Clearly, |S| = 50.
Count the multiples of 2 between 1 and 50:
⌊50/2⌋ = ⌊25⌋ = 25
(where ⌊x⌋ denotes the "floor of x", or the largest integer that is smaller than or equal to x; in other words, round <u>down</u> to the nearest integer)
Count the multiples of 3 between 1 and 50:
⌊50/3⌋ ≈ ⌊16.667⌋ = 16
Since LCM(2, 3) = 6, the sets of multiples of 2 and multiples of 3 have some overlap. Count the multiples of 6 between 1 and 50:
⌊50/6⌋ ≈ ⌊8.333⌋ = 8
Then by the inclusion/exclusion principle, we remove from S
25 + 16 - 8 = 33
elements, so that the new set S contains 50 - 33 = 17 elements.
Answer: A sequence of similar transformations of dilation and translation could map △ABC onto △A'B'C'.
Step-by-step explanation:
Similar transformations: If one figure can be mapped onto the other figure using a dilation and a congruent rigid transformation or a rigid transformation followed by dilation then the two figures are said to be similar.
In the attachment △ABC mapped onto △A'B'C' by a sequence of dilation from origin and scalar factor k followed by translation.
Do you mean what are axes?
Answer:
f(x) = 3x2
Step-by-step explanation:
I think the given the scatter plot is missing and it is my attachment for your question.
My answer:
f(x) = 3x2, it is a parabolic pathway. a =3 (positive) so the line is going up.
The other options are straight lines so they are wrong.
Since there is only addition and subtraction between the terms, we can drop the brackets.
= 2x - 2 + 7x + 21
For clarification, we can rearrange the equation.
= 2x + 7x - 2 + 21
Now we simplify by collecting like terms (the x's must stay together).
= 9x + 19
Hope this helps!