The width and height are given to one decimal place, and we have multiplied them together, the answer should be rounded to one decimal place. Therefore, the area of the rectangle is 25.1 cm²
To calculate the area of a rectangle, we need to multiply its width by its height.
The size of a patch on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina. Area can be interpreted as the quantity of material with a specific thickness required to create a model of the shape or as the quantity of paint required to completely cover the surface in a single coat.
Area = width x height
Substituting the given values, we get:
Area = 7.6 cm x 3.3 cm
Area = 25.08 cm²
Since the width and height are given to one decimal place, and we have multiplied them together, the answer should be rounded to one decimal place. Therefore, the area of the rectangle is 25.1 cm² (rounded to one decimal place).
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Please need help with this math problem
Answer:
maximum value = 135
Step-by-step explanation:
the maximum value is situated at the right end of the whisker.
each division on the number line is 5 units
so maximum value = 125 + 2 units = 125 + 10 = 135
10. Best Buy is having a 15% off sale on brands of computer regularly priced at $2250 How much does Jerome save on the computer the sales tax is 7. 5% what is the amount of on the computer How much is the total cost for the computer What would be the total price for the computer on sale
The total cost of the computer is $2418.75.
The total cost of the computer in sale $2,056.
The computer is regularly priced at $2250.
With the 15% discount, Jerome would save = $2250 × 15%
With the 15% discount, Jerome would save = $2250 × 15/100
With the 15% discount, Jerome would save = $337.50 on the computer
The sales tax is 7.5%.
So the tax on the computer would be = $2250 × 7.5%
The tax on the computer would bee = $2250 × 7.5/100
The tax on the computer would be = $168.75
The total cost for the computer on sale would be = $2250 - $337.50
The total cost for the computer on sale would be = $1,912.5
If the tax is 7.5% .
So he has to pay = $1,912.5 + $1,912.5 × 7.5% = $2,056
Therefore, the total price for the computer on sale would be $2,056,
The price of the computer not on sale = $2250 + $168.75 = $2418.75.
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A recipe calls for 6 cups of flour to make 24 pancakes. How many pancakes
can be made with a single cup of flour?
On the double number line below, fill in the given values, then use
multiplication or division to find the missing value:
cups of flour
pancakes
Sam depositied 500$ in a new bank account correct answer
Answer:
Bank a/c Dr
To cash a/c
(Being deposited cash into bank)
A lighthouse is fixed 130 feet from a straight shoreline. A spotlight revolves at a rate of 14 revolutions per minute, (281
rad/min), shining a spot along the shoreline as it spins. At what rate is the spot moving when it is along the shoreline
13 feet from the shoreline point closest to the lighthouse?
The spot on the shoreline is moving at a rate of about 1.764 feet per minute when it is 13 feet from the point on the shoreline closest to the lighthouse.
What is differentiation?
Differentiation is a mathematical operation that is used to find the rate at which a function changes. More specifically, it is the process of finding the derivative of a function.
The derivative of a function at a given point is a measure of how quickly the function is changing at that point. It gives the slope of the tangent line to the graph of the function at that point. The derivative can be thought of as the instantaneous rate of change of the function at that point.
Let's call the point on the shoreline closest to the lighthouse "P". We know that the distance from the spotlight to P is 130 feet, and we want to find the rate at which the distance from the spotlight to P changes when the spotlight is 13 feet from P.
