I'm having trouble with a couple math problems.?

Question

1) Find the graphs of the two lines 4x = 3y + 23 and 4y + 3x = -19
The answer is that they are supposed to be perpendicular lines, but when I work it out, the slopes aren't negative reciprocals, they're only reciprocals. What am I doing wrong?

2) Which of the following points are not solutions of 2y - 5x > 6?
(2.6, 5) is supposed to be one of the solutions, but when I work it out, it seems that it doesn't fit. I keep getting -3 > 6. What am I doing wrong?

3) Find f(-4) when f(x) = -x^2 - 2x.
We haven't learned how to do these and I can't find where in my book it says how to do it. Could you tell me how without telling me the answer?

For #2, there is another option that is supposed to be the answer, but there is also this option, which seems like it could also be the answer.

Answer 1

#1: I don't know what you're doing wrong - it seems that you lost a sign somewhere. The slopes are negative reciprocals -- for the first:

4x=3y+23
4x-23=3y
y=4x/3-23/3
M=4/3

4y+3x=-19
4y=-3x-19
y=-3x/4-19/4
M=-3/4

-3/4 is the negative reciprocal of 4/3

#2: In this case, you're not doing anything wrong. You do indeed get -3 when you substitute. Note that the problem asks for the points which are NOT solutions to 2y-5x>6 -- the point (2.6, 5) is listed among the answers because it does NOT satisfy the inequality.

#3: if f(x) = "something", then f(-4) is whatever you get when you replace every instance of x in "something" with -4.

Answer 2

1. this one kind of tricked you because you have to put it in y=mx+b form and it looks like it already is but reallly the y is where the x should be so you have to subtract that from both sides so it should end up being 4x-3y=23. then you take the 4x and put it back on the other side so then its -3y= -4x+23. after that you divide by the negative 3. that makes the negative 4 and negative 3 cancel out. so then you get y= 4/3x+23.

then the second part you have 4y + 3x = -19. so you take the 3x and bring it to the other side. 4y=-3x-19. then you divide by the four leaving y= -3/4 - 19.
then they're opp. recipricols.

2. i seem to have gotten the same answer as you.

3. f(-4) simply means find y when x is 4. so you just plug in 4 for the x's and you'll get y equals something.

i hope that helped you.
and i promise i'm pretty smart
i'm taking two math classes right now
and i have
100.2% and
104% in them :-P

good luck with them.
and let me know if you understand.

Answer 3

prob #1:

4x = 3y + 23
3y = 4x -23
y = (4/3)x -23 .... here the slope = 4/3

other
4y + 3x = -19
4y = -3x - 19
y = (-3/4)x - 19 ... here the slope = -3/4

the two slopes:
(4/3) * (-3/4) = -1

sounds like you made an algebraic 'bookkeeping error'

/****************************/
2y - 5x > 6 .... when (x,y) = (2.6, 5)

2(5) - 5(2.6) = 10 - 13 = -3

I agree that (2.6, 5) is NOT in the solution set.

lessee what *IS*
2y > 6 + 5x
y > 3 + 5x/2

sooo ..... if x>0 then y > 3.

you start out with x = 2.6 but
y>3 + 5x/2 = 3 + 13/2 = 19/2

"y" would HAVE to be > 9.5 = 19/2

/************************/

C
Find f(-4) when f(x) = -x^2 - 2x.

just "plug in" the value x = -4

f(-4) = -( (-4)^2) - 2(-4) = -(16) - (-8) = -16 + 8 = ... here I'm not going to tell you the answer ...


I *WOULD* however, suggest that you do more work than the homework assigned to you. The indications which I read tell me that there is a gap in your understading of this material. It's not terribly difficult, and the only way you will ever learn to do it is to spend time ... as much time as it takes .. EVERY day ... until the answers and the methods become crystal clear.


you can do this ... you will have to sacrifice your free time in order to gain mastery over the algebra.

It will pay off down the road ... maybe not this week or this month, but it WILL pay off


good luck

Answer 4

4x = 3y + 23 and 4y + 3x = -19
1st has slope of 4/3: 2nd has slope 0f -3/4 They are indeed negative reciprocals. If we rewrite the equations we get:
3y= 4x- 23 --> y = 4x/3 -23 <-- 1st EQ
4y+3x-19 --> 4y= -3x +19 --> y = -3x/4 +19.

