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
Answer:
"associative"
Step-by-step explanation:
The associative property lets you change the grouping of terms of a sum or of a product.
___
For example, you can rewrite
(5 + 4·3) -2
as
5 + (4·3 -2)
but the associative property does NOT allow you to change the grouping to ...
(5 +4)·3 -2 . . . . . not a valid rewrite
Perimeter: 2 1/8 + 3 1/2 + 2 1/2 = 7 (1 + 4 + 4)/8 = 7 9/8 = 8 1/8
Hope this will help you!
Answer:
{24, 18, 12, 6, 0} is the range of the above function
Step-by-step explanation:
solution:
let, x= -4
f(-2) = 12-3*(-2)
= 12+12
=24
let,x= -2
f(-2) = 12-3*(-2)
=12+6
18
let,x =0
f(0)= 12-3*0
=12-0
=12
let,x=2
f(2) = 12-3*2
=12-6
=6
let,x=4
f(4) = 12-3*4
=12-12
=0
Replacement = 11 total
probability of choosing a consonant = 7/11
without replacing the card
probability of choosing an e = 3/10
probability of choosing both = 7/11 * 3/10 = 21/110 <===
