4. Look at the figure below. Are triangles ABC and DEF congruent? Explain why or why not.

Mathematics

1 answer:

Debora [2.8K]4 years ago

3 0

Answer:

Yes

Step-by-step explanation:

You see that angle D and angle A are congruent, and you see that angle C and angle F are congruent. In addition, line AC is congruent to DF. This means that yes, those triangles are congruent because of the ASA postulate.

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AleksandrR [38]

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3 years ago

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A box holds 8 red and 4 blue beads. Three beads are taken from the box and not replaced. Determine: The probability that all thr

zubka84 [21]

Answer: $\dfrac{14}{55}, \dfrac{13}{55}$

Step-by-step explanation:

Given

There are 8 red and 4 blue beads

Three beads were taken from the box

(i)No of ways of choosing three red beads out of 12 beads is $^8C_3$

Total no of ways $^{12}C_3$

Probability is

$P=\dfrac{^8C_3}{^{12}C_3}=\dfrac{8\times 7\times 6}{12\times 11\times 10}=\dfrac{2\times 7}{11\times 5}\\P=\dfrac{14}{55}$

(ii)atleast two beads refers to minimum two beads

There can be two possibilities (2B,1 R), (3B, 0R)

$\Rightarrow P=\dfrac{^4C_2\times ^8C_1}{^{12}C_3}+\dfrac{^4C_3}{^{12}C_3}\\\\\Rightarrow P=\dfrac{6\times 8}{220}+\dfrac{4}{220}=\dfrac{52}{220}\\\\\Rightarrow P=\dfrac{13}{55}$