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2 years ago

Which equation exemplifies the commutative property of multiplication??

Mathematics

2 answers:

Studentka2010 [4]2 years ago

5 0

3: 12x1=1=12 because you’re changing the order of numbers you’re multiplying but the product stays the same

allsm [11]2 years ago

5 0

Answer: 3: 12x1=1x12

Step-by-step explanation:

An operation is said to be commutative if the answer to such mathematical operation remains the same no matter the way the variables are arranged. Commutative law is only true under operation addition and multiplication. For example, given two variables A and B, A and B are said to be commutative if

1. A+B = B + A (addition law)

2. AB = BA (multiplicative law)

Applying this to the question, the equation 12×1 = 1×12 exemplifies the commutative property of multiplication because the arrangements of the numbers does not affect the values to answers at both sides of the equation.

You might be interested in

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

2 years ago

A newspaper used a chart resembling the one to the right to illustrate the rising amounts that a video rental company spends to

Dmitry [639]

This question is incomplete- no bar chart was included.

The complete question was gotten from google.

Open the attachment below to see the bar chart'

Answer:

A newspaper used a chart resembling the one to the right to illustrate the rising amounts that a video rental company spends to provide streaming content online. Is this the bar chart of a categorical variable, or is it a time plot that uses bars to show the data? It is a time plot that uses bars to show the data; because it graphs a series of data recorded over time; presenting the values in sequential order.

Step-by-step explanation:

The chart used in the newspaper to illustrate the rising amounts that a video rental company spends to provide streaming content online is a time plot that uses bars to show the data; because it graphs a series of data recorded over time; presenting the values in sequential order.

6 0

2 years ago

A parking structure has three levels. There are 47 cars on the first level and 61 cars on the third level. How many cars are on

Anestetic [448]

54 I believe if this is what I think it is the end of the world as we see it the most hardest math riddle to have ever existed 61-47 = 14
47+7=54 54+7= 61 therefore the world as we know shall come to a end at 2:08 PM Central time

7 0

3 years ago

An alloy consists of nickel, zinc, and copper in the ratio 2:7:9.

Alexus [3.1K]

Answer:

0.4kg, 1.4kg and 1.8kg

Step-by-step explanation:

Given parameters:

Mass of alloy = 3.6kg

Ratio of elements in the alloy = 2:7:9

Unknown:

Mass of each element in the alloy = ?

Solution:

To find the mass of each element in the alloy, first find the sum of the ratio;

2+7+9 = 18

Mass of nickel = $\frac{2}{18}$ x 3.6 = 0.4kg

Mass of zinc = $\frac{7}{18}$ x 3.6 = 1.4kg

Mass of copper = $\frac{9}{18}$ x 3.6 = 1.8kg

The mass of each metal is 0.4kg, 1.4kg and 1.8kg

5 0

2 years ago

Find two numbers that multiply to 16 and also add to -8

mash [69]

Answer:

-4,-4

Step-by-step explanation:

let the numbers be x and y.

x+y=-8

y=-x-8

xy=16

x(-x-8)=16

-x²-8x=16

x²+8x+16=0

x²+4x+4x+16=0

x(x+4)+4(x+4)=0

(x+4)(x+4)=0

x=-4,-4

5 0

3 years ago