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3 years ago

If you rewrite the problem 14(22) as 14(20+2) so that you can use mental math, which of the following properties will you use?

1 answer:

7 0

For this case, the property you can use is the following:
Commutative property.
We have then that:
14 (20 + 2) = 280 + 28 = 308
Equivalently:
14 (2 + 20) = 28 + 280 = 308
Either way the result is exactly the same.
Answer:
Commutative property.

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3. Which polynomial is equal to

Nataly_w [17]

Which polynomial is equal to (-3x^2 + 2x - 3) subtracted from (x^3 - x^2 + 3x)?

<h3>Answer:</h3>

The polynomial equal to (-3x^2 + 2x - 3) subtracted from (x^3 - x^2 + 3x) is $x^3 + 2x^2 + x + 3$

<h3>Solution:</h3>

Given that two polynomials are: $(-3x^2 + 2x - 3)$ and $(x^3 - x^2 + 3x)$

We have to find the result when $(-3x^2 + 2x - 3)$ is subtracted from $(x^3 - x^2 + 3x)$

In basic arithmetic operations,

when "a" is subtracted from "b" , the result is b - a

Similarly,

When $(-3x^2 + 2x - 3)$ is subtracted from $(x^3 - x^2 + 3x)$ , the result is:

$\rightarrow (x^3 - x^2 + 3x) - (-3x^2 + 2x - 3)$

Let us solve the above expression

There are two simple rules to remember:

When you multiply a negative number by a positive number then the product is always negative.

When you multiply two negative numbers or two positive numbers then the product is always positive.

So the above expression becomes:

$\rightarrow (x^3 - x^2 + 3x) + 3x^2 -2x + 3$

Removing the brackets we get,

$\rightarrow x^3 - x^2 + 3x + 3x^2 -2x + 3$

Combining the like terms,

$\rightarrow x^3 -x^2 + 3x^2 + 3x - 2x + 3$

$\rightarrow x^3 + 2x^2 + x + 3$

Thus the resulting polynomial is found

5 0

3 years ago

The vertex form of the equation of a parabola is y= 3(x - 4)^2 -22. What is the standard form of the equation

Sunny_sXe [5.5K]

Answer:

option A

Step-by-step explanation:

We can find the standard form by expanding the equation:

y = 3(x-4)^2 - 22

y = 3(x^2 - 8x + 16) - 22

y = 3x^2 - 24x + 48 - 22

y= 3x^2 - 24x + 26

So the correct option is option A

8 0

3 years ago

Read 2 more answers

Consider the two data sets below:

alina1380 [7]

Answer:

Option c) The data sets will have the same values of their interquartile range.

Explanation:

1. The values are in order: they are in increasing oder, from lowest to highest value.

2. Calculate the interquartile range.

Interquartile range, IQR, is the third quartile, Q3, less the first quartile Q1:

IQR = Q3 - Q1

To find the first and the third quartile, first find the median:

Data Set 1: 19, 25, 35, 38, 41, 49, 50, 52, 59

[19, 25, 35, 38], 41, [49, 50, 52, 59]

↑

median = 41

Data Set 2: 19, 25, 35, 38, 41, 49, 50, 52, 99

[19, 25, 35, 38] , 41, [49, 50, 52, 99]

↑

median = 41

Now find the median of each subset: the values below the median and the values above the median.

Data set 1: First quartile

[19, 25, 35, 38],

↑

Q1 = [25 + 35] / 2 = 30

Third quartile

[49, 50, 52, 59]

↑

Q3 = [50 + 52] / 2 = 51

IQR = Q3 - Q1 = 51 - 30 = 21

Data set 2: First quartile

[19, 25, 35, 38]

↑

Q1 = [25 + 35] / 2= 30

Third quartile

[49, 50, 52, 99]

↑

Q3 = [52 + 50]/2 = 51

IQR = 51 - 30 = 21

Thus, it is shown that the data sets have will have the same values for the interquartile range: IQR = 21. (option c)

This happens because replacing one extreme value (in this case the maximum value) by other extreme value does not affect the median.

An outlier will change the range because the range is the maximum value less the minimum value.

5 0

2 years ago

Calculate the mean, median, mode, range, and 5 Number Summary of the following data set: 5,6,8,4,7,5,4,2,5,6,5,2,1,4

Artist 52 [7]

Answer:

mean = 4.57, median = 5 , mode = 5, range =7 ,

five number summary: Minimum value= 1 , First Quartile = 4, Median = 5

Third Quartile = 6, Maximum value = 8

Step-by-step explanation:

First arrange the data in ascending order.

1,2,2,4,4,4,5,5,5,5,6,6,7,8

Mean = sum of all numbers / total numbers

= 1+2+2+4+4+4+5+5+5+5+6+6+7+8 / 14

= 64 / 14

= 4.57

Median:

Since the given data is even number so, we can find median by taking mean of 2 middle numbers.

so the middle numbers are 7th and 8th data i.e, 5 and 5

Median =(5+5)/2

= 5

Mode:

The most repetitive number in the data set is mode

So Mode = 5

Range:

Range can be found by subtracting smallest number from largest number in the data set.

Smallest number = 1, Largest number = 8

Range= Largest number - Smallest number

= 8-1 = 7

Five no Summary

Minimum value= 1

First Quartile ( 25 % mark )= 4

Median = 5

Third Quartile (75 % mark) = 6

Maximum value = 8

First quartile can be found by : consider the data on left of the median and find median among them

Third quartile can be found by: consider the data on right of the median and find median among them

7 0

3 years ago

Interest after 1 year:

jasenka [17]

which class is this because I am in 7th class so that's why I can't give

5 0

2 years ago

Read 2 more answers