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1 year 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]1 year ago

4 0

It should be C. Equilateral triangles

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1 year ago

In a trapezoid the lengths of bases are 11 and 18. The lengths of legs are 3 and 7. The extensions of the legs meet at some poin

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Answer: The length of segments between this point and the vertices of greater base are $7\frac{5}{7}$ and 18.

Step-by-step explanation:

Let ABCD is the trapezoid, ( shown in below diagram)

In which AB is the greater base and AB = 18 DC= 11, AD= 3 and BC = 7

Let P is the point where The extended legs meet,

So, according to the question, we have to find out : AP and BP

In Δ APB and Δ DPC,

∠ DPC ≅ ∠APB ( reflexive)

∠ PDC ≅ ∠ PAB ( By alternative interior angle theorem)

And, ∠ PCD ≅ ∠ PBA ( By alternative interior angle theorem)

Therefore, By AAA similarity postulate,

$\triangle APB\sim \triangle D PC$

Let, DP =x

⇒ $\frac{3+x}{18} = \frac{x}{11}$

⇒ 33 +11x = 18x

⇒ x = 33/7= $4\frac{5}{7}$

Thus, PD= $4\frac{5}{7}$

But, AP= PD + DA

AP= $4\frac{5}{7}+3 =7\frac{5}{7}$

Now, let PC =y,

⇒ $\frac{7+y}{18} = \frac{y}{11}$

⇒ 77 + 11y = 18y

⇒ y = 77/7 = 11

Thus, PC= 11

But, PB= PC + CB

PB= 11+7 = 18

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1 year ago

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Answer:

We are given that,

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$y=-x^2+36$

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Let us consider the equation joining the points (-6,0) and (0,36), given by $y=6x+36$ .

So, the corresponding table for the linear equation is given by,

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So, from the figure, we get that,

Domain is the set of all real numbers.

Range is the set $\{ y|y\leq 36 \}$

Here, domain represents the points which are used to plot the path of the rainbow and range represents the points which are form the rainbow.

Not all points make sense in the range as the parabola is opening downwards having maximum point as (0,36).

2. X and Y-intercepts of the rainbow.

As, the 'x and y-intercepts are the points where the graph of the function cuts x-axis and y-axis respectively i.e. where y=0 and x=0 receptively'.

We see that from the figure below,

X-intercepts are (-6,0) and (6,0) and the Y-intercept is (0,36)

Here, these intercepts represents the point where the parabola intersects the individual axis.

3. Is the linear function positive or negative.

As the linear function is $y=6x+36$ represented by the upward flight of the drone.

So, the linear function is a positive function.

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So, from the figure, we see that the equations intersect at the points (-6,0) and (0,36).

Thus, the solution represents the position when both the drone and rainbow intersect each other.

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Answer:

positive correlation, likely causal

Explanation:

Correlation and causation are different.

Correlation means that the variables are related, meaning that when one changes the other also change. A positive correlation means that the variables change in the same way: when one increases the other also increases, and when one decreases the other also decreases. A negative correlation means that the variables change in opposite directions, i.e. when one increases the other decreases.

The correlations may be strong, moderated or weak. The correlation coefficient tells how strong the correlation is. The correlation coefficient may take values from - 1 to + 1.

A negative 1 correlation coefficient means a perfect negative correlation. A positive 1 correlation coefficient means a perfect positive correlation. Thus, in this case Brett's teacher found that the correlation coefficent was r = 0.97. That is pretty close to 1, and means that this is a strong positive correlation.

About causation, you only may feature a relationship as causal if one variable is the reason why the other variable changed in the way it did it. In this case, it is very reasonable to attribute a causation relationship between the minutes Brett stayed on task in class and the grade he earned on the homework that night, because the more Brett worked in class the better prepared he should be to do his homework, and that idea is reinforced by the high positive correlation coefficient r = 0.97. That is why you can assert that the teacher must have discored a positive correlation, likely causal.

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1 year ago

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