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Bingel [31]
3 years ago
5

304 students went on a field trip .7 buses were filled and 17 students traveled in cars. How many students were in each bus?? Sh

ow 2 step equations!!
Mathematics
2 answers:
Gemiola [76]3 years ago
8 0
304-17= 287.
287 divided by 7= 41 students per bus.
Anna71 [15]3 years ago
8 0

Answer:

There were 41 students in each bus.

Step-by-step explanation:

Consider the provided information.

304 students went on a field trip 7 buses were filled and 17 students traveled in cars.

We need to find How many students were in each bus.

Let the number of students in each bus is represented by x.

Thus the required equation is:

7x+17=304

Subtract 17 from both the sides.

7x=304-17

7x=287

x=41

Hence, there were 41 students in each bus.

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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.

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Answer:

a. 1/10 or 10%

b. 1/2 or 50%

Step-by-step explanation:

Since the combination of machines 1, 2 and 3 produce 100% of the total output when added together, then the probability of choosing a bolt at random that is defective is: 5 + 2 + 3 = 10% out of 100% or 10/100, which is 1/10 or 10%.

If the bolt that is choosen at random is defective, than the probability that it came from machine 1 is 5/10 or 1/2 which is also 50%.

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Answer:

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Step-by-step explanation:

Simplify the expression by combining like terms. Terms which look a like and sound a like should be added together.

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x^2 terms: 3x^2+5x^2=8x^2

x terms: 7x+12x=19x

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Together is is 8x^2+19x+3.

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