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Zigmanuir [339]
1 year ago
6

Angles A and B are complementary. If sin A = 5x + 9 and cos B = 3x + 21, what is the value of x? (1 point) 2 6 15 39

Mathematics
1 answer:
nadezda [96]1 year ago
7 0

The value of x is 6.

<h3>What are complementary?</h3>

Complementary angles are angles that sum up to 90°.

Analysis:

For angles A and B, to be complementary, the sine of angle A  must be equal to the cosine of angle B.

sin A = cos B

5X+9 = 3x+21

5x - 3x = 21 - 9

2x = 12

x = 6

In conclusion, the value of x to make angles A and B complementary is 6.

Learn more about complementary angles: brainly.com/question/98924

#SPJ1

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10. The sum of the digits of a three-digit number is 11. If the digits are reversed, the new number is 46
Zarrin [17]

Answer:

hope this helps

Step-by-step explanation:

The sum of the digits of a three-digit number is 11.

If the digits are reversed, the new number is 46 more than five times the old number.

If the hundreds digit plus twice the tens digit is equal to the units digit, then what is the number?

:

Write an equation for each statement:

:

"The sum of the digits of a three-digit number is 11."

x + y + z = 11

:

The three digit number = 100x + 10y + z

The reversed number = 100z + 10y + x

:

" If the digits are reversed, the new number is 46 more than five times the old number."

100z + 10y + x = 5(100x + 10y + z) + 46

100z + 10y + x = 500x + 50y + 5z + 46

combine on the right

0 = 500x - x + 50y - 10y + 5z - 100z + 46

499x + 40y - 95z = -46

:

"the hundreds digit plus twice the tens digit is equal to the units digit,"

x + 2y = z

x + 2y - z = 0

:

Three equations, 3 unknowns

:

x + y + z = 11

x +2y - z = 0

-----------------Addition eliminates z

2x + 3y = 11

From the 2nd equation statement, we know that the 1st original digit has to be 1

2(1) + 3y = 11

3y = 11 - 2

3y = 9

y = 3 is the 2nd digit

then

1 + 3 + z = 11

z = 11 - 4

z = 7

:

137 is the original number

:

:

Check solution in the 2nd statement

If the digits are reversed, the new number is 46 more than five times the old number."

731 = 5(137) + 46

731 = 685 + 46

7 0
3 years ago
1000 households were surveyed. 275 households own a desktop computer, 455 households own a DVD player, 405 households own two ca
icang [17]

Answer:

Step-by-step explanation:

From the given information,

Suppose

X represents the Desktop computer

Y represents the DVD Player

Z represents the Two Cars

Given that:

n(X)=275

n(Y)=455

n(Z)=405

n(XUY)=145

n(YUZ)=195

n(XUZ)=110

n((XUYUZ))=265

n(X ∩ Y ∩ Z) = 1000-265

n(X ∩ Y ∩ Z) = 735

n(X ∪ Y) = n(X)+n(Y)−n(X ∩ Y)

145 = 275+455 - n(X ∩ Y)

n(X ∩ Y) = 585

n(Y ∪ Z) = n(Y) + n(Z) − n(Y ∩ Z)

195 = 455+405-n(Y ∩ Z)

n(Y ∩ Z) = 665

n(X ∪ Z) = n(X) + n(Z) − n(X ∩ Z)

110 = 275+405-n(X ∩ Z)

n(X ∩ Z) = 570

a. n(X ∪ Y ∪ Z) = n(X) + n(Y) + n(Z) − n(X ∩ Y) − n(Y ∩ Z) − n(X ∩ Z) + n(X ∩ Y ∩ Z)

n(X ∪ Y ∪ Z) = 275+455+405-585-665-570+735

n(X ∪ Y ∪ Z) = 50

c. n(X ∪ Y ∪ C') = n(X ∪ Y)-n(X ∪ Y ∪ Z)

n(X ∪ Y ∪ C') = 145-50

n(X ∪ Y ∪ C') = 95

6 0
3 years ago
Hannah decided to make finger gelatin for a huge children’s party. She had to make 8 packs of gelatin. Each pack needed 2 cups o
Nadya [2.5K]

Answer:

4 quarts

Step-by-step explanation:

need 16 cups. In quarts that would be 4 quarts.

4 0
2 years ago
Read 2 more answers
Trina brings 6 cubic yards of compost for planting the trees. Each tree needs to be planted with 1/6 cubic yards of compost
kumpel [21]
If the question is asking how many trees can be planted with 6 cubic yards of compost, here is the solution.

6 divided by 1/6 means to take 6 wholes and break them into groups the size of 1/6.

One whole can be broken into 6 groups of 1/6 (6/6), so 6 wholes can be broken into 36 groups of 1/6 (6 x 6 = 36/6).

Mathematically, you will multiply 6 by 6/1  to get the 36.

You can plant 36 trees with 6 cubic yards of compost.
8 0
3 years ago
There are 110 sixth-grade students in a Florida middle school. 40% of the students enjoy playing video games on the weekends. Us
andreyandreev [35.5K]
40/100 - (I may be wrong)

Explanation: 40% of 110 is 44 so we make this a fraction 44/110 and then simplify to get 2/5 and after that we know that 2/5 is also 40/100, meaning 40 out of 100 students like video games.
7 0
2 years ago
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