1. Lesson 3.2: Solving Systems of Equations by Substitution
2. Problem: Solve the system of equations:
2x + 3y = 11
4x - y = 2
3. Work:
From the second equation, solve for y: y = 4x - 2
Substitute y = 4x - 2 into the first equation: 2x + 3(4x - 2) = 11
Simplify and solve for x: 2x + 12x - 6 = 11
Combine like terms: 14x - 6 = 11
Add 6 to both sides: 14x = 17
Divide by 14: x = 17/14
Substitute x = 17/14 into y = 4x - 2: y = 4(17/14) - 2
Simplify and solve for y: y = 17/7 - 2 = 1/7
Therefore, the solution to the system of equations is x = 17/14 and y = 1/7.
1. Assessment 4: Quadratic Functions and Equations
2. Problem: Solve the quadratic equation by factoring:
x^2 + 5x + 6 = 0
3. Work:
Find two numbers that multiply to 6 and add up to 5: 2 and 3
Rewrite the middle term using these numbers: x^2 + 2x + 3x + 6 = 0
Factor by grouping: x(x + 2) + 3(x + 2) = 0
Factor out the common factor: (x + 2)(x + 3) = 0
Set each factor to zero and solve for x:
x + 2 = 0 -> x = -2
x + 3 = 0 -> x = -3
Therefore, the solutions to the quadratic equation are x = -2 and x = -3.
1. Lesson 5.3: Exponential and Logarithmic Functions
2. Problem: Solve for x in the equation: 2^x = 16
3. Work:
Rewrite 16 as a power of 2: 16 = 2^4
Substitute 2^4 for 16 in the equation: 2^x = 2^4
Since the bases are the same, set the exponents equal to each other: x = 4
Therefore, the solution to the equation 2^x = 16 is x = 4.
Since the course is almost finished. I want you to find 3 problems that have to be worked out showing steps that you learned this semester that were either your favorite kind to solve OR something new to you that you learned this year.
1. Tell me where the problem is found -- give the lesson or assessment name. Each one must be from a different unit.
2. Write down the problem -- it can be copied and pasted, but NOT the work shown.
3. Show the work-- preferably written out, but can be typed. Give the proper steps. Just an answer will not work. Find a different problem if that is the case.
1 answer
1 answer