To do this, we can use the chain rule to differentiate the distance formula with respect to time. Let's call the distance between the spotlight and P "d". Then:
d²= 130² + x²
Taking the derivative of both sides with respect to time gives:
2d * dd/dt = 0 + 2x * dx/dt
We can solve for dd/dt by plugging in the values we know:
130² + 13² = d²
d = [tex]\sqrt{(130^2 + 13^2)}[/tex] = 130.325 ft
2(130.325) * dd/dt = 2(13) * dx/dt
dd/dt = (13/130.325) * dx/dt
We know that the spotlight revolves at a rate of 281 rad/min, or 281/2π ≈ 44.7 revolutions per minute. Each revolution of the spotlight covers a distance of 2π * 130 feet, so its speed is:
(2π * 130 ft/rev) * (44.7 rev/min) = 18410.8 ft/min
To find dx/dt when x = 13, we need to find the angular velocity of the spotlight at that point. The spotlight makes one full revolution every 60/14 ≈ 4.29 seconds, so its angular velocity is:
2π radians/rev ÷ 4.29 s/rev = 1.47 radians/s
At any given moment, the angle between the spotlight and the line connecting the lighthouse and P is equal to the arctangent of x/130. When x = 13, this angle is:
arctan(13/130) ≈ 5.71°
The rate at which the angle is changing is equal to the angular velocity of the spotlight, so we can use the formula for the derivative of the arctangent to find dx/dt:
dx/dt = 130 * tan(5.71°) * (1.47 radians/s)
dx/dt ≈ 17.602 ft/min
Finally, we can substitute this value into the expression we found for dd/dt:
dd/dt = (13/130.325) * 17.602
dd/dt ≈ 1.764 ft/min
So the spot on the shoreline is moving at a rate of about 1.764 feet per minute when it is 13 feet from the point on the shoreline closest to the
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Write the number for three million twenty thousand
Answer: 3,020,000
Step-by-step explanation:
three million twenty thousand
Answer: 3,020,000
Step-by-step explanation: 3,000,000 + 20,000 = 3020000
The ratio of Mr.X's score to Mr.Y's score was 8:9. If Mr.Y had scored 30 marks lower, the ratio would have had been 4:3. How many marks did Mr.Y score?
Answer:
Step-by-step explanation:30 x 2 = 60 because 8:9 get simplify by 2 and you just times the 30 with 2
Answer:
Let the common multiple be x
John's score is 8x Peter's is 9x
8x/9x-30=4/3
24x=36x-120
12x=120
x=10
John's score is 8 x 10=80
Correct me if im wrong:)
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which of the following is most likely to be possible? group of answer choices making a grouped frequency table from an ordinary frequency table making a normal curve from a bimodal distribution making an ordinary frequency table from a grouped frequency table making a bimodal distribution from a normal curve
The most likely option (b) to be possible is making a grouped frequency table from an ordinary frequency table.
A frequency table is a way of organizing data into classes or categories based on the number of times a particular observation or value occurs.
Now, let's examine the options provided. Making a grouped frequency table from an ordinary frequency table is possible, as we can simply group the values into intervals and calculate the frequencies for each interval. This allows us to better visualize and understand the distribution of the data.
Making a normal curve from a bimodal distribution is not possible, as a bimodal distribution has two distinct peaks or modes, while a normal distribution has only one. A normal curve is symmetrical and bell-shaped, and represents a continuous distribution of values.
Making an ordinary frequency table from a grouped frequency table is also possible, as we can simply list the intervals or classes and their corresponding frequencies, without the need to group them into intervals.
Finally, making a bimodal distribution from a normal curve is possible, as we can add two normal distributions with different means and standard deviations to create a bimodal distribution. However, it is important to note that a bimodal distribution may not always be appropriate for the given data.
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an army regiment with 400 soldiers has provision for 80 days. if 80 soldiers moved out of the regiment, how long would the food last at the same rate?
Answer: If the army regiment had 400 soldiers with provisions for 80 days, the food would last each soldier for 80 days / 400 soldiers = 0.2 days per soldier.
If 80 soldiers moved out, the number of soldiers remaining in the regiment would be 400 soldiers - 80 soldiers = 320 soldiers.
Since the amount of provisions has not changed, the food would last for 80 days / 320 soldiers = 0.25 days per soldier.
Therefore, the food would last the 320 soldiers for 0.25 days * 320 soldiers = 80 days.
Step-by-step explanation:
Solve for x *
est
45
O x = 50
O x = 8
O x = 48.2
O x = 40.5
20
S
18
R
The value of x for the similar triangles is given as follows:
x = 40.5.
What are similar triangles?Similar triangles share these two features:
Congruent angles, that is, angles that have the same measure.Proportional side lengths.A bisection divides a triangle into two similar triangles, hence the proportional relationship for the side lengths is given as follows:
x/45 = 18/20
18/20 = 0.9, hence:
x/45 = 0.9
x = 45 x 0.9
x = 40.5.
Meaning that the fourth option is the correct option.
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Fill in the table using this function rule.
y=2x-4
3
5
7
9
y
Answer:12
16
20
44 these are the answers
Step-by-step explanation:
Last week, Vanessa bought 14 shirts and 6 hats for a total of $198.
Today, Vanessa bought 10 shirts and 6 hats for a total of $150.
Assuming neither item has changed in price, what is the cost of a
shirt in dollars?
khora
Answer: Shirt-$12 Hat-$5
Step-by-step explanation:
14T + 6H = 198
10T + 6H = 150
4T=48
T=12$
10(12)+6H = 150
120 + 6H =150
H = 5$
54 is what percent of 200?
