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
A car trip from New York to Cincinnati took 12.5 hours. The return trip by the same route took 1 hour longer.
Let x be the speed of the car
Car trip from New York to Cincinnati
We know Distance D = speed * time
time = 12.5 hours and speed =x
D = 12.5x
Return trip
The return trip by the same route took 1 hour longer. So 12.5+1 = 13.5 hours
he average rate of speed was 4 mph less. So speed is x-4
Distance D = speed * time
time = 13.5 hours and speed =x-4
D = (x-4)*13.5
D= 13.5x-54
The distance of ongoing trip and return trip are same
So we equate both the distance equations D= 13.5x-54 and D= 12.5x
12.5x = 13.5x-54
Subtract 13.5 on both sides
-1x = -54
x=54
speed of ongoing trip = 54 miles per hour
Distance D = 12.5x = 12.5 * 54=675 miles
The length of the route = 675 miles
no it's 22 :D...............
I think the correct answer is linear
Answer:
A: enlargement B: 2
Step-by-step explanation:
im pretty sure this is correct
