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3 years ago

Find the area of the shaded region

Mathematics

1 answer:

wariber [46]3 years ago

6 0

31x^2 + 53x - 8

Use the FOIL method to find the area of the large rectangle. (7x - 2)(9 + 5x)

First term in each binomial: 7x * 9 = 63x
Outside terms: 7x * 5x = 35x^2
Inside terms: -2 * 9 = -18
Last term in each binomial: -2 * 5x = -10x

Now, just add them all up.

63x + 35x^2 - 8 - 10x

35x^2 + 53x - 8

Now find the area of the square.

2x * 2x = 4x^2

Now, subtract the areas.

31x^2 + 53x - 8

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You previously found the mean of this data set. Use that in answering the question. 63, 89, 92, 73, 79, 72, 34, 36, 94, 21, 25,

kicyunya [14]

Answer:

Sum of squares of differences = 11239.74

Step-by-step explanation:

We are given the following data set:

63, 89, 92, 73, 79, 72, 34, 36, 94, 21, 25, 93, 22, 90, 79

We have to calculate the sum of square of the data set.

Formula:

$\text{Sum of square of differences} = \sum (x_i -\bar{x})^2$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{962}{15} = 64.13$

Sum of squares of differences =

1.284444444 + 618.3511113 + 776.5511113 + 78.61777778 + 221.0177779 + 61.88444445 + 908.0177776 + 791.4844443 + 892.017778 + 1860.484444 + 1531.417778 + 833.2844446 + 1775.217777 + 669.0844446 + 221.0177779

= 11239.74

3 0

3 years ago

Work out the formula for the nth term of the<br>quadratic sequence:<br>5, 11, 19, 29

Sladkaya [172]

Answer:

n squared + 3n + 1

Step-by-step explanation:

5,11,19,29

Firstly look at the difference between each number. The first difference is 6 then 8 then 10 etc. After that you look at your created sequence - 6,8,10 etc. The difference is 2 each time. Then applying rules, you have to do the constant difference divided by 2 to get a coefficient of n squared. So in this case it's n squared because 2/2 = 1 so you don't have to place a 1 in front of the n squared. After you create a sequence from the n squared. That would be 1,4,9 etc. Then you need to see how to get from the sequence: 1,4,9 etc to your original sequence: 5,11,19 etc. So if you calculate it you will get 4,7,10 because firstly 5-1 = 4 then 11-4 = 7 etc. The sequence 4,7,10 is a linear sequence so the constant difference is 3 each time. So to get a nth term of a linear sequence you will start off as 3n then you will substitute 1 then 2 then 3 into the 3n. Therefore that would be 3,6 etc. So if you take the first substituted term, that would be 3 as said before then you will have to see how to get from the 3 to 4 so that is just adding 1. So the nth term of this linear sequence is 3n + 1. Check if it works at the end. So the overall nth term of the quadratic sequence is n squared as said before + 3n + 1.

8 0

3 years ago

Food bill: $36 Tip: 20% Sales tax (on food only) 6%

olasank [31]

Answer: To figure out the tip, you need to find 20% of $52.60.

0.2×52.6=10.52

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Dominique buys $14.95 worth of gasoline for her car. If the gas station charges $1.43 per gallon, how many gallons did she get?

Zolol [24]

Answer:

$10.45

Step-by-step explanation:

14.95 divided by 1.43 = 10.50

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3 years ago

Read 2 more answers

A hotel with 200 rooms has two types of rooms, and when it is completely booked, the hotel earns $18,250. Double rooms rent for

Mkey [24]

A) S + D = 200

B) 85 S + 110 D = 18,250 we multiply A) by -85

A) -85 S -85 D = -17,000 then we add to B) and get

25 D = 1,150

Double Bed Rooms = 46

Single Bed Rooma = 154

*************************************************

Double Check

46 * 110 = 5,060 154 * 85 = 13,090

Total = 18,150

3 0

3 years ago