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3 years ago

12

Mr and mrs smith buy 6tickets work out how much the tickets cost. Two for them and four for the children. The final price was 40

.50

1 answer:

mamaluj [8]3 years ago

4 0

Answer:

$6.75

Step-by-step explanation:

40.50/6

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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>

3 0

3 years ago

HELP I HAVE 10 MINUTES PLEASE GIVE ME A REAL ANSWER :

Dimas [21]

Answer:

the third one

Step-by-step explanation:

its easy

3 0

3 years ago

What is the slope of the line

posledela

Answer:

<h2>A . 6</h2>

Step-by-step explanation:

$\mathrm{For\:a\:line\:equation\:for\:the\:form\:of\:}\mathbf{y=mx+b}\mathrm{,\:the\:slope\:is\:}\mathbf{m}\\m=6$

3 0

3 years ago

Greenfield village is spread across 240 acres of land. Only 37% of the land is used for the exhibits, while the rest of the land

Sergeeva-Olga [200]

Answer:

The land which are used for exhibits are <u>89 acres</u> (approximately).

Step-by-step explanation:

Given:

Village is spread across 240 acres of land. 37% of land is used for the exhibits.

Now, we have to find acres of land which are used for exhibits.

So, here it is given that land used for exhibits is 37%, and we have to calculate the quantity from the percentage given:

According to question:

37% of 240 acres of land.

$\frac{37}{100}\times 240$

$0.37\times 240$

$88.80$

So, the land used for exhibits are 88.80 acres.

Therefore, the land which are used for exhibits are <u>89 acres </u>(approximately).

5 0

4 years ago

The heights of four students in Mrs. Patel;s class are 5 1/2 feet, 5.35 feet, 5 4/10 feet and 5.5 feet. What is the height in fe

kodGreya [7K]

5.35 feet. Just make them all decimals and compare

3 0

3 years ago

Read 2 more answers