Dr Walli's Responses in WyzAnt Answers

Hi Rita,

As a Bubbe (grandmother) myself I'd answer it this way:  

"Do you remember last year when it was almost your ___th birthday?  One month or so before the big day we started saying that you were almost __(the next age). We estimated and to do this we rounded the number up to the next year; the coming year. When you take a look at the number 33.6 what so you see first?  You see the 33. And you know that it will be 33 until it turns 34, just like you really stayed ___ until you turned ___.  But somewhere after the middle point; after 33 and 1/2 which we write 33.5 the number changes and starts calling itself (to anyone who will listen to a number) saying "I'm 34....almost." When it matter that we're very, very accurate we say you are __ year, 11 months and 29 days old. And when it matters very, very much we say a number like this one is 33.657890564677. When it matters a little less we say you are __ and 11 months old and, in the same way we say this number is 33.6.  It's short. It's easy. Nut when it hardly matters at we say you're almost ___ and we make it really easy and say that 33.6 is "34."

When there is something new you, or he. have never seen before, begin with what you do know.

Hope that helps.

Dr. Walli

This is a distribution problem.  Think of the 7 as something that will effect both things inside the parentheses.  7 (b + 3) = 7 times b plus 7 times 3    or     7b+21

Distribution can also happen when the parentheses come first; as in (3 - x) 4 = 12- 4x

And remember to pay close attention to the signs; positive or negative.  Multiplying two numbers whose signs that are the same will result in a positive number so:

8(4 + 3) = 8(4) + 8(3) = 32 + 24 = 56 

and

-8 (- 4 ) = -8 (-4) = 32

whereas multiplying 2 numbers that have opposite signs will always result in a negative number so,

3 (-6) = -18   and -3 (6) = -18

If you need help with distribution it is important to get that help very early in school. That makes algebra much easier.

Many standardized tests, including the SAT, ACT, GRE and GMAT do allow the use of a calculator, and I believe the ASVAB should too. I posed this argument to the Department of Defense in October of 2011 and an aide to the Undersecretary of the US Navy wrote back stating that it was under consideration.  As of today, Sept. 9, 2012, the change has not been made and paper and pencil are your only calculator.

I've been preparing students for this exam, with a very high rate of success, for many years and I've developed a "calculator sheet" that my students memorize and write on the scrap paper provided as soon as they sit down. It has all of the formulas you will need and other useful facts as well.  In addition, I have developed a 4 week series of notebooks that each of my students receives so your preparation will be very strong and secure.  In fact, many of the men and women I work with end up deciding to take their SAT/ACT exam at the same time so that they can expand their choice of college options.

I welcome your inquiry about ASVAB prep. and .....thank you, in advance, for defending our country.

Dr. Carranza

Lines can be defined in three ways:

1) the standard form Ax + By = C

2) the slope-intercept form Y = mX + b where m is the slope of the line and b is the Y intercept

3) the point slope formula with uses a point and the slope of the line in the form Y-Y1 = m (X-X1)

The point you state is (-14, -3)  so y= -3 and X = -14

"Perpendicular lines have slopes that are negative reciprocals of each other." What does that mean? It means that a pair of lines that intersect at right angles will have slopes that go in opposite directions and in opposite ways. Where line one has a slope of m, which can also be written m/1,  the perpendicular line has a slope of -1/m.

The line you state is -7X - 4Y = - 4

Let's rewrite this as - 4Y = -4 + -7x  (we added -7x to each side canceling it out on the left)

Not being a fan of negative numbers I would multiply both sides by (-1)

(-1) (-4Y) = -1 (-4 -7X) ----remember that + (-7) = -7

That becomes 4Y = 4 - (-7X)   which equals 4Y = 4+7X or    4Y = 7X + 4

Now divide each side by 4, canceling it out on the left.

Y = (7X + 4) / 4

Now distribute the dividend to get Y =  7/4 X + 4/4 or    Y = 7/4X + 1

That is a form you recognize as the Y intercept formula  Y = mX + b  where m = the slope

The perpaendicular line's slope will then be the negative reciprocol of 7/4   or   - 4/7 (flip it and change the sign)

The point can now be used with this slope to write the equation of the line in the Point -Slope formula required to be compliant with the question.

Y - (-3) = - 4/7 {(X - (-14)}

This becomes Y + 3 = - 4/7 X - 56/7   but on standardized exams this usually is not going to be the final answer. 

Subtract 3 from both sides gives you Y = - 4/7 X -56/7 - 3/1

But you must find a common denominator to subtract fractions  so it is - 4/7 X - 56/7 -21/7

or Y = - 4/7 X - 35/7    or Y = - 4/7 X -5

Whew!  That's a long answer and there are many short cuts that would have made this faster to explain but when you are learning algebra short cuts are a roadblock to becoming a math-master!  Honor yourself and take it step by step. This is your time to become gap-free in math and anytime I can help, give me a call and schedule a session of academic coaching.

Dr. Carranza