Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options.
18 x minus 15 = 72
50 x minus 25 = 72
18 x minus 9 = 72
3 (6 x minus 3) = 72
x = 4.5

In response to the aforementioned query, we may say that The slate roof has a total area of 0.26 square metres.

An area can be used to describe a surface's area. Surface area, also known as planar region, refers to the area of a form or planar layer, whereas planar region refers to the area of an open surface or the border of a three-dimensional object. An object's area is the entire amount of space occupied by its planar (2-D) surface or form. Use a pencil to mark a square on the paper. an individual having two dimensions. A shape's area on paper is the amount of space it occupies. Think of the square as being made up of smaller unit squares.

Height, breadth, and depth together make up volume.

Volume: 4.3 x 3.5 x 2.2 metres

33.77 cubic metres is the volume (rounded to 2 decimal places)

The stone outbuilding has a volume of 33.77 cubic metres.

Area = base x height x half

Height: 2.5 to 2.6 metres

Height = 0.10 metres

Height = (-0.1 m) | (0.1 m)

determine the size of each triangle's face:

Area = base x height x half

Area: 0.6 x 2.6 x 0.1 metres

0.13 square metres is the area.

Total area Equals twice the area

= 2 x 0.13 square metres total area

0.26 square metres is the total area (rounded to 2 decimal places)

The slate roof has a total area of 0.26 square metres.

To know more about area visit:

https://brainly.com/question/13194650

#SPJ1

The value of each variable in the triangle are:

x = 28 units

y = 7√6 units

z = 14√3 units

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Considering the upper triangle:

cos 45° = (14√2)/x

x = (14√2)/cos 45°

x = 28 units

hypotenuse =√((14√2)² + 28²) = 14√6 units

Considering the lower triangle:

The two triangles share the same hypotenuse.

Thus, hypotenuse = 14√6 units

sin 30° = y/hypotenuse

sin 30° = y/(14√6)

y = (14√6) * sin 30°

y = 7√6 units

cos 30° = z/hypotenuse

cos 30° = z/(14√6)

z = (14√6) * cos 45°

z = 14√3 units

Therefore, the value of each variable are x = 28 units, y = 7√6 units and z = 14√3 units.

Learn more about trigonometry on:

brainly.com/question/11967894

#SPJ1

Answer:

10000 meters

Step-by-step explanation:

1 kilometer=1000 meters

therefore 10 kilometers = 10×1000 = 10000meters

The probability of selecting a marble at random is 10/21, or 5/10.

Probability is the likelihood or chance of something happening. It is a mathematical measure of how likely an event is to occur, expressed as a number between 0 and 1. Probability can be used to make predictions and decisions about the future and to explain the likelihood of various outcomes. Probability is an important concept in many fields, including mathematics, finance, statistics, and science.

This is because there are 10 marbles out of a total of 21 total objects (3 golf balls, 8 tennis balls, and 10 metal marbles).

To know more about probability click-
https://brainly.com/question/24756209
#SPJ9

On solving the provided question we can say that value equation is

y = mx => -7 = m * 4 => m = -7/4 and x² + y² = 13 => x² + (-7)² = 13 => x

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence.

here, we have,

Squaring both sides and simplifying we get:

3m² + 56m + 36 = 0

The coordinates of the points A and B are (-12,103) and (-3,-89) respectively.

y = mx => -7 = m * 4 => m = -7/4

x² + y² = 13 => x² + (-7)² = 13 => x

So the equation of the tangent line is y = m(x - 0) + 0,

where m = -(x+4)/(y-7)

Now we can substitute the coordinates of the center of the circle into the equation of the tangent line to get y = -(x+4)/(y-7) * x

Squaring both sides and simplifying we get:

3m² + 56m + 36 = 0

b) To find the coordinates of the points A and B, we can use the equation of the tangent line and the equation of the circle.

We know that the equation of the tangent line is y = -(x+4)/(y-7) * x and the equation of the circle is (x+4)² + (y-7)² = 13.

We can substitute y = -(x+4)/(y-7) * x into the equation of the circle and solve for x.

This equation simplifies to 3x² + 56x + 36 = 0, which factors to

(x+12)(x+3) = 0

y = -(-12+4)/(y-7) * -12 = 8/(y-7) * 12 = 96/(y-7)

y = 96 + 7 = 103 and y = -96 + 7 = -89

The coordinates of the points A and B are (-12,103) and (-3,-89) respectively.

