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3 years ago

Why might you want to use the commutative property to change the order of the integers in the following sum before adding

1 answer:

4 0

Commutative Property is the property in which you can move around numbers in numerical operations like, addition and multiplication while retaining their result. In contrast to subtraction and division in which position is an important factor for every result, here it is regardless. Why might you want to use this property?Well, most importantly it suits the operation of addition and hence, to ensure the arrangement of the number is in symmetric proportion to its counterpart such as 3 + 2=2 + 3. Or rather, understanding that the equations in both sides are but the same and equal in sum. Thus, this is much more usable or will make more sense if used in a larger scale of complex equations and integers.

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What are the roots of the polynomial equation x^3-5x+5=2x^2-5? Use a graphing calculator and a system of equations. Round nonint

leonid [27]

The right answer is c. –2.24, 2, 2.24

This question needs to be solved in two ways. First, using a graphing calculator. Next, using a system of equations.

1. Using a graphing calculator.

We have the following polynomial equation:

$x^3-5x+5=2x^2-5$

By ordering this equation we have:

$x^3-2x^2-5x+10=0$

So, we can say that this equation comes from a function given by:

$f(x)=x^3-2x^2-5x+10$

Thus, by plotting this function, we have that the graph of this function is indicated in Figure 1. By zooming, we can see, in Figure 2, that the roots of the polynomial equation are the x-intercepts of $f(x)$ which are:

$x_{1}=-2.236 \\ \\ x_{2}=2 \\ \\ x_{3}=2.236$

Finally, rounding noninteger roots to the nearest hundredth we have:

$\boxed{Root_{1}=-2.24} \\ \\ \boxed{Root_{2}=2} \\ \\ \boxed{Root_{3}=2.24}$

2. Using a system of equations.

The ordered equation is:

$x^3-2x^2-5x+10=0$

By arranging to factor out we have:

$x^3-5x-2x^2+10=0$

Then, by factoring:

$x(x^2-5)-2(x^2-5)=0$

Term $(x^2-5)$ is a common factor, thus:

$(x-2)(x^2-5)=0 \\ \\ (x-2)(x-\sqrt{5})(x+\sqrt{5})=0 \\ \\ Finally: \\ \\ \boxed{Root_{1}=-\sqrt{5}=-2.24} \\ \\ \boxed{Root_{2}=2} \\ \\ \boxed{Root_{3}=\sqrt{5}=2.24}$

6 0

3 years ago

Read 2 more answers

Every evening, two weather stations issue weather forecast for the next day. The weather forecasts are independent. On average,

EleoNora [17]

Answer:

The probability is 0.6923

Step-by-step explanation:

Let's call R the event that the next day rains, S the event that the next day has sunny weather, R2 the event that the station 2 predicts rain and S1 the event that station 1 predict sunny weather.

The probability that the next day has sunny weather given that station 1 predicts sunny weather for the next day and station 2 predicts rain is calculated as:

P(S/S1∩R2) = P(S∩S1∩R2)/P(S1∩R2)

Where P(S1∩R2) = P(R∩S1∩R2) + P(S∩S1∩R2)

So, the probability P(R∩S1∩R2) that the next day rains, Station 1 predicts sunny weather and Station 2 predicts Rain is calculate as:

P(R∩S1∩R2) = 0.5 * 0.1 * 0.8 = 0.04

Because 0.5 is the probability that the next day rains, 0.1 is the probability that station 1 predicts sunny weather given that it is going to rain and 0.8 is the probability that station 2 predicts rain given that it is going to rain.

At the same way, the probability P(S∩S1∩R2) that the next day has sunny weather, Station 1 predicts sunny weather and Station 2 predicts Rain is calculate as:

P(S∩S1∩R2) = 0.5 * 0.9 * 0.2 = 0.09

Then, the probability P(S1∩R2) that station 1 predicts sunny weather for the next day, whereas station 2 predicts rain is:

P(S1∩R2) = 0.04 + 0.09 = 0.13

Finally, P(S/S1∩R2) is:

P(S/S1∩R2) = 0.09/0.13 = 0.6923

6 0

3 years ago

Each pound of fruit costs $4. Write an expression that shows the total cost of fruit use the variable you identified in the ques

Gnesinka [82]

The expression would be j • $4

5 0

3 years ago

Read 2 more answers

Which value of x makes 7+5(x-3)=227+5(x−3)=22 a true statement?

Greeley [361]

Answer: Your input has more than one equals sign.

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Please help ASAP ASAP ASAP

scZoUnD [109]

About 2.86 inches

Step by step explanation-

The formula for the volume of a cone is pi2 h/3 plugging the known numbers into formula you get
75=pi 5^2 h/2
H/3=0.955
H=2.86 inches

6 0

3 years ago