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2 years ago

Which set of shapes contains members that are always similar to one another?

2 answers:

8 0

Ok, Let me start from the word Similar , the word which is usually used in mathematics for geometrical shapes mainly polygons.

Similar Polygons= Two or more Polygons are said to be similar if their corresponding sides are proportional and Corresponding interior angles are equal.

I will answer this question by starting from

1. Option A:→ Trapezoids= Why two trapezoids can't be similar because if we consider parallel sides of trapezoids their length can vary. Suppose One trapezoid has parallel sides of length 7 m and 13 m , and other trapezoid has parallel sides of length 6 m and 11 m.So, neither the corresponding sides are proportional nor interior angles are equal.

So, the Statement is Incorrect that All Trapezoids are always similar to one another.

2. →B.isosceles triangles=One isosceles triangle (4,4,5, 50°,50°,80°) and Other isosceles triangle being (3,3,7,55°,55°,70°).

So, the Statement is Incorrect that All Isosceles triangles are always similar to one another.

3. →→C.Equilateral triangles=All equilateral triangles will always be similar because their all interior angles will always be 60°, whatever the length of their sides.So, two equilateral triangles will always be similar because ratio of their corresponding sides will always be equal and their corresponding interior angles will always be 60°.

4. →→D.Rectangles= Consider two rectangles having Dimensions (70 × 40) and (60 × 30).

So, the Statement is Incorrect that All Rectangles are always similar to one another.

5.→→E. Pentagons :=Two Regular pentagons are always similar to each other, but not all.

So, the Statement is Incorrect that All Pentagons are always similar to one another.

Option C i.e Set of equilateral triangles, is true statement about the set of shapes which contains members that are always similar to one another.

Elden [556K]2 years ago

4 0

It should be C. Equilateral triangles

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The answer would be $1.75 (Rounded off to the nearest cent).

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2 years ago

A worker drives a 0.500 kg spike into a rail tie with a 2.50 kg sledgeham-

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Total internal energy increases by 1760 J

Step-by-step explanation:

The kinetic energy of an object is the energy possessed by the object due to its motion.

It is calculated as

$KE=\frac{1}{2}mv^2$

where

m is the mass of the object

v is its speed

For the hammer in this problem:

m = 2.50 kg

v = 65.0 m/s

So its kinetic energy is

$KE=\frac{1}{2}(2.50)(65)^2=5281 J$

Then the problem says that 1/3 of the hammer's kinetic energy is converted into internal energy: therefore, the total internal energy increases by

$\frac{1}{3}KE=\frac{1}{3}(5281)=1760 J$

Learn more about kinetic energy:

brainly.com/question/6536722

#LearnwithBrainly

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2 years ago

High-power experimental engines are being developed by the Stevens Motor Company for use in its new sports coupe. The engineers

mamaluj [8]

Answer:

The 95% confidence interval the average maximum power is (596.0 to 644.0)

Step-by-step explanation:

Average maximum of the sample = x = 620 HP

Standard Deviation = s = 45 HP

Sample size = n = 16

We have to calculate the 95% confidence interval. The value of Population standard deviation is unknown, and value of sample standard deviation is known. Therefore, we will use one sample t-test to build the confidence interval.

Degrees of freedom = df = n - 1 = 15

Critical t-value associated with 95% confidence interval and 15 degrees of freedom, as seen from t-table = $t_{\frac{\alpha}{2}}$ = 2.131

The formula to calculate the confidence interval is:

$(x-t_{\frac{\alpha}{2} } \times \frac{s}{\sqrt{n} }, x+t_{\frac{\alpha}{2} } \times \frac{s}{\sqrt{n} })$

We have all the required values. Substituting them in the above expression, we get:

$(620-2.131 \times \frac{45}{\sqrt{16} }, 620+2.131 \times \frac{45}{\sqrt{16} })\\\\ =(596.0 , 644.0)$

Thus, the 95% confidence interval the average maximum power is (596.0 to 644.0)

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