Short leg = x-6m
Longer leg =x
Hypotenuse = x+6m
x² + (x-6)² =(x+6)²
x² + x²-12x+36 = x²+12x+36
2x²-12x+36= x² +12x+36
2x²-12x+36-36= x² +12x+36-36
2x² - 12x-12x = x²+12x-12x
2x² -24x-x² = x²-x²
x² -24x = 0
x(x-24)=0
x = 24
Short leg = 24-6m = 18
Longer leg =24
Hypotenuse = 24+6m=30
Check
a² + b² = c²
18² +24² =30²
324 +576 = 900
900=900
Answer:
Each answer is negative
Each equation has a four within it, either negative or positive
Step-by-step explanation:
-4x3=-12
3x-4=-12
5x-4=-20
Answer:
Step-by-step explanation:
1.) Get the equation in the form y = ax^2 + bx + c.
2.) Calculate -b / 2a. This is the x-coordinate of the vertex.
3.) To find the y-coordinate of the vertex, simply plug the value of -b / 2a into the equation for x and solve for y. This is the y-coordinate of the vertex.
1.) y = -x^2 - 10x + 24
2.) -(-10) / 2(-1) = -5
3.) y = -(-5)^2 - 10(-5) + 24
y = -25 + 50 + 24
y = 49
Answer:
Step-by-step explanation:
I used calculus for this, as I'm not sure there's any other way to do it and to do it as easily. This is the volume of a solid found by using the disk method of rotation:
![V=\pi\int\limits^a_b {[R(x)]^2-[r(x)]^2} \, dx](https://tex.z-dn.net/?f=V%3D%5Cpi%5Cint%5Climits%5Ea_b%20%7B%5BR%28x%29%5D%5E2-%5Br%28x%29%5D%5E2%7D%20%5C%2C%20dx)
where R(x) is the outer shell of the solid and r(x) is the space inbetween the solid and the axis of rotation. There is no space between the solid and the axis of rotation, so r(x) = 0. R(x) is the height of the solid which is 3. Therefore, f(x) = 3 and that's the function we put into the formula with the lower bound of 3 and the upper bound of 5:
and
and integrating:
and using the First Fundamental Theorem of Calculus:
V = π(9(5) - 9(3)) and
V = π(45 - 27) so
V = 18π units cubed or in decimal format,
V = 56.549 units cubed
Step-by-step explanation:
<h2>13. </h2>
<h2>14.</h2>
<h2>15.</h2>
![\implies\sf{ {x}^{3} = 216 } \\ \\ \implies\sf{ x = \sqrt[3]{216} } \\ \\ \implies\sf{ x = 6 }](https://tex.z-dn.net/?f=%20%20%5Cimplies%5Csf%7B%20%7Bx%7D%5E%7B3%7D%20%3D%20216%20%7D%20%5C%5C%20%20%5C%5C%20%20%5Cimplies%5Csf%7B%20x%20%3D%20%20%20%5Csqrt%5B3%5D%7B216%7D%20%20%7D%20%20%20%5C%5C%20%20%5C%5C%20%5Cimplies%5Csf%7B%20x%20%3D%20%206%20%7D%20%20)
