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3 years ago

Determine if the triangles, ΔZBX and ΔNBG, are similar. If so, identify the similarity criterion.

Mathematics

1 answer:

photoshop1234 [79]3 years ago

6 0

Answer:

Step-by-step explanation:

Consider triangles ZBX and NBG. In these triangles, angles ZBX and NBG are congruent as vertical angles (two opposite angles when two lines intersect).

From the diagram,

$\dfrac{XB}{BG}=\dfrac{5}{15}=\dfrac{1}{3}\\ \\\dfrac{ZB}{BN}=\dfrac{4}{12}=\dfrac{1}{3}$

Hence,

$\dfrac{XB}{BG}=\dfrac{ZB}{BN}$

Therefore, triangles ZBX and NBG are similar by SAS similarity theorem.

SAS Similarity Theorem states that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.

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What is number pattern

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A number patter is a list of numbers that follow a certain pattern like 2,4,6,8,10 is a pattern of 2's

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3 years ago

A dictionary contains the following 9 words: two, mice, three, squeaking, the, blind, deaf, birds, rabbits. What is the probabil

IgorC [24]

Answer:

The correct answer is B. 1/729

Step-by-step explanation:

1. Probability of any of the nine words would be randomly cited.

Using the Laplace Rule, we calculate that probability is 1/9

2. Now let's calculate the probability of any two - word phrase in specific order from those nine in the dictionary. We should remember that the probability of occurrence of two or more statistically independent events is equal to the product of their individual probabilities. So,

1/9 * 1/9 = 1/81

3. Using the same Multiplication Rule, we can calculate the probability of a random generation of the phrase "three blind mice", in that specific order. Because there are other phrases that could be generated with those three words, but in different order. The question was specific about the order.

1/9 * 1/9 * 1/9 = 1/729

The probability of randomly generating the phrase "three blind mice" is 1/729 or 0.137%

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3 years ago

Slope formula question (Algebra 2)

DaniilM [7]

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 5}}\quad ,&{{ 3}})\quad 
% (c,d)
&({{ 3}}\quad ,&{{ 1}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
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3 years ago

A monkey is swinging from a tree. On each swing, she travels along an arc that is 75% as long as the previous swing's arc. The t

mr_godi [17]

Answer:

Total length of the first swing=64 m

Step-by-step explanation:

The total length of all four swings can be expressed as;

Total length of all 4 swings=Length of first swing+length of second swing+length of third swing+length of fourth swing

where;

Total length of all 4 swings=175 m

Length of first swing=x

Length of second swing=75% of length of first swing=(75/100)×x=0.75 x

Length of third swing=75% of length of second swing

Length of third swing=(75/100)×0.75 x=0.5625 x

Length of fourth swing=75% of length of third swing

Length of fourth swing=(75/100)×0.5625 x=0.421875 x

replacing;

Total length of all 4 swings

175=x+0.75 x+0.5625 x+0.421875 x

2.734375 x=175

x=175/2.734375

x=64

Total length of the first swing=x=64 m

3 0

3 years ago

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Devide 60 in the ratio of 2:3

nevsk [136]

Answer:

Let the amounts be 2x and 3x.

Then 2x+3x=60

So, 5x=60

So, x=60/5=12

So, amounts are

2x=2*12=24

And 3x=3*12=36

Hope this helps you!

Step-by-step explanation:

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3 years ago

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