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3 years ago

What are the solutions of 3(x – 4)(2x – 3) = 0? Check all that apply.

Mathematics

2 answers:

lana66690 [7]3 years ago

6 0

Answer:

x = 4, x = 3/2

Step-by-step explanation:

3(x - 4)(2x - 3) = 0

x - 4 = 0 , or 2x-3 = 0

x = 4, x = 3/2

Stella [2.4K]3 years ago

3 0

Answer:

Its D and F

Step-by-step explanation:

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Find the angle between u =the square root of 5i-8j and v =the square root of 5i+j.

fenix001 [56]

Answer:

The angle between vector $\vec{u} = 5\, \vec{i} - 8\, \vec{j}$ and $\vec{v} = 5\, \vec{i} + \, \vec{j}$ is approximately $1.21$ radians, which is equivalent to approximately $69.3^\circ$ .

Step-by-step explanation:

The angle between two vectors can be found from the ratio between:

their dot products, and
the product of their lengths.

To be precise, if $\theta$ denotes the angle between $\vec{u}$ and $\vec{v}$ (assume that $0^\circ \le \theta < 180^\circ$ or equivalently $0 \le \theta < \pi$ ,) then:

$\displaystyle \cos(\theta) = \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|}$ .

<h3>Dot product of the two vectors</h3>

The first component of $\vec{u}$ is $5$ and the first component of $\vec{v}$ is also

The second component of $\vec{u}$ is $(-8)$ while the second component of $\vec{v}$ is $1$ . The product of these two second components is $(-8) \times 1= (-8)$ .

The dot product of $\vec{u}$ and $\vec{v}$ will thus be:

$\begin{aligned} \vec{u} \cdot \vec{v} = 5 \times 5 + (-8) \times1 = 17 \end{aligned}$ .

<h3>Lengths of the two vectors</h3>

Apply the Pythagorean Theorem to both $\vec{u}$ and $\vec{v}$ :

$\| u \| = \sqrt{5^2 + (-8)^2} = \sqrt{89}$ .
$\| v \| = \sqrt{5^2 + 1^2} = \sqrt{26}$ .

<h3>Angle between the two vectors</h3>

Let $\theta$ represent the angle between $\vec{u}$ and $\vec{v}$ . Apply the formula $\displaystyle \cos(\theta) = \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|}$ to find the cosine of this angle:

$\begin{aligned} \cos(\theta)&= \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|} = \frac{17}{\sqrt{89}\cdot \sqrt{26}}\end{aligned}$ .

Since $\theta$ is the angle between two vectors, its value should be between $0\; \rm radians$ and $\pi \; \rm radians$ ( $0^\circ$ and $180^\circ$ .) That is: $0 \le \theta < \pi$ and $0^\circ \le \theta < 180^\circ$ . Apply the arccosine function (the inverse of the cosine function) to find the value of $\theta$ :

$\displaystyle \cos^{-1}\left(\frac{17}{\sqrt{89}\cdot \sqrt{26}}\right) \approx 1.21 \;\rm radians \approx 69.3^\circ$ .

3 0

3 years ago

Carl has 200 songs on his mp3 player of these songs 24 all country songs what percent of curls songs are country songs

Leokris [45]

12% of carls songs are country songs.
I done this by doing 24 divide by 200 which is 0.12 meaning it would be 12%

Hope this helps!

5 0

3 years ago

Read 2 more answers

AMERICAN AIRLINES HAS A POLICY OF BOOKING AS MANY AS 15 PEOPLE ON AN AIRPLANE THAT CAN SEAT ONLY 14. (PAST STUDIES HAVE REVEALED

Blizzard [7]

Using the binomial distribution, there is a 0.0874 = 8.74% probability that not enough seats will be available.

<h3>What is the binomial distribution formula?</h3>

The formula is:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

For this problem, the values of the parameters are given by:

n = 15, p = 0.85.

The probability that not enough seats will be available is P(X = 15), as the only outcome in which not enough seats will be available is when all 15 people who bought the ticket show up, hence:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 15) = C_{15,15}.(0.85)^{15}.(0.15)^{0} = 0.0874$

0.0874 = 8.74% probability that not enough seats will be available.

More can be learned about the binomial distribution at brainly.com/question/24863377

#SPJ1

8 0

1 year ago

Given numbers of 1,2,5,7,8.

Gemiola [76]

The probability would be 2 out of 5

4 0

3 years ago

Kyle earns a fixed weekly salary of $200 plus a 10% commission on his sales that week. The total amount of Kyle's paycheck (y do

Arlecino [84]

Answer:

D. y= 200+ 0.1x

Step-by-step explanation:

Given data

Fixed Salary= $200

Commission= 10%

weekly sales = x

Hence the expression for the total amount he earns is given as

y= 200+ 0.1x

3 0

3 years ago