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Maximise:
This is the equation of a parabola that opens downwards (coefficient of x^2 is negative) so the maximum value of P (the dependent variable) will be found at the parabola's vertex. The x-coordinate of the vertex is given by:
and so the maximum value of P will be found at
Your equation is already in the standard form: (a = -25, b = 300, c = 0) so we can find the x-coordinate at which P will be the maximum.
Simplify.


To maximise profits, the manager should employ 6 clerks.
The maximum profit can be found by substituting 6 for x in the original equation for P.




Maximum profit is 900 (dollars ?)

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Minimise:

This is the equation of a parabola that opens upwards (Coefficient of x^2 is positive), so the minimum value of C would be at the parabola's vertex. The x-coordintate of the vertex is given by:
Your equation is already in standard form: so here: a = .009 and b = -1.8. The minimum value of C will be found at

Simplify.


Acme should produce 100 ball per hour to minimise the cost per hour.
It might be helpful to see the graph of the cost, C (vertical axis) versus x (horizontal axis) the number of balls produced:

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If row x has tiles, then:
row 4 has tiles.
row 5 has tiles.
row 6 has...well, you get the idea by now.

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First set up the equation of proportionality: Let F = flow in gallons and T = time in hours.
where k is the constant of proportionality. Solve for k.
Substitute F = 350 gallons and T = 20 mins = 1/3 hour.



Now you can solve the problem:
Substitute F = 3000 gallons and k = 1050

hrs
T = 2 hrs. 51 mins. 25.2 secs.

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Try some WD-40 for your rust problem. (lol)
The bridge is 3,100m + (1/10)(3,100m) + (1/8)(3,100m) = 3,100 + 310 + 387.5 = 3797.5 meters long.

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I was trying to use a more precise conversion factor by using 14.7868 ml per tablespoon.
If 1 tablespoon = 14.7868 ml, then 12 tablespoons = 12(14.7868) = 177.4416 ml
If you are allowed to use the approximate conversion factor of 1 tablespoon = 15 ml, I would go with that. So 12 tablespoons = 12(15) = 180 ml.

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First, a quick clarification. You have an expression not an equation.
An equation is some equal to something else and you will see the = sign in an equation.
An expression has no = sign.
Simplify:
Remember that: , so:

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Ok, you can show x squared like this...x^2 by using the caret (^). You get the caret by Shift-6 key. A little advice...use the same type letter (all upper case or all lower case) for the variable in your problems, rather than swithichjng from X to x and back again.
Solve: You can also write your equation:
You can solve this by factoring if you set y = 0
Apply the zero product principle.
and/or
If then,
If then,
The x-intercepts (also called zeros) are:


The x-coordinate of the vertex is found by:
The a and b come from the standard form of the quadratic equation: In your equation, a = 1 and b = 6

This the x-coordinate of the vertex. Find the y-coordinate by substituting this value of x into your equation and solving for y.
x = -3



The vertex is at (-3, -4)
Here's the graph.

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Yes! =

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Recall that the point=slope form is:
y = mx + b
You can find the slope of the new line when you remember that parallel lines have the same slope. The slope of the given line is easily seen when you compare the given equation with the general slope-intercept form.
y = 2x - 4 compare with:
y = mx + b and you can see that the slope of the given line, and of any line parallel to it, is m = 2
So you can start your new equation off with:
y = 2x + b Now, since this line passes through the point (8, -2), then the coordintates of the point (x = 8 and y = -2) must satisfy this equation. Substitute these values of x and y into you new equation:
-2 = 2(8) + b now you can solve this for b.
-2 = 16 + b Subtract 16 from both sides of the equation.
-18 = b Now you can write your final equation:
y = 2x - 18

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I expect it is possible that you can find a tutor here. I would also suggest that you check with school and ask about math tutoring. Most schools will provide their students with a tutor upon request or, if they can't, they can most-likely refer you to a local tutor.
The bottom line is that you need to get one-on-one tutoring in this subject if you so desperately need help.

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"Pre" means before so "Preimage" means the image before the tranformation.
In other words...the "before" picture in "Before-and-after"

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Here are the steps for solving this problem:
1) The slope-intercept form of a linear equation is: y = mx + b where m is the slope of the line and b is the y-intercept (where the line crosses the y-axis) of the line. Get your equation into the slope-intercept form.
(y = -(5/2)x + 5)
2) Find the slope of your new equation. Hint: If your new line is perpendicular to another line, then the slope of your new line is the negative reciprocal of the slope of the given line. (The negative reciprocal of -(5/2) is (2/5))
3) Substitute into the slope-intercept form (y = mx + b) the value you find for your slope (m) and the x and y-coordinates of the given point (3, -5) and then solve this for the value of b, the y-intercept.
4) Write the final equation in the form y = mx + b but with your value of m (found in step 2)and your value of b (found in step 3).