We know that the equation of the tangent line is y = mx and the equation of the circle is x² + y² = 13.

We can substitute the point (4, -7) for x and y in the equation of the tangent line and the equation of the circle and solve for m and x,y respectively.

y = mx => -7 = m * 4 => m = -7/4

x² + y² = 13 => x² + (-7)² = 13 => x

To know more about equation visit:

brainly.com/question/649785

#SPJ9

The sample size for the confidence interval is given as follows:

n = 185.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The margin of error is given as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The parameters for this problem are given as follows:

[tex]M = 0.071, \pi = 0.41[/tex]

Hence the sample size is obtained as follows:

[tex]0.071 = 1.96\sqrt{\frac{0.41(0.59)}{n}}[/tex]

[tex]0.071\sqrt{n} = 1.96\sqrt{0.41 \times 0.59}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.41 \times 0.59}}{0.071}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.41 \times 0.59}}{0.071}\right)^2[/tex]

n = 185.

More can be learned about confidence intervals at https://brainly.com/question/25890103

#SPJ1

Answer:

consonance

Step-by-step explanation:

consonance are words that end the same

spins and veins

[tex]83 + 61 + (4x + 16) = 180[/tex]

[tex]144 + 4x + 16 = 180[/tex]

[tex]4x + 160 = 180[/tex]

[tex]4x = 180 - 160[/tex]

[tex]4x = 20[/tex]

[tex]x = 20:4 \implies \bf x = 5[/tex]

Answer: 10.5 - 5.4n

Step-by-step explanation:

   To simplify, we will combine like terms.

Given:

   2.5 - 3.4n - 2n + 8

Add 2.5 + 8 and subtract -3.4n - 2n:

   10.5 - 5.4n

Answer:

[tex]-5.4n + 10.5[/tex]

Step-by-step explanation:

[tex]2.5 + 3.4n -2n + 8\\(-3.4n - 2n) + (2.5 + 8)\\-5.4n + 10.5[/tex]

(a) The number of students who took none of the three subjects is 169.

(b) The number of students who took PE but not BIO or ENG is 19.

(c) The number of students who took BIO and PE but not ENG is 8.

To find the number of students who took none of the three subjects, we can add up the numbers in the "none" region of the diagram.

From the given information, we know that 45 students took PE, 45 took BIO, and 45 took ENG, so the total number of students who took at least one subject is:

45 + 45 + 45 = 135

We also know that 4 students took all three subjects, so we need to subtract them from the total to avoid double-counting:

135 - 4 = 131

Therefore, the number of students who took none of the three subjects is:

300 - 131 = 169

(b) To find the number of students who took PE but not BIO or ENG, we need to look at the region of the diagram that only includes PE.

This includes the 12 students who took both PE and BIO, the 10 students who took both PE and ENG, and the 4 students who took all three subjects.

Therefore, the number of students who took PE but not BIO or ENG is:

45 - 12 - 10 - 4 = 19

(c) To find the number of students who took BIO and PE but not ENG, we need to look at the region of the diagram where BIO and PE overlap, but ENG does not.

This includes the 12 students who took both PE and BIO, as well as the 4 students who took all three subjects.

Therefore, the number of students who took BIO and PE but not ENG is:

12 - 4 = 8

Learn more about Venn diagram here: https://brainly.com/question/24713052

#SPJ1

The answer of the given expression  is -4.

What is expression ?

An expression is a combination of numbers, symbols, and operators that represents a mathematical quantity or relationship. It can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Expressions can be simple or complex and can be evaluated or simplified to a single value or another expression. Examples of expressions include 2x + 3, 4y - 7, (x + 5) / 2, and √(x² + y²).

We can solve the equation as follows:

|7x+4|/8 = 3

|7x+4| = 3*8

|7x+4| = 24

Now we have two cases to consider:

Case 1: 7x+4 is positive

|7x+4| = 7x+4

7x+4 = 24

7x = 20

x = 20/7

Case 2: 7x+4 is negative

|7x+4| = -(7x+4)

-7x-4 = 24

-7x = 28

x = -4

Therefore, the solutions are x = -4 and x = 20/7. However, we need to check if they satisfy the original equation:

For x = -4:

|7(-4)+4|/8 = 3

|-24|/8 = 3

3 = 3 (satisfied)

For x = 20/7:

|7(20/7)+4|/8 = 3

|24+4|/8 = 3

28/8 = 3.5 ≠ 3 (not satisfied)

So the only solution that satisfies the original equation is x = -4.

