The first step is to ignore the inequality symbol first and replace it with '=' sign. Then, find the x- and y-intercepts.
15x + 10y = 1,100
x-intercept:
15x + 0 = 1,100
x = 1,100/15 = 73.33
y-intercept:
0 + 10y = 1,100
y = 1,100/10 = 110
Now, plot points (73.33,0) and (0,110). Since the equality symbol is ≥, which has an equal sign to it, connect the points using a solid line.
Next, let's find a point on the graph. Suppose it is the origin at (0,0). Use this points to the equation.
15x + 10y ≥ 1,100
15(0) + 10(0) ? 1,100
0 ? 1,100
0 < 1,100
It makes the symbol ≥ false. Therefore, it means that the other region bounded by the line is the solution. So, you shade this area. The final graph is shown in the picture attached.
I believe there are 3 prime numbers between 21 and 35, they are 23, 29, and 31
Answer:
4x - 1 and x + 6 are the factors of given Trinomial
Step-by-step explanation:
The given Trinomial is:
![4x^{2}+23x-6](https://tex.z-dn.net/?f=4x%5E%7B2%7D%2B23x-6)
We can factorize this trinomial by mid-term splitting. The mid-term(23x) can be split up in two terms (24x and -x) such that their sum is 23x and their product(-24x²) is equal to the product of other two terms (4x² and -6)
So, the above expression can be written as:
![4x^{2}+23x-6\\\\ =4x^{2}+24x-x-6\\\\\text{Taking out commons, we get}\\\\=4x(x+6)-1(x+6)\\\\ =(4x-1)(x+6)](https://tex.z-dn.net/?f=4x%5E%7B2%7D%2B23x-6%5C%5C%5C%5C%20%3D4x%5E%7B2%7D%2B24x-x-6%5C%5C%5C%5C%5Ctext%7BTaking%20out%20commons%2C%20we%20get%7D%5C%5C%5C%5C%3D4x%28x%2B6%29-1%28x%2B6%29%5C%5C%5C%5C%20%3D%284x-1%29%28x%2B6%29)
Therefore, 4x - 1 and x + 6 are the factors of given Trinomial
Answer:
Step-by-step explanation:
4/9 - x²/25 = 0
- x²/25 = -4/9
x²/25 = 4/9
x² = 4*25/9
x = 2*5/3 = 10/3
x = 10/3