Steven bought 3 mirrors. He paid a total of $264. Which equation can be used to find the amount he paid for each mirror?

In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD=√2 cm.

Zielflug [23.3K]

Given that triangle ABC is right angle triangle. CD is altitude such that AD=BC

ABC is a right angle triangle so apply Pythogorean theorem

$AC^{2} + BC^{2} = AB^{2}$

$AC^{2} + AD^{2} = AB^{2}$ (Given that AD = BC)

$AC^{2} + AD^{2} = 3^{2}$ (Given that AB=3)

$AC^{2} + AD^{2} = 9$ ...(i)

ADC is a right angle triangle so apply Pythogorean theorem

$AD^{2} + CD^{2} = AC^{2}$

$AD^{2}+(\sqrt{2})^2= AC^{2}$

$AD^{2}+2= AC^{2}$

$AD^{2}=AC^{2} -2$ ...(ii)

Plug value (ii) into (i)

$AC^{2} + AC^{2}-2 = 9$

$2AC^{2} -2=9$

$2AC^{2} =11$

$AC^{2} =\frac{11}{2}$

$AC=\sqrt{\frac{11}{2} }$

Hence final answer is $AC=\sqrt{\frac{11}{2} }$

8 0

2 years ago

Read 2 more answers

What is the median of the following string of values?<br>16, 95, 3, 37.97. 13, 27.42, 64, 14

liubo4ka [24]

Answer:

21.71

Step-by-step explanation:

1) you need to order then by the size

3, 13, 14, 16, 27.42, 37.97 ,64, 95

2) if there is an odd amount of numbers then the median would be the center term. but if it an even number then you add the two middle terms together and divide them by 2.

16+27.42= 43.42

43.42 divided by 2=21.71

Hope this helped

4 0

2 years ago

Refer to the Trowbridge Manufacturing example in Problem 2-35. The quality control inspection proce- dure is to select 6 items,

Ivanshal [37]

Answer:

77.64% probability that there will be 0 or 1 defects in a sample of 6.

Step-by-step explanation:

For each item, there are only two possible outcomes. Either it is defective, or it is not. The probability of an item being defective is independent of other items. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$