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Maurinko [17]
2 years ago
8

AC ≅ AE; ∠ACD ≅ ∠AED

Mathematics
2 answers:
lana66690 [7]2 years ago
6 0
On online learning  its A,D,E
pshichka [43]2 years ago
4 0

Answers:

A) △ACF ≅ △AEB because of ASA.

D) ∠CFA ≅ ∠EBA

E) FC ≅ BE


Solution:

AC ≅ AE; ∠ACD ≅ ∠AED Given

The angle ∠CAF ≅ ∠EAB, because is the same angle in Vertex A

Then △ACF ≅ △AEB because of ASA (Angle Side Angle): They have a congruent side (AC ≅ AE) and the two adjacent angles to this side are congruent too (∠ACD ≅ ∠AED and ∠CAF ≅ ∠EAB), then  option A)  is true: △ACF ≅ △AEB because of ASA.

If the two triangles are congruent, the ∠CFA ≅ ∠EBA; and FC ≅ BE, by CPCTC (Corresponding Parts of Congruent Triangles are Congruent), then Options D) ∠CFA ≅ ∠EBA and E) FC ≅ BE are true

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Nevaeh has $560 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax. She buys
AnnyKZ [126]

Answer:

The number of outfits she purchase with the left money = 3

Step-by-step explanation:

The exact question is as follows :

Given - Nevaeh has $560 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax. She buys a new bicycle for $383.32. She buys 4 bicycle reflectors for $9.09 each and a pair of bike gloves for $21.07. She plans to spend some or all of the money she has left to buy new biking outfits for $39.75 each.

To find - Write and solve an inequality which can be used to determine  x  where x, the number of outfits Nevaeh can purchase while staying within her budget.

Proof -

Given that,

Total money Nevaeh have = $ 560

She spent money on bicycle = $ 383.32

She spend money on 1 reflector = $ 9.09

As she buy 4 bicycle reflector, So

Total money spent on bicycle reflector = $ 4×9.09 = $ 36.36

She spend money on a pair of bike gloves = $ 21.07

So,

Total money she spend on the items = $ 383.32 + 36.36 + 21.07

                                                              = $ 440.75

⇒Total money she spend on the items = $ 440.75

So,

Total money Left = $ 560 - $ 440.75 = $ 119.25

Now,

She plans to spend some or all of the money she has left to buy new biking outfits for $ 39.75 each.

Let us assume ,

The number of outfits she purchase with the left money = x

AS,

each outfit cost = $ 39.75

So, x outfits cost = $ 39.75 x

Now,

$ 39.75 x = $ 119.25     (because total money left = $ 119.25)

⇒ x = \frac{119.25}{39.75} = 3

∴ we get

The number of outfits she purchase with the left money = x = 3

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