PLEASE GIVE BRAINLIEST!
thank you and have a good day :)
Answer:
27%
Step-by-step explanation:
a percent is a part of 100
so if we get the denominator to 100, the numerator is the percent of the equation
54/200
in order to get 200 to 100, we have to divide by 2.
however we have to divide the numerator aswell as if we don't, we simply just half the equation.
54/2 = 27
200/2 = 100
27/100 is the new equation. referring back to the first statement, i made, the numerator would be the percent of the equation that is a part of 100
27%.
54/200 is equal to 27/100. all we did was divide both the numerator and denominator by 2.
Michael runs a distance of 5 1/4 miles in 45 3/4 minutes during a race. Which statements correctly represent
Michael's race? Select ALL the correct answers.
A. Michael's unit rate of minutes per mile was about 8.7.
B. Michael's average pace was about 0.11 miles per minute.
C.
Michael's unit rate of minutes per mile was about 6.9.
D. Michael's average speed during the race was about 6.9 miles per hour.
E.
Michael ran about 8.7 miles in 1 minute.
eria wall
Answer:
A. Correct
B. Correct
C. Not correct
D. Correct
E. Not correct
Step-by-step explanation:
We are told that Michael's race numbers are:
5.25 miles
45.75 minutes
Divide the miles by the minutes to get mIchael's running rate:
0.114754098 mi/min
This result matches option B. " Michael's average pace was about 0.11 miles per minute."
======
Check all the answer options:
A. Michael's unit rate of minutes per mile was about 8.7.
Take 0.11475409 mi/min and invert it to find min/mile:
1/(0.11475409 mi/min) = 8.71 min/mile
This is a correct statement.
B. Michael's average pace was about 0.11 miles per minute.
From above: This is a correct statement.
C. Michael's unit rate of minutes per mile was about 6.9.
Take the given numbers: (45.75 minutes)/(5.25 miles) = 8.71 min/mile
This is not a correct statement.
D. Michael's average speed during the race was about 6.9 miles per hour.
Take the calculated rate of 0.11475409 mi/min and covert it to miles/hour:
Use the conversion factor (60 min/1 hr)
(0.11475409 mi/min)*((60 min/1 hr)) = 6.89 miles/hr
This is a correct statement.
E. Michael ran about 8.7 miles in 1 minute.
We know from above that he runs at 6.89 miles per hour. Running 8.7 miles in 1 minute would mean he is running at (8.7)*(60) = 413 miles/hour.
Perhaps he had some good energy bars, but the data do not support this conclusion.
This is not a correct statement.
since the mode is the most frequently occurring data value, it group of answer choices is always larger than the mean can never be larger than the mean none of these alternatives is correct. is always larger than the median
Since the mode is the most frequently occurring data value so -
Option D : None of the alternatives is correct.
What is mode?
A mode is described as the value in a group of values that occurs more frequently. The value that appears the most frequently is called mode.
The distribution of the mean, median, and mode values will depend on how skewed the distribution is.
The total dependency of mean, median and mode of data is on the asymmetric form of the data.
As a result, mean or mode may be larger than or less than mode.
Therefore, the mode is neither large than mean or median and can never be larger than mean.
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Eric owes his brother $17. He recently got some money for his birthday and plans to use some of it to pay his brother back. Use the variable to represent the amount of money Eric got for his birthday, and use this variable to write an expression for the amount of money Eric will have left after he pays his brother back. Choose the expression for the amount of money Eric has after he pays his brother back.
A. 17-x
B. x-17
C. 17x
D. x+17
The expression for the amount of money Eric has after he pays his brother back is x- 17.
What is Expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
Given:
Eric owes his brother $17.
let x be the amount of money Eric got for his birthday.
If Eric gave the money back to his brother then he left with
= x - 17
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a student has scores of 77, 77.25, and 81.25 on his first three tests. he needs an average of at least 80 to earn a grade of b. what is the minimum score that the student needs on the fourth test to ensure a b?
The student needs a minimum score of 84.5 on the fourth test to ensure a grade of B.
To find the minimum score the student needs on the fourth test, we can use the formula for the average of four numbers:
Average = (sum of the numbers) / 4
We know that the student needs an average of at least 80 to earn a grade of B, and we also have the scores for the first three tests: 77, 77.25, and 81.25. So, we can set up the equation:
80 = (77 + 77.25 + 81.25 + x) / 4
where x is the score the student needs on the fourth test. Solving for x:
80 = (235.5 + x) / 4
320 = 235.5 + x
x = 320 - 235.5
x = 84.5
So, the student needs a minimum score of 84.5 on the fourth test to ensure a grade of B.
