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Varvara68 [4.7K]
4 years ago
8

Given: ABCD is a trapezoid, m∠1=m∠2, m∠3=m∠4, AB = CD, AC ∩ BD = O Prove: m∠AOD = m∠BCD

Mathematics
1 answer:
LiRa [457]4 years ago
6 0
Since AB = CD the trapezoid is isosceles, which means that ∡A = ∡D

Therefore also ∡2 = ∡3 (they are half of the congruent angles)

For the properties of parallel lines (BD and AD) crossed by a transversal (BD) we have ∡3 = ∡CBD.

Now consider triangles AOD and BCD:
∡OAD (2) = ∡ADO (3) = ∡CBD (3) = ∡CDB (4)

T<span>he sum of the angles of a triangle must be 180°, t</span>herefore:
∡AOD = 180 - ∡2 - ∡3
∡BCD = 180 - ∡3 - ∡4

∡AOD = ∡BCD because their measure is the difference of congruent angles.

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I really need the help please and thank you
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Answer:

B.  f^{-1}(x)=\frac{x-4}{5}

Step-by-step explanation:

To find the inverse of a function/equation:

  1. Replace f(x) with y: y=5x+4
  2. Switch x and y: x=5y+4
  3. Solve for y: x-4=5y   ->    y=\frac{x-4}{5}
  4. Write in standard inverse notation: f^{-1}(x)=\frac{x-4}{5}

I hope this helps!!

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The bureau of labor statistics reported the consumer price index as 211.4 in december 2007, and 231.1 in december 2012. by what
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The first step to determine the percentage of increase is to compute for the difference of consumer price index in value.

231.11 (consumer price index for 2012) – 211.4 (consumer price index for 2007) = 19.71 (increase)

To compute for the percentage of increase, you need to compare the increase to the consumer price index for 2007.

19.71/211.4 = 9.3% increase

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What is the sum of 1.57 and 6.88? 7 tenths, 3 hundredths, and 5 thousandths 8 ones, 4 tenths, and 5 hundredths 5 ones, 4 tenths,
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Step-by-step explanation:

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4 0
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Read 2 more answers
1. Which ordered pairs are solutions to the inequality –3x + y ≥ 7?
Murrr4er [49]
Q1. The answers are (–1, 8), (0, 7), (3, 18)

<span>–3x + y ≥ 7
</span>Let's go through all choices:

<span>(–2, –3) 
</span>(-3) * (-2) + (-3) ≥ 7
6 - 3 ≥ 7
3 ≥ 7       INCORRECT

(–1, 8) 
(-3) * (-1) + 8 ≥ 7
3 + 8 ≥ 7
11 ≥ 7       CORRECT

(0, 7) 
(-3) * 0 + 7 ≥ 7
0 + 7 ≥ 7
7 ≥ 7       CORRECT

(1, 9) 
(-3) * 1 + 9 ≥ 7
-3 + 9 ≥ 7
6 ≥ 7       INCORRECT

(3, 18) 
(-3) * 3 + 18 ≥ 7
-9 + 18 ≥ 7
9 ≥ 7       CORRECT



Q2. The answers are:
5x + 12y ≤ 80
x ≥ 4
<span>y ≥ 0
</span>
<span>x - small boxes
</span><span>y - large boxes

</span>He has x small boxes that weigh 5 lb each and y large boxes that weigh 12 lb each <span>on a shelf that holds up to 80 lb:
5x + 12y </span>≤ 80

Jude needs at least 4 small boxes on the shelf: x ≥ 4

Let's check if y can be 0:
5x + 12y ≤ 80
5x + 12 * 0 ≤ 80
5x + 0 ≤ 80
5x ≤ 80
x ≤ 80 / 5
x ≤ 16

x ≥ 4 can include x ≤ 16

So, y can be 0: y ≥ 0
8 0
3 years ago
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