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2 years ago

Determine if (−2,4) is a solution to the following system of inequalities.-3x > -7y -37x > -5y -4

Mathematics

1 answer:

nikklg [1K]2 years ago

5 0

Remember that ordered pairs are written in the form (x,y).

Then, to check if (-2,4) is a solution to the system of inequalities, both of the given inequalities should be verified when replacing x=-2 and y=4.

Replace x=-2 and y=4 into the inequalities and check if both of them are satisfied or not.

-3x > -7y - 3

$\begin{gathered} \Rightarrow-3(-2)>-7(4)-3 \\ \Rightarrow6>-28-3 \\ \Rightarrow6>-31 \end{gathered}$

Sice 6 is greater than -31, then this inequality is satisfied by (-2,4).

7x > -5y-4

$\begin{gathered} \Rightarrow7(-2)>-5(4)-4 \\ \Rightarrow-14>-20-4 \\ \Rightarrow-14>-24 \end{gathered}$

Since -14 is greater than -24, then this inequality is satisfied by (-2,4).

Since both inequalities are satisfied by (-2,4) then (-2,4) is a solution to the given system of inequalities.

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Fill in the blank to complete the following sentence. The two roots a +sqrt b and a- sqrt b are called ______ radicals.

katrin [286]

The two roots a + sqrt b and a - sqrt b are called conjugate radicals.

<u>Solution:</u>

Given that the two roots a + sqrt b and a - sqrt b are called ______ radicals.

Now let us write the each of the given two radicals in mathematical form.

So, first radical ⇒ a + sqrt b ⇒ $a+\sqrt{b}$ [ since sqrt means square root]

Now second radical ⇒ a - sqrt b ⇒ $a-\sqrt{b}$

We have to find the relation between $a+\sqrt{b} \text { and } a-\sqrt{b}$

Now, if observe $a+\sqrt{b}$ is conjugate of $a-\sqrt{b} \text { as }(a+\sqrt{b})(a-\sqrt{b})=a^{2}-b$

[ where radical is eliminated]

Hence, the two roots a +sqrt b and a- sqrt b are called conjugate radicals

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3 years ago

To get the volume of a ___, multiply 4/3 by pi and then by the cube of radius

Sladkaya [172]

Answer:

To get the volume of a <u>SPHERE</u>, multiply 4/3 by pi and then by the cube of radius.

Step-by-step explanation:

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4 years ago

Read 2 more answers

Find the solutions x2 = 27

Aneli [31]

Answer:

27 divided by 3 is 9

27 divided by 2 is 13.5

x = 13.5

Re written...

(13.5)2 = 27

make sense?

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3 years ago

What comes next in the sequence: 1, 3, 11, 43,

lianna [129]

There may be more than one solution, but if we take the difference between the numbers of the sequence, we get
3-1, 11-3, 43-11
=2,8,32
which are powers of 2
=2^1, 2^3,2^5
If we believe the next difference is 2^7=128, then the next in the sequence will be 43+128=171

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3 years ago

How to find the average squared distance between the points of the unit disk and the point (1,1)

ddd [48]

The unit disk can be parameterized by the function

$\mathbf p(r,\theta)=(r\cos\theta,r\sin\theta)$

where $0\le r\le 1$ and $0\le\theta\le2\pi$ . The squared distance between any point in this region $(x,y)=(r\cos\theta,r\sin\theta)$ and the point (1, 1) is

$(x-1)^2+(y-1)^2=(r\cos\theta-1)^2+(r\sin\theta-1)^2$
$=(r^2\cos^2\theta-2r\cos\theta+1)+(r^2\sin^2\theta-2r\sin\theta+1)$
$=r^2(\cos^2\theta+\sin^2\theta)-2r(\cos\theta-\sin\theta)+2$
$=r^2-2r(\cos\theta-\sin\theta)+2$

The average squared distance is then going to be the ratio of [the sum of all squared distances between every point in the disk and the point (1, 1)] to [the area of the disk], i.e.

$\dfrac{\displaystyle\iint_{x^2+y^2$
$=\dfrac{\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}[r^2-2r(\cos\theta-\sin\theta)+2]r\,\mathrm dr\,\mathrm d\theta}{\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}r\,\mathrm dr\,\mathrm d\theta}$
$=\dfrac{\frac{5\pi}2}\pi=\dfrac52$

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3 years ago