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3 years ago

Drag an expression or phrase to each box to complete the proof.

Mathematics

2 answers:

adelina 88 [10]3 years ago

5 0

Answer:

1st blank: ∠4≅∠1 and ∠3≅∠2

2nd blank: Angle-Angle similarity postulate

3rd blank: Substitution property of equality.

Step-by-step explanation:

Consider the provided figure.

Statement Reason

ΔACE, BD║AE Given

∠4≅∠1 and ∠3≅∠2 Corresponding angle postulate

ΔACE $\sim$ ΔBCD Angle-Angle similarity postulate

$\frac{CA}{CB}=\frac{CE}{CD}$ Definition of similar triangles

CA=CB+BA and CE=CD+DE Segment addition postulate

$\frac{CB+BA}{CB}=\frac{CD+DE}{CD}$ Substitution property of equality.

$\frac{CB}{CB}+\frac{BA}{CB}=\frac{CD}{CD}+\frac{DE}{CD}$ Addition of fractions.

$1+\frac{BA}{CB}=1+\frac{DE}{CD}$ Simplification of fractions

$\frac{BA}{CB}=\frac{DE}{CD}$ Subtraction property of equality.

QveST [7]3 years ago

3 0

<4 ≅ <1, 3 <≅ 2 Corresponding angles postulate

ΔACE ≈ ΔBCD Angle angle similarity postulate

(CB + BA)/CB = (CD + DE)/CD Substitution property of equality

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Express the terms of the following sequence by giving a recursive formula.

emmasim [6.3K]

The recursive formula for given sequence is: $a_n = a_{n-1}-7$

And the terms will be expressed as:

$a_1 = 11\\a_2 = a_{2-1} - 7 \\a_2= a_1 - 7\\a_2 = 11- 7\\a_2 = 4\\a_3 = a_{3-1} - 7 \\a_3= a_2 - 7\\a_3 = 4 - 7\\a_3 = -3\\a_4 = a_{4-1} - 7 \\a_4= a_3 - 7\\ a_4= -3 - 7\\a_4 = -10\\a_5 = a_{5-1} - 7 \\a_5= a_4 - 7\\a_5 = -10 - 7\\a_5 = -17\\$

Step-by-step explanation:

First of all, we have to determine if the given sequence is arithmetic sequence or geometric. For that purpose, we calculate the common difference and common ratio

Given sequence is:

11,4,-3,-10,-17...

Here

$a_1 = 11\\a_2 = 4\\a_3 = -3\\So,\\d = a_2 - a_1 = 4-11 = -7\\d = a_3-a_2 = -3-4 = -7$

As the common difference is same, given sequence is an arithmetic sequence.

A recursive formula is a formula that is used to generate the next term of the sequence using the previous term and common difference

So, the recursive formula for an arithmetic sequence is given by:

$a_n = a_{n-1} +d\\Putting\ d = -7\\a_n = a_{n-1}-7$

Hence,

The recursive formula for given sequence is: $a_n = a_{n-1}-7$

And the terms will be expressed as:

Keywords: arithmetic sequence, common difference

Learn more about arithmetic sequence at:

#LearnwithBrainly

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3 years ago

Help me asap plssss !! will crown brainliest !!

Finger [1]

Answer: 82

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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