Therefore, the answer of the given expression  is -4.

To know more about expression visit :

https://brainly.com/question/1859113

#SPJ1

If Huckleberry Finn uses offensive language, Huckleberry Finn should not be taught high school. Huckleberry Finn uses offensive language. Thus, Huckleberry Finn should not be taught in high school. The logical form of this argument is known as denying the antecedent. The Option C is correct.

If we represent the argument in logical symbols, it would look like this:

P: Huckleberry Finn uses offensive language.

Q: Huckleberry Finn should not be taught in high school.

The argument can be summarized as follows:

If P, then Q.

Not P.

Therefore, not Q.

This is the form of denying the antecedent, where the argument asserts that if P is true, then Q must also be true. However, the argument then proceeds to deny the antecedent by claiming that P is not true, and therefore, Q must not be true either.

Read more about antecedent

brainly.com/question/30723132

#SPJ1

In response to the query, we can state that As a result, interest accounted for $6.23 of Kyle's payment in month 2.

By dividing the principal by the interest rate, the passage of time, and other factors, simple interest is determined. Simple return equals principle plus interest plus hours is the formula used in marketing. The easiest way to compute interest is by using this method. The most typical method for calculating interest is as a portion of the principle amount. For example, if he borrows $100 from a buddy and agrees to pay back the loan at 5% interest, he will only pay his share of the 100% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and you must charge interest when you lend it. Typically, interest is determined as an annual percentage of the loan total. The loan's interest is the name given to this percentage.  

The yearly interest rate must be divided by 12 to obtain the monthly interest rate since it is given:

1.5% each month divided by 12 equals 0.125%.

initial balance is $5,020.

Amount paid: $45.08

Interest added equals 0.125% * $5,020 = $6.27

Principle paid equals $45.08 minus $6.27, or $38.81.

Final balance: $5,020 minus $38.81 equals $4,981.19

As a result, interest accounted for $6.27 of Kyle's payment in month 1.

Total starting balance: $4,981.19

Money received: $45.08; Interest owed: 0.125% * $4,981.19; Total: $6.23

Principal paid equals $45.08 minus $6.23, or $38.85.

Final balance: $4,981.19 minus $38.85 equals $4,942.34

As a result, interest accounted for $6.23 of Kyle's payment in month 2.

The amortisation table might look like this:

Month Starting Balance Payment: To Principal Ending Balance: To Interest Payment

[tex]1 $5,020.00 $6.27 $38.81 $4,981.19\s2 $4,981.19 $6.23 $38.85 $4,942.34\s3 $4,942.34 ...[/tex]

To know more about interest visit:

https://brainly.com/question/28792777

#SPJ1

Therefore, at least 49 street lights can be installed along one side of the street with equal distance between the lights.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The equals sign indicates that the two expressions are equal, and the goal of solving the equation is to find the value of x that makes this statement true. Equations can be solved using various algebraic techniques, such as simplifying and rearranging the expressions, applying operations to both sides of the equation, and factoring or expanding expressions. Solving an equation involves finding the values of the variables that make the equation true.

Here,

The distance between point A and B is AB, and the distance between point B and C is BC. Let's assume that the distance between each street light is "d".

Since there must be a street light at points A, B, and C, there will be a total of two gaps between these three street lights, which are AB and BC. Thus, the number of street lights required is equal to the sum of the lengths of AB and BC, divided by the distance "d" between the street lights, plus 1 for the street light at point B.

So, the total number of street lights required is

Number of street lights = (AB + BC) / d + 1

We know that AB = 1170 m and BC = 1625 m, and the distance between each street light should be equal. Therefore, we need to find the greatest common factor (GCF) of 1170 and 1625 to determine the distance between each street light.

1170 = 2 x 3 x 3 x 5 x 13

1625 = 5 x 5 x 13

The GCF of 1170 and 1625 is 65, which means the distance between each street light should be 65 meters.

