Are you good with Algebra? Please help.?

Question

I have mid term review and I would like to make sure that my answers are correct so that i learn from what is right and not wrong. Also, some of these questions i just don't understand how to find the answer or even what they're asking for. So here are a few of the questions I don't understand, and if you could solve them and explain in great detail how you got the answer i would appreciate it! [= please only answer the one's you know; also; best answer will also go to great detail
-Thank you!

Two adjacent sides of a rhombus are represented by 5x+7 and 6x-1. Find the value of x.

If y varies directly as x and y=24 when x=4, find the value of y when x=9.

Solve for x in terms of a, b, and c:
ax-3b=c

The line whose equation is y=4x+2 has a y-intercept whose coordinates are:
(1) (0,0) (2) (0,2) (3) (4,0) (4) (0,4)

Which equation represents the lin parallel to the y-axis and 4 units to the left of the y-axis?
(1) x=4 (2) x=-4 (3) y=-4 (4) y=4

more added later

thank you all very much so far! you guys have helped me a lot [=
yea i remember y=mx+b now
hhaa we learned it as Y is the Monkey crosXsing w+th Bananas lol
i have a few more that i'm a little confused about that i'lladd in the morning
happy holidays!

Answer 1

Rhombus question: the trick is that all sides of a rhombus have equal length. So of course that means 5x+7 = 6x-1 You just solve for x using normal rules of algebra.

The statement "y varies directly with x" means that
y = kx
for some (as yet unknown) constant k. Note that in this equation, k is the real unknown, not x. If y=24 when x=4, then you just substitute those values for x and y into the equation:
24 = 4k.
That means you can find k: k = 24/4 = 6.
To find y when x=9, you just substitute x and k into the equation and solve for y:
y = 24*9 = 216.

Third question, solving for x in term of the other values means making x the subject of the equation, i.e., using rules of algebra to put the equation in the form x = ...
To do this, you need to work out the *last* operation applied in the expression involving x and apply the inverse (the opposite) of that to both sides of the equation. Keep doing this until you just have x by itself:
ax - 3b = c
ax - 3b + 3b = c + 3b
ax = 3b
ax/a = 3b/a
x = 3b/a

If you're having trouble with the y intercept, then you're in serious need of revision. There is nothing difficult about this question at all. Given an equation of the form
y = mx + b
then the y intercept is b and the slope is m.
So when you see the equation
y = 4x + 2
you have try and match it with the form above:
y = (4)x + (2)
the (4) matches the m and the (2) matches the b.
You work the answer out from there.

This one is a little tricky and takes a bit of understanding. You have to think long and hard and try and comprehend what equations mean and what graphs represent. I can tell you that a graph represents the set of points that satisfy an equation, but you have to come to terms in your own mind as to what that means, and that means spending time in meditation over your maths.

The answer is x=-4 because the set of points (x,y) that satisfy x=-4 lie on a line parallel with the y axis and lie 4 units to the left (where x = -4).

Answer 2

1)
A rhombus by definition is a 4 sided shape with all congruent sides ie. a = b= c= d

Thus, 5x + 7 = 6x - 1 --> 6x - 5x = 7 + 1

Answer: x = 8

2)
If y varies directly with x, then there must be some number "k" such that:

y = k*x

Since you know x = 4 gives y = 24.... sub into y = k*x
24 = k (4)
k = 24/4 = 6

Thus the equation relating y and x is .... y = 6x

now all you have to do is substitute x = 9 to find y.....

y = 6(9) = 54

Answer: y = 54

3)
Rearrange the equation to isolate per variable....
ax = (c + 3b) (eq. 1)
3b = (c - ax) (eq. 2)
c = ax - 3b (eq. 3)

essentially x = (c + 3b)/a

then use system of equation and substitution if you want to solve for a certain variable....

4) y = 4x + 2
y intercept means that x = 0
thus y = 4(0) + 2

thus y = 2 and the coordinates are (x,y) ---> (0,2)

5) parallel means the same slope.... and since the y axis has a slope 0 from its coordinates of y = 0 thus a parallel line must also mean y = 0 and thus essentially meaning there is only an x value, y value does not count on an x axis..... ....and the left side of a cartesian plane means negative....
thus moving it 4 spaces to the left would mean a value of x = -4 and because y = 0 due to the line being parallel to the y axis....

Answer: x = - 4

Answer 3

1. Rhombus means that all sides are equal. So we have
5x + 7 = 6x + 1
6 = x

2. y = ax, but we don't know a, but a is constant. So figure a when x = 4 and y = 24
a = x/y
a = 4/24, or a = 1/6 = .166666666
y = ax
y = 1/6 * 9, or y = 1.5

3. ax - 3b = c
ax = c + 3b
x = (c + 3b)/a

4. y = mx + b is standard, learn it. m =slope, and b is the y intercept. Therefore (2) where the point is (0,2) is correct.

5. Parallel to the y axis means x never changes. Therefore, (2) x = - 4 is correct.

Answer 4

Hints: A rhombus has all sides equal.

If y varies directly, then y = k x, where k is a constant. You can find k from the (4,24) data point and then solve for y when x=9

You should know about gathering terms on different sides of the equal sign.

The y-intercept is computed by setting x=0 in the equation.

If a line is parallel to the y-axis, it means that the line has the general equation x= k, where k is found based on the info in the question.

Answer 5

in a rhombus, the sides are equal

so.... 5x+7 = 6x-1 solve for x
-5x -5x
7 = x-1
+1 +1
8 = x






and the last one, x=-4 (if its an equation that is simply x = "a number" then its parallel to the y-axis....and 4 units left of the y is -4

Answer 6

(x - y^5)^3 = x^3 - 3x^2y^5 + 3xy^10 - y^15