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3 years ago

Which of this shape will tessellate?

Mathematics

1 answer:

oksian1 [2.3K]3 years ago

5 0

Answer: You can consult:

Triangles, squares and hexagons are the only regular shapes which tessellate by themselves. You can have other tessellations of regular shapes if you use more than one type of shape. You can even tessellate pentagons, but they won't be regular ones. Tessellations can be used for tile patterns or in patchwork quilts!

Step-by-step explanation:

I'm not sure but hope it helps.

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a jigsaw puzzle has edge pieces and inside pieces. the ratio 3:22. there are 924 inside pieces. calculate the total number of pi

statuscvo [17]

Okay. So, 924 pieces are inside. Let’s divide to see how many times 22 goes into 924. 924/22 = 42. So now, multiply 3 by 42 to do the same thing the opposite way. The product is 126. There are 126 edge pieces in the puzzle. You can do 126/924 to get the fraction in simplest form to be 3/22. To find the total number of pieces, add both numbers up. The sum of the two numbers is 1,050. There are 1,050 total pieces in the puzzle.

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4 years ago

Someone PLease please help me

makvit [3.9K]

Answer is 1 . Righttttttttttttt

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3 years ago

Mrs. Smith has $20,000 to invest. She wants to earn $10,000 in interest. She is considering a savingsand loans bank that is offe

disa [49]

Answer:

Number of year to get $10,000 as interest = 7.5 year (Approx)

Step-by-step explanation:

Given:

Initial investment = $20,000

Interest on investment = $10,000

Rate of interest = 5.6% = 0.056

Find:

Number of year to get $10,000 as interest:

Computation:

$Interest\ on\ investment = Initial\ investment[(1+r)^n-1]\\\\10,000 = 20,000[(1+0.056)-1]\\\\0.5=(1.056)^n-1\\\\1.5 =(1.056)^n\\\\n=7.44$

Number of year to get $10,000 as interest = 7.44

Number of year to get $10,000 as interest = 7.5 year (Approx)

7 0

3 years ago

A moving company charges $40 plus point $.25 per mile to rent a van. Another company charges $25 plus point $.35 per mile to ren

nikdorinn [45]

Answer: 150 miles

Step-by-step explanation:

m = mile

40 + 0.25m = 25 + 0.35m

0.25 * 150 = 37.5

37.5 + 40 = 77.5

0.35 * 150 = 52.5

52.5 + 25 = 77.5

77.5 = 77.5

5 0

4 years ago

Find the three angles of the triangle with the given vertices: P(1,1,1), ????(1,−3,2), and ????(−3,2,5).

velikii [3]

Answer:

The three angles of the triangle are 90, 35.67 and 54.33 degrees.

Step-by-step explanation:

One way to find the angles of the triangle with vertices (1, 1, 1), (1, -3, 2), (-3, 2, 5) is using the definition of the dot product of two vectors, defined as:

a . b = |a| |b| cosФ [1]

Where |a| and |b| are the norms of vectors a and b, and cosФ is the cosine of the angle between either vector a and b.

If a = [ $\\ a_{1}, a_{2}, a_{3}$ ] and b = [ $\\ b_{1}, b_{2}, b_{3}$ ], then the dot product is simply a number (not a vector) obtained from:

a . b = $\\ a_{1}*b_{1} + a_{2}*b_{2} + a_{3}*b_{3}$

The norm of a vector (its length) is, for instance, |a| = $\\ \sqrt{{a_{1}^2 + {a_{2}}^2 + {a_{3}}^2}$ , for a vector in $\\ R^{3}$ .

Having all that into account, we can determine the angles of the triangle for each vertex using equation [1] and solving it for Ф.

<h3>Angle of the triangle for vertex in (1, 1, 1)</h3>

The vectors which form an angle from this vertex are the result of subtracting the vertex (1, 1, 1) to any of the remaining points (1, -3, 2) and (-3, 2, 5):

v(1, 1, 1) - v(1, -3, 2) = $\\ (1 - 1, 1 - (-3), 1 - 2) = (0, 1 + 3, -1) = (0, 4, -1)$

v(1, 1, 1) - v(-3, 2, 5) = $\\ (1 - (-3), 1 - 2, 1 - 5) = (1 + 3, -1, -4) = (4, -1, -4)$

The dot product for these vectors is:

[0, 4, -1] . [4, -1, -4] = [0 * 4 + 4 * -1 + -1 * -4] = 0 - 4 + 4 = 0

The norm for each vector is:

|(0, 4, -1)| = $\\ \sqrt{0^2 + 4^2 + -1^2} = \sqrt{0 + 16 + 1} = \sqrt{17}$

|(4, -1, -4)| = $\\ \sqrt{4^2 + -1^2 + -4^2} = \sqrt{16 + 1 + 16} = \sqrt{33}$

a . b = |a| |b| cosФ

$\\ 0 = \sqrt{17} * \sqrt{33} * cos{\theta}$

$\\ \frac{0}{\sqrt{17} * \sqrt{33}} = cos{\theta}$

$\\ cos^{-1}{0}} = cos^{-1}(cos{\theta})$

$\\ 90 = \theta$

In vertex (1, 1, 1) the angle of the triangle is 90 degrees. We have here a right triangle.

We have to follow the same procedure for finding the vectors for angles in vertices (1, -3, 2) and (-3, 2, 5), or better, after finding one of the previous angles, we find the remaining angle subtracting the sum of two angles from 180 degrees to finally obtaining the three angles in question.

Therefore, the other angles are 35.67 degrees and 180 - (90 + 35.67) = 180 - 125.67 = 54.33 degrees.

5 0

3 years ago

Which of this shape will tessellate?​

Which of this shape will tessellate?