What is the prime factorization for 180?

what is the polynomial function of lowest degree with leading coefficient of 1 and roots 2 and 1 + square root2

Marta_Voda [28]

If the roots to such a polynomial are 2 and $1+\sqrt2$ , then we can write it as

$(x-2)(x-(1+\sqrt2))$

courtesy of the fundamental theorem of algebra. Now expanding yields

$(x-2)(x-1-\sqrt2)=x^2-2x-(1+\sqrt2)x+2(1+\sqrt2)=x^2-(3+\sqrt2)x+2+2\sqrt2$

which would be the correct answer, but clearly this option is not listed. Which is silly, because none of the offered solutions are *the* polynomial of lowest degree and leading coefficient 1.

So this makes me think you're expected to increase the multiplicity of one of the given roots, or you're expected to pull another root out of thin air. Judging by the choices, I think it's the latter, and that you're somehow supposed to know to use $1-\sqrt2$ as a root. In this case, that would make our polynomial

$(x-2)(x-(1+\sqrt2))(x-(1-\sqrt2))=x^3-4x^2+3x+2$

so that the answer is (probably) the third choice.

Whoever originally wrote this question should reevaluate their word choice...

5 0

3 years ago

Jackson played a video game for 1/6 for hour. Hailey played a video game for 1/3 hour. Who played the video game for a greater a

viva [34]

Answer:

hailey played the game longer (1/3 hour).

Step-by-step explanation:

You are deciding which is greater: 1/6 or 1/3.in this case, a smaller denominator (such as 3) produces a greater value.1/3 has a smaller denom. than does 1/6, so 1/3 is greater than 1/6.hailey played the game longer (1/3 hour).

5 0

3 years ago

Find the slope of the line. (Please explain if you can, and answer in an integer/fraction.)

Setler [38]

Answer:

-2

Step-by-step explanation:

We can find the slope of a line by using two points

(-2,1) and (2,-7)

The slope is given by

m = (y2-y1)/(x2-x1)

= (-7-1)/(2- -2)

= (-8)/(2+2)

= -8/4

=-2

4 0

3 years ago

The area of a square is 49 square meters. How long is each side?

Artemon [7]

A square has 4 equal sides, which means when you need to work out the area, you're doing length × width, but the length and width are exactly the same, because it's a square (look at the picture if you don't understand this).

That means you just have to pick any side (let's call this side x), and multiply it by another side of the square. Now, because all of the sides are equal, you're doing x multiplied by x, which is the same as x².

Therefore, if the area is equal to x², and in this question, it's also equal to 49 (as stated in the question), we can equate them to each other:

x² = 49

Now to get the x by itself, we need to do the opposite of squaring, which is square rooting. Therefore, we square root both sides of the equation:

√x² = √49

The √ and the ² cancel out, so you're just left with x:

x = √49

The square root of 49 is just 7, so we can replace √49 with 7, and we get:

x = 7

Now remember, earlier, I called x the value of one side. Therefore, by remembering that, you know that the value of one side is equal to 7. And because all the sides are the same as each other, each side is equal to 7 metres.

Therefore, your final answer is 7 metres :)

3 0

3 years ago

If an employee notices that a bucket with sanitizing water is becoming dirt, he/she should ___.

ehidna [41]

This is pretty much a "common sense" question. It'd be best to get rid of the dirty sanitizing water and start fresh; in other words, he should change (throw out) the dirty water and make a fresh sanitizer.

By the way, this is the Math section; next time, please choose a different section more suited to your questions.

7 0

3 years ago