Answer:
- 30 chairs, 18 tables
- $3900
Step-by-step explanation:
If x and y represent the numbers of chairs and tables Pierre wants to make, then he wants to ...
Maximize 55x +125y
subject to the constraints ...
6x +10y ≤ 360 . . . . . limit on available boards
12x +40y ≤ 1080 . . . limit on available nails
y ≥ 6 . . . . . . . . . . . . . minimum number of tables to sell
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When there are two variables, it is often convenient to graph the constraints to find the feasible solution region. The graph shows the vertices of the feasible region to be (0, 27), (30, 18), (50, 6), and (0, 6).
Pierre's profit is maximized by selling 30 chairs and 18 tables. His maximum profit is $3900.
Answer:
The domains are not the same
Step-by-step explanation:
The domains are not the same because in the first graph, the left part of the graph is always approaching 2, not reaching it, while the right side is extending infinitely. In the second graph, the left side DOES reach three except it doesn't cross it.
So the notation for the first line would be
2<x<infinity
2\leq x <infinity
Answer:
1. $ 0.15 increases for each dollar.
2. There is $ 0.20 increases for each dollar in the 20% column .
3. $ 48.75 is calculated for $325.00 in the 15% column.
$ 65 tip will be calculated in the 20% column for $ 325
Step-by-step explanation:
a. The tip for each dollar would be
= $ 1 * (15%)
= $ 1 * 15/100
= $1 * 0.15
= $ 0.15
Therefore $ 0.15 increases for each dollar.
b. The tip for each dollar would be
= $ 1 * (20%)
= $ 1 * 20/100
= $1 * 0.20
= $ 0.20
There is $ 0.20 increases for each dollar in the 20% column .
c. The $ 325 bill can be broken down into
$ 100+ $100 + $100 +$25
The tip can be calculated
$ 100 * 15%+ $100* 15% + $100* 15% +$25* 15%
= $ 15+$ 15+$ 15+ $3.75
= $ 48.75
The tip can be calculated
$ 100 * 20%+ $100* 20% + $100* 20% +$25* 20%
= $ 20+$ 20+$ 20+ $5
= $ 65
$ 65 tip will be calculated in the 20% column for $ 325.
Answer:
Step-by-step explanation:
1.)1/4+3/4+1/4=5/4
2.)2+1=3
3.) 3·4+5=17/4
4.)17/4=2cubes
<h3>
Answer: AB is 14 units long.</h3>
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Explanation:
We're told that 
which means triangle ABC is similar to triangle DEF. The order of the letters is important as you'll see in the next two paragraphs.
AB and DE are the first two letters of ABC and DEF respectively. These two sides pair up as one corresponding pair. This forms the fraction AB/DE.
Through similar logic, we get the fraction BC/EF. We have BC and EF as the last two letters of ABC and DEF respectively. This fraction is equal to the previous fraction we set up (due to similar triangles having equal proportions).
Once again, the order of the letters matters to tell us how the sides and angles pair up together.
-----------------
In short, the key takeaway from that last section is that we can form this equation:
AB/DE = BC/EF
From here, we apply substitution and solve for x
So,
AB/DE = BC/EF
7x/7 = 4/x
7x*x = 7*4 .... cross multiplication
7x^2 = 28
x^2 = 28/7
x^2 = 4
x = sqrt(4)
x = 2
We only consider the positive square root because x is some side length. Negative x values are not allowed.
To wrap things up, use that x value to find AB
AB = 7x = 7*2 = 14
