ΔABC is dilated using a scale factor of 12 to produce ΔA'B'C'. Select all of the statements that apply to the transformation.
1 answer:
Answer:
Options (3) and (6)
Step-by-step explanation:
ΔABC is a dilated using a scale factor of to produce image triangle ΔA'B'C'.
Since, dilation is a rigid transformation,
Angles of both the triangles will be unchanged or congruent.
m∠A = m∠A' and m∠B = m∠B'
Since, sides of ΔA'B'C' = of the sides of ΔABC
Area of ΔA'B'C' =
Area of ΔABC > Area of ΔA'B'C'
Since, angles of ΔABC and ΔA'B'C' are congruent, both the triangles will be similar.
ΔABC ~ ΔA'B'C'
Therefore, Option (3) and Option (6) are the correct options.
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Please see the attached picture.
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Please see the attached picture.
<h2>Answer:</h2>
The graph is shown in the Figure below
<h2>Step-by-step explanation:</h2>In this exercise, we have an equation. On the left side we have a straight line with slope and there is no any y-intercept. On the right side, on the other had, we also have a straight line, but the slope here is
. Therefore, by plotting these two straight lines, we have that the solution is the origin, that is, the point
.
Answer:
d. can be equal to the value of the coefficient of determination (r2).
True on the special case when r =1 we have that
Step-by-step explanation:
We need to remember that the correlation coefficient is a measure to analyze the goodness of fit for a model and is given by:
The determination coefficient is given by
Let's analyze one by one the possible options:
a. can never be equal to the value of the coefficient of determination (r2).
False if r = 1 then
b. is always larger than the value of the coefficient of determination (r2).
False not always if r= 1 we have that and we don't satisfy the condition
c. is always smaller than the value of the coefficient of determination (r2).
False again if r =1 then we have and we don't satisfy the condition
d. can be equal to the value of the coefficient of determination (r2).
True on the special case when r =1 we have that
Answer: Choice B
a = 42, b = 5, c = 28, d = 33, e = 10
====================================================
Explanation:
Refer to the diagram below. We have a table of values in which some values (if not most) are unknown. We have variables as placeholders until we can figure out which numbers replace them.
Along the bottom row, we see that 70+e = 80, which solves to e = 10. I subtracted 70 from both sides.
That must mean the answer is between choice A or choice B.
--------------------------
Since e = 10, and b+5 = e (third column), we can replace the 'e' with 10 to get the equation b+5 = 10. That solves to b = 5. This rules out choice A.
The final answer is choice B
---------------------------
If you want to keep going to find a, c and d, then let's solve a+b = 47 which is the same as a+5 = 47 after replacing letter b with 5.
a+5 = 47 solves to a = 42 after subtracting both sides by 5.
Then along the first column, we see that a+c = 70 which is the same as 42+c = 70. Isolating c gets us c = 28
Lastly, c+5 = d is shown along the second row. Plug in c = 28 to find that d = c+5 = 28+5 = 33
So overall we have:
a = 42, b = 5, c = 28, d = 33, e = 10