Now we can calculate the total number of street lights required:

Number of street lights = (1170 + 1625) / 65 + 1

= 49

To know more about equation,

https://brainly.com/question/28243079

#SPJ9

flip the 2/3 then multiply

5 x 3/2 = 15/2 = 7.5

The longest distance between vertices on an 3- dimensional, 4-dimensional, 5-dimensional, and n-dimensional cube is the square root of 1.723, 2, square root 2.236, and square root of n respectively.

The ability to execute numerous tasks or calculations concurrently may greatly enhance a system's overall performance, which makes parallel processing important in computer science. A system can perform processes in parallel by employing many processors or cores, which cuts down on the time needed to do complicated calculations or activities.

The longest distance between vertices on an n-dimensional cube, is given by:

d = sqrt(n)

where d is the distance between vertices.

n is the number of dimensions.

For a 3-dimensional cube, we have:

d = sqrt(3) ≈ 1.732

For a 4-dimensional cube, we have:

d = sqrt(4) = 2

For a 5-dimensional cube, we have:

d = sqrt(5) ≈ 2.236

In general, for an n-dimensional cube, we have:

d = sqrt(n)

So the longest distance between vertices on an n-dimensional cube is the square root of n.

Learn more about cube here:

https://brainly.com/question/28134860

#SPJ1

ABC is an important tool for companies to utilize when they need to accurately assess their product costs and make decisions based on that information. ABC can also be used to create external reports that show customers and other stakeholders the cost of a product.

External reports are documents that are created by outside organizations or individuals and contain information that is relevant to a particular company or industry. They are used to provide insight and data that can help an organization make informed decisions.

Activity-based costing (ABC) is a method of product costing that assigns costs to products based on the activities that go into producing them. It is used to decide how much it costs a company to make a product, and then the company can use this information to set prices and make pricing decisions. With ABC, companies track the costs associated with activities and assign those costs to the products that use the activities. This is different from traditional costing methods that allocate costs to products based on a single cost driver, such as machine hours or direct labor hours. ABC is a more accurate way of determining the cost of a product because it takes into account all of the activities that go into making it. ABC can also be used to create external reports that show customers and other stakeholders the cost of a product. These reports can help a company make decisions about pricing and production efficiency, and can also be used to compare products and services to competitors. ABC is an important tool for companies to utilize when they need to accurately assess their product costs and make decisions based on that information.

For more questions elated to Activity-based costing,

https://brainly.com/question/15862944

#SPJ1

ABC is an impοrtant tοοl fοr cοmpanies tο utilize when they need tο accurately assess their prοduct cοsts and make decisiοns based οn that infοrmatiοn. ABC can alsο be used tο create external repοrts that shοw custοmers and οther stakehοlders the cοst οf a prοduct.

External repοrts are dοcuments that are created by οutside οrganizatiοns οr individuals and cοntain infοrmatiοn that is relevant tο a particular cοmpany οr industry. They are used tο prοvide insight and data that can help an οrganizatiοn make infοrmed decisiοns.

Activity-based cοsting (ABC) is a methοd οf prοduct cοsting that assigns cοsts tο prοducts based οn the activities that gο intο prοducing them. It is used tο decide hοw much it cοsts a cοmpany tο make a prοduct, and then the cοmpany can use this infοrmatiοn tο set prices and make pricing decisiοns. With ABC, cοmpanies track the cοsts assοciated with activities and assign thοse cοsts tο the prοducts that use the activities. This is different frοm traditiοnal cοsting methοds that allοcate cοsts tο prοducts based οn a single cοst driver, such as machine hοurs οr direct labοr hοurs.

ABC is a mοre accurate way οf determining the cοst οf a prοduct because it takes intο accοunt all οf the activities that gο intο making it. ABC can alsο be used tο create external repοrts that shοw custοmers and οther stakehοlders the prοduct cοst . These repοrts can help a cοmpany make decisiοns abοut pricing and prοductiοn efficiency, and can alsο be used tο cοmpare prοducts and services tο cοmpetitοrs. ABC is an impοrtant tοοl fοr cοmpanies tο utilize when they need tο accurately assess their prοduct cοsts and make decisiοns based οn that infοrmatiοn.

For more questions elated to Activity-based costing,

brainly.com/question/15862944

#SPJ1

Complete question:

What Activity-Based Costing in Product Costs for External Reports?

