The perimeter of an equilateral triangle is 10 inches more than the perimeter of a square, and the side of the triangle is 6 inches longer than the side of the square. Find the side of the triangle.

Answers

Answer 1

The side of the equilateral triangle is 14inches.

Let the side of the square be denoted as x inches

The formula for the perimeter of equilateral triangle is  

                           [tex]P_{t}[/tex] = 3a where a is the side of the triangle.

The formula for the perimeter of the square is

                           [tex]P_{s}[/tex] = 4x where x is the side of the square

We have been given that,

               [tex]P_{t} = 10 + P_{s}[/tex]      (1)

        and  a = 6 + x inches       (2)

Equation (1) can be written as

                  3a = 10 + 4x

From equation (2) ,

                  3( 6+x) = 10 + 4x

                  18 + 3x = 10 + 4x

                       x = 8

Substituting the value of x in equation (2) we get

                          a = 6+8

                           a = 14 inches

Hence the side of the triangle is 14 inches.

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Related Questions

Represent the following sentence as an algebraic expression, where "a number" is the letter x. 3 is decreased by a number.

Answers

Answer:

3-x

Step-by-step explanation:

Mr Moon bought a coffee and a sandwich every day for 100 days
from his local shop. In total, he spent £783.68. How much is one
coffee and sandwich? Round your answer to 2 decimal places.

Answers

Answer:

7.84

Step-by-step explanation:

783.68

[tex]783.63 \div 100 = 7.8363[/tex]

Approx to 7. 84

Both sets of values have an average of 13. Is Set A's standard deviation smaller, larger, or about the same as Set B's? Set A: 1 2 3 23 24 25 Set B: 9 10 11 14 16 18
a.)About the same
b.)Not enough information provided to tell
c.)Larger
d.)Smaller

Answers

Set A's standard deviation is larger than that of Set B (option c).

What are the standard deviations?

Standard deviation is used to determine how the values in a group differs from the mean of the values in the group. Standard deviation is a measure of variation of a dataset.

In order to determine the standard deviation, take the following steps:

Determine the average of the observation:Determine the difference between each value and the average and then square the result:Determine the average of the sum of the squared differences and then find the square root of the mean:

Standard deviation of Set A:

(1 - 13)² + (2- 13)² +  (3- 13)² +  (23- 13)² +  (24- 13)² +  (25 - 13)²

144 + 121 + 100 + 100 + 121 + 144 = 730

√730 / 6 = 11.03

Standard deviation of Set B:

(9 - 13)² + (10- 13)² +  (11- 13)² +  (14- 13)² +  (16- 13)² +  (18 - 13)²

16 + 9 + 4 + 1 + 9 + 25 = 64

√64 / 6 = 10.67

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Zach had surgery, which was his third claim of the year. He had a bill of $5000. Considering the prior visits, what is Zach’s portion of this bill and what is the responsibility of the insurance carrier?

Answers

Zach is supposed to pay $1000 for this surgery. The other $4000 is to be covered by his insurance.

Responsibility of insurance carriers:-

A primary function of an insurance agent is that of a communicator, counselor, and facilitator. The insurance agent can provide the best products and services for the prospective customer's various needs, such as life, property, health, and burglary insurance. When purchasing an insurance product, let the insurance agent know ahead of time how much money they have set aside for insurance coverage. In turn, the insurance agent will assist their clients in obtaining the lowest or best insurance product costs.

:- The insurance agent has a variety of responsibilities in the insurance industry, as noted below:

1) An insurance agent assists customers in promoting and selling insurance products and services.

2) Providing consumers with solid financial advice and personal service

3) Desires to work with individuals and their families and businesses.

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solve 2(x + 3)=-4(x+1) for x

Answers

[tex]\boxed{\begin{minipage}{5cm}\sf{2(x+3)=-4(x+1)}\\\sf{2x+6=-4x-4}\\\sf{6x+6=-4}\\\sf{6x=-10}\\\sf{x=-10/6}\\\sf{x=-5/3}\end{minipage}}[/tex]

45 is what percent of 180?

Answers

Answer:

It is 25% percent......

Answer:

Step-by-step explanation:

45 / 180 = 0.25

25%

Which of the following statements is true?
3/4 > 3/5
3/7 > 3/5
12/25 > 3/5
30/100 > 3/5

Answers

Answer:

3/4 > 3/5 is true.

Hope this helps :)

Explanation and Check below.

