Rewrite x^5+5x^3-9x+1 ______________ x^2+6 In q(x)+r(x)/b(x)
1 answer:
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Answer:
The system of inequalities " x + 2 y ≤ 5 and 3 x + y ≤ 4 " is represented by the graph ⇒ D
Step-by-step explanation:
To find the answer let us find the equation of each line
Blue line:
∵ The line passes through points (5 , 0) and (0 , 2.5)
- Find the slope of the line
∵ m = Δy/Δx
∴
∴ m = -0.5
- The form of the equation is y = m x + b, where b is the
y-intercept (value y at x = 0)
∵ y = 2.5 at x = 0
∴ b = 2.5
- Write the equation of the line
∴ y = - 0.5 x + 2.5
- Multiply both sides by 2
∴ The equation of the blue line is 2 y = - x + 5
- The shading is under the line and the line is solid, that means
2 y is less than or equal - x + 5
∴ The inequality of the blue line is 2 y ≤ - x + 5
Red line:
∵ The line passes through points (3 , -5) and (0 , 4)
- Find the slope of the line
∴
∴ m = -3
∵ y = 4 at x = 0
∴ b = 4
- Write the equation of the line
∴ y = -3 x + 4
∴ The equation of the red line is y = -3 x + 4
- The shading is below the line and the line is solid, that means
y is less than or equal -3 x + 4
∴ The inequality of the red line is y ≤ -3 x + 4
Let us find which answer is the same with this system of inequalities
∵ 2 y ≤ - x + 5
- Add x to both sides
∴ x + 2 y ≤ 5 ⇒ same as the first inequality of answer D
∵ y ≤ -3 x + 4
- Add 3 x to both sides
∴ 3 x + y ≤ 4 ⇒ same as the second inequality of answer D
The system of inequalities " x + 2 y ≤ 5 and 3 x + y ≤ 4" is represented by the graph
Answer:
<em>The PIN is 1147</em>
Step-by-step explanation:
<u>Prime numbers</u>
These are integer numbers that only divide exactly by themselves and by 1. To find the first possible prime number between 1,000 and 1,500, calculate the square root of 1,000.
Thus, the first prime to consider is 31. Write the consecutive primes from 31:
31 , 37 , 41 , 43
We can see the only two consecutive primes whose product lies in the given interval are 31 and 37. Thus, the PIN is 31*37=1147