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zhannawk [14.2K]
3 years ago
14

Which pairs of polygons are similar? Select each correct answer.

Mathematics
2 answers:
padilas [110]3 years ago
8 0
What was the answer please help me
kvasek [131]3 years ago
5 0

Answer: The first and fourth pair of polygons are similar.


Step-by-step explanation:

If two polygons are similar then their corresponding sides are proportional.

Let's check

  • In the first pair there are two rectangles and their dimensions are proportional as

\frac{22}{13.75}=\frac{16}{10}=1.6

  • In the second pair there are right triangles but their dimensions are not proportional as

\frac{18}{8}=2.25 and \frac{30}{17}=1.76

  • In the third pair there is one isosceles triangle and other is equilateral triangle, which can not be similar as they have different type of triangles.
  • In the fourth pair there are two right trapezoid and their dimensions are proportional as

\frac{7.5}{3}=\frac{30}{12}=\frac{12.5}{5}=\frac{20}{8}=2.5

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F divides HJ in the ratio 3:1. If H = (-11,7) and J = (5,3), what are the<br> coordinates of F?
Hatshy [7]

Answer:

The coordinates of HF are (1, 4)

Step-by-step explanation:

The parameters of the line are;

The coordinate of the end points are H = (-11, 7), and J = (5, 3)

The ratio by which the point F divides the line = 3:1

The segments in the line are HF, and FJ

Therefore;

The fraction of the length of HJ that is represented by HF = 3/(3 + 1) × HJ = 3/4 × HJ

HF = 3/4 × HJ

Which gives the coordinates of the point F as follows;

Coordinate of F = (-11 +(5 - (-11))×3/4, 7 + (3 - 7)×3/4) =  (1, 4)

The coordinates of F are (1, 4)

We check the length of HF, from the equation for the length to of a line to get;

l = \sqrt{\left (y_{2}-y_{1}  \right )^{2}+\left (x_{2}-x_{1}  \right )^{2}}

l_{HF} = \sqrt{\left (4-7  \right )^{2}+\left (1-(-11)  \right )^{2}} = \sqrt{\left (-3  \right )^{2}+\left (12  \right )^{2}} = 3\cdot \sqrt{17}

Similarly, we check the length of HJ, to get;

l_{HF} = \sqrt{\left (3-7  \right )^{2}+\left (5-(-11)  \right )^{2}} = \sqrt{\left (-4  \right )^{2}+\left (16  \right )^{2}} = 4\cdot \sqrt{17}

The length of HF = 3·√(17)

The length of HJ = 4·√(17)

Therefore, from HF = 3/4× HJ, we have;

HF = 3/4 × 4·√(17) = 3·√(17)

Therefore, the coordinates of HF are (1, 4)

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Answer:

option A

Step-by-step explanation:

given,                                                

the bank branch is offering $1,000 certificates of deposit.

Rate of interest per year = 4 % = 0.04                        

The bank is selling certificates with terms of 1, 2, 3, or 4 years

total amount =  A , in dollar              

time of investment = k years              

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A = P + P r t                                      

A = P (1 + r t)                                          

A = P (1 + 0.04 k)                            

the correct answer is option A

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Answer:

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Step-by-step explanation:

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