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zheka24 [161]
2 years ago
14

Simplify the problem; 18x^15

Mathematics
1 answer:
Maurinko [17]2 years ago
8 0

Answer: 6746640616477458432x


Step-by-step explanation: 18^15=6746640616477458432

so the answer is 6746640616477458432x


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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
Kevin and Randy Muise have a jar containing 92 coins, all of which are either quarters or nickels. The total value of the coins
Artemon [7]
<span>Let n = the number of nickles
Let q = the number of quarters
Then for your problem we have
(1) n + q = 43 and
(2) 5*n + 25*q = 100*6.95 (always work in cents to avoid decimal numbers) or
(3) 5*n + 25*q = 695
Now substitute n of (1) into (3) and get
(4) 5*(43 - q) + 25*q = 695 or
(5) 215 - 5*q + 25*q = 695 or
(6) 20*q = 695 - 215 or

(7) 20*q = 480 or
(8) q = 24
Then using (1) we get
(9) n + 24 = 43 or
(10) n = 19
Let's check these values.
Is (.05*19 + .25*24 = 6.95)?
Is (.95 + 6.00 = 6.95)?
Is (6.95 = 6.95)? Yes
Answer: Kevin and Randy have 19 nickles and 24 quarters in the jar.</span>
7 0
2 years ago
Boys height: 5 ft 6 inches<br> Boys shadow: 8 ft<br> Tree Ht: ?<br> Tree shadow: 46 ft
igor_vitrenko [27]

Answer:

43.6

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
What's the most efficient way to revise for a maths test? (Can really do with some advise ) ​
Rudiy27

Answer:

Step-by-step explained  

Sleep,eat well,drink plenty of water.Attened any revision plans.

7 0
3 years ago
Read 2 more answers
Which table represents a function with a slope of 1/2 and a y-intercept of 4
Volgvan

Answer:D

Step-by-step explanation: trust me ima sophomore use this for help y=1/2x+4 then x value change it to the number in the x section then if the y appears just like in the box the y section it’s correct

8 0
2 years ago
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