Hi there!
Since the triangle is equilateral, all of its sides are congruent. This means that to solve, we can set the two given equations equal to each other.
2(x - 8) = 1/2x + 8
2x - 16 = 1/2x + 8
1.5x - 16 = 8
1.5x = 24
x = 16
Now that we know what x is, we can plug that in for x in the equation for ZY.
2(16 - 8) = ZY
ZY = 2(8)
ZY = 16 units
And here is the work to show that XZ is also 16.
1/2(16) + 8 = XZ
XZ = 8 + 8
XZ = 16
Hope this helps!! :)
If there's anything else that I can help you with, please let me know!
Answer:
The slope of a line parallel to this line is -7/6, and the slope of a line perpendicular to this line is 6/7.
Step-by-step explanation:
7x+6y=8
6y=8-7x
6y=-7x+8
y=-7/6x+8/6
y=-7/6x+4/3
Parallel lines have the exact same slopes, but perpendicular lines have negative reciprocal slopes.
Answer:
The radius is increasing at a rate of approximately 0.044 in/s when the diameter is 12 inches.
Because 
the radius is changing more rapidly when the diameter is 12 inches.
Step-by-step explanation:
Let 
be the radius, 
the diameter, and 
the volume of the spherical balloon.
We know 
and we want to find 
The volume of a spherical balloon is given by
Taking the derivative with respect of time of both sides gives
We now substitute the values we know and we solve for :
The radius is increasing at a rate of approximately 0.044 in/s when the diameter is 12 inches.
When d = 16, r = 8 and is:
The radius is increasing at a rate of approximately 0.025 in/s when the diameter is 16 inches.
Because the radius is changing more rapidly when the diameter is 12 inches.
The quadratic equation is;
x²+5x-6 = 0
x²+6x-x-6 = 0
x(x+6)-1(x+6) = 0
(x+6)(x-1) = 0
So,
x+6 = 0 and x-1 = 0
x=-6 and x = 1
Thus the answer is
x = -6,1
Answer:
D
Step-by-step explanation
You multiply 7x2 first, that equals 14. Then you add 13+4, which equals 17. You then subtract those two and get 3.