Step-by-step explanation:

1. To compare fractions with the same numerators, look at the denominators and the greater one is the smaller number.

2. To compare fractions with the same denominator, look at the numerator and the answer will be the bigger number.

3. To compare fractions with different denominators, find the Least Common Multiple (LCM).

3/4 > 3/5 ✓

3/7 > 3/5 ✘

12/25 > 3/5 = 12/25 > 15/25 ✘

30/100 > 3/5 = 30/100 > 60 ✘

without using tables solve for x in: Log10(x²+4)=2+Log10x-Log10 20​

Answers

The value of x for a given logarithm is 49.9.

Log10(x²+4)=2+Log10x-Log10 20​=

x = 49.9

2 = log10( 100)

so we have

log10( x [tex]\times[/tex]2 4) = log10( 100) log10( x)- log10( 20).

factor out log10 from RHS.

also log10( [tex]x[/tex] x  2 4) = log10( 100x/ 20).

log10 cancel log10.so, break the quadratic equation after simplification to have x = 49.9 or0.080

That is, the logarithm of a given integer x is the exponent to which another set number, the base b, must be increased in order to produce x. In the most the logarithm counts the number of times the same factor appears in repeated addition; for illustration, since 1000 = 10 10 10 = 103, the" logarithm base 10" of 1000 is 3, or log10( 1000) = 3. When no mistake is conceivable, or when the base does not important, the logarithm of x to base b is expressed as logb( x), without logb x, or indeed without the base, logx.

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Tanisha read 4 books in 5 months. If she reads at a constant rate, how many books
did she read each month? Give your answer as a whole number or a FRACTION in
simplest form.

Answers

Answer:

4/5

Step-by-step explanation:

The denominator is the total.

The numerator/top.

The rate of reading book by Tanisha is 4/5 book per month.

What is ratio?

Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

The book read by Tanisha in 5 months = 4 book.

To find the book read by Tanisha each month,

Use ratio property,

In 5 months = 4 book

in 1 month = 4/5 book.

In one month, the book read by Tanisha is 4/5 fraction.

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if fx(x)=3x -1 and g(x)x^2 then what is (fog)(x)

Answers

The result function of  (fog)(x) in the given functions is 3x² - 1.

What is the result function of (fog)(x)?

Given the functions in the questions;

fx(x) = 3x - 1g(x) = x²(fog)(x) = ?

Set up the composite result function and simplify.

(fog)(x) = f(g(x) = f(x²)

Evaluate f(x²) by substituting in the value of g into f

fx(x) = 3x - 1

f(x²) = 3(x²) - 1

Now, simplify

f(x²) = 3(x²) - 1

f(x²) = 3x² - 1

Therefore the result function of  (fog)(x) in the given functions is 3x² - 1.

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4 tablets each day 28 day supply with 55 tablets per bottle how many bottles are needed and how many additional tablets

Answers

Answer:

Approximately 3 bottles

Step-by-step explanation:

28*4 = 112 tablets in a month

122/55 = 2.218 bottles

Basically, you will need to buy 3 bottles.

There are 10 numbers listed below. 13.5 12.5 10.8 9 11 10 12.5 13 10.5 12 What is the mode of these numbers?

Answers

Answer:

12.5

Step-by-step explanation:

13.5 12.5 10.8 9 11 10 12.5 13 10.5 12

The mode is the number that appears the most number of times.

We place the numbers in ascending order just for convenience.

9 10 10.5 10.8 11 12 12.5 12.5 13 13.5

Every number appears once except 12.5 that appears twice.

Answer: 12.5

Find the equation of the line using the given information. The slope is undefined and it passes through the point (x, y) = (8, 6).

Answers

Answer:

x= 8

Step-by-step explanation:

Vertical lines have undefined slopes, with an equation of x= ____. This is because when using the slope formula, the denominator would be a zero. The coordinates of points that lie on a vertical line have the same y-coordinate, but different x-coordinate value.

Given that the line passes through (8, 6), the line has an equation of x= 8.

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A choir bakes and sells cookies to raise money for their end-of-year production. Lin sells 3 times as many cookies as Noah. Jada sells 5 more cookies than Lin. Elena sells 7 more cookies than Jada. Diego sells 4 fewer cookies than Noah, and Andre sells twice as many as Diego. If the six students sold 317 cookies, write and solve an equation to determine how many cookies Noah sold.

