1. What is the intercept (y-intercept) of the function y = 2.5x + 8
is it 8?
2. What is the x-intercept of the function y = 2.5x + 8
i'm honestly not sure...
3. What is the slope of the function y = 2.5x + 8
um...is it 2.5?
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
i'm really confused on this one.
y = 2.5x + 8
this is the slope-intercept form, so
slope = 2.5
y-intercept = 8
you got those right
The x-intercept is where y=0, so
2.5x+8 = 0
2.5x = -8
x = -16/5 = -3.2
The Pythagorean Theorem states that in a right triangle with sides a and b and hypotenuse c,
a^2+b^2 = c^2
So, to see whether your triangle is a right triangle, you need
6^2+8^2 = 12^2
36+64 = 144
100 = 144
Bzzzt! So it is not a right triangle.
Just FYI, the most basic right triangle has sides 3,4,5
If you scale up by a factor of 2, that gives sides of 6,8,10
So, 6,8,12 cannot be a right triangle.
Thank you!
1. Yes, you are correct. The y-intercept of the function y = 2.5x + 8 is 8. It is the point where the line crosses the y-axis.
2. To find the x-intercept of the function y = 2.5x + 8, we set y = 0 and solve for x. In this case, we have 0 = 2.5x + 8. Solving for x gives us x = -8/2.5 or x = -3.2. Therefore, the x-intercept is -3.2.
3. Yes, you are correct. The slope of the function y = 2.5x + 8 is 2.5. The slope represents the rate of change of y with respect to x.
4. To determine if the triangle with sides 6, 10, and 12 is a right triangle, we can use the Pythagorean Theorem, which 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 other two sides.
Let's call the sides of the triangle A, B, and C, where A = 6, B = 10, and C = 12. We can now check if A^2 + B^2 = C^2.
6^2 + 10^2 = 36 + 100 = 136
12^2 = 144
Since 144 is not equal to 136, the triangle with sides 6, 10, and 12 is not a right triangle.
1. To find the y-intercept of a function, you can set x to 0 and solve for y. In the equation y = 2.5x + 8, when x is 0, the equation becomes y = 2.5(0) + 8. Simplifying this, we get y = 8. Therefore, the y-intercept of the function is 8, as you correctly mentioned.
2. To find the x-intercept of a function, you can set y to 0 and solve for x. In the equation y = 2.5x + 8, when y is 0, the equation becomes 0 = 2.5x + 8. Solving this equation, we subtract 8 from both sides to isolate 2.5x, giving us 2.5x = -8. Dividing both sides by 2.5, we find x = -8/2.5. Simplifying this, x = -3.2. Therefore, the x-intercept of the function is -3.2.
3. The slope of a linear function is the coefficient of x. In the equation y = 2.5x + 8, the coefficient of x is 2.5. So, the slope of the function is indeed 2.5, as you mentioned.
4. To determine if a triangle is a right triangle using the Pythagorean Theorem, you need to check if the sum of the squares of the two shorter sides (legs) of the triangle is equal to the square of the longest side (hypotenuse). In this case, the sides given are 6, 10, and 12. To apply the Pythagorean Theorem, we compare 6^2 + 10^2 to 12^2.
Calculating, we find that 6^2 + 10^2 equals 36 + 100 = 136, and 12^2 equals 144. Since these values are not equal, the sum of the squares of the two shorter sides is not equal to the square of the longest side. Therefore, the triangle with sides 6, 10, and 12 is not a right triangle.