Answer:346.5

Step-by-step explanation: At first,we have calculate the radius of the given circle,by using the following mathematical formula.

Radius = Diameter/2 = 21/2 = 10.5 cm

Now,we have to calculate the area of the circle by using the following mathematical formula,

Area of the circle = π×r² = 22/7 × 10.5 × 10.5 = 346.5 cm²

please lmk if this an option or answer for you.

The equation of circles that have a diameter of 12 units and a center that lies on the y-axis is  (x + 6)² + y² = 144

The equation of a circle with center (h, k) and radius r is given by

(x - h)² + (y - k)² = r²

To determine which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis, we must have that

for the circle to lie on the y - axis, k = 0 and r² = 144

So, comparing the equations that meet this criteria, we have

(x + 6)² + y² = 144

We cannot select the circle  (x – 4)² + y² = 36. Although it lies on the y - axis, its radius is not equal to 12.

So, the circle is (x + 6)² + y² = 144

Learn more about equation of a circle here:

https://brainly.com/question/28849755

#SPJ1

Answer:

She got $21.70 an hour

Step-by-step explanation:

130.20/6= 21.7

The range is 75, variance is 607.70 and standard deviation is 24.65

Standard deviation is a statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance.

Given is a data set :- 23 53 67 61 66 91 27 85 98 44 73,

We need to find the range, variance, and standard deviation for the given sample data.

Range :-

Range = the difference between the highest and lowest numbers

Highest = 98

Lowest = 23

Range = 98 - 23 = 75

Mean :-

The mean of the data is calculated by the sum of all data is divided by the total number of data =

23+53+67+61+66+91+27+85+98+44+73 / 11 = 62.54

Variance :-

Variance is calculated by formula:

σ² = (xi-mean)² / n-1

σ² = (23-62.54)²+(53-62.54)²+(67-62.54)²+(61-62.54)²+(91-62.54)²+(66-62.54)²+(27-62.54)²+(85-62.54)²+(98-62.54)²+(44-62.54)²+(77-62.54)² / 10

= 1563.4+91.0116+19.9+2.37+809.98+11.97+1263.09+504.45+1257.41+343.73+209.09 / 10

σ² = 607.70

The standard deviation, we take the variance and get the square root of it :-

σ = √607.70

σ = 24.65

Hence, the range is 75, variance is 607.70 and standard deviation is 24.65

Learn more about standard deviation click;

https://brainly.com/question/29088233

#SPJ1

The 20% percentage of bill $169.86 is $33.9.

A value or ratio that may be stated as a fraction of 100 is referred to in mathematics as a percentage. Divide the number by the total and multiply by 100 to find the percent of a given number. Therefore, the percentage refers to a portion per hundred. Per 100 is what the word percentage signifies. The letter "%" stands for it.

Here the total bill amount= $169.86

The percentage for tip is 20%.

Then the tip amount = 20% of bill

=> 20% of 169.86

=> 20% × 169.86

=> [tex]\frac{20}{100}\times 169.86[/tex]

=> $33.9

Hence the bill amount is $33.9.

To learn more about percentage refer the below link

https://brainly.com/question/24877689

#SPJ1

If Molly bought a watch in Singapore for 58 Singapore dollars.  the difference between the amounts that Molly and Louis paid for their watches, in pounds, is £1.06.

To compare the prices paid by Molly and Louis in the same currency, we need to convert their respective amounts to pounds.

First, we convert Molly's purchase of 58 Singapore dollars to pounds:

58 Singapore dollars x £0.57/1 Singapore dollar = £33.06

Next, we convert Louis's purchase of 336 Hong Kong dollars to pounds:

336 Hong Kong dollars x £1/10.50 Hong Kong dollars = £32.00

Molly paid £33.06 for the watch, while Louis paid £32.00. The difference in the amounts paid is:

£33.06 - £32.00 = £1.06

So, the difference between the amounts that Molly and Louis paid for their watches, in pounds, is £1.06.

