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3 years ago

4. What are the elements needed to prove similarity between two figures? Explain.

1 answer:

8 0

Two geometrical objects are called similar if they both have the same shape, or one has the same shape as the mirror image of the other. More precisely, one can be obtained from the other by uniformly scaling (enlarging or reducing), possibly with additional translation, rotation and reflection. This means that either object can be rescaled, repositioned, and reflected, so as to coincide precisely with the other object. If two objects are similar, each is congruent to the result of a particular uniform scaling of the other. A modern and novel perspective of similarity is to consider geometrical objects similar if one appears congruent to the other when zoomed in or out at some level.

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Can somebody prove this mathmatical induction?

Flauer [41]

Answer:

See explanation

Step-by-step explanation:

1 step:

n=1, then

$\sum \limits_{j=1}^1 2^j=2^1=2\\ \\2(2^1-1)=2(2-1)=2\cdot 1=2$

So, for j=1 this statement is true

2 step:

Assume that for n=k the following statement is true

$\sum \limits_{j=1}^k2^j=2(2^k-1)$

3 step:

Check for n=k+1 whether the statement

$\sum \limits_{j=1}^{k+1}2^j=2(2^{k+1}-1)$

is true.

Start with the left side:

$\sum \limits _{j=1}^{k+1}2^j=\sum \limits _{j=1}^k2^j+2^{k+1}\ \ (\ast)$

According to the 2nd step,

$\sum \limits_{j=1}^k2^j=2(2^k-1)$

Substitute it into the $\ast$

$\sum \limits _{j=1}^{k+1}2^j=\sum \limits _{j=1}^k2^j+2^{k+1}=2(2^k-1)+2^{k+1}=2^{k+1}-2+2^{k+1}=2\cdot 2^{k+1}-2=2^{k+2}-2=2(2^{k+1}-1)$

So, you have proved the initial statement

4 0

4 years ago

What is the missing side and what is the answer rounded to the nearest tenth?

pogonyaev

The missing side is 17 and rounded it is 20

4 0

3 years ago

A negative correlation means ________. Group of answer choices there is a relationship between two variables, but it is not stat

lisov135 [29]

Answer: one variable decreases as the other increases

Step-by-step explanation:

5 0

3 years ago

Graph ƒ(x) = 2x - 3.

Naya [18.7K]

Ok so your gonna go on the graph and your gonna go to -3 and make a dot then from that point you go up two times and over to the right once and that's your slope

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3 years ago

A science class has 3 girls and 1 boy in the seventh grade and 5 girls and 5 boys in the eighth grade. the teacher randomly sele

brilliants [131]

In the science class,
there are 3 girls and 1 boy (grade 7)
and 5 girls and 5 boys (grade 8)
There is a total of 14 pupils being 8 girls and 6 boys
The probability of choosing a boy will be $\frac{6}{14}$
Which can be simplified into $\frac{3}{7}$ by dividing 2 from the numerator as well as the denominator.

8 0

3 years ago