Find the tangent of the smaller acute angle in a right triangle with side lengths 5, 12, and 13. Write your answer as a fraction.

To find out how much black cord the design needs, we must find the perimeter of the figures. In this case, it would be: 107.42ft

To find the perimeter of four-sided figures, we just have to add the length of their sides as shown below:

To find the area of the triangle we must add its sides, in this case it is a triangle that has all the sides equal so it would be like this:

2ft + 2ft + 2ft = 6ft

Finally, the perimeter of the circle is calculated by multiplying 2 * number pi * radius. So the operation would look like this:

2*3.14*1.5=9.42ft

Now all that remains is to add all the sides and we will know how much black cord we need

9.42ft + 24ft + 28ft + 52ft = 107.42ft

Additionally, the area of the figures is calculated as follows:

Rectangle:

Square:

Triangle:

Circle:

To find the area shown for each figure, simply subtract the area of the superimposed figure as shown below:

Finally, to know how many yards of fabric we need for each figure, we must take into account that one square foot is equal to 0.11 square yards, so we will have to multiply these values as shown below:

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The value of x in the given figure is 31.76.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

In the given triangle, there are two triangles.

Let us find the length of the perpendicular line by using pythagoras theorem.

16² + a² = 22²

256 + a²  = 484

a²  =484-256

a² = 228

a=15.09 = 15

Now let us find the value of x.

Now 44-16= 28

28²+15² = x²

784 + 225 =  x²

1009 = x²

Square root on both sides

x=31.76

Hence, the value of x in the given figure is 31.76.

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Answer:

the answer is 5

Step-by-step explanation:

³√125 or this can also be written as 125^⅓

it means cube root of 125

And the cube root of ³√125 is 5

then the cube of 5³ is 125

The fraction of crayons that are blue triangle is 1/5.

The ratio of blue rounds to non-blue crayons is

The fraction of footballs that are brown rubber footballs is 8/15 and here are 4 times as many rubber footballs as non-rubber footballs

A fraction represents a part of a whole.

1. Let's say Alexa had a total of 5x crayons in the bag.

the number of blue crayons in the bag is 2x,

There is one triangle for every two round crayons,

(1/2) × 2x = x (By condition)

So, the fraction of crayons that are blue triangle is x / 5x = 1/5.

The number of blue round crayons is 2x.

The number of non-blue crayons is 5x - 2x = 3x,

The ratio of blue rounds to non-blue crayons is 2x / 3x = 2/3.

2.

4 out of 5 wall footballs are rubber, 4/5 of the footballs in the bag are rubber.

The fraction of rubber footballs that are brown is 2/3.

The fraction of footballs that are brown rubber footballs is (4/5) × (2/3) = 8/15.

The fraction of non-brown rubber footballs is (4/5) - (8/15) = 4/15.

The ratio of rubber footballs to non-rubber footballs is (4/5) / (1/5) = 4.

So there are 4 times as many rubber footballs as non-rubber footballs

Hence,  the fraction of crayons that are blue triangle is 1/5.

The ratio of blue rounds to non-blue crayons is

The fraction of footballs that are brown rubber footballs is 8/15 and here are 4 times as many rubber footballs as non-rubber footballs

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Answer:

Below

Step-by-step explanation:

x = first number  

x+1 = second number

x *  (x+1) = 272

x^2  +x  = 272

x^2 + x - 272 = 0     Use Quadratic Formula to find:

x=   16    x+1 = 17          OR       x =   -17     x+1 = -16

The Weight of mini horse is 465 lbs.

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

A calf and a mini-horse weigh 705 lbs combined.

The ratio of their weights is 16:31 respectively.

let the Common ratio be x.

So, weight of calf = 16x and Weight of mini horse = 31x

Thus, 16x + 31x = 705

47x = 705

x= 705/ 47

x= 15

Then, the Weight of mini horse = 31x = 31(15)= 465 lbs.

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The length and breadth of the room is 4 meters

A square is a 2D figure in which all the sides are of equal measure. Since all the sides are equal, the area would be length times width, which is equal to side × side. Hence, the area of a square is side square.

A square has it's sides equal

A = l²

The area of 2 walls = 128/2 = 64

Therefore the length of each sides = √64

= 4meters

The height of the room = Volume/ height

= 256/128 = 2

The breadth of the room will also be 4meters

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48 miles per hour is the most accurate rate of speed Morris is traveling

A measurement unit is a standard quantity used to express a physical quantity.

Given that Aneesha's speed is 50 miles per hour.

We need to convert to feet per second.

By given 1 mile = 5,280 feet

50×5280=264000 feet

Now divide by 36000

264000/36000

73.33 feet/second is the Aneeshas speed.

Morris is traveling 3 feet per second less than Aneesha, so his speed is:

73.33 - 3 = 70.33 feet/second

70.33× 3600  = 253,188 feet/hour

253,188 ÷ 5280  = 48 miles/hour

Hence,  Morris is traveling at a speed of 48 miles per hour.

