8TH GRADE MATH

Mathematics

1 answer:

IRISSAK [1]2 years ago

3 0

Answer: choice G)

Corresponding angles are congruent; therefore, 2x+52 = 76

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Explanation:

Let's go through the answer choices one by one

We can rule out choice F because 4x and 104 are alternate exterior angles. They are equal because line a and line b are parallel. So 4x = 104 is a valid equation to solve for x.
Choice G is the answer because 2x+52 and 76 are not corresponding angles. One possible pair of corresponding angles are 2x+52 and 104. These two angles are in the southeast corner of each 4 corner angle configuration, which is why they correspond to one another. The pairing 2x+52 and 76 are instead supplementary, so those two angles add to 180.
We can rule out choice H because 4x and 2x+52 are congruent vertical angles. Vertical angles form when we have an X shape from the intersection of two lines. Specifically vertical angles are opposite one another like the diagram shows.
We can rule out choice J because the angles (4x) and (x+50) are supplementary. This means they add to 180. This applies to any pair of same side exterior angles. They are on the same side of the transversal line t. They are exterior because they are outside of the parallel lines a and b.

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The recursive rule for a sequence is an=an-1+7, where a1=15.What is the explict rule for this sequence

posledela

well, the recursive rule of aₙ = aₙ₊₁ + 7, where a₁ = 15, is simply saying that

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well, that's the recursive rule.

so then let's use that common difference and first term for the explicit rule.

$\bf n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\ \cline{1-1} a_1=15\\ d=7 \end{cases} \\\\\\ a_n=15+(n-1)7\implies a_n=15+7n-7\implies a_n=7n+8$