Given:
Consider the pentagon MVEDR is dilated with the origin as the center of dilation using the rule 
to create pentagon M'V'E'D'R'.
To find:
The correct statement.
Solution:
If a figure dilated by factor k, then the rule of dilation is
Here,
If k>1, then the image is larger than the original figure.
If k<1, then the image is smaller than the original figure.
We have,
Here, M'V'E'D'R' is image and MVEDR is original figure. The scale factor is
Pentagon M'V'E'D'R' is smaller than pentagon MVEDR because the scale factor is less than 1.
Therefore, the correct option is B.
Answer:
$4
Step-by-step explanation:
The two purchases can be written in terms of the cost of an adult ticket (a) and the cost of a student ticket (s):
7a +16s = 120 . . . . . . . . price for the first purchase
13a +9s = 140 . . . . . . . . price for the second purchase
Using Cramer's rule, the value of s can be found as ...
s = (120·13 -140·7)/(16·13 -9·7) = 580/145 = 4
The cost of a student ticket is $4.
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<em>Comment on Cramer's Rule</em>
Cramer's rule is particularly useful for systems that don't have "nice" numbers that would make substitution or elimination easy methods to use. If you locate the numbers in the equation, you can see the X-patterns that are used to compute the numerator and denominator differences.
The value of a is (16·140 -9·120)/(same denominator) = 1160/145 = 8. I wanted to show you these numbers so you could see the numerator X-pattern for the first variable.
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Of course, graphical methods can be quick and easy, too.
Answer:
the largest interval of x values where f(x) is increasing is (-1,1).
Step-by-step explanation:
the domain of f(x) is all real numbers.
As we can conclude from the table that the function f(x) is decreasing from (-3, -1) and the function is increasing from (-1, 1) .
Graphically we can also show this that for the x-values in (1,-1) function is increasing.
The first one cause no input have more than one output.
Take the complex zero 1+i. There must be another zero 1-i to balance it, so we have the factors (x-1-i)(x-1+i)=x²-2x+1+1=x²-2x+2.
So the polynomial is (x+3)(x²-2x+2)=x³-2x²+2x+3x²-6x+6=x³+x²-4x+6, option D.
