Answer:
Yes, the shapes are similar. Note, the angles are equivalent and the sides are scales of each other satisfying the requirements for similarly.
Step-by-step explanation:
For a shape to be similar there are two conditions that must be met. (1) Must have equivalent angles (2) Sides must be related by a scalar.
In the two triangles presented, the first condition is met since each triangle has three angles, 90-53-37.
To test if the sides are scalar, each side must be related to a corresponding side of the other triangle with the same scalar.
9/6 = 3/2
12/8 = 3/2
15/10 = 3/2
Alternatively:
6/9 = 2/3
8/12 = 2/3
10/15 = 2/3
Since the relationship of the sides is the scalar 3/2 (Alternatively 2/3), then we can say the triangles meet the second condition.
Given that both conditions are satisfied, then we can say these triangles are similar.
Note, this is a "special case" right triangle commonly referred to as a 3-4-5 right triangle.
Cheers.
1/3 + 1/3 + 1/3 + 1/3 + 1/3 + 1/3 = 6/3
The answers are:
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[B]: "√12 " ; AND:
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[D]: "<span>√20" .
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Note: "Irrational numbers" have decimals that are: 1) non-terminating; AND: 2) non-repeating.
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Consider the answer choices given; and consider the given information that there "should be no more than one answer.
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Consider the following answer choices:
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Choice A) "</span><span>√9" = 3 . Rule out this choice.
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Choice C) "</span><span>√16" = 4 . Rule out this choice.
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Choice E) "</span><span>√25" = 5. Rule out this choice.
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We are left with 2 (two) remaining answer choices:
[B]: "</span>√12" ; and: [D]: "<span>√20" .
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If there are more than one answer, then these two choices should be the correct answer. However, let us explore these two choices, using a calculator.
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[B]: </span>"√12" = 3.4641016151377546
[D]: "√20" = 4.4721359549995794
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These two answer choices should the correct answers.
6x + 5x + (x + 16) + (3x - 1) = 360
11x + x + 16 + 3x - 1
15x + 15 = 360
15x = 345
x = 23
6(23) = 138
((23) + 16) = 39
(3(23) - 1) =68
5(23) = 115
138 + 39 + 68 + 115 = 360
Slope-intercept form:
y=1/3x+11/3
