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3 years ago

1. What plane is parallel to plane HGK?*

Mathematics

1 answer:

MrRa [10]3 years ago

4 0

Answer:

The answer should be BAD

Step-by-step explanation:

They are all parallel from each other and will never touch

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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:

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

I NEED HELP PLEASE, THANKS! :)

eduard

Answer:

2444

Step-by-step explanation:

The total cost is the integral of the marginal cost.

$\displaystyle C=\int_{144}^{625}{\dfrac{94}{\sqrt{x}}}\,dx=\left. 2\cdot 94\sqrt{x}\right|_{144}^{625}=188(25 -12)=\boxed{2444}$

The total cost of producing units 144 through 625 is 2444.

_____

If all you need is a number, a graphing calculator can give you that.

8 0

3 years ago

Suppose a farm has pens for raising insects. A pen is shaped as a rectangle that measures x meters wide and 2x meters long and h

Ludmilka [50]

Answer:

1.2 meters.

Step-by-step explanation:

Length of pen = 2x meters

width of pen = x meters

shape of pen is rectangular

we know that area of rectangle is given by length * width

Thus, area of the pen is x*2x = $2x^2$

It is also given that area of pen is 2.8 square meters.

Equating numerical value of area with area in terms of x, we have

$2x^2 = 2.88\\=> x^2 = 2.88/2\\=> x^2 = 1.44\\=> x = 1.2$

Thus value of x is 1.2 meters.

5 0

3 years ago

I need to find measure of angle "u" m

garik1379 [7]

Answer:

30°

Step-by-step explanation:

TW UV

If an ARC subtends an angle in the circle (on the opposite side of the circumference), the measure of that angle will be HALF of the Arc. In other words, the Arc's measure will be DOUBLE of that angle.

The measure of the angle would be SAME if the angle subtended in the center of the circle, thought.

Now, looking at the image, we can see that:

Arc TW subtends Angle V and Angle U

*on the opposite side of the circumference*

So,

Angle V (measure given to be 30) is HALF of Arc TW, so

Arc TW = 2 * 30 = 60

So, Angle U is half of Arc TW

60/2 = 30

Hence,

∠U = 30°

7 0

3 years ago

In jaime's math class, 9 students chose soccer as their favorite sport. This amount represents 3/8 of the entire class. The equa

Daniel [21]

Answer:

Step-by-step explanation:

3/8=9

6/8=18

8/8 would be 6/8 plus 2/3 of nine which is six

6+18=24

7 0

3 years ago