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SSSSS [86.1K]
2 years ago
11

What is the converse of the linear pairs theorem

Mathematics
1 answer:
marysya [2.9K]2 years ago
6 0
The converse of a logicalstatement is a s tatement formed by reversing the parts of the statement.

For example, the logical statement "A implies B" has a converse of "B implies A"

The linear pairs theorem states that "<span>if two angles form a linear pair, then they are supplementary".</span>

The converse of the linear pairs theorem is therefore, "if two angles are suplementary, then they form a linear pair".
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Suppose the roots of the polynomial $x^2 - mx + n$ are positive prime integers (not necessarily distinct). Given that $m &lt; 20
Vsevolod [243]

Answer:

<em>18</em> values for n are possible.

Step-by-step explanation:

Given the quadratic polynomial:

$x^2 - mx + n$

such that:

Roots are positive prime integers and

$m < 20$

To find:

How many possible values of n are there ?

Solution:

First of all, let us have a look at the sum and product of a quadratic equation.

If the quadratic equation is:

Ax^{2} +Bx+C

and the roots are: \alpha and \beta

Then sum of roots, \alpha+\beta = -\frac{B}{A}

Product of roots, \alpha \beta = \frac{C}{A}

Comparing the given equation with standard equation, we get:

A = 1, B = -m and C = n

Sum of roots,  \alpha+\beta = -\frac{-m}{1} = m

Product of roots, \alpha \beta = \frac{n}{1} = n

We are given that m  

\alpha and \beta are positive prime integers such that their sum is less than 20.

Let us have a look at some of the positive prime integers:

2, 3, 5, 7, 11, 13, 17, 23, 29, .....

Now, we have to choose two such prime integers from above list such that their sum is less than 20 and the roots can be repetitive as well.

So, possible combinations and possible value of n (= \alpha \times \beta) are:

1.\ 2,  2\Rightarrow  n = 2\times 2 = 4\\2.\ 2, 3 \Rightarrow  n = 6\\3.\ 2, 5 \Rightarrow  n = 10\\4.\ 2,  7\Rightarrow  n = 14\\5.\ 2, 11 \Rightarrow  n = 22\\6.\ 2, 13 \Rightarrow  n = 26\\7.\ 2, 17 \Rightarrow  n = 34\\8.\ 3,  3\Rightarrow  n = 3\times 3 = 9\\9.\ 3, 5 \Rightarrow  n = 15\\10.\ 3, 7 \Rightarrow  n = 21\\

11.\ 3,  11\Rightarrow  n = 33\\12.\ 3, 13 \Rightarrow  n = 39\\13.\ 5, 5 \Rightarrow  n = 25\\14.\ 5, 7 \Rightarrow  n = 35\\15.\ 5, 11 \Rightarrow  n = 55\\16.\ 5, 13 \Rightarrow  n = 65\\17.\ 7, 7 \Rightarrow  n = 49\\18.\ 7, 11 \Rightarrow  n = 77

So,as shown above <em>18 values for n are possible.</em>

3 0
3 years ago
12.1.33 Question Help Suppose that 62​% of families living in a certain country own an HDTV and 16​% own a computer. The Additio
poizon [28]

Answer:

Step-by-step explanation:

Suppose :

62% own an HDTV

16% own a computer

Using the addition rule : suggests that (62% + 16%) = 78% either own an HDTV or a computer.

The reasoning is wrong because ; since it is possible to own both an HDTV and also own a computer at the same time, the outcome of the addition rule is wrong as both events are independent. If both event cannot occur at the same time (mutually exclusive event) , then, the addition rule may be applied,. But since both can occur independently and each family can own an HDTV while also owning a computer, then the addition rule is wrong for the scenario described.

6 0
3 years ago
Angle psr measures 99°. what is the measure of psq in degrees?
Snezhnost [94]
Assuming that point s is the vertex of the angle and that line sq is between angle psr. We can get the correct measurement of angle psq by subtracting 99 degrees with the measurement of the angle made by qsr. Hope this helps. Have a nice day.
6 0
3 years ago
Please help if you can
dolphi86 [110]

Answer:

x=4 or x=-5/7

Step-by-step explanation:

4 0
3 years ago
Autum school holding a voleturing challeng. Students are encouraged to volunteer for at least 1 1/2 hours per week. Volenteers a
Pani-rosa [81]

Given :

Challenge given is to volunteer for about 1 1/2 hours per week .

Autum did at a rate of 6 3/4 hours per week .

To Find :

The comparison ( ratio )  her volunteers rate with the challenge rate .

Solution :

Simplifying challenge rate in in normal fraction , 1\dfrac{1}{2}=\dfrac{2+1}{2}=\dfrac{3}{2} .

Also , simplifying her rate , 6\dfrac{3}{4}=\dfrac{(6\times 4)+3}{4}=\dfrac{27}{4} .

Now , ratio of his work by challenge is :

R=\dfrac{\dfrac{27}{4}}{\dfrac{3}{2}}\\\\\\R=\dfrac{27\times 2}{4\times 3}\\\\R=\dfrac{9}{2}

Therefore , the ratio is 9/2 or 4 1/2 .

Hence , this is the required solution .

8 0
3 years ago
Read 2 more answers
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