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3 years ago

Quick! Is this line parallel, perpendicular, or neither?

Mathematics

2 answers:

svetoff [14.1K]3 years ago

8 0

This line would be neither. Parallel lines are lines that will never intersect. Perpendicular lines will meet and create four 90 degree angles. These lines do not meet the criteria, so the answer is neither.

Elanso [62]3 years ago

5 0

I'm pretty sure this is neither

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Suppose the roots of the polynomial $x^2 - mx + n$ are positive prime integers (not necessarily distinct). Given that $m < 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>

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3 years ago

What is the best name for the part of the figure identified by

BigorU [14]

It is Line of symmetry

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3 years ago

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What are three equivalent ratios for 5/45

Burka [1]

$\frac{5}{45}=5:45\ and\ \frac{5}{45}=\frac{5:5}{45:5}=\frac{1}{9}\\\\\frac{5}{45}=\frac{1}{9}\to\boxed{1:9}\\\\\frac{5}{45}=\frac{1}{9}=\frac{1\cdot2}{9\cdot2}=\frac{2}{18}=\boxed{2:18}\\\\\frac{5}{45}=\frac{1}{9}=\frac{1\cdot3}{9\cdot3}=\frac{3}{27}=\boxed{3:27}\\\\\frac{5}{45}=\frac{1}{9}=\frac{1\cdot4}{9\cdot4}=\frac{4}{36}=\boxed{4:36}\\\vdots$

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3 years ago

a bag contains 8 red 4 blue and 4 yellow marbles what is the probrability of randomly choosing 2 blue marbles without replacemen

enyata [817]

Answer:

12.5%

Step-by-step explanation:

8+4+4=16

2/16*100=12.5

12.5%

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4 years ago

Solve for n: 3(n+6)≥3n+8

hodyreva [135]

Answer:

infinite solutions

Step-by-step explanation:

3(n+6)≥3n+8

3n+18≥3n+8 (distributive property)

18≥8 (subtracted 3n from both sides)

this will always be true so there are infinite solutions

7 0

3 years ago

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