Answer:
a = 2x, b = 3.
Step-by-step explanation:
8x^3+27 = (2x)^3 + 3^3
a = 2x and b = 3.
We can cube root 8x^3 getting 2x and cube root 27 getting 3.
Answer: perimeter = 96mm, Area = 564mm².
Step-by-step explanation:
From the diagram, it is a trapezium, it has a rectangle joined together by a right angled triangle. Now to find the perimeter, we add all the dimensions together. To get the other side of the rectangle, which is also the perpendicular height of the figure, we take the Pythagoras. Let the perpendicular height = x
Therefore,
25² = ײ + 7²
625 = x² + 49
x² = 625 - 49
x² = 576
x. = √576
= 24.
Now the perimeter
= 20 + 25 + 7 + 20 + 24
= 96mm.
Area of the figure will be
= 1/2( a + b )h
Where a = 20, b = 20 + 7 = 27 and h = 24, now substitute for the values
( 20 + 27) x 24
---------------------
2
= 47 x 24/2
= 47 x 12
= 564mm²
Answer: (f·g)(x) = -5x³ - 31x² + 62x + 18
(f·g)(-1) = -70
(fog)(x) = 25x² - 130x + 155
(fog)(-1) = 310
<u>Step-by-step explanation:</u>
f(x) = x² + 8x + 2 g(x) = -5x + 9
(f·g)(x) = (x² + 8x + 2)(-5x + 9)
= -5x³ + 9x²
- 40x² + 72x
<u> - 10x + 18</u>
= -5x³ - 31x² + 62x + 18
(f·g)(-1)= -5(-1)³ - 31(-1)² + 62(-1) + 18
= -5(-1) - 31(1) - 62 + 18
= 5 - 31 - 62 + 18
= -70
****************************************************************************************
(fog)(x) = (-5x + 9)² + 8(-5x + 9) + 2
= 25x² - 90x + 81
- 40x + 72
<u> + 2</u>
= 25x² - 130x + 155
(fog)(-1) = 25(-1)² - 130(-1) + 155
= 25 + 130 + 155
= 310
<em>It wasn't clear if you wanted multiplication or composition so I solved both.</em>
Let n = length
let n-4 = width since it is 4 meters shorter
2( n+n-4) =72 Two of the length and width added together equal the perimeter
combine like terms
2(2n -4) = 72 Now use the distributive law on the left side of the equation
4n -8 = 72 Now add 8 to both sides
4n -8 +8 = 72 +8
4n = 80 Finally divide each side by 4
n=20
so the length is 20 and the width is 4 less or 16.
Let's see if our answer works.
20 + 16 + 20 +16 =? 72
72 =72 yes, it does. Length = 20 Width = 16
Im guessing he answered 30 correct, let me know if im correct
