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Sholpan [36]
3 years ago
5

There are 15 non fiction books and 37 fiction books in the teacher’s collection. Which of the following expresses the ratio of f

iction books to non fiction books in simplest form?
A. 15:37
B. 15/37
C. 37:15
D. 3:5
Mathematics
2 answers:
fomenos3 years ago
6 0
To simplify a ratio, first make into the fraction form. a:b = \frac{a}{b}

Then find the prime factors of both the numerator and denominator.

\frac{15}{37} = \frac{(3)(5)}{(1)(37)}

Now cancel out any common factors. But if there isn't any common factors, then the fraction or ratio is in its simplest formula.

And that is the case here.

And because the question wants the answer in ratio form, make the fraction back into a ratio.

So, A. 15:37 is the answer.
saveliy_v [14]3 years ago
6 0

Answer:

The answer is A. 15:37 Good luck to you! Stay safe and Healthy!

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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.

4 0
1 year ago
How is factor 36 related to factor 72
Lady bird [3.3K]

Answer:by 2

Step-by-step explanation:

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Write an equation in point-slope form of the line through point J (4,1) with slope -4.
Marysya12 [62]

\bf J(\stackrel{x_1}{4}~,~\stackrel{y_1}{1})~\hspace{10em}slope = m\implies -4\\\\\\ \begin{array}{|c|ll}\cline{1-1}\textit{point-slope form}\\\cline{1-1}\\y-y_1=m(x-x_1)\\\\\cline{1-1}\end{array}\implies y-1=-4(x-4)

8 0
3 years ago
1. How do I find slope? What does a positive or negative slope mean?
gavmur [86]

Answer:

If your looking at a graph, you find the slope by going to a random point, and using rise/run to go to the next point. A negative slope means the function is decreasing, and a positive slope means the function is increasing.

6 0
2 years ago
Rewrite the quadratic function in vertex form.<br> Y=3x^2-12x+4
chubhunter [2.5K]

Answer:

\large\boxed{y=3(x-2)^2-8}

Step-by-step explanation:

The vertex form of an equation of a parabola y = ax² + bx + c:

f(x)=a(x-h)^2+k

(h, k) - vertex

h=\dfrac{-b}{2a},\ k=f(h)

We have the equation:

y=3x^2-12x+4\\\\a=3,\ b=-12,\ c=4

Substitute:

h=\dfrac{-(-12)}{2(3)}=\dfrac{12}{6}=2\\\\k=f(2)=3(2^2)-12(2)+4=3(4)-24+4=12-24+4=-8

Finally:

y=3(x-2)^2+(-8)=3(x-2)^2-8

4 0
3 years ago
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