Answers

The equation used to determine how many cookies Noah sold is 317 = 13n + 5 where number of cookies Noah sold is 24

Equation

Total cookies sold = 317Noah = nLin, l = 3nJada, j = 5 + 3nElena, e = 7 + (5 + 3n)Diego, d = n - 4Andre, a = 2(n - 4)

Total = Noah + Lin + Jada + Elena + Diego + Andre

317 = n + 3n + (5 + 3n) + {7 + (5 + 3n)} + (n - 4) + {2(n - 4)}

317 = n + 3n + 5 + 3n + 7 + 5 + 3n + n - 4 + 2n - 8

317 = 13n + 5

317 - 5 = 13n

312 = 13n

divide both sides by 13

n = 312 / 13

n = 24 cookies

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1190 1172 1217 1207 1197
1202 1197 1168 1204 1189
1185 1191 1198 1185 1183
1205 1207 1197 1201 1225
1172 1208 1187 1197 1179
1231 1208 1211 1205 1194
1210 1250 1217 1177 1221
1185 1177 1202 1221 1204
1182 1204 1218 1194 1198
1187 1198 1198 1183 1227
Use this data for problems 1 thru 4.
1. Calculate the mean, median and mode of this data.
Mean=1199.3
Median=1797
Mode=1197

2. Calculate the Coefficient of skewness of the data using Pearson’s formula. Is the data skewed?
Yes it positively skewed because the mean is greater than the mode. -112.238
3. What is the range of the above data?
82
4. What is the standard deviation of the data. Assume it is a sample.
STANDARD deviation=15.97593

Answers

For the given data-set, we have that:

1. The mean is of 1199.3, the median is of 1198 and the distribution is bimodal, with 1197 and 1198 as modes.

2. The Pearson coefficient is of 0.24, and since it is positive, the data is positively skewed.

3. The range is of 82.

4. The standard deviation is of 16.47.

What are the mean, the standard deviation, the range, the median and the mode of a data-set?

The mean of a data-set is given by the sum of all the observations in the data-set, divided by the cardinality of the data-set, which is the number of values in the data-set.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the cardinality of the data-set.The range is the difference between the maximum value and the minimum value of the data-set.The median is the middle value of the data-set, the value which 50% of the data-set is smaller than and 50% of the data-set is greater than.The mode is the value that appears the most times in the data-set.

Using a calculator, which just applies the concepts explained above, as the data-set is too large, the measures are given as follows:

Mean: 1199.3.Median: 1198.Mode: 1197 and 1198. (each appeared 4 times).Range: 82 (difference between 1250 and 1168).Standard deviation: 16.47.

What is the Pearson's Skewness Coefficient?

The Pearson Skewness Coefficient is given by:

P = 3(Mean - Mode)/Standard Deviation

The meaning of the coefficient is:

If the coefficient is positive, the distribution is right skewed.If the coefficient is negative, the distribution is left skewed.If the coefficient is close to 0, the distribution is bell shaped.

For this problem, the coefficient is given by:

P = 3(1199.3 - 1198)/16.48 = 0.24.

The Pearson coefficient is of 0.24, and since it is positive, the data is positively skewed.

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The candlestick chart to the right shows market action for a
particular stock for five days in September. The lengths of
the candlesticks for September 8 and 11 are approximately
the same. Explain what this means about trading prices on
both of those days.

Answers

The lengths of the candlesticks for September 8 and 11 are approximately the same because this physical object stands in for the price range between the opening and closing prices for that trading day.

The close was lower than the open if the true body is filled in or is completely black. Real bodies that are empty indicate that the close was higher than the open.

Let's consider a case study over a longer time frame, say a week. In this example, the candle records prices from Monday through Friday of the work week. The price at which the market starts on Monday at 9:15 a.m., the first business day of the week, will be the opening price. The highest and lowest prices ever recorded will be set during that particular week.

Over a century before the West created the bar and point-and-figure charts, candlestick charts were invented in Japan. While there was a correlation between rice price and supply and demand in the 1700s, a Japanese man by the name of Homma found that traders' emotions had a significant impact on the markets.

Hence, predict the short-term direction of the price, traders utilise the candlesticks to help them make trading decisions.

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What is the solution set for 7x − 3 =18, given the replacement set {0, 1, 2, 3, 4}?


x = 0

x = 1

x = 2

x = 3

x = 4

Answers

Answer:

x = 3

Step-by-step explanation:

Let's solve your equation step-by-step.

7x−3=18

Step 1: Add 3 to both sides.

7x−3+3=18+3

7x=21

Step 2: Divide both sides by 7.

7x/7 = 21/7

x=3

What is the correct answer?

Answers

Answer: 7x=9

because x is 2 and 7+2= 9

Kassim has a water barrel in his garden. The water barrel is full and Kassim wants to know how much water is in the barrel. The barrel is a cylinder which is 1.1m high and has a diameter of 70cm. Give your answer in cm3 to three decimal places. Use 3.14 as an approximate to [tex]\pi \pi[/tex]

Answers

The amount of water in the barrel is 423,115 cm³.

