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2 years ago

Simplify the radical expression

Mathematics

2 answers:

eimsori [14]2 years ago

6 0

5(45b)^1/2 times 6(48b)^1/2

LenKa [72]2 years ago

3 0

To multiply two radicals together, we can simply multiply both the values inside the radicals together and put that in a radical.
So for 5*sqrt(45b) * 6*sqrt(48b), we get 30*sqrt(45b*48b) = 30*sqrt(2160b^2). This value can be simplified further by taking out b^2 and 12^2 from the radical giving us the answer 360b*sqrt(15).

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On Tuesday at 2 p.m., the ocean’s surface at the beach was at an elevation of 2.2 feet. Winston’s house is at an elevation of 12

bekas [8.4K]

A) The elevation of Tammy's house is 42.35 feet.

6 0

2 years ago

Juanita wants to perform row operations on the augmented matrix for the system below (See pictures). Which matrix should Juanita

Artist 52 [7]

Answer:

The second option

Step-by-step explanation:

The given system of equation is

x+2y=3

-x+y+z=2

y-2z=-3

The augment matrix is obtained by combining the coefficient matrix with the constant matrix to obtain;

$\left[\begin{array}{cccc}1&2&0&|3\\-1&1&1&|2\\0&1&-2&|-3\end{array}\right]$

Note that the absence of z, in the first equation means its coefficient is zero. The same thing applies to x in the last equation.

The correct choice is the second option.

5 0

2 years ago

Sociologists want to test whether the number of homeless people in a particular urban area is increasing. In 2010, the average n

Kobotan [32]

Answer:

The test statistic value is 15.3.

Step-by-step explanation:

The hypothesis for this test is:

H₀: The average number of homeless people is not increasing, i.e. μ = 42.3.

Hₐ: The average number of homeless people is increasing, i.e. μ > 42.3.

Given:

$\bar x=45.3\\\sigma=6.2\\n=1000$

As the population standard deviation is provided use a single mean z-test for the hypothesis testing.

The test statistic is:

$z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}=\frac{45.3-42.3}{6.2/\sqrt{1000}}=15.3$

Thus, the test statistic value is 15.3.

7 0

2 years ago

Find a polynomial $f(x)$ of degree $5$ such that both of these properties hold: $\bullet$ $f(x)$ is divisible by $x^3$. $\bullet

frosja888 [35]

There seems to be one character missing. But I gather that f(x) needs to satisfy

• $x^3$ divides $f(x)$

• $(x-1)^3$ divides $f(x)^2$

I'll also assume f(x) is monic, meaning the coefficient of the leading term is 1, or

$f(x) = x^5 + \cdots$

Since $x^3$ divides $f(x)$ , and

$f(x) = x^3 p(x)$

where $p(x)$ is degree-2, and we can write it as

$f(x)=x^3 (x^2+ax+b)$

Now, we have

$f(x)^2 = \left(x^3p(x)\right)^2 = x^6 p(x)^2$

so if $(x - 1)^3$ divides $f(x)^2$ , then $p(x)$ is degree-2, so $p(x)^2$ is degree-4, and we can write

$p(x)^2 = (x-1)^3 q(x)$

where $q(x)$ is degree-1.

Expanding the left side gives

$p(x)^2 = x^4 + 2ax^3 + (a^2+2b)x^2 + 2abx + b^2$

and dividing by $(x-1)^3$ leaves no remainder. If we actually compute the quotient, we wind up with

$\dfrac{p(x)^2}{(x-1)^3} = \underbrace{x + 2a + 3}_{q(x)} + \dfrac{(a^2+6a+2b+6)x^2 + (2ab-6a-8)x +2a+b^2+3}{(x-1)^3}$

If the remainder is supposed to be zero, then

$\begin{cases}a^2+6a+2b+6 = 0 \\ 2ab-6a-8 = 0 \\ 2a+b^2+3 = 0\end{cases}$

Adding these equations together and grouping terms, we get

$(a^2+2ab+b^2) + (2a+2b) + (6-8+3) = 0 \\\\ (a+b)^2 + 2(a+b) + 1 = 0 \\\\ (a+b+1)^2 = 0 \implies a+b = -1$

Then $b=-1-a$ , and you can solve for a and b by substituting this into any of the three equations above. For instance,

$2a+(-1-a)^2 + 3 = 0 \\\\ a^2 + 4a + 4 = 0 \\\\ (a+2)^2 = 0 \implies a=-2 \implies b=1$

So, we end up with

$p(x) = x^2 - 2x + 1 \\\\ \implies f(x) = x^3 (x^2 - 2x + 1) = \boxed{x^5-2x^4+x^3}$

6 0

1 year ago

Rewrite in simplest radical form 1/x^-3/6. Please show each step of your process.

antiseptic1488 [7]

To simplify the given radical form, we must recall some properties of exponents as shown below. 1. 1/x⁻ⁿ = xⁿ 2. x¹/² = √x Now, going back to 1/x⁻³/⁶, we have 1/x⁻³/⁶ = x³/⁶ x³/⁶ = x¹/² x¹/² = √x Using the properties provided, we have a simplified form of √x. Answer: √x

7 0

2 years ago

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