An integer is all whole numbers and zero, are the numbers you are talking about negatives?
Answer:
1) 
2) ![\sqrt[3]{-1331}=-11](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B-1331%7D%3D-11)
3) Evaluating 
we get 
4) 
5) 
Step-by-step explanation:
1) 
Prime factors of 1225 : 5x5x7x7
Prime factors of 1024: 2x2x2x2x2x2x2x2x2x2
2) ![\sqrt[3]{-1331}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B-1331%7D)
We know that ![\sqrt[n]{-x}=-\sqrt[n]{x} \ ( \ if \ n \ is \ odd)](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7B-x%7D%3D-%5Csqrt%5Bn%5D%7Bx%7D%20%5C%20%28%20%5C%20if%20%5C%20n%20%5C%20is%20%5C%20odd%29)
Applying radical rule:
![\sqrt[3]{-1331}\\=-\sqrt[3]{1331} \\=-\sqrt[3]{11\times\11\times11}\\=-\sqrt[3]{11^3} \\Using \ \sqrt[n]{x^n}=x \\=-11](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B-1331%7D%5C%5C%3D-%5Csqrt%5B3%5D%7B1331%7D%20%5C%5C%3D-%5Csqrt%5B3%5D%7B11%5Ctimes%5C11%5Ctimes11%7D%5C%5C%3D-%5Csqrt%5B3%5D%7B11%5E3%7D%20%5C%5CUsing%20%5C%20%5Csqrt%5Bn%5D%7Bx%5En%7D%3Dx%20%5C%5C%3D-11)
So,
3)
It can be written as:
Evaluating we get
4) 
Put value of x, y and z in equation and solve:
So,
5) 
We know (-a)^n = (a)^n when n is even and (-a)^n = (-a)^n when n is odd
So,
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:
The four small cones combined will hold more ice cream than the big one.
Step-by-step explanation:
The expression that can be used to represent x is not shown.
x is the price of the shoes
5% commission on every pair of shoes sold. $1.00 is the value of the commission received.
$1/5% = 1 / 0.05 = 20
The price of the shoes is 20.
