For this, you would use simultaneous equations.
w=walnuts
a=almonds
3w+6a=51
5w+4a=55
Find a way to make one of the unknowns equal. since we are trying to work out the price of a pound of walnuts, I am going to make a equal on each side to leave us with w. This leaves us with:
15w+12a=165
6w+12a=102
Then take them away to leave w:
9w=163
Then solve:
w=163/9
= 18.11111111...
Then round it to 2 decimal places as the measurement is currency.
So 1 pound of walnuts equals $18.11
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:
b. 4x^2 + 3x - 6
Step-by-step explanation:
The values of f(x) for the extremes of x are more positive than the value of f(x) for the middle x, so we know the parabola opens upward. That eliminates choice D.
It is probably easiest to evaluate the other expressions to see which one matches the given f(x) values. For the purpose, it is usually easier to use the Horner form of the equation.
a. f(-2) = (3(-2) +4)(-2) -6 = -2(-2) -6 = -2 ≠ 4
b. f(-2) = (4(-2) +3)(-2) -6 = -5(-2) -6 = 4 . . . . matches the given data point
c. Because (b) matches, we know this one will not.
The appropriate choice is B.
To find the mean, you have to add all the numbers then divide it by how many numbers there are.
In this case, you'll need to add all those numbers and divide it by 4.
The mean is 1995.
Answer:
A = 58.7 degrees
B = 66.9 degrees
C = 34.1 degrees
Step-by-step explanation:
<u><em>For <A:</em></u>
Tan A = 
Tan A = 
Tan A = 1.6
A = 
A = 58.7 degrees
<u>For <B:</u>
Sin B = 
Sin B = 
Sin B = 0.92
B = 
B = 66.9 degrees
<em><u>For <C:</u></em>
Sin C =
Sin C = 
Sin C = 0.56
C = 
C = 34.1 degrees