Learn more about price here:https://brainly.com/question/1153322

#SPJ1

Answer:

Step-by-step explanation:

i dont undrestand either sorry

y = 5(10)ˣ is the equation for the  exponential function

The general form of the exponential function is y = abˣ

From the table, when x = 0, y = 5. Substitute the values into the function:

y = abˣ

5 = ab⁰             (Note: b⁰ = 1)

5 = a(1)

5= a

a = 5

Also, from the table, when x = 1, y = 50. Substitute the values into the function:

y = abˣ

50 = 5 × b¹

50 = 5b

5b = 50

b = 50/5 = 10

We can now write the equation for the exponential function:

y = abˣ

y = 5(10)ˣ

Therefore, the equation for the exponential function is y = 5(10)ˣ

Learn more about exponential function on:

brainly.com/question/29409105

#SPJ1

The two measures of these data that best describe the typical number of minutes Addison spent reading each day are mean and median.

Mean is the average value of a set of numbers, found by adding up all the numbers and dividing by the total count of numbers. Median is the middle value in a set of numbers when they are listed in order.

To find the mean of the data set, we add up all the values and divide by the total count:

(90 + 60 + 89 + 94 + 60 + 93) / 6 = 85.33

To find the median of the data set, we first put the values in order:

60, 60, 89, 90, 93, 94

Since there are an even number of values, we take the average of the two middle values:

(89 + 90) / 2 = 89.5

Therefore, the mean is 85.33 minutes and the median is 89.5 minutes, which are the two measures that best describe the typical number of minutes Addison spent reading each day.

Using arithmetic οperatiοns it is οbtained that Brandοn must mοw 15 lawns at $25 per lawn tο break even, meaning his revenue will cοver his cοsts.

A subject οf mathematics knοwn as arithmetic οperatiοns deals with the study and use οf numbers in all οther branches οf mathematics. Basic οperatiοns including additiοn, subtractiοn, multiplicatiοn, and divisiοn are included.

Let x be the number οf lawns Brandοn mοws.

Use the arithmetic οperatiοn οf multiplicatiοn.

His revenue frοm mοwing × lawns at $25 per lawn is -

Revenue = Price per lawn × Number οf lawns

Revenue = $25 × x

Revenue = $25x

Use the arithmetic οperatiοn οf additiοn.

His tοtal cοst includes the equipment cοst οf $300 and the variable cοst οf $5 per lawn, sο his tοtal cοst is -

Cοst = Equipment cοst + Variable cοst

Cοst = $300 + $5x

Tο break even, his revenue must be equal tο his cοst.

Use the arithmetic οperatiοn οf additiοn.

Sο we can set the revenue equal tο the cοst and sοlve fοr x -

Revenue = Cοst

$25x = $300 + $5x

$20x = $300

x = 15

Therefοre, Brandοn must mοw 15 lawns at $25 per lawn.

To learn more about arithmetic operation from the given link

https://brainly.com/question/20628271

#SPJ1

Answer:

6902

Step-by-step explanation:

divide through by multiples of the given values

Answer:

It should be 88 questions

Step-by-step explanation:

86/88 x 100 = 97.7 round to the nearest whole number and you get 98%

The perimeter of triangle ABC is approximately 50.9 units.

The perimeter of a triangle is the total distance around the outside of the triangle. It is defined as the sum of the lengths of all three sides of the triangle.

To find the perimeter of triangle ABC, we need to know the lengths of all three sides. We are given the measure of angle C (40 degrees), the length of side AC (13 units), and the measure of angle B (49 degrees).

To find the length of side BC, we can use the law of sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides. In other words:

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the lengths of the sides, and A, B, and C are the measures of the opposite angles.

Using this formula, we can write:

13/sin(40) = BC/sin(91)

Solving for BC, we get:

BC = (13 * sin(91)) / sin(40)

BC ≈ 21.12

To find the length of side AB, we can use the fact that the sum of the angles in a triangle is 180 degrees. We know the measures of angles B and C, so we can find the measure of angle A as follows:

A = 180 - B - C

A = 180 - 49 - 40

A = 91 degrees

Now we can use the law of sines again to find the length of side AB:

AB/sin(49) = 13/sin(91)

Solving for AB, we get:

AB = (13 * sin(49)) / sin(91)

AB ≈ 16.78

Finally, we can add up the lengths of all three sides to find the perimeter:

Perimeter = AB + AC + BC

Perimeter = 16.78 + 13 + 21.12

Perimeter ≈ 50.9 units

Therefore, the perimeter of triangle ABC is approximately 50.9 units.

To know more about perimeter of triangle visit :

https://brainly.com/question/24299023

#SPJ1