Can I have some math help please?

Question

My teacher ALREADY assigned 30 problems for homework! I got most of them but there's a few that I'm stuck on. Some help would and maybe a walkthrough be nice.

Solve for x.

y= - 2/3 x +8

* the - and the x are in the middle of the fraction.

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Find the slope.

2x-3y=18

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Graph y = 40x +160, x Greater than or equal to 0.

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Cost Analysis. A small company manufactures picnic tables. The weekly fixed cost is $1,200 and the variable cost is $45 per table. Find the daily total cost of producing x picnic tables. How many picnic tables can be produced for a total weekly cost of $4,800?

Any help on any of these problems would be greatly appreciated!!!

Answer 1

Ok, first one - you're solving for x so you're trying to get it to the other side of the equation on it's own

y = - 2/3 x + 8

Add 2/3 x to both sides

y + 2/3 x = -2/3x + 8 + 2/3x

x cancels on the right hand side

y + 2/3 x = 8

Subtract y from both sides,

y + 2/3 x - y = 8 - y

2/3 x = 8 - y

Now you want to get rid of the 2/3 in front of x so we'll multiply by 3 to start and then divide by 2

3 * (2/3 x) = 3 * (8 - y)

2 x = 24 - 3y

2 x / 2 = (24 - 3y) / 2

x = 12 - 3/2 y

For the second question, the slope is whatever is in front of x when y is alone on the left hand side, so first move the x to the right hand side by subtracting 2x from each side

2x - 3y - 2x = 18 - 2x

-3y = 18 - 2x

Divide by -3 to get y on it's own

-3y / -3 = (18 - 2x) -3

y = 18/(-3) - 2x/(-3)

y = -6 + 2/3 x

y = 2/3 x - 6

So the slope is 2/3

Next, to graph the slope y = 40x + 160, the easiest way to do this is to first find the points where x = 0 and y = 0

If x = 0, y = (40 x 0) + 160 = 0 + 160 = 160

If y = 0, 0 = 40x + 160

40x = -160 (subtracting 160 from both sides)

x = -40 (dividing by 40 on both sides)

Now mark off the point on the x-axis (the horizontal one) where x = -40. Then mark of the point on the y-axis where y = 160.

Draw a line between the two (in pencil).

But the question also says, x >= 0. So rub out the line anywhere to the left of where the y-axis crosses the x-axis and there's your answer.

Last question...

Ok, the fixed cost is going to be the same all the time, the variable cost is how much extra you'll pay to make each table.

First, they're asking for a daily cost.

Assuming (and they should tell you this in the question!!!), that they work 5 days a week, the fixed cost works out to $1,200 / 5  = $240.

The variable cost will just be the cost of however many tables are made in a day. Since x tables are made, the variable cost is $45*x. (We don't need to divide by 5 because if 3 tables are made in a day, it's going to cost us $45 each for those 3 tables and if more are made, it will cost more)

This gives a daily total cost of 240 + 45x

For weekly costs, we don't need to divide fixed costs by 5 so we have that the total cost is fixed costs ($1,200) plus variable costs for making x tables ($45x) =

1,200 + 45x

To work out how may tables for a cost of 4,800, set the costs = the maximum cost of 4,800.

1,200 + 45x = 4,800

so 45x = 3,600 (subtracting 1,200 on each side)

45x / 45 = 3,600 / 45

x = 80

So you can make 80 tables for that amount of money.

Hope the explanations helped.

Answer 2

1) For the first one, you can't solve for x. There are two variables; x and y. There can be multiple answers.

2) For the second one, you subtract 2x from both sides, getting:

- 3y= - 2x+18

Then you divide everything by -3 getting:

y= - 2/3 x - 6.

3) Can't exactly show you on the computer.

4) Not sure, sorry.

Answer 3

The answer is 3.12

Answer 4

y= - 2x/3  +8

y-8 = - 2x/3

3y-24 = -2x

-3y/2 + 12 = x

2x-3y=18

2x-18=3y

2x/3 -6 = y

slope = 2/3