MATHEMATICS HIGH SCHOOL

Disha has £6.she buys some pineapples at 80p each and has 40p left over.
how many pineapples did she buy?
must show all your workings.

Answers

Answer 1
Answer: Well here's an easy way:

Subtract 40p from £6.00 and you get £5.60

then divide that by the 80p per pineapple.

Answer: 7 Pineapples.

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What two numbers multiply to 44 and add up to 12?

Answers

This pattern of question is always coming up. Since we can't easily guess, then let us set up simultaneous equation for the statements.

let the two numbers be x and y.

Multiply to 44.      x*y = 44 ..........(a)

Add up to 12.      x + y = 12 .........(b)

From (b)

y = 12 - x .......(c)

Substitute (c) into (a)

x*y = 44

x*(12 - x) = 44   

12x - x² = 44

-x² + 12x = 44

-x² + 12x - 44 = 0.       

Multiply both sides by -1

-1(-x² + 12x - 44) = -1*0

x² - 12x + 44 = 0.   

This does not look factorizable, so let us just use quadratic formula

comparing to ax² + bx + c = 0, x² - 12x + 44 = 0,  a = 1, b = -12, c = 44 

x = (-b + √(b² - 4ac)) /2a   or (-b - √(b² - 4ac)) /2a


x = (-(-12) + √((-12)² - 4*1*44) )/ (2*1)    

x = (12 + √(144 - 176) )/ 2

x = (12 + √-32 )/ 2

√-32 = √(-1 *32) = √-1 * √32 = i * √(16 *2) = i*√16 *√2 = i*4*√2 = 4i√2

Where i is a complex number.  Note the equation has two values. We shall include the second, that has negative sign before the square root.

x = (12 + √-32 )/ 2      or     (12 - √-32 )/ 2   

x = (12 + 4i√2 )/ 2              (12 - 4i√2 )/ 2 

x = 12/2 + (4i√2)/2                12/2 - (4i√2)/2

x = 6 + 2i√2            or         6 - 2i√2

Recall equation (c):

y = 12 - x, When x = 6 + 2i√2,  y = 12 - (6 + 2i√2) = 12 - 6 - 2i√2 = 6 - 2i√2

When x = 6 - 2i√2,  y = 12 - (6 - 2i√2) = 12 - 6 + 2i√2 = 6 + 2i√2


x = 6 + 2i√2,  y = 6 - 2i√2

x = 6 - 2i√2,  y = 6 + 2i√2

Therefore the two numbers that multiply to 44 and add up to 12 are:

6 + 2i√2 and 6 - 2i√2
xy=44\n x+y=12\n\n xy=44\n x=12-y\n\n (12-y)y=44\n 12y-y^2=44\n y^2-12y+44=0\n y^2-12y+36+8=0\n (y-6)^2=-8

No solutions in real numbers.

In complex numbers:
(y-6)^2=-8\n y-6=-√(-8) \vee y-6=√(-8)\n y=6-2\sqrt2 i \vee y=6+2\sqrt2 i\n\n x=12-(6-2\sqrt2i) \vee x=12-(6+2\sqrt2i)\n x=12-6+2\sqrt2i \vee x=12-6-2\sqrt2i\n x=6+2\sqrt2i \vee x=6-2\sqrt2i

These numbers are 6-2\sqrt2i and 6+2\sqrt2i.

Tara works in a clothing store where she earns a base salary of $100 per day plus 12% of her daily sales. she sold $800 in clothing on saturday and $1500 in clothing on sunday. how much did she earn over the two days?

Answers

Saturday: $100 + ($800 x 0.12) = 196
Sunday: $100 + ($1500 x 0.12) = 280 
$196 + $280 = $476

Answer:

Wha she said and she is correct!

Step-by-step explanation:

Cylinder has a height of 14 centimeters and its circle bases have a radius of 10 centimeters. find the surface area of the cylinder.2(100  ) + 140   square centimeters
1,400  + 140   square centimeters
2(100  ) + 280   square centimeters
2(1,400  ) + 2(140  )  square centimeters

Answers

200 plus 140 is 300 
1400 plus 140 is 1540
200 plus 280 is 480
and 2800 plus 280 3080

Simplify (3x2 − 3 + 9x3) − (4x3 − 2x2 + 16).x3 − 5x2 + 25
−x3 + x2 − 25
5x3 + x2 + 13
5x3 + 5x2 − 19

Answers

Answer: 5x³ + 5x² - 19

Answer:

The answer is D

Step-by-step explanation:

Let's simplify step-by-step.

3x2−3+9x3−(4x3−2x2+16)

Distribute the Negative Sign:

=3x2−3+9x3+−1(4x3−2x2+16)

=3x2+−3+9x3+−1(4x3)+−1(−2x2)+(−1)(16)

=3x2+−3+9x3+−4x3+2x2+−16

Combine Like Terms:

=3x2+−3+9x3+−4x3+2x2+−16

=(9x3+−4x3)+(3x2+2x2)+(−3+−16)

=5x3+5x2+−19

Answer:

=5x3+5x2−19

a class has a pizza party. there are 14 students that will have pizza. Each pizza has 8 slices. the teacher wants to buy the least amount of pizzas so that there are the same number of slices for each student. how many pizzas should be purchased?

Answers

The teacher could get a whole pie and five individual slices but if not then...... The teacher can get one whole pie and cut each slice into 2 but there will be a remainder of 1 slice which the teacher can have......hope this helps

What is (9+9)+45?????????

Answers

Answer:

60

Step-by-step explanation:

Answer: 63

Step-by-step explanation:

PEMDAS, so parentheses come first,

9+9=18

And the next in your problem would be Addition.

So,

18+45=63
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