Answer:
Hence, ption B is true.
Step-by-step explanation:
Given the expression
solving the expression
as
so the expression becomes
Group like terms
Add similar elements
Therefore, we conclude that:
Hence, option B is true.
Answer:
The correct answer is option b)
50a+10b<1000; 200a+360b < 7200; a> 0; b>0
Step-by-step explanation:
We are given that Two kind of crated cargo namely A and B to be shipped by truck.
<u>Cargo A:</u>
Volume of each crate of cargo A = 50 cubic ft
Weight of each crate of cargo A = 200 pounds
Let number of crates of cargo A to be shipped = a
Total volume of 'a' crates of cargo A = 50a cubic ft
Total weight of 'a' crates of cargo A = 200a pounds
<u>Cargo B:</u>
Volume of each crate of cargo B = 10 cubic ft
Weight of each crate of cargo B = 360 pounds
Let number of crates of cargo B to be shipped = b
Total volume of 'b' crates of cargo B = 10b cubic ft
Total weight of 'b' crates of cargo B = 360b
Total volume allowed in the truck is 1000 cubic ft
Total volume of 'a' crates of Cargo A and Total volume of 'b' crates of Cargo B = 50a+10b cubic ft (This sum should be less than volume of truck so that it can fit in the truck)
So, the inequality becomes
....... (1)
Total weight allowed (load limit) in the truck is 7200 pounds
Total weight of 'a' crates of Cargo A and Total weight of 'b' crates of Cargo B = 200a+360b cubic ft (This sum should be less than volume of truck so that it can fit in the truck)
So, the inequality becomes
....... (1)
And number of crates of cargo A and B are always a positive number.
So, a > 0 and b > 0.
So, the correct answer is option b.
<em>b. 50a+10b<1000; 200a+360b < 7200; a> 0; b>0</em>
Answer:
y = 2x³ +x² -3x +6
Step-by-step explanation:
The polynomial correlation function of a graphing calculator can work with the table of function values to give you the equation. (See attached)
_____
If you want to solve this by hand, you can write the equations for the unknown coefficients in the polynomial function, then solve those. First of all, notice that you are given the y-intercept, (0, 6), so you know one of the coefficients already. That leaves a system of 3 equations in 3 unknowns that need to be solved.
___
<em>Writing the equations</em>
... ax³ +bx² +cx +6 = y . . . . the generic linear equation in a, b, c that you're writing
For x = -1:
... -a +b -c +6 = 8
For x = 1
... a + b + c + 6 = 6
For x = 2
... 8a +4b +2c +6 = 20
In augmented matrix terms, this set of linear equations looks like ...
___
<em>Solving the equations</em>
There are a number of ways to solve these. Again, a graphing calculator often has solution functions, such as reducing a matrix to row-echelon form, that will solve this in a keystroke or two.
If you add the first two equations, you get ...
... 2b = 2 ⇒ b = 1
Substituting that into the first equation allows you to simplify it to ...
... -a -c = 1
Dividing the third equation by 2 (and substituting for b) makes it ...
... 4a +c = 5
Adding these equations gives ...
... 3a = 6 ⇒ a = 2
Then ...
... c = -a -1 = -2 -1 = -3
And our polynomial function is ...
... y = 2x³ +x² -3x +6