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Answer:

Length: 17 cm

Width: 4 cm

Step-by-step explanation:

Let x be the width of the rectangle.

length : 4x+1

x+x+4x+1+4x+1= 42

10x= 40

x= 4

4x+1= 4(4)+1

= 17

Answer: √177

Step-by-step explanation:

6²+9²=c²

36+81=c²

117=c²

√117=√c²

√177 = c

(√177 can also be watered down to ±3√13 but √177 is one of the answer choices so yeah)

Answer:

1/4

Step-by-step explanation:

You cannot subtract (or add) a fraction with different denominators so first, you need to find a common denominator. You can do this by finding the least common multiple (LCM).

Here the denominators are 2 and 4 so the LCM is 4.

After you find the LCM you need to multiply the denominator by a number that equals the LCM. Then multiply the numerator by that same number.

So convert both 1/2 and 1/4

1/4 x 1/1 = 1/4

1/2 x 2/2 = 2/4

Now we can just subtract the numerator from each other.

2/4 - 1/4 = 1/4

We cannot simplify the difference any more so keep it the same.

Answer:

Proportional relationship between two quantities x and y means that the quotient y/x stays constant, i.e. that there is a constant c such that y=cx. In our case we have that y=3x+5 which means that x and y are NOT proportional.

Answer:

Check the explanation provided

Step-by-step explanation:

This equation does not represent a proportional relationship because it's graph does not pass through the origin (i.e. 0,0)

[tex]y = mx + c[/tex]

where m =  gradient OR slope

               = 3

           c  = y-intercept

               = 5

For the equation to have a proportional relationship, the value of c MUST BE '0’

Answer:

1, The Commutative Property of Addition

Step-by-step explanation:

you’re only changing the order

It is possible for equivalent expressions to make the left and right expressions have the same value

An expression is combination of variables, numbers and operators.

We have to check whether it is  possible to make the left and right expressions have the same value

If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

For example 2x+4=2(x+2)

When we plug in x as 2

2(2)+4=2(2+2)

4+4=2(4)
8=8

Hence, its possible to make the left and right expressions have the same value when the expressions are equivalent.

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Answer:  

x = -3

Step-by-step explanation:

I did this before

Answer:

Step-by-step explanation:

The simple interest formula is given by I = Prt, where P is the principal amount, r is the interest rate (per compounding period), and t is the time in years.

In this case, the interest rate is 5% per month, so we need to convert it to the equivalent annual interest rate, given by r = (0.05 x 12) = 0.6 (since there are 12 months in a year).

The time is 1.5 years, so t = 1.5.

So, the simple interest is:

I = Prt = 1000 x 0.6 x 1.5 = 900

The future value of the investment is the principal amount plus the interest earned, given by:

Future value = P + I = 1000 + 900 = 1900

So, the future value of the investment is $1900.

Answer: the future value of the simple interest investment, where 5% interest is paid monthly for 1.5 years on $1000, is $18074.06.

Step-by-step explanation:

To determine the future value of a simple interest investment, we need to calculate the interest earned over the investment period and add it to the original investment amount. Here's a step-by-step explanation for calculating the future value of a simple interest investment with a 5% interest rate paid monthly for 1.5 years on $1000:

Step 1: Convert the annual interest rate to a monthly rate.

Since the interest rate is 5% per year and the interest payments are made monthly, we need to convert the annual interest rate to a monthly interest rate. We can do this by dividing the annual interest rate by 12:

Monthly interest rate = Annual interest rate / 12

Monthly interest rate = 5% / 12 = 0.05 / 12 = 0.00417

Step 2: Calculate the interest payment for each month.

For each month, we can calculate the interest payment by multiplying the monthly interest rate by the current balance:

Interest payment = Monthly interest rate * Current balance

Let's calculate the interest payment for the first month:

Interest payment = 0.00417 * $1000 = $4.17

Step 3: Add the interest payment to the current balance to get the new balance.

After each interest payment, we can add it to the current balance to get the new balance:

New balance = Current balance + Interest payment

New balance = $1000 + $4.17 = $1004.17

Step 4: Repeat the steps for each month.

We can repeat steps 2 and 3 for each of the 12 months in the first year and then for the 6 months in the second year.

Step 5: Add up the final balance.

After all 18 interest payments have been made, the final balance will be the sum of all the new balances:

Final balance = $1004.17 + $1004.17 + ... + $1004.17 (18 times) = $1004.17 * 18 = $18074.06

So, the future value of the simple interest investment, where 5% interest is paid monthly for 1.5 years on $1000, is $18074.06.

Tasha can make 1 1/6 an improper number making 1 1/6=7/6. Then she can subtract 7/6-5/6, which is 2/6. Simplified 1/3.

Now it's not impossible! ;D

First find the amount the price increased.

    amount of change
                 = (percent change) x (starting value)

                 = (8%) x ($20)

                 = (0.08) x ($20)

                 = $1.60

(Remember to convert the percent to a decimal before multiplying.)

