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:
The equation for a line that is parallel to y + 5 = 3(x - 1) and goes through the point (3,-4) will be:
Step-by-step explanation:
Given the equation
y + 5 = 3(x - 1)
Writing in the slope-intercept form
y=mx+b
where m is the slope and b is the y-intercept
y = 3(x-1) -5
y = 3x-3-5
y = 3x - 8
Thus, the slope = m = 3
We know that the parallel lines have equal slopes.
So, the slope of a parallel line is also 3
Using the point-slope form of the line equation
substituting the values m = 3 and the point (3, -4)
y-(-4)=3(x-3)
y+4 = 3x-9
y = 3x-9-4
y = 3x-13
Thus, the equation for a line that is parallel to y + 5 = 3(x - 1) and goes through the point (3,-4) will be:
Answer:3.14
Step-by-step explanation:
r=pi*r sqaured
Answer:
Cone volume formula
To calculate its volume you need to multiply the base area (area of a circle: π * r²) by height and by 1/3: volume = (1/3) * π * r² * h
Step-by-step explanation:
