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3 years ago

What do we know about a system of linear equations when is has

Mathematics

1 answer:

Radda [10]3 years ago

4 0

Linear systems that have infinite solutions have the same slope and they have the same line on the graph

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When 8 is added to 3times a certain number, the result is the same as adding 12 to twice the number. find the number

White raven [17]

Answer:

The number is 4

Step-by-step explanation:

<u>Choose a variable for the number.</u>

let the number be "x"

<u>Make an equation</u> with the information from the problem. Break down each part of the problem and change it to the algebraic form (numbers and symbols).

"When 8 is added to" 8 +

"3 times a certain number" 3x

"the result is the same as" =

"adding 12 to" 12 +

"twice the number" 2x

Put the equation back together with each of the parts.

8 + 3x = 12 + 2x

<u>Now isolate "x"</u> to the left side to find the number.

8 + 3x - 2x = 12 + 2x - 2x Subtract 2x from both sides

8 + x = 12 "x" is only on the left side

8 - 8 + x = 12 - 8 Subtract 8 from both sides

x = 4 Solved for the number

Therefore the number is 4.

5 0

3 years ago

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in s

nikdorinn [45]

We are given zeros of the polynomial : 7, -11, and 2 + 8i.

Note: The radical zero always comes with the pair of plus and minus sign.

Therefore, another zero would be 2-8i.

Now, in order to find the polynomial with the zeros 7, -11, 2 + 8i and 2-8i, we need to find the factors of the polynomial.

The factors of the polynomial would be (x-7)(x+11)(x-2-8i)(x-2+8i).

Let us multiply those factors to get the standard form of the polynomial.

$\left(x-2-8i\right)\left(x-2+8i\right)=\left(x-2-8i\right)\left(x-2+8i\right) =x^2-4x+68$

$\left(x-7\right)\left(x+11\right)=x^2+11x-7x-77$ = $x^2+4x-77$

$\left(x^2-4x+68\right)\left(x^2+4x-77\right)=x^4-9x^2-16x^2+308x+272x-5236\\$

$=x^4-25x^2+580x-5236$ .

<h3>Therefore, correct option is 4th option $f(x) = x^4 - 25x^2 + 580x - 5236$ .</h3>

8 0

3 years ago

Please help I need this! Pls!!

ZanzabumX [31]

Answer:

Step-by-step explanation:

To find how many it is greater, divide the size of the largest email by the smallest email and both should in bytes. So, convert megabytes and kilo bytes to bytes.

4 kilo bytes = 4* 10³ bytes

8 megabytes = 8 * 10⁶ bytes

$\sf \dfrac{8*10^6}{4*10^3}= 2 *10^{(6-3)}$