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Algebra

The use of letters to substitute unknown numbers to form an equation. Solve the equation to get the unknown number using different methods such as simultaneous equations and more.

500 Questions

Are both the y and x axis negative in quadrent 1?

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NO!

Quadrant 1 is top right (x,y) Both positive

Quadrant 2 is top left ( -x,y) ('x' is negative, 'y' is positive)

Quadrant 3 is bottom left (-x,-y)(Both negative)

Quadrant 4 is bottom right ( x,-y). ( 'x' is positive , and 'y' is negative).

Divide x2 - x - 12 by x - 4?

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x^2 -x -12 / (x - 4)

Factor ise the top line

(x + 3)(x - 4) / (x - 4)

Cancel down by 'x-4'

Hence

x + 3 is the answer!!!!

Hcf of 14 and 49?

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14 = 7 x 2

&

49 = 7 x 7

'7' is common to both numbers, so seven is the HCF ( Highest common factor).

What is o-o in chess?

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o-o means castling on king's side

&

o-o-o means castling on queen's side. THat is NOT with the Queen , but the King and the Queen's Castle.

1 over tan x equals what?

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1/ Tan = 1/ (Sin/Cos) = Cos/Sin = Cot (Cotangent)

What slope is 7x plus 5y equals 35?

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-7/5

For equations in Standard Form (Ax + By = C), slope equals -A/B. Or you could put the equation in Slope-Intercept form (y = mx + b) by solving for y and then finding the slope (m).

Why didn't the piano work?

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The answer to this riddle is "The piano only knew how to play."

What is 10 minus 5 times 2 plus 8 divided by 2?

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If the question is writen out "10-5x2+8/2=" then with the correct order of operations it would be "10-(5x2)+(8/2)=". This simplifies to "10-10-+4=". Finally, this comes to "4"

Twos complement of a given 3 or more bit binary number of non-zero magnitude is the same the original number if all bits except the?

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ANSWER: MSB IS 1

In the 2's complement representation, the 2's complement of a binary number is obtained by first finding the one's complement (flipping all the bits), and then adding 1 to the result. This representation is commonly used to represent signed integers in binary form.

Now, if all bits except the sign bit are the same, taking the 2's complement of the binary number will result in the negative of the original number. The sign bit (the leftmost bit) is flipped, changing the sign of the entire number.

For example, let's take the 4-bit binary number

1101

  1. The 2's complement would be obtained as follows:

Find the one's complement:

0010

Add 1 to the one's complement:

0011

What is the diameter of a 22 circumference circle?

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Remember the circle eq'n

C = pi d

AlgebraicaLLY REARRGANGE

d = C / pi

d = 22/3.141502....

d = 7.002817496... ~ 7.0

If a circle has a diameter of 7 what is the circumference?

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Remember the circle equation

C = pi d

Substituting

C = 3.141592....X 7

C = 21.99114858.... units. ~ 22.0 units.

If it takes 2 hours to travel 90 miles how many miles how far can you travel in 7 hours?

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We can solve this problem using the concept of speed.

  1. We know the speed: The information states that it takes 2 hours to travel 90 miles. Therefore, the speed is 90 miles / 2 hours = 45 miles per hour.

  2. Now, we need to find the distance with a different travel time: You want to know how far you can travel in 7 hours with the same speed of 45 miles per hour.

  3. Use the formula: Distance = Speed × Time

  4. Plug in the known values: Distance = 45 miles per hour × 7 hours = 315 miles

Therefore, if it takes 2 hours to travel 90 miles at a constant speed of 45 miles per hour, you can travel 315 miles in 7 hours with the same speed.

How long will a helicopter flying at a speed of 160 miles per hour take to travel a distance of 350 miles?

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Time = 350 miles / 160 miles per hour

Time ≈ 2.1875 hours

However, to express the time in minutes, it's more convenient to convert the decimal part:

2.1875 hours * 60 minutes per hour ≈ 131.25 minutes

Therefore, the helicopter will take approximately 131 minutes, or 2 hours and 11 minutes to travel 350 miles at 160 mph.

How long does it take a helicopter going 200 mph to go 18 miles?

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11.11 minutes distance equal rate divided by time.....time equals rate divided by distance.

How do you write your height in numeric value?

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suppose your height to be 150 cm

then you would write it as CL

Where do the x axis and y axis intersect?

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At the point of the origin which is at (0, 0)

How do you factor 20x2 plus 22x-12?

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20x^2 + 22x - 12

Since '2' is a common factor

Then

2(10x^2 + 11x -6)

To factor the bracket bit , we write down all the factors of '10' & '6'

Hence

10 ; 1,2,5,10,

6 ; 1,2,3,6.

We then select a pair of numbers from each factors to multiply together and then add/subtract to reach '11'.

They are ( 2,5) & ( 2,3)

3 x 5 = 15 & 2 x 2 = 4

15 - 4 = 11

So (2,3) & ( 2,5) are the selected factors.

Open brakets. ( 5x 2)(2x 3)

To select the signs, we note that '6' is a minus '-6' , so the signs are differen(+/-).

We also note that 11x is positive (+) , so the larger multiple is the positive multip;le and the small is the negative.

Hence

(5x - 2)(2x + 3)

Overall it is

2(5x - 2)(2x + 3)

What number is next in this series 5 7 11 19 35?

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Note the difference between each pair is doubled compared to the previous pair.

5 ; 7 = 2^1

7 ; 11 = 2^2

11 : 19 = 2^3

19 : 35 = 2^4

So 35 : x = 2^5 = 32

So 35 + 32 = 67 .

Factor expression 16x2 - 25y2?

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Remember both 16 & 25 are squared numbers.

16 = 4^2 & 25 = 5^2

Hence we can write

(4x)^2 - (5y)^2

Remember two squared terms with a NEGATIVE Between them will factor.

( 4x - 5y)(4x + 5y)

Note the difference signs.

NNB Two squared terms with a positive (+) between them DOES NOT factor.