We can use proportions
12/x = 10/5
12*5 = 10x
60 = 10x
x = 6
Check
12/6 = 10/5
2 = 2
Answer:
11. 78
12. 4x² - 3x - 1
Step-by-step explanation:
11. Sum of n whole numbers = ½(n² + n)
Multiply
½*n² + ½*n
= n²/2 + n/2
To find the sum of the first 12 whole number, substitute 12 for n into the equation.
= 12²/2 + 12/2
= 144/2 + 12/2
= 72 + 6
= 78
12. Area of trapezoid = ½(a + b)*h
Where,
a = 5x - 4
b = 3x + 2
h = x + 1
Area = ½(5x - 4 + 3x + 2)*(x + 1)
Area = ½(8x - 2)*(x + 1)
Area = ½[8x(x + 1) -2(x + 1)]
= ½[8x² + 8x - 2x - 2]
Add like terms
= ½(8x² - 6x - 2)
= ½(8x²) - ½(6x) - ½(2)
= 4x² - 3x - 1
Answer:
Cost of Blanket = 32
Step-by-step explanation:
Let the cost of a blanket be = b , cost of a scarf be = s. Blanket price x Blanket Quantity & Scarf Price x Scarf Quantity sum up to be total sales.
So, Day 1 : 2b + 5s = 104 (i) , Day 2 : 3b + 4s = 128 (ii)
Solving equations : Multiplying (i) by 3 , & (ii) by 2 , we get
6b + 15s = 312 ,
(-)6b + (-)8s = (-)256
By elimination method, 15s - 8s = 312 - 256 → 7s = 56 → s = 56 / 7 = 8 .
Putting s value in any equation i], 2b + 5 (8) = 104 → 2b + 40 = 104 → 2b = 104 - 40 = 64 → b = 64 / 2 = 32
