bookshelf = $20
Cost to build a table = $45
Amount available to spend = $600
Let x = number of bookshelves built.
Let y = number of tables built.
The total number of bookshelves and tables = 18.
Therefore
x + y = 18.
That is,
y = 18 - x (1)
The total amount available to build x bookshelves and y tables = $600. Therefore
20x + 45y = 600
That is (dividing through by 5),
4x + 9y = 120 (2)
Substitute (1) into (2).
4x + 9(18 - x) = 120
4x + 162 - 9x = 120
-5x = -42
x = 8.4
From (1),obtain
y = 18 - 8.4 = 9.6
Because we cannot have fractional bookshelves and tables, we shall test values of x=8, 9 and y=9,10 for profit
Note: The profit is $60 per bookshelf and $100 per table.
If x = 8, then y = 18-8 = 10.
The profit = 8*60 + 10*100 = $1480
If x = 9, then y = 18-9 = 9.
The profit = 9*60 + 9*100 = $1440
The choice of 8 bookshelves and 10 tables is more profitable.
Answer: 8 bookshelves and 10 tables.
Answer:
<h2>21/32</h2>
Step-by-step explanation:
-7/8 × -3/4 = 21/32
-7 × -3 = 21
-8 × -4 = 32
21/32
<u><em>IMPORTANT: This number is not negative, because a negative times a negative is a positive.</em></u>
By the way, if you didn't know how to arrive at the fraction here's how.
First, Address input parameters & values.
Input parameters & values: The decimal number = 0.65625. Then, write it as a fraction
0.65625/1
Multiply by 100000 both the numerator & denominator
(0.65625 x 100000)/(1 x 100000) = 65625/100000
65.625% = 65.625/100 or 65625/100000
Find LCM (Least Common Multiple) for 65625 & 100000.
3125 is the LCM for 65625 & 100000
Divide by 3125
65625/100000 = (65625 / 3125) / (100000 / 3125)
= 21/32
I'm always happy to help :)
Answer:
Step-by-step explanation:
The domain of all polynomials is all real numbers. To find the range, let's solve that quadratic for its vertex. We will do this by completing the square. To begin, set the quadratic equal to 0 and then move the -10 over by addition. The first rule is that the leading coefficient has to be a 1; ours is a 2 so we factor it out. That gives us:
The second rule is to take half the linear term, square it, and add it to both sides. Our linear term is 2 (from the -2x). Half of 2 is 1, and 1 squared is 1. So we add 1 into the parenthesis on the left. BUT we cannot ignore the 2 sitting out front of the parenthesis. It is a multiplier. That means that we didn't just add in a 1, we added in a 2 * 1 = 2. So we add 2 to the right as well, giving us now:
The reason we complete the square (other than as a means of factoring) is to get a quadratic into vertex form. Completing the square gives us a perfect square binomial on the left.
and on the right we will just add 10 and 2:
Now we move the 12 back over by subtracting and set the quadratic back to equal y:
From this vertex form we can see that the vertex of the parabola sits at (1,-12). This tells us that the absolute lowest point of the parabola (since it is positive it opens upwards) is -12. Therefore, the range is R={y|y ≥ -12}
