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
One of the errors made by Margie by saying the set of numbers 0, 1, -1, -21, 4, 3 is that the -21 should be the first number on the list.
The given set of numbers is:
0, 1, -1, -21, 4, 3.
Margie says that the set of numbers above is in order from least to greatest
Kindly note that:
The negative number with the highest magnitude is the lowest
The positive number with the highest magnitude is the highest
Arranging this number by carefully following the note above, the set of numbers above from the least to greatest is:
-21, -1, 0, 1, 3, 4
It is obvious that Margie made a mistake in arranging the numbers, and one of the mistake is that the -21 should be the first number on the list since it is the most negative
Learn more here: brainly.com/question/25874786
We know, C = 2πr
So, 34.5 = 2 * 3.14 * r
r = 34.5 / 6.28
r = 5.49 m
In short, Your Answer would be 5.49 m
Hope this helps!
Answer:
3.2
Step-by-step explanation:
5a+2a(5−b)
Distribute:
=5a+(2a)(5)+(2a)(−b)
=5a+10a+−2ab
Combine Like Terms:
=5a+10a+−2ab
=(−2ab)+(5a+10a)
=−2ab+15a
