Answer:
a) one solution
b) no solution
Step-by-step explanation:
Systems of equations can be described as having one solution, no solution or infinite solutions:
One solution: 'x' and 'y' are equal to only one value
No solution: 'x' and 'y' can not be solved with the given equations
Infinite solutions: values for 'x' and 'y' include all real numbers
In order to evaluate the systems, putting them in the same format is your first step:
a) - y = -5x - 6 or y - 5x = 6
y - 5x = -6
Since both equations have the same expression 'y - 5x', but there are equal to opposite values, this system would have no solution, as this would not be possible to calculate.
b) y + 3x = -1
y = 3x -1 or y - 3x = -1
Solving for 'y' by adding the equations and eliminating 'x', gives us:
2y = -2 or y = -1
Using y = -1 to plug back into an equation and solve for 'x': -1 + 3x = -1 or x = 0. Since 'x' and 'y' can be solved for a value, the system has just one solution.
Answer:
f(x) = 3x² - 15x + 12
Step-by-step explanation:
Given f(x) has roots x = a and x = b, then
(x - a) and (x - b) are the factors
f(x) is then the product of the factors
f(x) = a(x - a)(x - b) ← where a is a multiplier
Given roots are x = 4 and x = 1, then
(x - 4) and (x - 1) are the factors
With a = 3, then
f(x) = 3(x - 4)(x - 1) ← expand factors using FOIL
= 3(x² - 5x + 4) ← distribute
= 3x² - 15x + 12
So in total, there are 7 marbles, (3 black + 4 red = 7 total marbles) and we want to find out how much black marbles are able to come out. So it would be 3/7. :)
x
Answer:
b^20/a^12
Step-by-step explanation:
b to the power of 20 over a to the power of 12
Answer:
first one is not. parallel second one is not and the third one is
