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Liula [17]
3 years ago
5

The snack bar at your school has added sushi to its menu. The ingredients for one roll include sushi​ rice, seaweed​ sheets, cuc

umbers, cream​ cheese, and 2 oz of smoked salmon. One roll can be cut into 9 servings. Write an expression for the amount of salmon needed to make s servings of sushi. How much salmon is needed to make 18 ​servings? 36 ​servings? 90 ​servings? 100 ​servings?
Mathematics
1 answer:
amid [387]3 years ago
5 0

Answer:

The answer si:  

- 16 servings - 6 oz of salmon

- 24 servings - 9 oz of salmon

- 80 servings - 30 oz of salmon

- 100 servings - 37.5 oz of salmon

1 roll is 8 servings and it is also made of 3oz of smoked salmon. That means that 3oz of smoked salmon is needed fo 8 servings.

Now, let's made some proportions:

16 servings:

3 oz is for 8 servings, how much oz is for 16 servings:

3 : 8 = x : 16

x = 3 · 16 ÷ 8 = 6 oz

24 servings:

3 oz is for 8 servings, how much oz is for 24 servings:

3 : 8 = x : 24

x = 3 · 24 ÷ 8 = 9 oz

80 servings:

3 oz is for 8 servings, how much oz is for 80 servings:

3 : 8 = x : 80

x = 3 · 80 ÷ 8 = 30 oz

100 servings:

3 oz is for 8 servings, how much oz is for 100 servings:

3 : 8 = x : 100

x = 3 · 100 ÷ 8 = 37.5 oz

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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.

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1 year ago
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Ilia_Sergeevich [38]
Assume L=1.5W, where W=width, L= Length of the triangle.

Therefore,

Perimeter (P) = 2(W+L) = 2(W+1.5W) = 2(2.5W) = 5W=20 => W=20/5 = 4 in

Then, L=1.5W = 1.5*4 = 6 in

Area, A= L*W = 6*4 = 24 in^2
8 0
3 years ago
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