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aalyn [17]
3 years ago
10

Evaluate the following real numbers:

Mathematics
1 answer:
makkiz [27]3 years ago
5 0

Answer:

Q.1 Answer is 9

Q.2 Answer is 0.04

Q.3 Answer is 11/12

Q.4 Answer is 3/2

Q.5 Answer is 1/12

Q.6 Answer is 3/5

Q.7 Answer is 1

Q.8 Answer is -15

Q.9 Answer is 10

Q.10 Answer is 108

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Given: △ABC, AB=5sqrt2 <br> m∠A=45°, m∠C=30°<br> Find: BC and AC
Marysya12 [62]

BC is 10 units and AC is 5+5\sqrt{3} units

Step-by-step explanation:

Let us revise the sine rule

In ΔABC:

  • \frac{AB}{sin(C)}=\frac{BC}{sin(A)}=\frac{AC}{sin(B)}
  • AB is opposite to ∠C
  • BC is opposite to ∠A
  • AC is opposite to ∠B

Let us use this rule to solve the problem

In ΔABC:

∵ m∠A = 45°

∵ m∠C = 30°

- The sum of measures of the interior angles of a triangle is 180°

∵ m∠A + m∠B + m∠C = 180

∴ 45 + m∠B + 30 = 180

- Add the like terms

∴ m∠B + 75 = 180

- Subtract 75 from both sides

∴ m∠B = 105°

∵ \frac{AB}{sin(C)}=\frac{BC}{sin(A)}

∵ AB = 5\sqrt{2}

- Substitute AB and the 3 angles in the rule above

∴ \frac{5\sqrt{2}}{sin(30)}=\frac{BC}{sin(45)}

- By using cross multiplication

∴ (BC) × sin(30) = 5\sqrt{2} × sin(45)

∵ sin(30) = 0.5 and sin(45) = \frac{1}{\sqrt{2}}

∴ 0.5 (BC) = 5

- Divide both sides by 0.5

∴ BC = 10 units

∵ \frac{AB}{sin(C)}=\frac{AC}{sin(B)}

- Substitute AB and the 3 angles in the rule above

∴ \frac{5\sqrt{2}}{sin(30)}=\frac{AC}{sin(105)}

- By using cross multiplication

∴ (AC) × sin(30) = 5\sqrt{2} × sin(105)

∵ sin(105) = \frac{\sqrt{6}+\sqrt{2}}{4}

∴ 0.5 (AC) = \frac{5+5\sqrt{3}}{2}

- Divide both sides by 0.5

∴ AC = 5+5\sqrt{3} units

BC is 10 units and AC is 5+5\sqrt{3} units

Learn more:

You can learn more about the sine rule in brainly.com/question/12985572

#LearnwithBrainly

6 0
3 years ago
(i) 809, 708, 607, _____, _ class 4<br>__class 4​
schepotkina [342]

Answer:

809, 708, 607, 506, 405, 304, 203, 102, 1, -100

Step-by-step explanation:

809, 708, 607, _____, _______

First term = 809

Second term = 708

Third term = 607

Difference between first term and second term = 809 - 708

= 101

Difference between second term and third term = 708 - 607

= 101

Therefore, the common difference is 101

Fourth term = 607 - 101

= 506

Fifth term = 506 - 101

= 405

Sixth term = 405 - 101

= 304

Seventh term = 304 - 101

= 203

Eighth term = 203 - 101

= 102

Ninth term = 102 - 101

= 1

Tenth term = 1 - 101

= - 100

809, 708, 607, 506, 405, 304, 203, 102, 1, -100

4 0
2 years ago
Can someone help me with this please it would be a big help
Anuta_ua [19.1K]
Answer in order

----------
answer
A. -4.6 - (0.4 + 7.2)

----------------
answer
B. -10 + (-90) + (-40)

--------
answer

associate property of addition

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

answer
Commutative <span>Property
</span>
--------------------

answer
-147
7 0
3 years ago
4a-(a+6)=12-36 please help i am confused again lol
andreev551 [17]

Answer:

a=6

Step-by-step explanation:

4 0
2 years ago
Collins has a part-time job as a dog walker. The table below shows the amount of money Collins earned for different numbers of h
kondor19780726 [428]

Answer:

See below.

Step-by-step explanation:

Part A:

For Dog walking, he earns $30 for 5 hours of work.

He earns $36 for 6 hours of work.

$30/5 hours = $6/hour

$36/6 hours = $6/hour

He earns $6/hour dog walking.

For 8 hours, he earns 8 hours * $6/hour = $48

To earn $66, he works 66/6 = 11 hours.

5 30

6 36

8 48

11 66

Part B:

He earns $7/hour for yard work, so multiply the number of hours by 7 to find the money he earns.

Table for yard work

Hours     Money

5             $35

6             $42

8             $56

Part C:

For 5 hours, he earns $35 for yard work and $30 as a dog walker.

$35 - $30 = $5

3 0
3 years ago
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