can u please explain this algebra probs?

Question

We'll be having our finals this tuesday and I need some help with the ff probs:

1.) A rectangular building whose depth is twice its frontage is divided into two parts by partition that is 30 ft from, and parallel to, the front wall. If the rear portion of the building contains 3500 ft^2, find the dimensions of the building.

2.) A man purchased some shares of stock for S1560. Later, when the price had gone up S24 per share, he sold all but 10 of them for S1520. How many shares had he bought?

3.) Draw a sketch of a line passing through the point P(-1,6) and having slope m = -2. Also sketch a line through the same point having slope m= -1/2

4.) Draw a sketch of a line passing through the equation 5x+2y-10=0 by finding the axis and y axis intercept?
**is the answer here (2,0) and (0,5)


****and oh, how do you do the find the equation that lies parallel to the given equation and the perpendicular one too...


thanks so much!!!
really need to Ace this exam..


hahaah

in college... but my math is basic math because i failed the diagnostic

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Answer 1

I'll do the first 3 for you as examples, except for drawing the sketches (once you have an equation for a line, you can use it to plot/sketch any number of arbitrary points that lie on it)

1. width of building (or its "frontage") in feet = w
total depth/length of building in feet = l = 2w

length of front partition = 30 ft

length of rear partition = 2w - 30

Area of rear partition = width of r.p * length of r.p. = 3500 ft^2

w * (2w - 30) = 3500

2w^2 - 30w - 3500 = 0

w^2 - 15w - 1750 = 0

(w - 50)(w + 35) = 0

w = 50 ft.....(a width of -35 ft doesn't make sense)

l = 2w = 100 ft


2. Let s = # of shares originally purchased

Let p = the original share price

2 variables......2 equations needed for a solution

(a) original purchase: s * p = 1560

(b) sale of shares: (s - 10) * 24 = 1520

NOTE: I couldn't get a sensible solution if the share price increases by $24, so I assumed you meant to say that the share price increases TO $24.....

From Equation (b): s = (1520/24) + 10

~ 73.333 shares originally bought

From Equation (a): p = 15460/s

~ $21.273/share


3. The equation of a line has this form: y = mx + b

m = slope of the line

b = a constant* (*when x = 0, y = b = y-intercept)

If m = -2 and the line passes through (-1, 6), then....

6 = (-2)*(-1) + b -------------> b = 6 - 2 = 4

y = -2x + 4

Aside from point (-1,6), you could plot (0, 4), (1,2), etc., etc.


If a line passes through (-1, 6) again, but m = -1/2 instead:

6 = (-1/2)*(-1) + b -------------> b = 6 - 0.5 = 5.5

y = -0.5x + 5.5

Aside from (-1,6), you could plot (0, 5.5), (1,5), etc., etc.


Hope this helps you a little......good luck on your final exam

Answer 2

8x-5=4x+4-2x 8x-4x+2x=4+5(collecting all the like terms) 4x+2x=9 6x=9 x=9/6 x=3/2 answer is x=3/2 and not -1/6

Answer 3

Surely your textbook would show you how it's done. If not, you need to contact your teacher pronto and do some heavy cramming on Monday.

Answer 4

wat grade are you?? ill answer your question... im just typing it...pls reply..