Let
If M is the midpoint, the x and y coordinates of M are the average of the x and y coordinates of P and Q:
We can solve this expression for the coordinates of Q:
Plug in the values for the coordinates of M and P to get
The answer is
-5/8+9/2=3 7/8 or 31/8
so you should put 31 in the green box
<span>Based in the information given in the problem, you must apply the The Angle Bisector Theorem. Let's call the triangle: "ABC"; the internal bisector of the angle that divides its opposite side: "AP"; and "x": the longest and shortest possible lengths of the third side of the triangle.
If BP= 6 cm and CP= 5 cm, we have:
BP/CP = AB/AC
We don't know if second side of the triangle (6.9 centimeters long) is AB or AC, so:
1. If AB = 6.9 cm and AC = x:
6/5 = 6.9/x
x = (5x6.9)/6
x = 5.80 cm
2. If AC= 6.9 cm and AB= x:
6/5 = x/6.9
x = 6.9x6/5
x = 8.30 cm
Then, the answer is:
The longest possible length of the third side of the triangle is 8.30 cm and the and shortest length of it is 5.80 cm.</span>
Answer:
Step-by-step explanation:
we know that
DGH ~ DEF ---> given problem
Remember that
If two triangles are similar, then the rtio of its corresponding sides is proportional and its corresponding angles are congruent
so
substitute the given values
Minimum value is equal to x=8, y=-4First find the derivative of the original equation which equals= d/dx(x^2-16x+60) = 2x - 16at x=8, f'(x), the derivative of x equals zero, so therefore, at point x = 8, we have a minimum value.Just plug in 8 to the original equation to find the answer for the minimum value.
