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Flauer [41]
3 years ago
12

Evaluate 1.80/Y for y= 0.009 express your answer is in simplest form.

Mathematics
1 answer:
igomit [66]3 years ago
3 0

Evaluate 1.80/Y for y= 0.009

We replace 0.009 for y

So fraction becomes \frac{1.80}{0.009}

Now , to simplify the fraction we try to remove the decimal from denominator

0.009 have three digits after the decimal point, so we multiply by 1000 to remove the decimal point. Multiply top and bottom by 1000 to make equivalent fraction.

\frac{1.80*1000}{0.009*1000}

\frac{1800}{9} = 200

Answer is 200

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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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1 year ago
If triangle ABD is similar to Triangle EFG, find BC and FH
Liula [17]

Answer:

B. BC=12, FH=9

Step-by-step explanation:

I guessed and it was right

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2 years ago
Select all the options below that correctly fill in the blank. A ____ is a subcategory of polygon.
yaroslaw [1]

Answer:

triangle is a subcategory of polygon

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3 years ago
Becky put $100 into in the account to use for school expenses. The account earns 11% interest, compounded annually. How much wil
Mnenie [13.5K]

Answer: $187 will be in the account after 6 years.

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = $100

r = 11% = 11/100 = 0.11

n = 1 because it was compounded once in a year.

t = 6 years

Therefore,.

A = 100(1 + 0.11/1)^1 × 6

A = 100(1 + 0.11)^6

A = 100(1.11)^6

A = $187

5 0
3 years ago
Estelle is raking leaves in the yard. After 1 hour, she has 2 bags of leaves. After 3 hours, she has 6 bags of leaves. Which gra
kenny6666 [7]
Y= 2x
Every hour 2 bags
Afer 1 hour. 2 bags
After 2 hours 4 bags
After 3 hours. 6 bagds
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