Answer:
5040 different combinations
Step-by-step explanation:
0-9 = 10 numbers
1st digit can be 1 0f 10
2nd digit can be 1 of 9
3rd digit can be 1 of 8
4th digit can be 1 of 7
10×9×8×7=5040
By comparing the given shape with easier ones like triangles and rectangles we will see that the area of the shape is 8 square units.
<h3>
How to simplify the shape.</h3>
So the given shape is a little bit complex, but you can actually see that it is a triangle with a base of 8 units with a height of 4 units, where a rectangle of 2 in by 3 in was removed, and also removed a triangle of height of 2 inches and base of 2 inches.
Remember that:
- A triangle of height H and base B has an area = B*H/2
- A rectangle of length L and width W has an area = L*W.
Then the area of the given shape is:
A = 8*4/2 - 3*2 - 2*2/2
A = 16 - 6 - 2
A = 8
So the given shape has an area of 8 square units.
If you want to learn more about areas, you can read:
brainly.com/question/14137384
Step-by-step explanation:
Total books = 368.
Sociology books = 92.
Psychology books = 3 times sociology books
= 3 x 92 = 276
Total = 276 + 92 = 368
Answer:
g(-4) = -1
g(-1) = -1
g(1) = 3
Explanation:
If you are given a function that is defined by a system of equations associated with certain intervals of x, just find which interval makes x true, and then substitute x into the equation of that interval.
For example, given g(-4), this is an expression which is asking for the value of the equation when x = -4. So -4 is not ≥ 2, so ¼x - 1 will not be used. -4 is also not ≤ -1 and ≤ 2, so -(x - 1)² + 3 will not be used either. So in turn, we will just use -1 which is always -1 so g(-4) will just be -1, right because there is no x variable in -1 so it will always be the same.
Using the same idea as before g(-1) is g(x) when x = -1 so -1 will not be a solution because -1 is not less than -1 (< -1). -1 is not ≥ 2 either so we will be using the second equation because -1 is part of the interval -1≤x≤2 (it is a solution to this inequality), therefore -(x - 1)² + 3 will be used.
As x = -1, -(x - 1)² + 3 = -(-1 - 1)² + 3 = -(-2)² + 3 = -4 + 3 = -1.
It is a coincidence that g(-1) = -1.
Now for g(1), where g(x) has an input of 1 or the value of the function where x = 1, we will not use the first equation because x = 1 → x < -1 → 1 < -1 [this is false because 1 is never less than -1], so we will not use -1.
We will use -(x - 1)² + 3 again because 1 is not ≥ 2, 1≥2 [this is also false]. And -1 ≤ 1 < 2 [This is a true statement]. Therefore g(1) = -(1 - 1)² + 3 = -(0)² + 3 = 3
Answer: f(x) = x-7
explanation: the function is already being translated down 5, so subtracting 2 more units leaves you with this new equation
