Calculus Path

Statistics Path

MTH070
Elementary Algebra
Pre-PreCalculus, part 1

vs.

MTH062
Quantitative Literacy 1
Math for "Real" Life

Which class is right for you?
Is calculus in your future or NOT?

Systems Equations

Solve for `x` and `y`:
`-x+3y=-4`
`-3x-4y=27`

Choose a variable to eliminate. Eliminate `x` first. Multiply equation 1 by `-3`:
`-3*(-x+3y=-4)`
`-3x-4y=27`

Distribute:
`3x-9y=12`
`-3x-4y=27`

Add the equations together:
`-13y=39`

Solve for `y`:
`y=39/-13=-3`

Substitute into one of the equations and solve for `x`:
`-x+3(-3)=-4`
`-x-9=-4`
`-x-9+9=-4+9`
`-x=5`
`x=-5`

We think the solution is `(-5,-3)`.

CHECK:
Plug both values into the other equation to check:
`-3(-5)-4(-3)=15+12=27`
It checks!!!

§ 1-2 Eighteen Trillion and Counting

Problem situation: How Big Is a Billion or a Trillion?

zero to 1 million

So, where on the number line is 1 billion? Make a mark for 1 billion on the number line.

In news about politics and government, BIG numbers are talked about often. Below is a chart showing the national deficit over time.

US debt 1900 to 2020

On a scale from 0 to 1 trillion, 1 billion is very close to zero, since 1 trillion is 1000 billion!

zero to 1 billion to 1 million

Imagine a stack of 1,000 one‚Äźdollar bills, which is about 4.3 inches tall.
Complete the table below:

$ Amount Height (inches) Height (feet) Height (miles)
$1,000 4.3
$1 million 4,300 358
$1 billion 4,300,000 358,333 68
$1 trillion 4,300,000,000 358,333,333 68,866

This means that a stack of $1 bills, 3.5 trillion high, would reach the moon.

Polynomial Division

`(x^3-3x^2+4x-5)/(x-2)`

Use long division to find the quotient and remainder:
`x-2 \ bar(")"\ x^3-3x^2+4x-5)`

What do you multiply by `x` to get `x^3`?
Guess: `x^2` and multiply:

`x^2`
`x-2` `)x^3` `-3x^2` `+4x` `-5`
`x^3` `-2x^2`

Now subtract:

`x^2`
`x-2` `)` `x^3` `-3x^2` `+4x` `-5`
`-(x^3` `-2x^2)`
`-1x^2` `+4x`

What would you multiply by `x` to get `-1x^2`?

Guess: `-1x` and multiply.

`x^2` `-1x`
`x-2` `)` `x^3` `-3x^2` `+4x` `-5`
`-(x^3` `-2x^2)`
`-1x^2` `+4x`
`-1x^2` `+2x`

Now subtract:

`x^2` `-1x`
`x-2` `)` `x^3` `-3x^2` `+4x` `-5`
`-(x^3` `-2x^2)`
`-1x^2` `+4x`
`-(` `-1x^2` `+2x)`
`2x` `-5`

What would you multiply by `x` to get `2x`?

Guess: `2` and multiply.

`x^2` `-1x` `+2`
`x-2` `)` `x^3` `-3x^2` `+4x` `-5`
`-(x^3` `-2x^2)`
`-1x^2` `+4x`
`-(` `-1x^2` `+2x)`
`2x` `-5`
`2x` `-4`

Now subtract.

`x^2` `-1x` `+2`
`x-2` `)` `x^3` `-3x^2` `+4x` `-5`
`-(x^3` `-2x^2)`
`-1x^2` `+4x`
`-(` `-1x^2` `+2x)`
`2x` `-5`
`-(` `2x` `-4)`
`-1`

Solution: `(x^3-3x^2+4x-5)/(x-2)``=``x^2-x+2+(-1)/(x-2)`

CHECK:
`(x-2)(x^2-x+2)-1=``x^3-3x^2+4x-5` check.

§ 2-1 A Taxing Set of Problems

Problem Situation: Calculate income tax for tax bracket

If Taxable Income Is: The Tax Is:
Not over $18,150 10% of the taxable income
Over $18,150 but not over $73,800 $1,815 plus 15% of the excess over $18,150
Over $73,800 but not over 148,850 $10,162.50 plus 25% of the excess over $73,800

EZ 2014

Suppose a couple, married with no kids, filing jointly, earned $93,000 with no other interest or income.

Based on the standard standard married filing jointly deduction, their taxable income is `$93,000-$20,300=$72,700`

According to the tax table above their income tax is
`$1,815+0.15*($72,700-$18,150)=``$9,997.50`

Compare this to line 15 of the table below: tac table 2014

Disclaimer:

You should check with your advisor before taking a math class leading to calculus. Algebra classes are known to cause stress, anger, depression, and occasionally rashes, as well as lead to calculus. Please consult a physician if negative symptoms persist.

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