The tangent of the smaller acute angle in a right triangle is tanФ = 5/12 taking side 5 as opposite side and 12 as adjacent side.
We know a right-angled triangle has three sides they are -: Hypotenuse,
Opposite and Adjacent or (base and perpendicular)
The Formula of tangent is opposite side/ adjacent side
Given, a right triangle with side lengths 5, 12, and 13.
We can see that largest side i.e., 13 is a hypotenuse of triangle and other two sides are base and perpendicular length.
Tangent taking side 5 as opposite side and 12 as adjacent side
tanФ = 5/12.
Tangent taking side 12 as opposite side and 5 as adjacent side
tanФ = 12/5
so, the tangent of the smaller acute angle in a right triangle is 5/12.
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A calf and a mini-horse weigh 705 lbs combined. The ratio of their weights is 16:31 respectively. How much does the mini-horse weigh?
The Weight of mini horse is 465 lbs.
What is Ratio?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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6. Sofia rearranged the equation 3x+7+2x-8=21
into 3x+2x+7-8=21 in order to combine like
terms more easily. Which of the following properties
did she use to make this manipulation?
(1) The commutative property of addition
(2) The additive property of equality
(3) The distributive property
(4) The associative property of multiplication
Answer:
1, The Commutative Property of Addition
Step-by-step explanation:
you’re only changing the order
volume of a square room is 256 cubic meter.
Area of 4 walls is 128 Sq.m
Find length and breath.
The length and breadth of the room is 4 meters
What is area of square?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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Tasha is trying to solve 1 ⅙ - ⅚. She says it’s impossible because you only have ⅙, so you can’t take away ⅚. Explain how Tasha can solve this problem. Please help me
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
Easy question. My friend asked me this random question while I'm trying to sleep. If you get with someone on 12/27/2021 when will your 1 month, 2 month, and 3 month anniversary be? Remember February only has 28 days..
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.
Please Helppppp I dont understandddd
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
How to find the perimeter of figures?To find the perimeter of four-sided figures, we just have to add the length of their sides as shown below:
16ft + 16ft + 10ft + 10ft = 52ft7ft + 7ft + 7ft + 7ft = 28ftTo 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:
16ft*10ft=160ftSquare:
7ft*7ft=49ftTriangle:
1.73ft * 2ft / 2 = 1.73ft1.73*4=6.92ftCircle:
3.14*1.5²=7.06ftTo find the area shown for each figure, simply subtract the area of the superimposed figure as shown below:
160ft - 49ft = 11ft49ft - 8ft - 6.92ft = 34.08ftFinally, 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:
160ft * 0.11 = 17.6 = 18 yards49ft * 0.11 = 5.39 = 6 yards6.92ft * 0.11 = 0.76 = 1 yard7.06ft * 0.11 = 0.77 = 1 yardLearn more about inches in: https://brainly.com/question/16311877
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why does the equation y = 3x + 5 not represent a proportional relationship?
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’
find two consecutive numbers whose product is 272
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
Determine the future value of a simple interest investment where 5% interest paid monthly for
1.5 years on $1000.
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.
Aneesha travels at a rate of 50 miles per hour. Morris is traveling 3 feet per second less than Aneesha. Which is the most accurate rate of speed Morris is traveling?
1 mile = 5,280 feet
45 miles per hour
46 miles per hour
47 miles per hour
48 miles per hour
48 miles per hour is the most accurate rate of speed Morris is traveling
What is Unit of measurement?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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1.Which best describes a linear function?
(a) Building a tower of blocks, Collin starts with 25 blocks on the first level, 16 on the second level, and
9 on the third level. The function represents the relationship between the number of blocks on each
level after x levels.
(b) On a summer day, the temperature outside increases 3 degrees Fahrenheit per hour after 6 AM.
The function represents the relationship between the
temperature outside after x hours after 6 AM.
(c) Patty's company makes gift boxes in the shape of cubes. As the size of the gift box changes, the
length of each side increases by 6 inches. The function represents the relationship between the volume
of
each gift box after x increases in side length.
Xo
(d) The water in an outdoor pool is evaporating. Each day, only 95% of the water from the day before
remains. The function represents the relationship between the amount of water in the pool after x days.
()
Find the value of X. Round to the nearest tenth
The value of x in the given figure is 31.76.
What is Trigonometry?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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The population of a city has decreased by 26% since it was last measured. If the current population is 40,700, what was the previous population?
The previous population, of the city is 55,000
What is percentage?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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For two adjacent angles x° and (x + 30)° that make up a 90° angle, what is x
In the given situation, the required value of x for the given pair of adjacent angles is 30°.
What are adjacent angles?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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The measure of central location most often reported for annual income and property value data is the _____.
a. mode
b. median c. aggregate mean d. weighted mean
The measure of central location most often reported for annual income and property value data is the mode.
What is the mode?There are three measures of central tendency of a data-set, which are defined as follows:
Mean.Median.Mode.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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The length of a rectangle is 1 cm more than 4 times the width. The perimeter is 42 cm. Find the length and the width.
Equation: Length:
Solve: Width:
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
What's the length of the hypotenuse of right ΔDEF shown?
Question 13 options:
A)
√87
B)
12
C)
15
D)
√117
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)
Sanjeev has to buy enough wallpaper to cover a rectangular wall that has an area of
242 square feet. The wall is 11 feet tall. How wide is the wall?
What is 0700 military time?
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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What is the answer it is so confusing
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
Find the difference. use your answer in the simplest terms, using the slash ( / ) as the fraction bar.
1/2 - 1/4
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.
How to convert microgram to mg?
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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Can someone help please this so due tonight
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
What is Fraction?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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Is it possible to make the left and right expressions have the same value? Explain your thinking.
It is possible for equivalent expressions to make the left and right expressions have the same value
What is Expression?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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If tan A=7/12, what is cos A?
The foundation of a building is in the shape of a rectangle, with a length of 20 meters (m) and a width of 18 m.
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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Elwyn's bill for dinner at a restaurant was $75. He wants to leave a 20% tip. How much should he leave for the tip? What is his total bill for dinner and tip?
Mr. Newton wants to buy a shirt in Leavenworth Kansas that cost $20.The sales tax in Leavenworth is 8%. What would be the total price of the shirt after adding the sales tax?
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.
Solve for x.
7-3x/2 = 8
x = [?]
Answer:
x = -3
Step-by-step explanation:
I did this before
Andy has $1,000 in an account. The interest rate is 15% compounded annually. To the nearest cent, how much will he have in 2 years? Use the formula B=p(1+r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
To the nearest cent, Andy will have $1,322.50 in 2 years.
What is interest ?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.
According to given information :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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