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Factor completely:
First, factor an x.
Now factor the parentheses.
Done!

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This is a "combinations" (order doesn't matter) problem in which you want to know the number of combinations of 12 things taken 4 at a time.
The left side is Combination of 12 things taken 4 at a time.

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Factor:
First, factor out an x
Now factor the parentheses.
Does this help?

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Yes there is. Quadratic equations are always solvable by using the quadratic formula:
For your equation, this would look like:




The roots are:

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First, rewrite your equation in standard form:
becomes:
Solve by factoring.
Now apply the zero product principle.
and/or
If then,
If then,
The roots are:
x = -3
x = 5

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Recall that:
means: Applying this to your problem:
means:
Add 7 to both sides.
Finally, divide both sides by 3.

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Simply substitute the given values of x and y (-3, 4) into the two equations and solve for the respective values of b and m.
1)
5x + 7y = b Substitute x = -3 and y = 4.
5(-3) + 7(4) = b Simplify.
-15 + 28 = b
b = 13
2)
mx + y = 22 Substitute x = -3 and y = 4.
m(-3) + 4 = 22 Subtract 4 from both sides of the equation.
-3m = 18 Finally, divide both sides of the equation by -3.
m = -6

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Yes! Note that the given equation is already in the slope-intercept form:
y = mx + b where: m = the slope and b = the y-intercept. Compare this with the given equation.
y = 3x + 2 and you can easily see that m = 3 so the slope of your line is 3.

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1)
First convert 3/8 to a decimal. Just divide 3 by 8 to get 0.375.
Next, you need to find out how many times does 0.0125 go into 0.375, so this is a division problem.

Answer: You can get thirty 0.0125-grain doses from 3/8 grains of a drug.
2)
If 1000 tablets contain 11.5 grams of an antihistamine, you need to find out how much antihistamine 1 tablet contains. Do it like this:
(1000 tablets)/1000 = 11.5 grams/1000
1 tablet = 0.0115 grams Now, to find out how much antihistamine is in 475 tablets, do it like this:
1 tablet = 0.0115 grams
475 (1 tablet) = 475(0.0115) grams
475 tablets = 5.4625 grams of antihistamine.
3) You can use proportions on this problem.
Solve for x. Multiply both sides of the equation by 1.2ml
Do the math.

Answer: The patient would receive 11.2 mg of the drug.

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1)
Use a proportion to find the number of mg, then convert to mcg.


Convert to micrograms: 1 mg = 1,000 mcg

2)1 tablespoonful qid (four times a day) for 3 days (4 X 3) = 12 tablespoonsful.
1 Tablespoonful = 15 ml approximately. Perhaps your PDR has the exact conversion factor for this but I think it's more like 14.7868 ml per tbsp.
12 tbsp = 180 ml approximately.
12 tbsp = 177.4412 ml more precisely.
3) Flow rate of 30 drops per minute over 6 hours (30 drops/min)(60 min/hr)(6 hrs) = 10,800 drops at 18 gtts/ml (18 drops/ml) = 600 ml.

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Simplify:
First, cube the parentheses by multiplying the exponent outside by every exponent on the inside.
Now multiply by the (4AB)

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Simplify:
Remember: In the top, square everything inside the parentheses and in the bottom, raise everything inside the parenteses to the 4th power.
Cancel the 16's
Now cancel in the top with in the bottom to get:

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Yes, that's what GCF means...Greatest Common Factor.
Factor out the GCF:

Look at the three terms to find a common element. First, all of the coefficients (the integers in front of the variables) are divisible by 5, so 5 is a factor of these integers.
Now look at the variables for a common factor. They all have at least one x and one y, so xy would be a factor. So you can factor out the 5 and the xy to get:

To check the answer, just multiply the by the and you should get back what you started with. Try it!

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I can see why you're having trouble solving this problem.
Your opening statement..."The length of a rectangle is 6 times more than its width..." implies that the length, L = 6W but what I believe you should have written is..."The length is 6 more than its width..." which would translate into L = W + 6, So let's work it on that assumption.
A = L*W but L = W+6, so:
A = (W+6)*W = 72 cm^2 Simplify and solve for W
Subtract 72 from both sides of the equation.
Solve this quadratic equation by factoring.
Apply the zero product principle.
and/or
If then, Discard this solution, width must be positive.
If then, The width is 6 cm.

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Notice that the first term (16y^2) and the last term (25x^2) are perfect squares, this suggests that the factors may be identical, so try:
Use the FOIL method to check it out.
=

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I hope I've got this right.
Solve for f. Add 3 to both sides of the equation.
Multiply both sides by 7.

What kind of equation is this? It's a linear equation.

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Remember that:

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I assume that the use of logarithms is expected.
Subtract 1 from both sides of the equation.
Take the log of both sides.
Divide both sides by
You can do this on your calculator or use a table of logarithms.
to the nearest thousandth.
Check:
= 64.031