How much water is in the barrel?

A cylinder is a three-dimensional object. It is a prism with a circular base. In order to determine the amount of water in the barrel, the volume of the barrel has to be determined.

Volume of a cylinder = nr^2h

Where:

n = 3.14

r = radius = diameter / 2 = 70 / 2 = 35cm

h = height = 1.1m

100cm = 1 meter

1.1 x 100 = 110 cm

Volume of a cylinder = 3.14 x 35² x 110 = 423,115 cm³

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with reference to the figure below, find x, y, z, t such that n(U) =50, n(A) = 25, n(B) = 13 and n(A’nB’) = 12


(pls help i’m gonna cry)

Answers

Accordingly the Venn diagram The required values of x = 12 , y = 13 , z = 24 and t = 13.

A Venn diagram uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items.

In Venn diagram, if two sets A and B do not intersect, then n(A∩B)=0 and n(A∪B) = n(A) + n(B).

Given: n(U) = 50, n(A) = 25, n(B) = 13 and n(A'∩B')=12

We have to determine the values of x, y, z, and t.

According to the given figure,

n(A') = n(U) - n(A)

n(A')=  50 - 25

n(A') = 25

n(B') = n(U) - n(B)

n(B') = 50 - 13

n(B') = 37

n(A∩B) = n(A') - n(A'∩B')

n(A∩B) = 25 - 12

n(A∩B) = 13

So, y = n(A∩B) = 13

As  in the Venn diagram, we know that,

x + y = n(A')

x = n(A') - y

x = 25 - 13

x = 12

y + z = n(B')

13 + z = 37

z = 37 - 13

z = 24

t = n(U) - [n(A) + n(B)]

t = 50 - [25+13]

t = 50 - 37

t = 13

Therefore, the values of x, y, z and t are 12, 13, 24, and 13.

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My question is in pictures

Answers

The standard price night cost at Night-Time Rest Days is $ 26.30 .

Average = Sum of all the observations/Number of observations

Substituting the values in the formula, we get that:

⇒ $ 20.60 = $( 22.45 + 18.55 + 24.50 + 11.20 + x )/5

⇒ $ 20.60 = $ (76.7 + x)/5

⇒ 20.60 × 5 = 76.7 + x

Solving to find the value of x, we get that

⇒ 103 = 76.7 + x

⇒ x = 103 - 76.7

⇒ x = 26.3

Therefore, the standard price night cost at Night-Time Rest Days is $ 26.30 .

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I need help with this please

Answers

Answer:

133

Step-by-step explanation:

SP is part of a line and line is 180°

so:

m∠PQR + m∠RQS= 180°

(3x-5)  + ( x+1) = 4x-4=180

4x = 184

x= 46

m∠PQR = 3X-5 = 3(46)-5 =133

Answer:

133

Step-by-step explanation:

Supplementary angles are angles that sum to 180°, meaning they form a straight line.

Solving for x

Since we know that these 2 angles will sum to 180 (remember they are supplementary) we can add their expression together and set it equal to 180.

(3x-5) + (x+1) = 180

Next, combine like terms.

4x - 4 = 180

Add 4 to both sides

4x = 184

Divide by 4

x=46

Solve for m∠PQR

Now that we know the value of x, we can find the measure of PQR. Simply plug 46 in for x and solve.

3(46) - 5 = 133

This means that m∠PQR = 133°.

Mrs.Cody needs 1 3/4 yards of fabric to make a pillow. How many yards of fabric will she need to make 12 pillows?

Answers

Answer:

21 yards

Step-by-step explanation:

1 3/4 * 12 = (12 + (3/4 of 12)) = 12 + 9 = 21

Someone please help me with this problem
Simplify (6^2)^2

Answers

Answer: 1296

Step-by-step explanation:

(6^2)^2=

(6^(2*2))=

6^4=1296

(6^2)^2
Solve the equation in the parenthesis.
(6^2) = 6*6 = 36
Equation now looks like this
(36)^2
Which looks like this
36*36
1296
Thus, the answer is 1296.

Hope this helps.

PLEASE HELP ME!!! DUE TODAY, I WILL GIVE 20 POINTS!!!! NO EXPLAINATION NEEDED!!!! FIRST PERSON TO ANSWER GETS BRAINLIEST AWARD!!!!