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At a restaurant, Gabe buys 1 cheese pizza and 3 pepperoni pizzas. A cheese pizza costs $11.00. In total, Gabe spends $57.59, including 6% tax on the cost of the pizza and a $3.00 tip.
What is the cost of each pepperoni pizza?
Answer:
$13.53
Step-by-step explanation:
Let's call the cost of a pepperoni pizza x.The total cost of the cheese and pepperoni pizzas before tax and tip is 1 * $11.00 + 3 * x = $57.59 - $3.00Simplifying the expression on the right side: $54.59 - $3.00 = $51.59Now we can solve for x:1 * $11.00 + 3 * x = $51.593 * x = $51.59 - $11.003 * x = $40.59x = $13.53So each pepperoni pizza costs $13.53
Jana needs to rent a moving van for one day. Reliable Rentals charges $20 for the day and $0.50
for each mile. Dependable Rentals charges $10 for the day and $0.80 for each mile. Jana wrote
and solved the equation below to find the number of miles for which the costs of renting from the
companies will be the same. She used m to represent the number of miles.
20-0.5m= 10+ 0.8m
20= 10 + 1.3m
10 = 1.3m
= 13 = 100 = 77/3
The costs will be equal if the van is driven about 8 miles.
m=
Answer:
20 + .50M = 10 + .80M subtract .50M, 10 from both sides
10 = .30M divide both sides by .30
10 / .30 = M = about 33 + 1/3 miles driven equalize the cost
[Jana used " -.50M" in the original set up instead of " +.50M" ]
Step-by-step explanation:
what are the multiplicative inverses of the other elements (you may want to use trial and error for finding the inverses)?
To find the multiplicative inverse of an element in a set, we need to find another element in the set that, when multiplied by the first element, gives the multiplicative identity element. All elements in the set have a multiplicative inverse except for 0.
To find the multiplicative inverse of an element in a set, we need to find another element in the set that, when multiplied by the first element, gives the multiplicative identity element (usually 1).
For example, in the set {1, 2, 3, 4, 5} under multiplication modulo 6, we have:
The multiplicative inverse of 1 is 1 (1 x 1 = 1 mod 6).
The multiplicative inverse of 2 is 4 (2 x 4 = 8 = 1 mod 6).
The multiplicative inverse of 3 is 5 (3 x 5 = 15 = 3 x 1 = 1 mod 6).
The multiplicative inverse of 4 is 2 (4 x 2 = 8 = 2 x 4 = 1 mod 6).
The multiplicative inverse of 5 is 3 (5 x 3 = 15 = 3 x 5 = 1 mod 6).
Note that every element in the set has a multiplicative inverse except for 0. This is because any number multiplied by 0 is 0, not 1.
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What is the shape of the graph of the function? g(x)= 3/2 ⋅( 2/3 ) ^x
Answer:
Shape of the graph is exponentially decreasing
The horizontal asymptote is y = 0
The y intercept is at x = 0 and is at y = 3/2
Graph attached
Step-by-step explanation:
Not sure what exactly the question is asking for.
Here is what I figured out
Shape of the graph is exponentially decreasing
The horizontal asymptote is y = 0
The y intercept is at x = 0 and is at y = 3/2
We can also rewrite this equation as:
[tex]g(x) = \dfrac{3}{2} \cdot \dfrac{2}{3} \cdot \left(\dfrac{2}{3}\right)^{x-1}\\\\\\= \left(\dfrac{2}{3}\right)^{x-1}[/tex]
how many three-digit numbers satisfy the property that the middle digit is the absolute value of half the difference of the first and the last digits?
A total of [tex]10 + 4 + 4 = \boxed{18}[/tex] three-digit numbers that satisfy the given property.
Let the three-digit number be written as abc, where a, b, and c are the hundreds, tens, and ones digits, respectively. We want b to be the absolute value of half the difference between a and c. In other words, we want b = [tex]\left|\frac{a-c}{2}\right|.[/tex]
Since a, b, and c are digits, we know that [tex]0 \leq a, b, c \leq 9.[/tex] Since b is the absolute value of a number, we know that b is non-negative.
