Algebra 2 solutions
Introduction :
Algebra: a branch of mathematics in which symbols represent numbers or quantities and express relationships that hold for all members of a set.
Some differences between algebra and other math courses:
Algebra 2 solutions:
Example 1:
Lunch at our favorite fast food stand now cost dollar 6.50. The price has steadily increased 4% per year for many
years. What will lunch cost in 10 years? The initial value is dollar 6.50, the multiplier is 1.04, and the time is 10 years.
Substituting into the formula:
y = 6.50(1.04)10 = 9.62 dollars
What did it cost 10 years ago?
y = 6.50(1.04)-10 = 4.39 dollars
How long before lunch costs 10 dollars?
The initial value is 6.50 dollars, the multiplier is 1.04, and the time is unknown but the final value is 10 dollars.
Substituting into the formula:
10 = 6.50(1.04)x
This time we must solve an equation.
(1.04)x = 10 / 6.50 = 1.538
x = `log(1.538)/log(1.04)` ≈ 11 years
Example 2:
Adding equations one and two eliminates z.
x + y - z = 12
3x + 2y + z = 6
------------------------
4x + 3y =18 (**)
Adding equations two and three also eliminates z.
3x + 2y + z = 6
2x + 5y - z = 10
--------------------------------
5x + 7y = 16 (***)
Now we have two equations in two variables. Multiplying (**) by 5 and (***) by -4 eliminates x.
5(4x + 3y =18) = 20x + 15y = 90
-4(5x + 7y = 16) = -20x - 28y = -64
------------------------------
-13y = 26
y = -2
Using y = -2 into (**) gives x = 6.
Using y = -2 and x = 6 in any of the original equations gives z = -8
The solution is (6, -2, -8).
algebra 2 solutions:
Example 3:
y = x2 + 8x +10
We need to make x2 + 8x into a perfect square list.
Taking half of the x coefficient and squaring it will accomplish the task.
The 16 that was put into the parenthesis must be compensated for by subtracting 16.
Factor and simplify
y = x2 + 8x +10
y = (x2 + 8x + ?) + 10
? = ` (8/2)^2 ` = 16
y = (x2 + 8x + 16) + 10 - 16
y = (x + 4)2 - 6. The locator's is (-4, -6).
Example 4:
Here are two examples.
24/(x+1) = 16/1
Multiply both sides by the common denominator (x + 1)
(x + 1)`( 24/ (x+1))` = (x + 1)`(16/1)`
Then simplify.
24 = 16(x + 1)
24 = 16x + 16
8 = 16x
`8/16` = `(16x)/16`
x = `1/2`
`5/(2x) +1/6` = 8
Multiply each term by the common denominator 6x.
`5/(2x) + 1/6 = 8`
`6x( 5/(2x) + 1/6)` = 6 x (8)
Then simplify.
`6x( 5/(2x) ) + 6x(1/6)` = 48x
15 + x = 48x
15 = 47x
x =`15/47`
I like to share this Common Denominator Calculator with you all through my blog.
Algebra: a branch of mathematics in which symbols represent numbers or quantities and express relationships that hold for all members of a set.
Some differences between algebra and other math courses:
- Algebra is more abstract than previous courses.
- Since mastery of basic concepts is necessary to progress through the course, Algebra might require more practice than previous courses.
- Algebra is the basis for all future courses involving mathematics. (Source: Wikipedia)
Algebra 2 solutions:
Example 1:
Lunch at our favorite fast food stand now cost dollar 6.50. The price has steadily increased 4% per year for many
years. What will lunch cost in 10 years? The initial value is dollar 6.50, the multiplier is 1.04, and the time is 10 years.
Substituting into the formula:
y = 6.50(1.04)10 = 9.62 dollars
What did it cost 10 years ago?
y = 6.50(1.04)-10 = 4.39 dollars
How long before lunch costs 10 dollars?
The initial value is 6.50 dollars, the multiplier is 1.04, and the time is unknown but the final value is 10 dollars.
Substituting into the formula:
10 = 6.50(1.04)x
This time we must solve an equation.
(1.04)x = 10 / 6.50 = 1.538
x = `log(1.538)/log(1.04)` ≈ 11 years
Example 2:
Adding equations one and two eliminates z.
x + y - z = 12
3x + 2y + z = 6
------------------------
4x + 3y =18 (**)
Adding equations two and three also eliminates z.
3x + 2y + z = 6
2x + 5y - z = 10
--------------------------------
5x + 7y = 16 (***)
Now we have two equations in two variables. Multiplying (**) by 5 and (***) by -4 eliminates x.
5(4x + 3y =18) = 20x + 15y = 90
-4(5x + 7y = 16) = -20x - 28y = -64
------------------------------
-13y = 26
y = -2
Using y = -2 into (**) gives x = 6.
Using y = -2 and x = 6 in any of the original equations gives z = -8
The solution is (6, -2, -8).
algebra 2 solutions:
Example 3:
y = x2 + 8x +10
We need to make x2 + 8x into a perfect square list.
Taking half of the x coefficient and squaring it will accomplish the task.
The 16 that was put into the parenthesis must be compensated for by subtracting 16.
Factor and simplify
y = x2 + 8x +10
y = (x2 + 8x + ?) + 10
? = ` (8/2)^2 ` = 16
y = (x2 + 8x + 16) + 10 - 16
y = (x + 4)2 - 6. The locator's is (-4, -6).
Example 4:
Here are two examples.
24/(x+1) = 16/1
Multiply both sides by the common denominator (x + 1)
(x + 1)`( 24/ (x+1))` = (x + 1)`(16/1)`
Then simplify.
24 = 16(x + 1)
24 = 16x + 16
8 = 16x
`8/16` = `(16x)/16`
x = `1/2`
`5/(2x) +1/6` = 8
Multiply each term by the common denominator 6x.
`5/(2x) + 1/6 = 8`
`6x( 5/(2x) + 1/6)` = 6 x (8)
Then simplify.
`6x( 5/(2x) ) + 6x(1/6)` = 48x
15 + x = 48x
15 = 47x
x =`15/47`
I like to share this Common Denominator Calculator with you all through my blog.