1. What is the intercept (y-intercept) of the function y = 2.5x + 8
2. What is the x-intercept of the function y = 2.5x + 8
3. What is the slope of the function y = 2.5x + 8
4. The sides of a triangle are 6,10, and 12. Using Pythagorean Theorem, determine if the triangle is a right triangle (has 90 degree angle). Recall that in the right triangle, A^2 +B^2 = C^2
1,2,3 the equation is in slope-intercept form. That should tell you something
just check 6^2 + 8^2 vs 12^2
1. To find the y-intercept of the function y = 2.5x + 8, you need to know that the y-intercept is the value of y when x is equal to 0. In this equation, the y-intercept is the constant term, which is 8. Therefore, the y-intercept is 8.
2. To find the x-intercept of the function y = 2.5x + 8, you need to set y equal to 0 and solve for x. In other words, you want to find the value of x when y is equal to 0. Rewriting the equation as 2.5x + 8 = 0, you subtract 8 from both sides to isolate the term with x. This gives you 2.5x = -8. Finally, divide both sides by 2.5 to solve for x. The x-intercept is x = -8/2.5 = -3.2.
3. The slope of the function y = 2.5x + 8 is the coefficient of the x-term. In this equation, the coefficient of x is 2.5. Therefore, the slope is 2.5.
4. To determine if the triangle with sides 6, 10, and 12 is a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, let's label the sides A, B, and C, with side C being the hypotenuse. The lengths of the sides are A = 6, B = 10, and C = 12. Applying the Pythagorean theorem, we can check if A^2 + B^2 is equal to C^2.
Calculating A^2 + B^2, we have 6^2 + 10^2 = 36 + 100 = 136.
Now, calculating C^2, we have 12^2 = 144.
Since A^2 + B^2 is not equal to C^2 (136 is not equal to 144), the triangle with sides 6, 10, and 12 is not a right triangle.