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defon
3 years ago
11

GEOMETRY PLEASE HELP

Mathematics
1 answer:
marysya [2.9K]3 years ago
7 0

Answer:

see explanation

Step-by-step explanation:

(5)

Since ∠EBA = 90° then ∠ABD = 90° ( straight angle ) and

∠ABC + ∠CBD = ∠ABD, that is

2x + 3x - 10 = 90, simplifying

5x - 10 = 90 ( add 10 to both sides )

5x = 100 ( divide both sides by 5 )

x = 20, thus

∠ABC = 2x = 2 × 20 = 40°

∠CBD = 3x - 10 = (3 × 20) - 10 = 60 - 10 = 50°

(6)

4x - 18 = 3x + 7 ( vertical angles are congruent )

Subtract 3x from both sides

x - 18 = 7 ( add 18 to both sides )

x = 25

7y = 5y + 28 ( vertical angles are congruent )

Subtract 5y from both sides

2y = 28 ( divide both sides by 2 )

y = 14

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The candy jar has 251 pieces of candy. Sophia adds 31 pieces of candy to it. If the candy is divided equally between 6 campers,
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Answer:

47

Step-by-step explanation:

251+31= 282

282 divided by six = 47

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I need help with #61 to #64 ASAP please and thank you …. Could someone please help me with it… I need to get it done ASAP
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Problem 61

The nth triangular number is

T(n) = n(n+1)/2

I'll rewrite this into

T(n) = 0.5n(n+1)

The triangular number right after this is

T(n+1) = 0.5(n+1)(n+2)

I replaced every n with n+1 and simplified

Let's see what we get when we add up the two expressions

T(n) + T(n+1)

0.5n(n+1) + 0.5(n+1)(n+2)

0.5n^2+0.5n + 0.5(n^2+3n+2)

0.5n^2 + 0.5n + 0.5n^2 + 1.5n + 1

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(n+1)^2

This shows that the sum of any two consecutive triangular numbers results in a square number

Here's a few examples

  • 0+1 = 1
  • 1+3 = 4
  • 3+6 = 9
  • 6+10 = 16
  • 10+15 = 25

Note each sum is a perfect square, which visually would plot out a square figure.

For quick reference, the set of the first few triangular numbers is {0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55,...}

<h3>Answer: Square number</h3>

==========================================================

Problem 64

Let's say we go with n = 5.

This means,

T(n) = 0.5n(n+1)

T(n-1) = 0.5(n-1)(n-1+1)

T(n-1) = 0.5n(n-1)

T(5-1) = 0.5*5(5-1)

T(4) = 10

This says that when n = 5, the 4th triangular number is 10

Triple that result and add on n = 5

3*T(4) + n = 3*10+5 = 35

This result is beyond obvious which category of figurate number it belongs to. It's not a triangular number since it's not in the form n(n+1)/2. It's not a square number either.

Through a bit of trial and error, you should find it's a pentagonal number

Pentagonal numbers are of the form n(3n-1)/2

If you plugged n = 5 into that, it leads to 35

n(3n-1)/2 = 5*(3*5-1)/2 = 5*14/2 = 70/2 = 35

The diagram shown below represents the first few pentagonal numbers. The number of blue dots corresponds to the pentagonal number itself. Note the equal spacing when dealing with dots on each segment (eg: some interior blue dots are midpoints, others are quarter points, etc.)

<h3>Answer: Pentagonal number</h3>

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