What value of x makes this equation true?
2 answers:
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Answer:
Triangle DEF is a right, scalene triangle. It is not isosceles, obtuse, acute, or equilateral
Step-by-step explanation:
All we know about m and n are that they are not equal to each other and they are positive. This was given in the problem. See image. Once it is graphed you can see on the graph the lengths of DE and EF. Use Pythagorean theorem to calculate DF. see image.
DE is horizontal and EF is vertical, so you can see their slopes or calculate using a formula. Calculate the slope of DF. Slope is y-y on top of a fraction and x-x on the bottom of the fraction.
Lastly, use midpoint formula to find the midpoints. Average the x's and average the y's to find the x- and y-coordinates of the midpoints. See image.
Finally, DEF is a right triangle. The graph as well as the slopes show us that DE and EF form a right angle. So DEF must be a right triangle (and not obtuse nor acute) We were told that m doesNOT equal n, so the triangle cannot have two equal sides, so it cannot be isosceles (2 equal sides) nor equilateral (3 equal sides) It has 3 different lengths of sides; that is called scalene.
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Answer:
in order by function: 0.6, 8, 7/3, 2, 1/2
Step-by-step explanation:
The functions are given in the form ...
f(x) = a·b^x
The "b" value is the value immediately to the left of the exponent. (It's not rocket science; it's pattern matching.) Note that the minus sign in g(x) is part of 'a', not part of 'b'.
From the top-down, the functions listed on the left have the b-values shown above.
