what is the solution sets of the following
a) 2x^-7x-5
b)5y^-16y+3
c)10x^+5y-6
d)10x^-13x+4
e)12y^-11y-5
f)10c^-21c+9
g)3m^+5m-2
you are missing the exponents
if (a) should be 2x^2 - 7x - 5
a) 2x^2 - 7x - 5
does not factor, solve by using the quadratic formula or completing the square
if you are stuck, post your work and someone will help
tutors do not do your homework
Complete the square to solve -x^2-7x+6=-2x^2
Are these equations equal to zero?
If so, then I noticed that each one factors quite easily.
I will do the last one
g)
3m^2 + 5m - 2 =0
(3m - 1)(m + 2) = 0
3m-1 = 0 or m+2 = 0
m = 1/3 or m = -2
do the others the same way.
You can check your answers by subbing them back in.
e.g. if m = -2
LS = 3(4) + 5(-2) - 2
= 12 - 10 - 2
= 0
= RS
so my answer of m=-2 is correct
To find the solution sets of the given expressions, we need to determine the values of the variables (x, y, c, m) that make the expressions equal to zero.
a) 2x^2 - 7x - 5 = 0:
To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula. Let's use factoring.
Factor the equation: (2x + 1)(x - 5) = 0
Setting each factor equal to zero: 2x + 1 = 0 or x - 5 = 0
Solving each equation:
For 2x + 1 = 0, subtract 1 from both sides and divide by 2: x = -1/2.
For x - 5 = 0, add 5 to both sides: x = 5.
The solution set is {-1/2, 5}.
b) 5y^2 - 16y + 3 = 0:
We will use factoring for this quadratic equation.
Factor the equation: (5y - 1)(y - 3) = 0
Setting each factor equal to zero: 5y - 1 = 0 or y - 3 = 0
Solving each equation:
For 5y - 1 = 0, add 1 to both sides and divide by 5: y = 1/5.
For y - 3 = 0, add 3 to both sides: y = 3.
The solution set is {1/5, 3}.
c) 10x^2 + 5y - 6 = 0:
This equation contains two variables, x and y, so we cannot determine a single solution set without additional information.
d) 10x^2 - 13x + 4 = 0:
We will use factoring for this quadratic equation.
Factor the equation: (2x - 1)(5x - 4) = 0
Setting each factor equal to zero: 2x - 1 = 0 or 5x - 4 = 0
Solving each equation:
For 2x - 1 = 0, add 1 to both sides and divide by 2: x = 1/2.
For 5x - 4 = 0, add 4 to both sides and divide by 5: x = 4/5.
The solution set is {1/2, 4/5}.
e) 12y^2 - 11y - 5 = 0:
We will use factoring for this quadratic equation.
Factor the equation: (4y + 1)(3y - 5) = 0
Setting each factor equal to zero: 4y + 1 = 0 or 3y - 5 = 0
Solving each equation:
For 4y + 1 = 0, subtract 1 from both sides and divide by 4: y = -1/4.
For 3y - 5 = 0, add 5 to both sides and divide by 3: y = 5/3.
The solution set is {-1/4, 5/3}.
f) 10c^2 - 21c + 9 = 0:
We will use factoring for this quadratic equation.
Factor the equation: (2c - 1)(5c - 9) = 0
Setting each factor equal to zero: 2c - 1 = 0 or 5c - 9 = 0
Solving each equation:
For 2c - 1 = 0, add 1 to both sides and divide by 2: c = 1/2.
For 5c - 9 = 0, add 9 to both sides and divide by 5: c = 9/5.
The solution set is {1/2, 9/5}.
g) 3m^2 + 5m - 2 = 0:
We will use factoring for this quadratic equation.
Factor the equation: (3m - 1)(m + 2) = 0
Setting each factor equal to zero: 3m - 1 = 0 or m + 2 = 0
Solving each equation:
For 3m - 1 = 0, add 1 to both sides and divide by 3: m = 1/3.
For m + 2 = 0, subtract 2 from both sides: m = -2.
The solution set is {1/3, -2}.