(877) 999-2681  | BECOME A TUTOR | BECOME A STUDENT  |  Sign In
Search 73,793 tutors SEARCH
WyzAnt Tutoring Tutor Tutor United States

## I can provide your "A-HA" moment

### Apopka, FL (32712)

 Travel Radius 20 miles Hourly Fee \$75.00 Save up to 15%
 Background Check Passed 1/10/2010 Your first hour with any tutor is always 100% refundable!

# Michael's Responses in WyzAnt Answers

#### i need to see how to work a couple of these slope intercepts and parallel and perpendicular problems

write the equation for the slope intercept

a is (14,-2) and b is (-3,15)

+ more- less
Asked by Amber from Middleport, OH
20

Hi Amber,

There are two main forms that you can write a line in:

Point-Slope: y-y1 = m(x-x1)
We use point-slope when we know the slope m and a point (x1, y1)

Slope-Intercept: y = mx + b
We use slope-intercept when we know the slope m and the y-intercept b

There is no fundamental difference between the lines produced by these two equations - in other words, we can convert between Slope-Intercept and Point-Slope form with a little bit of algebra.

Sometimes, however, the problems don't give us all the bits we need for either form directly, but we have to figure them out.  That is the situation in this case, where we are given two points, but not the slope.

So the first step is to calculate the slope:

`m = (y2 - y1) / (x2 - x1)   = (15 - -2) / (-3 - 14)   = 17 / -17   = -1`

Now, since we know the slope, and we ALSO know two different points, we can plug one of the points and the slope into the point-slope formula:

`y-y1 =  m(x-x1)  Starting equationy-15 = -1(x- -3) Plug in m=-1 and (x1,y1) = (-3,15)y-15 = -1(x+3)   Minus a negative -> add a positive`

But since the problem wants the answer in slope-intercept form, we must convert to this form using our basic algebra rules:

`y-15    = -1(x + 3)    Starting equationy-15    = -x - 3       Distribute -1 across (x + 3)y-15+15 = -x - 3 + 15  Add 15 to both sidesy       = -x + 12      Combine terms, DONE`

So the line, in slope-intercept form, is y = -x + 12.

Now you might ask why I plugged in (-3, 15) instead of (14, -2).  Well it doesn't actually matter - we could have plugged in either point and we would have gotten the same answer in the end.

#### In regards to the big bang heory, where did the matter come from to have the big bang?

I believe in the creationist theory, my question is posed toward darwinist...

+ more- less
Asked by Malik from Duarte, CA
20

The Big Bang theory posits that matter (and anti-matter) were both created as part of the Big Bang.  In other words, matter didn't cause the big bang, matter was produced BY the big bang.  This is a result of the equivalence of matter and energy (Albert Einstein's E=mc2).

However, you also seem to be asking about Darwinism, which has absolutely nothing to do with the Big Bang theory.  Darwinism is an explanation for life on planet Earth, and Big Bang is an explanation for the existence of the universe as a whole - two very fundamentally different questions.

#### How do you figure out the difference of two squares if the numbers aren't square?

3m2-12 = ?

+ more- less
Asked by Katrina from New York, NY
10

Daniel posted a good answer....   to complement his answer, I'd also point out that there is a way to factor this even without factoring out the three first.  The key is to realize that you don't have to restrain yourself to whole numbers, but you can use square roots.  Thus, the following is also an acceptable answer:

`  (√3 m + √12)(√3 m - √12) = (√3 m + 2√3)(√3 m - 2√3)`

That is "square root of 3, times m, plus two times square root of 3" and "square root of 3, times m, minus two times square root of 3".  Both would yield the same answers for m when put into an equation.

This is an important technique when the problem doesn't simplify to a "perfect square" as yours does after factoring out the three.  For example, a simpler example is:

`m2 - 2 = (m + √2)(m - √2)`

(To be clear, this is NOT the answer to your question - it is a different example.)

