To factorize 10y² - 3y - 1:
Look for two numbers whose product is 10 × (-1) = -10 and whose sum is -3.
These numbers are -5 and 2.
Rewrite the middle term:
10y² - 5y + 2y - 1
Now, factor by grouping:
(10y² - 5y) + (2y - 1)
5y(2y - 1) + 1(2y - 1)
Common factor (2y - 1):
(2y - 1)(5y + 1)
Given:
x + y = 6
y + z = 7
z + x = 9
Add the three equations:
2(x + y + z) = 22
Divide by 2:
x + y + z = 11
The average of x, y, and z is:
(x + y + z)/3 = 11/3
A scale has 90cm and 100cm long arms, if we place 100kg on 90cm, 90kg weight should we need to put at 100cm arm to balance the scale
Given A = [1 2] and B = [3; 2], let's calculate the product AB:
AB = [1_3 + 2_2]
= [3 + 4]
= [7]
Slope AB = (-2-2)/(5-1) = -4/4 = -1
Slope BC = (2-5)/(1-(-2)) = -3/3 = -1
Since slopes AB and BC are equal (-1), the points A, B, and C are collinear.
In the expression x√a, 'a' is called the radicand.
The radical symbol (✓) indicates a root, and the number or expression inside it (in this case, 'a') is the radicand.
a - b = 4
ab = 5
The formula for a³ - b³ is:
a³ - b³ = (a - b)(a² + ab + b²)
We can also use the identity:
a³ - b³ = (a - b)³ + 3ab(a - b)
Substituting the given values:
a³ - b³ = (4)³ + 3 * 5 * 4
= 64 + 60
= 124
Means x = 5, y = 2
Putting value of x and y in expression
8 × 5 + 9 × 2 = 58
8 × 5 + 2 × 2 = 44
58 : 44 = 29 : 22
To solve the system of equations:
x - y = 5 ... (1)
2x + y = 1 ... (2)
Multiply equation (1) by 1 and equation (2) by 1:
x - y = 5
2x + y = 1
Add both equations:
3x = 6
Divide by 3:
x = 2
Substitute x into equation (1):
2 - y = 5
Subtract 2 from both sides:
-y = 3
Multiply by -1:
y = -3
The solution is:
{(2, -3)}