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
Triangular prism
length of slanted side:
sqrt(3^2 + 4^2) = 5
SA = 2(1/2)(8)(3) + 8(12) + 2(5)(12) =240
V = (1/2)(8)(3)(12) = 144
cuboid
SA = 2(7x6) + 2(7x5) + 2(6x5) = 214
V = 7x6x5 = 210
The answer to this question has to be 8
Answer:
Let x be the discounting price of a surfing lessons per person
Let y be the discounted price of a surfing lessons per person
The cost of taking a surfing lesson and go parasailing is $130
x + y = 130--------------(i)
25 people take
Surfing lessons, and 30 people go parasailing and a total of $3,650 is collected
25x + 30y = 3650--------------(ii)
We solve for y using equ (i):
y = 130 - x ------------(iii)
Substitute equ (iii) to equ (ii) and solve for x
25x + 30(130 - x) = 3650
25x + 390 - 30x = 3650
-5x = -250
-x = 50
We solve for y using equ (iii):
y = 130 - x
y = 130 - 50
y = 80
So, the discounted price to take a surfing lesson is $50 and the discounted price to go parasailing is $80
Answer:
Y=2×+13
Step-by-step explanation:
2×+3=0
2×=0-3
you use 3 to divide it self =×
×=3
