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To find the smallest value, you need to find the vertex of the porabola. The vertex is the point that is the lowest on the porabola (or highest if a is negative). The x value produces the lowest (or highest) value of the porabola, so we only need to find one half of the point.

To find the x value, plug the coefficients into \({-b \over 2a}\)

\({-(-9) \over 2(1)}\)

=9/2

=4.5 will produce the lowest value of the porabola

8 x 40 = 320 m^2    =  

320 m^2   /  (.3048 m/f )^2 =  3444.45 ft^2

3444.45 ft^2 / 400 ft^2/gal  =  8.61 gal =~ 9 gallons of paint required

Are you the real AoPS?

If the area of the square is 25 inches, each side is 5 inches because 5*5 = 25.

If each side is 5 inches, can you figure out the total perimeter?

You are very welcome!

:P

A car license plate contains three letters followed by four digits. How many different plates can be made if no two consecutive letters can be the same, if the letters I, O and Q cannot be used, and if the number 0 cannot be used?   So that is 23 letters and 9 digits to choose from.

Letters

First 2 the same, the third different

23*1*22 =  506 

or it could be the second 2 that are the same so times 2

1012

1012*9^4 = 6639732  

Yeah I did oops

I was testing to see if you actually understood

Here is the graph that we were talking about

Hi Nirvana,

Asking genuine questions is never dumb.      BUT     not asking them is always dumb.

____________________

The gradient is the slope of a line.

Have a look through the explanation on this site.

sorry, typos, this is the real question:

The country of Mathlandia still clings to its old-fashioned currency of pounds, shillings and pence. In fact, 4 pounds is equal to 3 shillings, and 2 shillings is 1 pound and 10 pence. How many pence is a shilling worth?

1)     Circumference of a circle = 2Pi (radians)

        234Pi / 2Pi = 117 revolutions/second.

2)  Circumference of a circle also =2*r*Pi

      2 * 4 * Pi =25.13 inches

      9 revolutions/second  x  25.13 inches =226.17 inches/second - angular velocity.

Though I'm assuming you mean 23 and 22 not 26 and 25

23 x 22 x 21 x 9 x 9 x 9 x 9{if you allowed to repeat the numbers} =69,717,186 different license plates.

23 x 22 x 21 x 9 x 8 x 7 x 6{if you are not allowed to repeat the numbers} =32,133,024 different l. plates.

Thank you so much!

26 total letters - I, O and Q = 23 letters you can use

10 total letters - 0 = 9 numbers you can use

There are 26 options for the first of the three letters, and 25 options for the second because it can be anything but the first letter, and 25 options for the third letter because it can't be the second letter but it can be the first letter

26*25*25=16250 ways to make the letters

Try to use the same logic I used to count the number of ways to make the numbers, and then multiply the number of ways to count the letters by the number of ways to count the numbers 

Solve for t:
t^2 - 9 t - 36 = 0

The left hand side factors into a product with two terms:
(t - 12) (t + 3) = 0

Split into two equations:
t - 12 = 0 or t + 3 = 0

Add 12 to both sides:
t = 12 or t + 3 = 0

Subtract 3 from both sides:
 
t = 12       or        t = -3

For the first problem, an equilateral triangle has sides that are all the same length. One of the sides of the triangle is on a side of the square, and all four sides of a square are the same length, so the sides of the triangle and the sides of the square are the same length. To find the side length of the square, first think about how you would find the area given a side... you would square the side. What number squared is 25?

To get the prerimiter of the square add up all the sides of the figure, so 3 sides of the square and 2 sides of the triangle.

I would help with the 2nd and 3rd but the images are blocked for some reason 

For the last problem, a line of symetry is when everything of either side of a line is the same, so if you folded the figure on the line everything would line up. Think about how you could split the octagon in half... maybe draw a line through the middles of two opositie sides? Or from opposite corners?

I gave the first problem a try, not quite sure what to do with the second one.

The wording of this problem is weird, I'll do what I can.

To 150 items at the regular price is 4*150=$600

The sale price for the item is .9*4=$3.60

*holding cost per unit per day* *thinks*

Does this mean that to hold an item for a day you don't use it it costs $0.30?

If so, holding one item for 2 days before it means paying .30+.30+3.6=$4.20 for the item, and most of the items will be held for far more than 2 days before they are used so the average price per item will be way above $4 and the company should not take advantage of the discount price.

Tell me if I interperated this problem incorrectly and I'll try again.

a=67,  b=11, c=4, d=7

For first expression =2 /5

For 2nd expression =651 / 11

but let me ask you this...

what is a gradient in mathematics?
sorry lol im dumb :')

The answer is \(31121314\), each number is counting the quantity of numbers before it in increasing magnitude. (Three ones, one two, one three, one four).

You must separate the terms of each sequence by commas "," . OK?

$130 - $2 = $128 that Alex has left for 14 shirts.

Let the price of each shirt =P

1.05P x 14 = 128

14.7P = 128      Divide both sides by 14.7

P = 128 / 14.7

P = $8.71 - price of a shirt. But, since the price of a shirt is a "whole number", then it would have to be "rounded down" in order for Alex to be able to buy 14 shirts. In other words, the greatest possible price would have to be $8 per shirt, because: $8 x 1.05 (sales tax) x 14 shirts =$117.60. If the price of the shirt was "rounded up" to $9 per shirt, then: $9 x 1.05 x 14 =$132.30 which Alex couldn't afford.

3/4×8/9×15/16×24/25×35/36×48/49×63/64×80/81×99/100

= 11 / 20

x = 1/2 - 2y^2.

Therefore, all possible values of:

x + 2y^2 = 1/2