The cubic function is f(x) = x^3
You need to perform three transformations to the cubic function to obtain
f(x) = - (x + 2)^3 - 5.
Those transfformations are:
1) Shift f(x) = x^3, 2 units leftward to obtain f(x) = (x + 2)^3
2) reflect f(x) = (x + 2)^3 across the x-axis to obtain f(x) = - (x + 2)^3
3) shift f(x) = - ( x + 2) ^3, 5 units downward to obtain f(x) = - (x + 2)^3 - 5
Average of 10 people = 65
65 × 10 = 650
average of 5 people = 35
35 × 5 = 175
650 + 175 = 825
825 ÷ 15 = 55
the average reading time for the entire book club each day is 55 minutes a day
Answer:
384 cm²
Step-by-step explanation:
The shape of the figure given in the question above is simply a combined shape of parallelogram and rectangle.
To obtain the area of the figure, we shall determine the area of the parallelogram and rectangle. This can be obtained as follow:
For parallelogram:
Height (H) = 7.5 cm
Base (B) = 24 cm
Area of parallelogram (A₁) =?
A₁ = B × H
A₁ = 24 × 7.5
A₁ = 180 cm²
For rectangle:
Length (L) = 24 cm
Width (W) = 8.5 cm
Area of rectangle (A₂) =?
A₂ = L × W
A₂ = 24 × 8.5
A₂ = 204 cm²
Finally, we shall determine the area of the shape.
Area of parallelogram (A₁) = 180 cm²
Area of rectangle (A₂) = 204 cm²
Area of figure (A)
A = A₁ + A₂
A = 180 + 204
A = 384 cm²
Therefore, the area of the figure is 384 cm²
Answer:
number of ways = 120
Step-by-step explanation:
The number of ways five children can pose for a photograph line up in a row is given by the number of permutations of 5 elements in 5 different positions (positions in the line), then
number of ways = number of permutations of 5 elements = 5! = 5 * 4 * 3 * 2 * 1 = 120
Since the first children that occupies the line can be on any of the positions (5 positions) , but then the second one can choose any of the 4 remaining positions (since the first children had already occupied one) , the third can choose 3 ... and so on.
Answer:
3x + 2y = 16
x = 2 , y = 5
Step-by-step explanation:
Given that George bought x quarts at $3.00 per quart & y quarts at $2.00 per quart and he bought 7 quarts for $16.00
Considering the total cost
3x + 2y = 16
For the cost of each
x + y = 7
solving the 2 equations simultaneously be substitution
x = 7 - y
3(7 - y) + 2y = 16
21 - 3y + 2y = 16
-3y + 2y = 16 - 21
-y = - 5
Divide both sides by -1
y = 5
x = 7 -y
x = 7 - 5
= 2
