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Zolol [24]
2 years ago
13

If TR=11 ft, find the length of PS

Mathematics
1 answer:
Klio2033 [76]2 years ago
5 0

Answer:

PS = 31.5 ft

Step-by-step explanation:

∠PTS = 180 - 16 = 154°

164°(π/180) = 41π/45 radians

PS = rθ = 11(41π/45) = 31.48573...

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Mia buys 5 yards of ribbon to make bracelets.She needs 18 inches of ribbon to make 1 bracelet.How many bracelets can Mia make if
snow_tiger [21]
To find the number of bracelets Mia can make, she will convert 5 yards to inches and then break that into groups of 18 inches.

5 x 36 = 180 inches

180/18= 10

Mia can make 10 bracelets.
8 0
3 years ago
In triangle RST, m∠R > m∠S + m∠T. Which must be true of triangle RST? Check all that apply.
solmaris [256]

Answer:

1. m∠R > 90°

2. m∠S + m∠T < 90°

4. m∠R > m∠T

5. m∠R > m∠S

Step-by-step explanation:

<h3>General strategy</h3>
  1. prove the statement starting from known facts, or
  2. disprove the statement by finding a counterexample

Helpful fact:  Recall that the Triangle Sum Theorem states that m∠R + m∠S + m∠T = 180°.

<u>Option 1.  m∠R > 90°</u>

Start with m∠R > m∠S + m∠T.

Adding m∠R to both sides of the inequality...

m∠R + m∠R > m∠R + m∠S + m∠T

There are two things to note here:

  1. The left side of this inequality is 2*m∠R
  2. The right side of the inequality is exactly equal to the Triangle Sum Theorem expression

2* m∠R > 180°

Dividing both sides of the inequality by 2...

m∠R > 90°

So, the first option must be true.

<u>Option 2.  m∠S + m∠T < 90°</u>

Start with m∠R > m∠S + m∠T.

Adding (m∠S + m∠T) to both sides of the inequality...

m∠R + (m∠S + m∠T) >  m∠S + m∠T + (m∠S + m∠T)

There are two things to note here:

  1. The left side of this inequality is exactly equal to the Triangle Sum Theorem expression
  2. The right side of the inequality is 2*(m∠S+m∠T)

Substituting

180° > 2* (m∠S+m∠T)

Dividing both sides of the inequality by 2...

90° > m∠S+m∠T

So, the second option must be true.

<u>Option 3.  m∠S = m∠T</u>

Not necessarily.  While m∠S could equal m∠T, it doesn't have to.  

Example 1:  m∠S = m∠T = 10°;  By the triangle sum Theorem, m∠R = 160°, and the angles satisfy the original inequality.

Example 2:  m∠S = 15°, and m∠T = 10°;  By the triangle sum Theorem, m∠R = 155°, and the angles still satisfy the original inequality.

So, option 3 does NOT have to be true.

<u>Option 4.  m∠R > m∠T</u>

Start with the fact that ∠S is an angle of a triangle, so m∠S cannot be zero or negative, and thus m∠S > 0.

Add m∠T to both sides.

(m∠S) + m∠T > (0) + m∠T

m∠S + m∠T > m∠T

Recall that m∠R > m∠S + m∠T.

By the transitive property of inequalities, m∠R > m∠T.

So, option 4 must be true.

<u>Option 5.  m∠R > m∠S</u>

Start with the fact that ∠T is an angle of a triangle, so m∠T cannot be zero or negative, and thus m∠T > 0.

Add m∠S to both sides.

m∠S + (m∠T) > m∠S + (0)

m∠S + m∠T > m∠S

Recall that m∠R > m∠S + m∠T.

By the transitive property of inequalities, m∠R > m∠S.

So, option 5 must be true.

<u>Option 6.  m∠S > m∠T</u>

Not necessarily.  While m∠S could be greater than m∠T, it doesn't have to be.  (See examples 1 and 2 from option 3.)

So, option 6 does NOT have to be true.

4 0
1 year ago
the equation 4(x+9)=76 models this situation which choice shows the sequence of operations neede to slove this problem using bot
laiz [17]

Answer:

Step-by-step explanation:

Here you go mate

Use PEMDAS

Parenthesis,Exponent,Multiplication,Division,Addition,Subtraction

Step 1

4(x+9)=76  Equation/Question

Step 2

4(x+9)=76  Remove parenthesis by multiplying 4

4x+36=76

Step 3

4x+36=76  Subtract 36 from sides

4x=40

Step 4

4x=40  Divide sides by 4

answer

x=10

Hope this helps

5 0
3 years ago
★write the pair of integer in which multiplication is -45 and difference is 12.
vladimir1956 [14]

Answer:

(3 and 15)

Step-by-step explanation:

If the product of both of these two numbers needs to be a negative 45 then there are no pair of integers that comply with both requirements.

If the multiplication in the question is wrong and it is a positive 45 then the pair of integers that would comply with these requirements would be (3 and 15). Multiplying this pair together would give you 45 and the difference between them is also 12 meaning it complies with both requirements that were asked for in the question.

5 0
2 years ago
Helllppppppppppppppppppppppppppppp
Georgia [21]

The equation: n - 4 = -15

Now let's solve our equation for n.

n - 4 = -15

Add 4 to both sides.

n = -11

4 0
3 years ago
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