Answer:
4*(n)^2
Step-by-step explanation:
Answer:
21x^2-2x+1
Step-by-step explanation:
The area of shaded region= The area of the floor - area of the identical islands
The area of shaded region=(5x+1)^2-2*(2x)(x+3)=25x^2+1+10x-4x^2-12x=21x^2-2x+1
Answer:
The sides are 30 ft, 40 ft and 50 ft.
Step-by-step explanation:
The length of the triangle are as follows x - 4 , x + 6 and 2x - 18 . The hypotenuse should be 2x - 18 . The hypotenuse is the longest side of a right angle triangle.
Using Pythagoras theorem the length of the sides can be found.
a² + b² = c²
(x - 4)² + (x + 6)² = (2x - 18)²
(x - 4)(x - 4) + (x + 6)(x + 6) = (2x - 18)(2x - 18)
x²- 4x - 4x + 16 + x² + 6x + 6x + 36 = 4x² - 36x - 36x + 324
2x² - 8x + 12x + 16 + 36 = 4x² - 72x + 324
2x² + 4x + 52 = 4x² - 72x + 324
2x² - 4x² + 4x + 72x + 52 - 324 = 0
-2x² + 76x - 272 = 0
2x² - 76x + 272 = 0
divide through by 2
x² - 38x + 136 = 0
find the number you can multiply to give you 136 and add to give you - 38. The number are - 34 and - 4.
x² - 4x - 34x + 136 = 0
x(x - 4) - 34(x - 4) = 0
(x - 4)(x - 34 ) = 0
x = 4 or 34
we can only use 34 since using 4 will result to negative number.
x - 4 = 34 - 4 = 30 ft
x + 6 = 34 + 6 = 40 ft
2x - 18 = 68 - 18 = 50 ft
Answer:
Pears: 30
Step-by-step explanation:
Constant:
3x + 5x + 2x = 150
10x = 150
x = 15
Multiply ratio with constant from above:
oranges : apples
3 * 15 : 5 * 15
45 : 75 ==> 45 oranges: 75 apples
pears : apples
2 * 15 : 5 * 15
30 : 75 ==> 30 pears: 75 apples
Check:
45 oranges + 75 apples + 30 pears = 150 fruits
You could roll a 6-sided die 3 times to simulate this. This is a good simulation because it has one side for each possible tool, and each roll is independent, just as selecting the tool with replacement would be.
