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3 years ago

Which expression represents the follow-

Mathematics

1 answer:

Varvara68 [4.7K]3 years ago

4 0

Answer:

the sum of x and 5.

x + 5

the sum of is adding

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Leave the answer in simplest form ?

lions [1.4K]

Tan is opposite÷ adjacent.
So tan(d) = 7÷24. It is already in the simplest form.

Rate and Thanks!

4 0

3 years ago

Help!!!!!

guapka [62]

3*-6-2*-11=14

-18+22=14

22=14+18

8 0

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:

18 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 18 values for n are possible.

3 0

3 years ago

12s+ 3p =b There’s the question and I need help understanding it

yaroslaw [1]

Answer:

Step-by-step explanation:

8 0

3 years ago

(Quick please ) !!!!!!!!!!!!!!!! Help me!!!!! find the surface area of the rectangular prism!!!!!! thank you

Aleks [24]

You can do this !

The rectangular prism has

   -- length = 10 cm
   -- width = 7 cm
   -- height = 3 cm.

-- The area of the top and bottom is (length x width) each.

-- The area of the left and right sides is (length x height) each.

-- The area of the front and back is (width x height) each.

There. I just laid out all the schmartz you need to answer this question.
The rest is all simple arithmetic, and you're perfectly capable of turning
the crank and getting the answer. You don't need anybody else to do
that part for you.

Don't forget your units. The area of each flat face is (cm) times (cm),
and that product will be some cm² , for area.

3 0

3 years ago