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Ksju [112]
3 years ago
15

The supplement of the complement of an angle less the complement of an angle exceeds the quotient of the supplement of the angle

and the number 3 by 73. Find the angle.
Mathematics
1 answer:
djverab [1.8K]3 years ago
5 0

Complement of an angle = 90° - x.

Supplement of the complement of an angle = 180 - (90 - x).

= 180 - 90 + x

= 90 + x

Supplement of the complement of an angle less the complement of an angle = (90 + x) - (90 - x)

= 90 + x - 90 + x

= 2x

Now, the quotient of the supplement of the angle and the number 3 is \frac{180-x}{3}.

It is given that supplement of the complement of an angle less the complement of an angle exceeds the quotient of the supplement of the angle and the number 3 by 73.

Therefore, 2x = \frac{180x}{3} +73

2x=\frac{180-x+219}{3}

Multiply both sides by 3.

6x = 180 - x + 219

= 399 - x

Add x to both sides.

6x + x = 399

7x = 399

Divide both sides by 7.

x = 57

Hence, the required angle = 57°.

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olga_2 [115]

Answer: it will take 9 hours.

Step-by-step explanation:

The rain is falling at the rate of 1.5 inches per hour. This means that the height of water in the barrel is increasing in arithmetic progression.

The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + d(n - 1)

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = 18 inches

d = 1.5 inches

The expression becomes

Tn = 18 + 1.5(n - 1)

For the number of hours it would take to collect 30 inches of rain in the barrel, Tn = 30

Therefore,

30 = 18 + 1.5(n - 1)

1.5(n - 1) = 30 - 18

1.5(n - 1) = 12

n - 1 = 12/1.5 = 8

n = 8 + 1

n = 9

6 0
3 years ago
Sunscreen should be applied every 2 hours. Over the summer, Cece spends at least 84 hours outside.
maria [59]

Answer:

42

Step-by-step explanation:

84 divide 2

answer 42

answer =42

4 0
2 years ago
Could someone help me with this question? i don't know how to really work this out Order Of Operations
lozanna [386]

Answer:

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Step-by-step explanation:

2[45/(11-8)^2]

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3 0
2 years ago
The length of a rectangle 4 yd is longer than its width. If the perimeter of the rectangle is 68 yd, find its length and width.
natulia [17]

w + 4

------------------------

l l

l l w

l l

------------------------

Perimeter would be the sum of all the sides so: (w+4) + w + (w+4) + w

Perimeter is 60 yards according to your problem so: (w+4) + w + (w+4) + w = 60 yds

1.Simplify/combine like terms:

w + 4 + w + w + 4 + w =

4w + 8 =

Now it's a 2-step algebra equation

4w + 8 = 60

2.Subtract 8 on both sides

4w = 56

3.Divide both sides by 4

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4 0
2 years ago
2 ACTIVITY: Estimating a Percents
meriva

Answer: 45%

Step-by-step explanation:

Converting the word problem into words, we have:

18= x/100*40

Solving for it, we get that x=45.

7 0
2 years ago
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