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Olin [163]
2 years ago
13

Complete the following proof.

Mathematics
1 answer:
Ivan2 years ago
7 0

Using the circle theorems, we have proven that m ∠RTW = 15°

<h3>Circle theorems </h3>

From the question, we are to prove that m ∠RTW = 15°

In the given diagram,

measure of arc ST = 30°

∴ m ∠SRT = 30°

m ∠SRT = ∠T + ∠W ( <em>Exterior angle of a triangle equals the sum of the two remote angles</em>)

Also,

∠T = ∠W (<em>Radii of the same circle</em>)

∴ m ∠SRT = ∠T + ∠T

m ∠SRT = 2 × ∠T

30° = 2 × ∠T

∠T = 30° /2

∠T = 15°

∴ m ∠RTW = 15°  

Hence, we have proven that m ∠RTW = 15°

Learn more on Circle theorems here: brainly.com/question/27111486

#SPJ1

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You have a total of ​$1760 to invest. Account A pays 7​% annual interest and account B pays 4​% annual interest. How much should
posledela

Answer:

You should invest $820 in account A and $940 in account B

Step-by-step explanation:

* Lets use the system of linear equations to solve the problem

- Simple Interest Equation I = Prt , Where:

# P = Invested Amount

# I = Interest Amount

# r = Rate of Interest per year in decimal; r = R/100

# t = Time Period involved in months or years

* Lets solve the problem

- The total money invested is $1760

- Account A pays 7​% annual interest

- Account B pays 4​% annual interest

- Let A represent the amount of money invested in the account A

- Let B represent the amount of money invested in the account B

- You would like to earn $ 95 at the end of one year

∴ The interest from both accounts at the end of one year is $95

- Lets write the equations

# Account A :

∵ Account A has $A invested

∴ P = $A

∵ Account A pays 7​% annual interest

∴ r = 7/100 = 0.07

∵ t = 1 year

∵ I = Prt

∴ I = A(0.07)(1) = 0.07A

# Account B :

∵ Account B has $B invested

∴ P = $B

∵ Account A pays 4​% annual interest

∴ r = 4/100 = 0.04

∵ t = 1 year

∵ I = Prt

∴ I = B(0.04)(1) = 0.04B

- The total amount of interest from both accounts at the end of one

  year is $95

∴ I from A + I from B = 95

∴ 0.07A + 0.04B = 95 ⇒ multiply both sides by 100

∴ 7A + 4B = 9500 ⇒ (1)

- The total money to invest in both accounts is $1760

∵ Account A has $A invested

∵ Account B has $B invested

∴ A + B = 1760 ⇒ (2)

* Lets solve the system of equations to find the amount of money

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- Multiply equation (2) by -4 to eliminate B

∵ A + B = 1760 ⇒ × -4

∴ -4A - 4B = -7040 ⇒ (3)

- Add equation (1) and (3)

∵ 7A + 4B = 9500 ⇒ (1)

∵ -4A - 4B = -7040 ⇒ (3)

∴ 7A - 4A = 9500 - 7040

∴ 3A = 2460 ⇒ divide both side by 3

∴ A = 820

- Substitute the value of A in equation (1) or (2)

∵ A + B = 1760 ⇒ (2)

∴ 820 + B = 1760 ⇒ subtract 820 from both sides

∴ B = 940

- From all above

* You should invest $820 in account A and $940 in account B

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Shawn drew a rectangle that had a width of 4.2 inches and a length of 8.1 inches. Find the perimeter of Shawn's rectangle
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Answer:

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Hope this helps :)

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