Now add the tax onto the price:

      $20 + $1.60 = $21.60

The price, including sales tax, is $21.60.

In the given situation, the required value of x for the given pair of adjacent angles is 30°.

When two angles have a similar vertex and side, they are referred to as neighboring angles.

The vertex of an angle is the point at which the rays that make up its sides come to an end.

When adjacent angles have the same vertex and side, they can be a complimentary angle or supplemental angle.

The definition of adjacent is next to or nearby.

Two next-door residences are an illustration of proximity.

Typically, we think of those who live on our street as neighbors.

So, we have:

x + x + 30 = 90

Now, solve for x as follows:

x + x + 30 = 90

2x + 30 = 90

2x = 90 - 30

2x = 60

x = 60/2

x = 30

Therefore, in the given situation, the required value of x for the given pair of adjacent angles is 30°.

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To convert micrograms (μg) to milligrams (mg), you can divide the number of micrograms by 1000. So, the formula for converting micrograms to milligrams is: mg = μg / 1000.

To convert micrograms to milligrams, divide the number of micrograms by 1000. This is because there are 1000 micrograms in 1 milligram. For example, if you have a measurement of 5000 micrograms and you want to convert it to milligrams, you would divide 5000 by 1000 to get 5 milligrams. This conversion is useful in many fields, including medicine, where medication dosages are often measured in milligrams, and scientific research, where precise measurements of small amounts of substances are necessary.

For example, let's say you have a measurement of 5000 micrograms and you want to convert it to milligrams:

mg = 5000 μg / 1000

mg = 5 mg

Therefore, 5000 micrograms is equal to 5 milligrams.

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Answer:

Step-by-step explanation:

If you got together on December 27, 2021, your 1-month anniversary would be on January 27, 2022, which is exactly 31 days later.

Your 2-month anniversary would be on February 27, 2022, which is exactly 61 days later. Since February has only 28 days in 2022, it means that your 2-month anniversary would fall on the last day of February.

Your 3-month anniversary would be on March 27, 2022, which is exactly 90 days later.

To the nearest cent, Andy will have $1,322.50 in 2 years.

Interest is the cost of borrowing money, or the return on lending money. It is typically expressed as a percentage of the amount borrowed or lent, known as the principal.

Using the formula [tex]B=p(1+r)^t[/tex], where p=$1,000, r=0.15 (15% expressed as a decimal), and t=2, we can calculate the balance B after 2 years:

[tex]B = $1,000(1+0.15)^2 \\ \\B = $1,000(1.15)^2\\\\B = $1,000(1.3225)\\\\B = $1,322.50\\\\[/tex]

Therefore, to the nearest cent, Andy will have $1,322.50 in 2 years.

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The measure of central location most often reported for annual income and property value data is the mode.

There are three measures of central tendency of a data-set, which are defined as follows:

Among those three measures, the mode is the one that gives the observation that appears the most often in a data-set, hence the correct option is given by option a.

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0700 military time is 7:00 AM in the 24-hour time format used by the military, also known as the 24-hour clock.

The 24-hour clock is a timekeeping system that uses a continuous count of 24 hours, instead of two sets of 12 hours for AM and PM. In this system, each hour of the day is numbered from 0 to 23, and is referred to as "military time" or "24-hour time". So, 0700 military time is equivalent to 7:00 AM, with the "0" indicating the first hour of the day. This system is commonly used in the military, as well as in other fields where precise and standardized timekeeping is important, such as aviation and public transportation.

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The previous population, of the city is 55,000

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100.

Given that, a city's current population is 40,700, decreased by 26% after it was measured last time, the

Let the previous population, of the city, be x,

Therefore,

x - 26% of x = 40,700

x(1-26%) = 40,700

0.74x = 40,700

x = 55,000

Hence, the previous population, of the city is 55,000

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The distance from the top left corner of the foundation to the bottom right corner is 27 meters.

The distance between two points in space can be calculated using the Pythagorean theorem. In this case, we want to find the distance from the top left corner of the foundation to the bottom right corner.

To do this, we will use the length and width of the foundation, which are 20 meters and 18 meters respectively.

The Pythagorean theorem states that in a right triangle, the square of the distance (c) between the two points is equal to the sum of the squares of the other two sides (a and b). Mathematically, this can be represented as

=> c² = a² + b².

In our case, the two sides are the length (20m) and width (18m) of the foundation. To find the distance, we will first find the square of c by adding the squares of a and b. So,

=> c² = 20² + 18² = 400 + 324 = 724.

To find the distance, we will take the square root of c².

So,

c = √724 = 26.83

When we rounded to the nearest meter, c = 27m.

Complete Question:

The foundation of a building is in the shape of a rectangle, with a length of 20 meters(m) and a width of 18m. To the nearest meter, what is the distance from top left corner of the foundation to the bottom right corner.

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