Answer:
The correct answer is first option 60%
Step-by-step explanation:
The radius of a circle is inscribed in an equilateral triangle with side a = a/2√3
<u>To find the area of equilateral triangle</u>
Here side be 'a'
Area of equilateral = √3a²/4
<u>To find the area of circle</u>
Here radius = a/2√3
Area = πr²
= π(a/2√3)
= 3.14a²/12
<u>To find the probability</u>
probability = area of circle/area of triangle
= 3.14a²/12/ √3a²/4
= 3.14/3√3
= 0.6043 ≈ 60.43 % 60 %
The correct answer is first option 60%
Hello there!
3x - y = 3
-x + y = 3
We need to solve 3x - y = 3 for y
Let start by adding -3x to both sides
3x - y = 3
3x - 3x - y = 3 - 3x
-y = 3 - 3x
We cannot leave the variable with a negative sign. We must multiply both sides by -1
-y * -1= (3 - 3x)-1
y = 3x - 3
Substitute 3x -3 for y in -x+y=3
-x + y = 3
-x + 3x - 3 = 3
2x - 3 = 3
2x = 3 + 3
2x = 6
x = 6/2
x = 3
Now substitute 3 for x in y=3x -3
y = 3x - 3
y = 3(3) - 3
y= 9 - 3
y= 6
Thus,
The answer is x=3 and y=6
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Distance = Speed × Time
Distance = (4.5 mi)/(0.75 h) × (3.5 h) = 21 mi
The walker will cover 21 miles in 3.5 hours at that pace.
Samuel needs to estimate the product of 24 x 395.
First method
We round the number to nearest tens
24 can be rounded to 20 because we have 4 on ones place
395 can be rounded to 400 because we have 5 in ones place so we add 1 with 9 and it becomes 10 . so we add 1 with 3 and got 400
20 * 400 = 8000
Second method:
We round the number to nearest hundreds place
24 have no number in hundreds place so it remains 24
395 can be rounded to 400 because we have 9 in tens place.
24 * 400 = 9600
Using transformations and congruency concepts, it is found that with these following transformations, the triangles will be congruent.
- A reflection, then a translation.
-
A rotation, then a reflection.
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- Two triangles are congruent if they have the <u>same lengths</u> of the sides and the <u>same angles.</u>
- In a reflection, there is a rule that changes the <u>coordinates (x,y)</u>, but does <u>not </u>change <u>the lengths</u> of the sides of the triangles, thus they will still be congruent.
- A <u>reflection is also a special case of rotation</u>, thus, in a rotation, the triangles are also congruent.
- A translation is also similar to a reflection, using rules to shift the triangle up, down, left or right according to it's coordinates, not changing the sides or angles, thus congruent.
- In a dilation, the <u>lengths of the sides are changed</u>, thus, the triangles will not be congruent.
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Thus, from the bullet points above, the correct options are:
- A reflection, then a translation.
- A rotation, then a reflection.
A similar problem is given at brainly.com/question/24267298
