What two numbers multiply to 44 and add up to 12?
Answers
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
No solutions in real numbers.
In complex numbers:
These numbers are
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Answers
Answer:
22/25
Step-by-step explanation:
0.88×100/1×100=88/100
88÷4/100÷4=22/25
Answer: 22/25
Step-by-step explanation:
i took the test
Answers
Answer:
18 miles
Step-by-step explanation:
the ratio is miles/minute
10/50=0.2
so no just multiply the amount of minute you want 0.2*90= 18 miles
Answer and Step-by-step explanation:
In an hour and a half, Dana would go 18 miles since she's going a mile at regular intervals, so if she's trekking for an additional forty minutes, she will bicycle 8 miles. This implies that you'd increase five minutes by 8 miles (recall it's a mile for every 5 minutes) and that would give you forty. At that point simply add that to the 50 minutes she's been cycling as of now.
Answers
We multiply both sides of the equation by 3x:
We multiply both sides of the equation by 2:
From here, we clear the value of x:
Answer:
You can not divide by zero, but you can rewrite the expression to clear x.
The value of x is given by:
Taking the LCM on the left side
(9 + x)/(3x) = (5/6)
54 + 6x = 15x
From this step, it is visible that x is no longer in th denominator and even if it is 0, the equation is solvable.
9x = 54
x = 6
f(x) = x^4 + 64x^2
Answers
we are given with the function f(x) = x^4 + 64x^2 and is asked to factor the function. The greatest common factor of the terms is x^2 . hence taking out x^2 from the set, the result is x2 *(x2 + 64).(x2 + 64) is equal to (x+8)^2 - 16x. hence the linear factorization is x^2 * ( (x+8)^2 - 16x)
y=x^4+64x&
In IR, y=x^2(x^2+64).
In C, y=x²(x+8i)(x-8i)
Answers
+ 09.73
____
31.33
look at the colomns and add them together. Or use a calculator.
Answer:
31.33
Step-by-step explanation:
9.73
+------- = 31.33 or just 9.73 + 21.6= 31.33 recommend if you are solving 21.6 things and need help, use the calculator, yw have an amazing dayヾ(≧▽≦*)o
Answers
this means legnth=7 times width
l=legnth
l=7w
legnth is 7w inches