100 POINTS

Mathematics

2 answers:

Andru [333]3 years ago

6 0

Answer:

(1, -7)

Step-by-step explanation:

P(3,4)

3 up ---> y = 4 + 3 = 7

2 left ----> x = 3 - 2 = 1

new point (1, 7)

after 180 rotation around origin

point is (-1, -7)

now reflection over y-axis

(1, -7)

Lisa [10]3 years ago

3 0

Answer:

$(1,-7)$

Step-by-step explanation:

Refer to the image below

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$\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ S_n=\displaystyle\sum \limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio} \end{cases} \\\\[-0.35em] ~\dotfill$

$\bf S_{20}=\displaystyle\sum \limits_{n=1}^{\stackrel{\stackrel{n}{\downarrow }}{20}}~\stackrel{\stackrel{a_1}{\downarrow }}{3}(\stackrel{\stackrel{r}{\downarrow }}{1.5})^{n-1}\implies S_{20}=3\left(\cfrac{1-1.5^{20}}{1-1.5} \right)\implies S_{20}=3\left(\cfrac{1-\stackrel{\approx}{3325.3}}{-0.5} \right) \\\\\\ S_{20}=3\left(\cfrac{-3324.3}{-0.5} \right)\implies S_{20}=3(6648.6)\implies S_{20}=19945.8$