2y-5x > 6
2y > 5x+6
y>5x/2 + 3
So for (2.6,5) we get 5 >5*2.6/3 +3 = 7.333 which is false.
(2.6 , 5) is definitely not a solution.

Find f(-4) when f(x) = -x^2 - 2x.
Thes are easy. You just plug in -4 for x and get:
f(-4) = -(-4)^2 - 2(-2) = -16 +4 = -12
f(1) = -(-1)^2 -2(-1) = -1 +2 = 1

Answer 5

For #1 - you need to look at your book which has the graphs printed on the page. Write both equations in the slope-intercept form which is, y = mx + b > Let's solve the 1st equation.

a. First: subtract "3y" from both sides...

4x - 3y = 3y - 3y + 23
4x - 3y = 23

*Subtract "4x" from both sides

4x - 4x - 3y = - 4x + 23
- 3y = - 4x + 23

Sec: isolate "y" > divide everything by "- 3"

- 3y/-3 = - 4x/-3 + 23/-3
y = 4x/3 - 23/3

Let's solve the 2nd equation.

b. 4y + 3x = -19

First: subtract "3x" from both sides...

4y + 3x - 3x = - 3x - 19
4y = - 3x - 19

Sec: divide everything by "4"

4y/4 = - 3x/4 - 19/4
y = -3x/4 - 19/4

3. Find f(- 4) when f(x) = -x^2 - 2x. *You need the answer in order to understand the steps.

First: the problem gives you the value/number for the x-variable.
Sec: replace "- 4" with the x-variable in the expression...

- (- 4)^2 - 2(- 4)
- (- 4)(- 4) + 8
- (16) + 8

Third: eliminate the parenthesis > distribute the negative sign to 16...

- 16 + 8 = - 8

Answer 6

1) They are indeed perpendicular lines. Look the slopes are opposite reciprocals
4x = 3y + 23 4y + 3x = -19
-13+4x=3y 4y=-3x-19
-13/3 +4x/3=y y=-3x/4 -19/4

2) 2(2.6) - 5(5) > 6
-19>6
Are you sure that (2.6,5) is one of the answers. I don't think so.

3) You replace -4 whereever you have X and do the corresponding operations.

Answer 7

1) well to find the slopes we'll put them into standard form and get the slopes:
4x = 3y + 23
3y = 4x - 23
y = (4/3)x - 23/3

4y + 3x = -19
4y = -3x - 19
y = (-3/4)x - (19/4)

so, (4/3) and (-3/4) are negative reciprocals, not sure, your error must have been in the rearranging

2) 2(5) - 5(2.6) = -3, not >6, therefore that must be the option that is not the solution.

3) just substitute x = -4 into the equation f(x)=-x^2-2x

Answer 8

I havent touched algebra in a long time but here are a few of my calculus tricks that might help:
1. The easiest way to chart variables is to reduce elements by their power and disregard small numbers, for example 3 + x^2 will be 2x.
So 4y(^1) + 3x(^1) (that is x to the power of 1) will be y + x = 0 and here is your simplified graph, now plug in a few numbers and see the results. (1, -1) (-1, 1) one graph look like straight diagonal line \ the other should be x - y = 0 (1, 1) (-1, -1) diagonal line to the other direction /

2. not enough info to help

3. f(-4) = -(-4)^2 - 2(-4)
= -(-4 X -4) - 2 X (-4)
= -(16) - (-8)
= -16 + 8
= -8

I hope that help

Answer 9

The slope of the first line is 4/3 and the slope ofthe second -3/4
so one slope is reciproc.and changed sign from the other.They are perp.
You should put the equ. of each line in the form y=m*x+n where m is the slope
2) 2*5 -5*2.6 = -3 There is nothing wrong with your doing
3) you should put the number instead x so

f(-4)=-(-4)^2 -2(-4) =-16 +8 -8

Answer 10

(a million) examine the area on your e book approximately circles and then attempt this project your self. that's fairly consumer-friendly. (2) replace y=4x into the 1st equation and you have got a quadratic equation in x. remedy it and you have got a huge decision for x. Then y=4x says y is 4 situations that huge variety. (3) Draw it on the x-y airplane. there are various angles that have an analogous terminal area as 80 stages. as an occasion, 80 + 360 = 440 stages. (4) csc is reciprocal of sin so turn the fraction the different way up (5) parabola. ellipse, circle, hyperbola equations all have the two x^2 and y^2