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3 years ago

Given: bisects ∠BAC; AB = AC Which congruence theorem can be used to prove △ABR ≅ △ACR?

Mathematics

2 answers:

astraxan [27]3 years ago

8 0

Answer: SAS

Step-by-step explanation:

Here ABC is a triangle, In which angle BAC is bisected by line AR where, $R\in BC$ .

Thus in triangles ABR and ACR,

AB= AC ( given)

Therefore $AB\cong AC$

$\angle BAR\cong \angle CAR$ ( by the property of angle bisector)

And, $AR\cong AR$ (reflexive)

Thus by SAS postulate,

△ABR ≅ △ACR.

Therefore, Option D is correct.

mote1985 [20]3 years ago

5 0

Answer:

The answer is SAS

Step-by-step explanation:

I got it right on edge

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a dvd costs twice as much as a music cd. Jack buys 2 dvds and 2 cds and spends $45. Determine how much one cd costs. in dollars

VMariaS [17]

$dvd=d \\ cd=c \\ \\ \left \{ {{d=2c} \atop {2d+2c=45}} \right. \\ \\ 2(2c)+2c=45 \\ 4c+2c=45 \\ 6c=45 \\ c=7.5 \\ \\ d=2(7.5) \\ d=15$

One CD costs $7.50.
One DVD costs $15.00.

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3 years ago

Read 2 more answers

A club surveyed its members to decide on food for an event. Out of 125 members surveyed, 89 preferred pizza, 23 of those preferr

RSB [31]

Answer:

$\begin{array}{cccc}&\text{Prefer Pizza}&\text{Do not Prefer Pizza}&\text{Total}\\\text{Prefer Punch}&23&29&52\\\text{Do not Prefer Punch}&66&7&73\\\text{Total}&89&36&125\end{array}$

Step-by-step explanation:

There are 125 members.

89 of them preferred pizza and 23 of 89 preferred punch, so 89-23=66 preferred only pizza.

52 members preferred punch, 23 of them preferred both pizza and punch, so 52-23=29 preferred only punch.

Now,

66 members preferred only pizza,

23 members preferred both,

29 members preferred only punch,

125-66-23-29=7 members did not prefer both

The two-way table is

$\begin{array}{cccc}&\text{Prefer Pizza}&\text{Do not Prefer Pizza}&\text{Total}\\\text{Prefer Punch}&23&29&52\\\text{Do not Prefer Punch}&66&7&73\\\text{Total}&89&36&125\end{array}$

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2 years ago

The museum's show for July features 30 oil paintings by different artists. All artists show the same number of paintings and eac

boyakko [2]

Answer: We have many options:
1) 15 artists, with 2 paintings per artist.
2) 10 artists, with 3 paintings per artist.
3) 6 artists, with 5 paintings per artist.
4) 5 artists, with 6 paintings per artist.
5) 3 artists, with 10 paintings per artist.
6) 2 artists, with 15 paintings per artist.

by different artists, then the number of artists must be more than 1.
each artist shows more than 1 painting: >1 painting/artist

(30 oil paintings)/(2 paintings/artist)=15 artists
(30 oil paintings)/(3 paintings/artist)=10 artists
(30 oil paintings)/(5 paintings/artist)=6 artists
(30 oil paintings)/(6 paintings/artist)=5 artists
(30 oil paintings)/(10 paintings/artist)=3 artists
(30 oil paintings)/(15 paintings/artist)=2 artists

5 0

2 years ago

A manufacturer of tablets receives its LED screens from three different suppliers, 45% from supplier B1, 30% from supplier B2, a

Shalnov [3]

Answer:

a) 0.83 = 83% probability that a LED screen will meet specifications.

b) 0.2892 = 28.92% probability that a LED screen that meets specifications was sent by the second supplier.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

45% from supplier B1, 30% from supplier B2, and the rest from supplier B3.

So 100 - (45 + 30) = 100 - 75 = 25% from supplier B3.

a) Find the probability that a LED screen will meet specifications.

95% of 45%(supplier B1)

80% of 30%(supplier B2)

65% of 25%(supplier B3). So

$p = 0.95*0.45 + 0.8*0.3 + 0.65*0.25 = 0.83$

0.83 = 83% probability that a LED screen will meet specifications.

b) Calculate the probability that a LED screen that meets specifications was sent by the second supplier.

Conditional probability.

Event A: Meets specifications.

Event B: Sent by second supplier.

0.83 = 83% probability that a LED screen will meet specifications.

This means that $P(A) = 0.83$

Meets specifications and is sent by the second supplier.

80% of 30%, so

$P(A \cap B) = 0.8*0.3 = 0.24$

Probability:

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.24}{0.83} = 0.2892$

0.2892 = 28.92% probability that a LED screen that meets specifications was sent by the second supplier.

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3 years ago

Cheese Or Pickles? WILL GIVE BRAINLIEST

Setler [38]

Answer:

<em>Pickles. My friends are allergic to cheese. </em>

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