Answers

Answer:

CD=2

BC=3

A1B1=2.4

D1E1=3.2

For the boxes on the bottom:

BC=B1C1     CD=C1D1

A1B1=AB      D1E1=DE      

Answer:

BC = 3

CD = 2

A1 B1 = 2.4

D1 E1 = 3.2

Find the distance of segment NP given its two endpoints: N(8, 14) and P(-21, -39).

Answers

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ N(\stackrel{x_1}{8}~,~\stackrel{y_1}{14})\qquad P(\stackrel{x_2}{-21}~,~\stackrel{y_2}{-39})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ NP=\sqrt{(~~-21 - 8~~)^2 + (~~-39 - 14~~)^2} \implies NP=\sqrt{( -29 )^2 + ( -53 )^2} \\\\\\ NP=\sqrt{ 841 + 2809 } \implies NP=\sqrt{ 3650 }\implies NP\approx 60.42[/tex]

You're going on a 1211-mile trip, and your car gets about 29 miles per gallon. Gas prices along your route average $3.10. Estimate the cost of gasoline for this trip by rounding the distance to 1200 miles, the mileage to 30 miles per gallon, and the cost of gas to $3.00 per gallon. Calculate the answer without using estimation and compare the two results. (Round your answers to the nearest cent.)

Answers

There is a difference of actual and approximations 9.46 dollars.

What is unitary method ?

Unitary method is a mathematical way of first deriving the value of a single unit then multiplying the given unit to obtain the required result.

According to the given question we have to compare the results where in first case we put actual values and on the second case we round the values.

In the first case

You're going on a 1211 mile trip, and your car gets about 29 miles per gallon.

So, the total fuel consumption will be (1211/29) gallons which is

= 41.76 gallons.

Given 1 gallon of gas costs 3.10 dollars.

∴ 41.76 gallons of gas will cost ( 41.76×3.10) dollars which is

= 129.456 dollars.

= 129.46 dollars.

In the second case

It is a 1200 mile trip and the fuel economy of the car is 30 miles per gallon.

So, the total fuel consumption will be

= 1200/30

= 40 gallons.

Given 1 gallon of gas costs 3 dollars.

∴ 40 gallons of gas costs (40×3) dollars which is

= 120 dollars.

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Adventure Travel has an Adjusted Trial Balance for Year Ended December 31, 20XX with the following account balances:

DEBITS: Cash: 25,000; Accounts Receivable: 15,000; Office Supplies: 4,300; Office Equipment: 29,600

CREDITS: Accumulated depreciation - office equipment: 5,000; Salaries Payable: 2,800; Long-term notes payable: 22,200; Common Stock: 20,000; Retained Earnings: 10,260

DEBIT: Cash Dividends: 1,000

CREDITS: Fees Earned: 75,000

DEBITS: Salaries Expense: 32,800; Rent Expense: 16,800; Depreciation expense - office equipment: 3,960; Advertising expense: 4,000; Office supplies expense: 2,800.

Total Debits = 135,260; Total Credits = 135,260

You have just determined Net Income for Adventure Travel in the previous question. Now, you must prepare the Statement of Retained Earnings.

What is the Retained Earnings Balance as of the Ending of the Year, December 31, 20XX? Specify whole number.

Answers

The Retained Earnings Balance as of the Ending of the Year, December 31, 20XX is $23,900

What is net income?

The net income is the excess of fees earned by Adventure Travel  in the year ended  over its total expenses, in essence, we need to determine its total expenses first and foremost, which comprises of salaries expense, rent expense, depreciation expense, advertising expense and office supplies expense

total expenses=32,800+16,800+3960+4000+2800

total expenses=60,360

fees earned=75,000

net income =fees earned-total expenses

net income=75,000-60,360

net income=$14,640

Now the closing retained earnings comprises of beginning retained earnings plus the net income minus the cash dividends paid

Retained earnings=$14,640+$ 10,260-$1,000

Retained earnings=$23,900

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Solve this system by substitution (Pls answer step by step so I can understand thank you!)

Answers

Answer:

-3

Step-by-step explanation:

1) -x-y = 9

2) -3x+y = 3

By adding 3x to each side on equation #2, you get that y = 3+3x.

Now, we can substitute the value of y into the second equation. If you do this, you will get that [tex]-x-(3+3x)=9[/tex].

Simplifying gives you: [tex]-4x-3=9[/tex]

Adding three to both sides: [tex]-4x=12[/tex]

And finally dividing by negative four: [tex]x=-3[/tex]

You will get x = -3

PLEASE HELP I NEED TO FINISH

Answers

Answer: x=-4

Step-by-step explanation:

Other Questions
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