Answer:
1 false
2 true
3 true
4 false
5 true
Step-by-step explanation:
f(a) = (2a - 7 + a^2) and g(a) = (5 – a).
1 false f(a) is a second degree polynomial and g(a) is a first degree polynomial
When added together, they will be a second degree polynomial
2. true When we add and subtract polynomials, we still get a polynomial, so it is closed under addition and subtraction
3. true f(a) + g(a) = (2a - 7 + a^2) + (5 – a)
Combining like terms = a^2 +a -2
4. false f(a) - g(a) = (2a - 7 + a^2) - (5 – a)
Distributing the minus sign (2a - 7 + a^2) - 5 + a
Combining like terms a^2 +3a -12
5. true f(a)* g(a) = (2a - 7 + a^2) (5 – a).
Distribute
(2a - 7 + a^2) (5) – (2a - 7 + a^2) (a)
10a -35a +5a^2 -2a^2 -7a +a^3
Combining like term
-a^3 + 3 a^2 + 17 a - 35
6x^2 -7x + 2 with a factor of 2x -1
If you divide the trinomial by the factor you will get the other factor.
See attachment
The saying "A picture is worth a thousand words" comes to mind here. You can list all of the possible points in a solution region, or you can list a few points to give the general pattern. Though this method requires a bit more work than simply graphing and showing the solution shaded region. A visual is often more efficient at conveying a message especially to those who aren't proficient with algebra. I'm sure there are other reasons why graphs are the better choice, but that's all I could think of really.
Answer: {x,y}={-1,2}
step-by-step explanation:
// Solve equation [2] for the variable x
[2] 2x = 5y - 12
[2] x = 5y/2 - 6
// Plug this in for variable x in equation [1]
[1] 2•(5y/2-6) + 3y = 4
[1] 8y = 16
// Solve equation [1] for the variable y
[1] 8y = 16
[1] y = 2
// By now we know this much :
x = 5y/2-6
y = 2
// Use the y value to solve for x
x = (5/2)(2)-6 = -1
Solution :
{x,y} = {-1,2}
Two is equivalent to twenty and 84
