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Sergio [31]
3 years ago
7

Here’s another way to think about the number line model for 2 – (-3): if we were adding 2 + (-3), we’d first move two units to t

he right. Then, we’d move three units to the left, because we move left when adding negative integers. But instead, we’re subtracting -3. Addition and subtraction are inverse operations, or opposite operations; they undo one another. So we move in the opposite direction, right, and end up with a sum of 5. As a result, the number line models for 2 – (-3) and 2 + 3 are identical. This shows that subtracting a negative integer is the same as adding a positive integer.
Subtracting -9 from any number is the same as

A
subtracting 9 from that number.
B
subtracting 0 from that number.
C
adding 9 to that number.
D
adding -3 to that number.
Mathematics
1 answer:
CaHeK987 [17]3 years ago
7 0

Subtracting -9 from any number is the same as

<u></u>

<u>A</u>

<u>subtracting 9 from that number.</u>

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<span>The object's speed is 8/5 miles per hour or 1.6 mph.</span>
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What two numbers multiply to 44 and add up to 12?
djverab [1.8K]
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
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Answer:

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