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3 years ago

PLEASE HELP FAST triangle abc is translated 4 units down and 6 units right, resulting in triangle A’B’C’

Mathematics

1 answer:

Lina20 [59]3 years ago

6 0

Answer:

D. (6,-1)

Step-by-step explanation:

Translating is just sliding slide the point B down 4 units from where it is and then move over 6 units to the right.

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How do i complete the square y= X2+8X-4

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x²+8x+16-16-4
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How long is the coastline of canada

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B. Mercury, Venus, and Earth are the three planets closest to the sun. Would their combined distance from

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3 years ago

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>

3 0

3 years ago

The area of a square garden is 50 m3. How long is the diagonal?

katen-ka-za [31]

Answer:

10 m

Step-by-step explanation:

If the area of a square is 50 m2, then the length of each side will be $\sqrt{50}$ m, to get the diagonal length, after dividing the square by joining the points of the diagonal with a line, it forms two right angles with length $\sqrt{50}$ m each.

the diagonal length represent the hypotenuse side of each of the right angle, knowing the pythagoras theorem:

$(hyp)^{2} = (opp)^{2} + (Adj)^{2}$ , so we have:

$(diagonal)^{2} = 50 + 50$

$(diagonal)^{2} = 100$

diagonal = 10 m

6 0

3 years ago