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3 years ago

Use the diagram, which is not drawn to scale to find AD if you know that AC=24 & BC=12

Mathematics

2 answers:

eduard3 years ago

5 0

Answer:

B. 18

Step-by-step explanation:

Firdavs [7]3 years ago

4 0

Answer:

Option b. $AD=18\ units$

Step-by-step explanation:

step 1

In the right triangle ABC

<em>Find the sine of angle CAB</em>

$sin($ ---> the sine of angle CAB is equal to divide the opposite side angle CAB (BC) by the hypotenuse (AC)

substitute

$sin($

simplify

$sin($ ---->equation A

step 2

In the right triangle BDC

<em>Find the sine of angle CBD</em>

$sin($ ---> the sine of angle CBD is equal to divide the opposite side angle CBD (DC) by the hypotenuse (BC)

substitute

$sin($ ----> equation B

step 3

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

Triangles ABC and BDC are similar by AA Similarity Theorem

therefore

m∠CBD≅m∠CAB

equate equation A and equation B

$\frac{DC}{12}=\frac{1}{2}$

solve for DC

$DC=\frac{12}{2}=6\ units$

step 4

Find the value of AD

$AD=AC-DC$

substitute the values

$AD=24-6=18\ units$

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66 cards are drawn from a standard deck without replacement. What is the probability that at least one of the cards drawn is a s

Novay_Z [31]

Answer:

0.8397

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the cards are chosen is not important. Also, they are drawn without replacement. So we use the combinations formula to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

What is the probability that at least one of the cards drawn is a spade?

Either none is a spade, or at least one is a spade. The sum of the probabilities of these outcomes is 1.

The standard deck has 52 cards, of which 13 are spades. So

Probability that none are spades:

Desired outcomes:

6 cards from a set of 52 - 13 = 39. So

$D = C_{39,6} = \frac{39!}{6!33!} = 3262623$

Total outcomes:

6 cards from a set of 52. So

$T = C_{52,6} = \frac{52!}{6!46!} = 20358520$

Probability:

$p = \frac{D}{T} = \frac{3262623}{20358520} = 0.1603$

Probability that at least one is a spade:

1 - 0.1603 = 0.8397

The answer is 0.8397

8 0

4 years ago

Hi if i have 8,000 saving for 12,000 how much more do i need?

Murljashka [212]

Answer: 4,000

Step-by-step explanation: 12,000 - 8,000 = 4,000 Hope it helped!! :)

8 0

3 years ago

2x-y and 7y= -7 +3x solve by substitution

miss Akunina [59]

Answer:

x = -7/11, y = -14/11

Step-by-step explanation:

2x = y ------- (1)

7y = -7+3x -------- (2)

from (1)

2x = y

y = 2x ------- (3)

substitute (3) into (2)

7y = -7+3x

7(2x) = -7+3x

14x = -7+3x

14x-3x = -7

11x = -7

x = -7/11

substitute x = -7/11 into (3)

y = 2x

y = 2(-7/11)

y = -14/11

x = -7/11, y = -14/11

7 0

3 years ago

What is yyou useing properies to find the sum or product

sineoko [7]

Can you say it again

3 0

3 years ago

Read 2 more answers

PLEASE HELP! a rectangular picture frame has a perimeter of 58 inches.the height of the frame is 16 inches.what is the width of

PIT_PIT [208]

Perimeter is adding all the sides together. If the height is 16, 16×2 for the two sides would be 32. And 58-32=26.
26 is the other two sides added together so 26÷2=13
13 is the answer

8 0

3 years ago