catmg

Hi websiteNOPE199,

The answer is 96390, you can just plug it into a calculator. 

Generally, I like to use the standard algorithm for multiplying large numbers. 

Here's a link to a video: https://www.khanacademy.org/math/cc-fifth-grade-math/multi-digit-multiplication-and-division/imp-multi-digit-multiplication/v/multiplication-6-multiple-digit-numbers

I hope this helped. :)))

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I'm sorry Guest!

I can't seem to access the file, perhaps change sharing restrictions?

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Hi Guest!

Background

To solve this question, we should use the quadartic equation. 

If you don't know what that is, here's a wiki page: https://en.wikipedia.org/wiki/Quadratic_equation

Whether or not a quadratic has a real answer is based on it's discriminant, b^2 - 4ac. 

If the discriminant is negative, then the solutions won't work since you can't square root a negative number. 

Equation

6x - x^2 = k

x^2 - 6x + k = 0

Discriminant

b^2 - 4ac

(-6)^2 - 4(1)(k)

36 - 4k 

Solving

So, we're looking for the greatest k value where 36 - 4k is non-negative. 

The smallest non-negative number is 0. 

36 - 4k = 0

36 = 4k

k = 9

Answer

Thus, our answer is 9. 

I hope this helped. :))))

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Hello Guest!

_ _ _ _ _ _

Let each of those spots represent a book. 

There are 4 spots where the math books can be, making 4*3 = 12 different placements of them.

After the placing the math books, there are 4 other books that can be placed in 4*3*2*1 ways. 

Thus, our answer is (4*3)*(4*3*2*1) = 228

I hope this helped. :)))

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Hi Guest!

The easiest way to do this problem would be to graph it, and look for the point of intersection, x = 1/3, y = -2/3. 

However, I'm going to assume that you don't have a graphing calculator on hand. 

I'm going to try to make it so that the only x remains in the equation.  

3x + y = 1/3

2x - 3y = 8/3

One way to cancel out y in this equation, 2x - 3y = 8/3, is to add 3y. 

3x + y = 1/3

9x + 3y = 1

Then, we can just add. 

(9x + 3y) + (2x - 3y) = 1 + 8/3

11x = 11/3

x = 1/3

Knowing x, we can just plug it in for y. 

2(1/3) - 3y = 8/3

2/3 - 3y = 8/3

-3y = 6/3

y = -2/3

I hope this helped. :))))

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Hello ss333!

Background

The line on top of ABCD means to read it as a number instead of A*B*C*D. 

Equation

line(ABCD) + line(BCD) + line(CD) + line(D) = 2012

(1000A + 100B + 10C + D) + (100B + 10C + D) + (10C + D) + (D) = 2012

1000A + 200B + 30C + 4D = 2012. 

Letter A

First, let's try to find A. 

A has to be 1 or 2, since if A was 3, then 1000*A = 3000, which is bigger than 2012. 

However, if we try setting A as 2, we find out that B would be 0 since 200B + 30C + 4D = 12. 

B can't be 0 since B has to be a positive digit, making A 1. 

Equation

A = 1

1000(1) + 200B + 30C + 4D = 2012. 

200B + 30C + 4D = 1012

100B + 15C + 2D = 506

Letter B

Following the same logic as letter A, B has to be in the range 1-5 since if B was 6, 100*B = 600, which is greater than 506. 

However, if B were 5, then C would be 0, and if B were less than or equal to 3, then C would be greater than 10, which isn't a digit number, making B 4. 

Equation

B = 4

100(4) + 15C + 2D = 506. 

15C + 2D = 106. 

Letter C

Following the same letter as A and B, C has to be in the range 1-7 since if C were greater than 7, then 15C > 106. 

However, if C were less than 6, then D would be greater than 10 and not a digit. 

Similarly, if C were greater than 6, then D would be a decimal number.

Thus C has to be 6. 

Equation

15(6) + 2D = 106. 

2D = 16

D = 8

Answer

A = 1

B = 4

C = 6

D = 8

1+4+6+8 = 19.

Our final answer is 19. 

I hope this helped. :)))))))

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Hello Guest!

Another way of thinking about drawing 3 balls, is not drawing 1 ball. Since there are 4 balls and 3 colours, we can represent them as A, A, B, C. 

To draw 3 different balls, we just need to not draw an A ball. Since there are 2 A balls, the chance of not drawing an A ball is 1/2. 

I hope this helped. :)))

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Hello Guest!

Variables: 

If we set line QZ as x, then line AQ would be 42 - x. 

QZ = x

AQ = 42 - x

BQ = 8

QY = 28

Similar:

The first thing to note is that triangle ABQ is similar to triangle ZYQ. 

That also means that the side length ratios are the same. 

That means BQ/AQ = QY/QZ 

Equation:

BQ/AQ = QY/QZ can be written as 8/(42 - x) = x/28.

8/(42 - x) = x/28

1176 - 28x = 8x

1176 = 36x

x = 98/3

Answer:

Since x is QZ, our answer is 98/3. 

However, I am not the most confident. 

I hope this helped.  :)))))

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Hello Cryingcathuehue, 

Slope

To start, a line is parallel to another when both lines have the same slope so we need to find the slope of the line 2x + 3y = 21. 

We can do this by turning the equation in the form of y = mx + b, where m is the slope. 

2x + 3y = 21

3y = -2x + 21

y = (-2/3)x + 7

Thus, the slope of the line much be -2/3

Finding j

So we know the line has a slope of -2/3. Slope is also known as y/x. So for every time the y goes down by -2, the x goes up by 3. 

From -9 to 17, the y went up by 26, meaning that the x went down by 39. -2:3 = -26:39. 2 - 39 = -37. 

Answer

j = -37

I hope this helped. :)))

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