Answer:
Width =15
Length =33
Step-by-step explanation:
Take width as x
And length as 2x+3
Perimeter as 96
Formula of the perimeter of a rectangle is 2l+2w
X+×+2×+3+2×+3=96
6x+6=96
6x=96-6
6×=90
X=15
Width =x and x =15 so width =15 while length =33
Perimeter of a parallelogram = 2(l+b)
= 2 (65+42)
= 2*107
= 214 cm
Answer:
A.) gf(x) = 3x^2 + 12x + 9
B.) g'(x) = 2
Step-by-step explanation:
A.) The two given functions are:
f(x) = (x + 2)^2 and g(x) = 3(x - 1)
Open the bracket of the two functions
f(x) = (x + 2)^2
f(x) = x^2 + 2x + 2x + 4
f(x) = x^2 + 4x + 4
and
g(x) = 3(x - 1)
g(x) = 3x - 3
To find gf(x), substitute f(x) for x in g(x)
gf(x) = 3( x^2 + 4x + 4 ) - 3
gf(x) = 3x^2 + 12x + 12 - 3
gf(x) = 3x^2 + 12x + 9
Where
a = 3, b = 12, c = 9
B.) To find g '(12), you must first find the inverse function of g(x) that is g'(x)
To find g'(x), let g(x) be equal to y. Then, interchange y and x for each other and make y the subject of formula
Y = 3x + 3
X = 3y + 3
Make y the subject of formula
3y = x - 3
Y = x/3 - 3/3
Y = x/3 - 1
Therefore, g'(x) = x/3 - 1
For g'(12), substitute 12 for x in g' (x)
g'(x) = 12/4 - 1
g'(x) = 3 - 1
g'(x) = 2.
Answer:
C
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
Here [ a, b ] = [ - 10, 10 ], thus
f(b) = f(10) = 10² + 9(10) + 18 = 100 + 90 + 18 = 208
f(a) = f(- 10) = (- 10)² + 9(- 10) + 18 = 100 - 90 + 18 = 28, thus
average rate of change = 
= 
= 9
Answer:
196
Step-by-step explanation:
Since the largest share was 56 and the largest ratio is 14, then
56 ÷ 14 = 4 ← value of 1 part of the share, thus
8 parts = 8 × 4 = 32
6 parts = 6 × 4 = 24
9 parts = 9 × 4 = 36
14 parts = 14 × 4 = 56
12 parts = 12 × 4 = 48
Total the amounts
total = 32 + 24 + 36 + 56 + 48 = 196
