MATHEMATICS COLLEGE

Find the solutions to x2-2x+10=0. The quadratic formula has been started for you.

Answers

Answer 1

Answer:

Answer

The solution to the quadratic equation is

$x=1\pm3i$

EXPLANATION

Problem Statement

The question gives us the beginning of the application of the Quadratic formula on a quadratic equation. We are required to simplify the expression and get in more certain terms, the values of x.

The expression given is:

$\begin{gathered} x^2-2x+10=0 \n \n x=\frac{2\pm\sqrt[]{(-2)^2-(4)(1)(10)}}{2} \end{gathered}$

Solution

Let us begin to simplify the expression below:

$\begin{gathered} x=\frac{2\pm\sqrt[]{(-2)^2-(4)(1)(10)}}{2} \n \n x=\frac{2\pm\sqrt[]{(-2*-2)^{}-(4*1*10)}}{2} \n \n x=\frac{2\pm\sqrt[]{4-40}_{}}{2} \n \n x=\frac{2\pm\sqrt[]{-36}}{2} \n \n \text{From the laws of indices, we have:} \n \sqrt[]{a* b}=\sqrt[]{a}*\sqrt[]{b} \n \n x=\frac{2\pm\sqrt[]{-1*36}}{2} \n \n x=\frac{2\pm(\sqrt[]{-1})(\sqrt[]{36})}{2} \n \n \text{ We know that, } \n \sqrt[]{-1}=i \n \n x=(2\pm(i)(6))/(2) \n \n x=(2\pm6i)/(2) \n \n x=(2(1\pm3i))/(2) \n \n 2\text{ Crosses out} \n \n x=1\pm3i \end{gathered}$

Final Answer

The solution to the quadratic equation is

$x=1\pm3i$

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Six-four million, one hundred eighty-six thousand, three hundred square miles in standard form

Answers

Answer:

64,186,300

Step-by-step explanation:

Six-four million - 64 million.

One hundred eighty six thousand - 186,000

You won't have space for the zeros, so you remove them.

And last, three hundred - 300.

So, now combine all of the numbers.

Your answer is 64,180,300.

Hope it helps!

Final answer:

The number six-four million, one hundred eighty-six thousand, three hundred is written as 64,186,300 in standard form.

Explanation:

The student is asking for a numerical representation of a written number, specifically six-four million, one hundred eighty-six thousand, three hundred. In standard form, this would be written as 64,186,300. The "million" denotes six zeros following the 64, the "thousand" indicates three zeros following the 186, and the "three hundred" is written as 300 at the end. So, in simpler terms, the number is written as 64,000,000 + 186,000 + 300 = 64,186,300.

Learn more about Standard form here:

brainly.com/question/37011468

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The population of a city (in millions) at time t (in years) is P(t)=2.6 e 0.005t , where t=0 is the year 2000. When will the population double from its size at t=0 ?

Answers

Answer:

year 2139

Step-by-step explanation:

The population will double when the factor e^(.005t) is 2.

e^(.005t) = 2

.005t = ln(2)

t = ln(2)/0.005 = 138.6

The population will be double its size at t=0 when t=138.6. That is the population will be about 5.2 million in the year 2139.

The population will double by the year 2139 from its value of 2.6 million in year 2000.

Population function :

$P(t) = 2.6 {e}^(0.005t)$

Population size at t = 0

$P(0) = 2.6 {e}^(0.005(0)) = 2.6(1) = 2.6$

Population at t = 2.6 million.

For the population to double ;

2.6 × 2 = 5.2 million :

$5.2 = 2.6 {e}^(0.005t)$

We solve for t

$(5.2)/(2.6) = {e}^(0.005t)$

$2 = {e}^(0.005t)$

Take the In of both sides

$ln(2) = 0.005t$

$t \: = ln(2) / 0.005 = 138.629$

The population will double after 139 years

Therefore, the population will double by the 2139 (Year 2000 + 139 years) = year 2139.

Learn more : brainly.com/question/11672641?referrer=searchResults

Write the equation in vertext form

Vertex: (3,6) ; y-intercept: 2

Answers

Y= a(x-3)^2+6
2= a(0-3)^2+6
2=a(-3)^2+6
2=a(9)+6
2-6=9a
-4=9a
-4/9=a

Therefore the equation in vertex form is
y = -4/9 (x-3)^2+6

Plzzz help fast I need the answer

Answers

Answer: (The first number are the years and the second are the amount of Komodo's) (0, 0) (1, 4) (2, 20) (3, 100) (4, 500) (5, 2,500)

Step-by-step explanation:

If there are 4 Komodo's in the first year because that's when they moved in, then there would be zero in the 0 year.

If they keep multiplying their population by 5 each year then for every year, you would multiply the existing population of that year by 5

Starting at year 1 which is (1, 4) multiply that by 5 to get 20 and so on to get the function.

I hope this helps!

Hello, there are three questions and pictures of them in the links If you could solve them that would be awesome, thank you!

Answers

Answer:

1. 1 * $x^(3/6)$ = $x^(3/6)$ (it will be equal to the sixth root of x cube)

2. No, the expression $x^(3)$ X $x^(3)$ X $x^(3)$ will be equal to $x^(3 + 3 + 3 )$ since the powers of numbers with the same base are added

3. B and D 1/ $x^(-1)$ is the same as 'x'

as mentioned in the last answer, powers of numbers with same base are added. hence, option D will be $x^(3/3)$ which will be equal to x

Can someone plz help me on this

Answers

Step-by-step explanation:

I know it's not B because it has the most explanation and C is the only answer that dosnt relate

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