#### tan^2x-sin^2x=tan^2xsin^2x

The directions say to prove the identity. I understand how these two functions work, but I don't understand how to go through the process of getting from the left side to the right side.

+ more- less
Asked by Lauren from Naples, FL
10

When trying to prove trig identities, it is often helpful to convert TAN functions into SIN/COS functions:

tan2x - sin2x = (tan2x)(sin2x)

Proof Step 2: Replace tan with sin/cos
(sin2x/cos2x) - sin2x = (sin2x/cos2x)(sin2x)

Proof Step 3: Obtain a common denominator on left, simplify right
(sin2x - sin2x cos2x) / cos2x = sin4x / cos2x

Proof Step 4: Cancel cos2x from both denominators
sin2x - sin2x cos2x = sin4x

Proof Step 5: Factor out sin2x from left
(sin2x)(1 - cos2x) = sin4x

Proof Step 6: Use trig identity 1-cos2x = sin2x
(sin2x)(sin2x) = sin4x

Proof Step 7: Simplify, DONE.
sin4x = sin4x

#### the product of four consecutive even integers es 1680. what are the four numbers?

four consecutive even entegers

+ more- less
Asked by Juan from Boston, MA
10

Juan,

I believe that you have copied your problem incorrectly.  There are no 4 consecutive EVEN integers that multiply out to 1680.

You can see this for yourself - lets pick the first 4 even integers: 2, 4, 6, 8.  The product of these even integers is 384 - too small.  The next potential set is 4, 6, 8, 10, and the product of these four is 1920, which is too big.

Therefore, you must have copied or typed the problem wrong.

Assuming that you didn't mean to say EVEN integers, there is a solution.  If we assign the first number in the sequence to this variable 'n', then the four numbers would be:

n, n+1, n+2, n+3

The product of these is:

n(n+1)(n+2)(n+3) = 1680

Which we can FOIL.  I've done this in three steps - first FOILing the first two terms 'n' and 'n+1' and FOILing 'n+2' and 'n+3', then FOILing the two results, and then combining terms and collecting them on the left side of the equation:

n(n+1)(n+2)(n+3) = 1680
(n2 + n)(n2 + 5n + 6) = 1680
(n4 + 5n3 + 6n2 + n3 + 5n2 + 6n) = 1680
n4 + 6n3 + 11n2 + 6n - 1680 = 0

Now we have to solve this equation for n.  There are several ways to do this, none of which are easily described in this forum.  I used a program called "Octave" to find the solutions; it is similar to Matlab.  However, there are two REAL answers: n = -8 and n = 5.

So, ASSUMING that you are NOT looking for EVEN integers, but any integers, the answer is EITHER: (5, 6, 7, 8) OR (-8, -7, -6, -5).  Multiplying either of these sets of numbers results in 1680.  Notice that both sets of numbers are the same, except one is positive and one is negative.  But since it is an even number of integers, the answers to the multiplication are both positive.

## Other Apopka, FL Tutors

### Michael's Hourly Rate

Hourly Fee: \$75.00

Save up to 15% with a discount package

Cancellation: 4 hours notice required

#### How do I receive a discount?

Save between 5 and 15% on tutoring by purchasing credit with one of our prepaid discount packages. You can buy one of our standard 5, 10 or 15% packages or customize your own package based on how much tutoring you need. The credit you purchase can be used towards any tutor at any time and does not expire. If you do not use the entire package, we will simply deduct what you did spend on tutoring from your original purchase price and give you a refund. Discount packages start as low as \$190.

Credit For Only You Save
\$200 - \$399 \$190 - \$379 5%
\$400 - \$999 \$360 - \$899 10%
\$1,000 + \$850 + 15%

Your first hour with any tutor is protected by our Good Fit Guarantee: You don't pay for tutoring unless you find a good fit!

## Background Check Status for Michael B.

Michael B. passed a background check on 1/10/2010. You may run an updated background check on Michael once you send an email.