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3 years ago

∠LMN and ∠PQR are complementary angles. Find m∠LMN if m∠LMN = (4x-2) and m∠PQR= (9X+1)

Mathematics

1 answer:

kow [346]3 years ago

4 0

Answer:

Step-by-step explanation:

Since ∠LMN and ∠PQR are complementary it means that the sum of their angles is 90°

To find m∠LMN , add both m∠LMN and m∠PQR and equate it to 90 to find x then substitute the value of x into the expression for m∠LMN

That's

m∠LMN + m∠PQR = 90

4x - 2 + 9x + 1 = 90

13x - 1 = 90

13x = 90 + 1

13x = 91

Divide both sides by 13

x = 7

From the question

m∠LMN = (4x-2)

m∠LMN = 4(7) - 2 = 28 - 2

We have the final answer as

Hope this helps you

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Isaac's dad built a shelf for his video games that is 42inches wide. Each video game is 6/8inches wide. How many video games can

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Answer:

Step-by-step explanation:

to find the answer, divide 42 by 6/8

42 x 8/6 = 56

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4 years ago

1. What is the slope of the line that passes through points (-8,3) and (1,9)?

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Answer:

The slope should be 8 1/3 which is also 25/3

Step-by-step explanation:

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3 years ago

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four component system Assume A, B, C, and D function independently. If the probabilities that A, B, C, and D fail are 0.1, 0.2,

ArbitrLikvidat [17]

Answer:

then the probability of failure goes between 0.00003 (0.003%) and 0.5212 (52.12%) depending on the system configuration

Step-by-step explanation:

the solution depends on the system configuration, that is , if some component ( lets say A) is run in parallel from other , or is in series

if a component is run in parallel then the system fails only if all the components in parallel fails

but if the system is connected in series , the system will fail only if one of the components the serie fails.

Therefore denoting the events A= fails A , B= fails B , C= fails C , D= fails D , we have:

- lower bound of probability of failure = all components are in parallel

probability of failure P(A∩B∩C∩D)=P(A)*P(B)*P(C)*P(D)= 0.1 * 0.2 * 0.05 * 0.3 = 0.00003 (0.003%)

- upper bound of probability of failure = all components are in parallel

probability of failure P(A∪B∪C∪D)= P(A) + P(B) + P(C) +P(D) - P(A ∩ B) - P(A ∩ C) - P(A ∩ D)- P(B ∩ C) - P(B ∩ D) - P(C ∩ D) + P(A ∩ B ∩ C) + P(A ∩ B ∩ D) + P(A ∩ C ∩ D) + P(B ∩ C ∩ D) - P(A ∩ B ∩ C ∩ D) = (P(A) + P(B) + P(C) +P(D)) - ( P(A)*P(B) + P(A)*P(C) + P(A)*P(D) + P(B)*P(C) + P(B)*P(D) + P(C)*P(D) ) + P(A)*P(B)*P(C) + P(A)*P(B)*P(D)+ P(A)*P(C)*P(D)+ P(B)*P(C)*P(D) - P(A)*P(B)*P(C)*P(D)

replacing values

P(A∪B∪C∪D)= 0.5212 (52.12%)

then the probability of failure goes between 0.00003 (0.003%) and 0.5212 (52.12%) depending on the system configuration

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3 years ago

Snow Dome Ski Resort has 75 inches of snow. It is currently snowing there at a rate of 1 inch per hour. Mt. Winterpark Ski Resor

Nastasia [14]

Answer:

a. See explanation for table

b. The 7th hour

Step-by-step explanation:

Given

Ski Resort

$Base\ Snow = 75in$

$Rate = 1in$ hourly

Mt. Winterpark

$Base\ Snow = 68in$

$Rate = 2in$ hourly

First, we need to illustrate the amount of snow as an equation in both cases.

$Amount = Base\ Snow + Rate * Time$

Let x be number of hours. and y be the amount of snow

So:

Ski Resort

$y= 75 + 1* x$

$y= 75 + x$

Mt. Winterpark

$y= 68 + 2 * x$

$y= 68 + 2x$

Next, we make a table to show the data.

When $x = 0$

Ski Resort: $y = 75 + 0 = 75$

Mt. Winterpark: $y = 68 + 2(0) = 68$

When $x = 1$

Ski Resort: $y = 75 + 1 = 76$

Mt. Winterpark: $y = 68 + 2(1) = 70$

When $x = 2$

Ski Resort: $y = 75 + 2 = 77$

Mt. Winterpark: $y = 68 + 2(2) = 72$

When $x = 3$

Ski Resort: $y = 75 + 3 = 78$

Mt. Winterpark: $y = 68 + 2(3) = 74$

When $x = 4$

Ski Resort: $y = 75 + 4 = 79$

Mt. Winterpark: $y = 68 + 2(4) = 76$

When $x = 5$

Ski Resort: $y = 75 + 5 = 80$

Mt. Winterpark: $y = 68 + 2(5) = 78$

When $x = 6$

Ski Resort: $y = 75 + 6 = 81$

Mt. Winterpark: $y = 68 + 2(6) = 80$

When $x = 7$

Ski Resort: $y = 75 + 7 = 82$

Mt. Winterpark: $y = 68 + 2(7) = 82$

When $x = 8$

Ski Resort: $y = 75 + 8 = 83$

Mt. Winterpark: $y = 68 + 2(8) = 84$

When $x = 9$

Ski Resort: $y = 75 + 9 = 84$

Mt. Winterpark: $y = 68 + 2(9) = 86$

When $x = 10$

Ski Resort: $y = 75 + 10 = 85$

Mt. Winterpark: $y = 68 + 2(10) = 88$

Hence, the table is:

x ---- Ski Resort ---- Mt. Winterpark

0 --------75 ----------- 68

1 --------76 ----------- 70

2 --------77 ----------- 72

3 --------78 ----------- 74

4 --------79 ----------- 76

5 --------80 ----------- 78

6 --------81 ----------- 80

7 --------82 ----------- 82

8 --------83 ----------- 84

9 --------84 ----------- 86

10 -------85 ----------- 88

(b)

From the table, the amount of snow is the same at the 7th hour and the snow is 82 inches

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3 years ago

Eremy works two jobs. He makes $8/hr working at a deli and $12/hr working for a landscaper. Let x represent the number of hours

bezimeni [28]

Answer:

A.) combinations of the hours he can work at the two jobs and earn at least $300

Step-by-step explanation:

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3 years ago

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