4. To determine if a triangle is a right triangle, given that you know the length of its sides, you have to check if its lengths follow the Pythagorean theorem.
This theorem states that the square of the hypothenuse (c) is equal to the sum of the squares of the legs of the triangle (a and b), following the expression:
The triangle is:
We have to check that a²+ b² is equal to c².
The square of the hypothenuse is:
The sum of the squares of the legs of the triangle is:
As you can see, the sum of the squares of the legs of the triangle is 100, which is the same as the square of the hypothenuse. The triangle follows the Pythagorean theorem and can be considered a right triangle.
Answer: D. 94.25 in²
Step-by-step explanation:
To find the total area, we will break the shape up into two different parts.
[] The rounded part is 39.25 in². Let us assume the rounded part is exactly half of a circle.
Area of a circle:
A = πr²
Use 3.14 for pi:
A = (3.14)r²
Find the radius:
d / 2 = r, 10 / 2 = 5 in
Subsittue:
A = (3.14)(5)²
A = 78.5 in²
Divide by 2 since it is only half:
78.5 in² / 2 = 39.25 in²
[] The triangle is 55 in².
Area of a triangle:
A = b*h/2
A = 11 * 10 / 2
A = 110 / 2
A = 55 in²
[] Total area. We will add the two parts together.
55 in² + 39.25 in² = 94.25 in²
This is a table with 6 lines.
In each line, the number in the first column is the 'x' value.
All you have to do on each line is ...
--- substitute the 'x' value in (100 + 23x), simplify it,
and write the result in the middle column
then
--- substitute the 'x' number in 90(1.2ˣ) , simplify it,
and write the result in the last column.
On the first line, x=0.
100 + 23x = 100 + 0 = 100. Write 100 in the middle column.
90(1.2ˣ) = 90(1) = 90. Write 90 in the last column.
Then go on to the second line, where x=1.
You'll make it.
The greatest common factor is 6
36: 1, 2, 3, 4, 6, 9, 12, 18, 36
42: 1, 2, 3, 6, 7, 14, 21, 42
Hope this helps : )
