Mathematics, 20.10.2019 15:30 velazquezemmy45

Rachel traveled to five different areas (a, b, c, d, and e) to study the number of buckeye butterflies and the number of monarch butterflies living there. the table shows her findings. area buckeye butterflies monarch butterflies
a 15 16
b 27 36
c 12 25
d 24 32
e 44 33
the relationship between the number of buckeye butterflies and the number of monarch butterflies is not proportional across all areas. which two areas have buckeyes and monarchs in the same proportion?

areas a and b,
areas c and e,
areas b and d, < correct answer
areas c and d

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Answer from: gmac24

As we can see our our ration in Area B and Area D gives the same answer, so they are in proportion

Step-by-step explanation:

Given that

Rachel traveled to 5 areas to find number of Buckeye and Monarch butterflies.

Areas Rachel Traveled to = A, B, C, D, E

The table given below shows her findings.

Area Buckeye Monarch

A 15 16

B 27 36

C 12 25

D 24 32

E 44 33

Now lets find the ratio of Buckeye and Monarch Butterflies in these areas

Area A

Buckeye : Monarch = 15:16 = 0.9375

Area B

Buckeye : Monarch = 27:36 = 0.75

Area C

Buckeye : Monarch = 12:25= 0.48

Area D

Buckeye : Monarch = 24:32 = 0.75

Area E

Buckeye : Monarch = 44:33 = 1.334

As we know that if two ratios give same answer after solving the fraction then these ratios are in proportion.

As we can see our our ration in Area B and Area D gives the same answer, so they are in proportion.

Answer from: zappygal923

Area A = 15/16 = 0.9375
Area B = 27/36 = 0.75
Area C = 12/25 = 0.48
Area D = 24/32 = 0.75
Area E = 44/33 = 1.33

From the above, areas B and D have buckeyes and monarchs in the same proportion

Answer from: Quest

I’m pretty sure it’s i think : /

Answer from: Quest

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

ac ≅ ab (given)< cax ≅ < bax (given)ax ≅ ax (common side)

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

ac ≅ ab (given)< cay ≅ < bay (since < cax ≅ < bax is given and xy is the extension of line ax)ay ≅ ay (common side)

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)

Use a paragraph, flow chart, or two-column proof to prove the angle congruency. given: ∠cxy ≅ ∠bxy

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Rachel traveled to five different areas (a, b, c, d, and e) to study the number of buckeye butterfli...

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