Case 1: [tex]a \geq c[/tex]
If [tex]a \geq c[/tex], then[tex]b = \frac{a-c}{2}[/tex]. Since b must be non-negative, we have two
subcases to consider:
Subcase 1: a=c
In this subcase, b=0, which means that the number abc is of the form a00, where [tex]0 \leq a \leq 9[/tex]. There are 10 such numbers.
Subcase 2: a>c
In this subcase, [tex]b = \frac{a-c}{2}[/tex] is a positive integer. Since a and c must have the same parity (i.e., they are either both even or both odd), we have two
sub-subcases to consider:
Sub-subcase 1: a and c are both even
In this sub-subcase, a and c are both integers between 0 and 8 inclusive (since they are even and cannot be equal to 0 or 9). There are 4 such pairs of values for a and c: (2,0), (4,2), (6,4), and (8,6). For each pair, the value of b is uniquely determined, so there are 4 corresponding numbers abc.
Sub-subcase 2: a and c are both odd
In this sub-subcase, a and c are both integers between 1 and 9 inclusive (since they are odd and cannot be equal to 0 or 8). There are 4 such pairs of values for a and c: (9,7), (7,5) , (5,3), and (3,1). For each pair, the value of b is uniquely determined, so there are 4 corresponding numbers abc.
Case 2: a < c
If a < c, then[tex]b = \frac{c-a}{2}[/tex]. Since b must be non-negative, we have only one
subcase to consider:
Subcase: c- a is even
In this subcase, c-a is an even integer between 2 and 8 inclusive (since it cannot be equal to 0 or 9). There are 4 such even integers: 2, 4, 6, and 8. For each even integer, the values of a and c that satisfy c-a are uniquely determined, and the value of b is then uniquely determined. So there are 4 corresponding numbers abc.
Putting everything together, we have a total of [tex]10 + 4 + 4 = \boxed{18}[/tex] three-digit numbers that satisfy the given property.
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which of these statements about a normally distributed data set is true? a.) the smaller the standard deviation, the less concentrated the data will be. b.) the concentration of the data set is not related to the standard deviation. c.) the smaller the standard deviation, the more concentrated the data will be. d.) the greater the standard deviation, the more concentrated the data will be.
The Statement which is true is (c) the smaller the standard deviation, the more concentrated the data will be.
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
A standard deviation close to zero indicates that data points are close to the mean, whereas a high or low standard deviation indicates data points are respectively above or below the mean.
The smallest possible value for the standard deviation is 0, and that happens only in contrived situations where every single number in the data set is exactly the same
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if written backwards, the number, one thousand, one hundred twenty-five, would be written five thousand, two hundred eleven.
True False
The statement "if written backwards, the number, one thousand, one hundred twenty-five, would be written five thousand, two hundred eleven " is true
The given statement is
If written backwards, the number, one thousand, one hundred twenty-five, would be written five thousand, two hundred eleven
We have to check the given statement is true or false
The given number is
One thousand one hundred and twenty five
Write the number in numeric terms
One thousand one hundred and twenty five = 1125
Write the number in backwards
= 5211
Then the number will be
Five thousand two hundred and eleven
Therefore, the given statement is true
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Meredith's new Pomeranian puppy is 7 inches tall and 9 inches long. She wants to make a drawing of her new Pomeranian to put in her locker. If the sheet of paper she is using is 3 inches long by 5 inches, find an appropriate scale factor for Meredith to use in her drawing. (please answer I need help)
Answer:
2.3333 inches
Step-by-step explanation:
To find the appropriate scale factor, we need to determine how many times smaller the piece of paper is compared to the dog. We can start by finding the ratio of the length of the paper to the length of the dog:
3 inches / 9 inches = 1/3
Similarly, the ratio of the width of the paper to the height of the dog is:
5 inches / 7 inches = 5/7
So, the smaller of these two ratios, 1/3, is the appropriate scale factor for Meredith to use in her drawing. This means that the length of the dog in the drawing will be 9 inches * 1/3 = 3 inches, and the height will be 7 inches * 1/3 = 2.3333 inches.
an airline would like to decide on an appropriate flight overbooking policy. since a certain percentage of ticketed passengers will cancel at the last minute, to avoid empty seats, they sell more tickets than there are seats, hoping that just about the right number of passengers will show up. we will assume that the rate of passages that cancel a flight at the last minute is equal to 5%. for a flight with 220 seats, the airline wants to find how sensitive various probabilities are to the number of tickets it issues. first, estimate the number of tickets to be sold such that, on average, all the seats in the flight will be occupied. second, using an appropriate probabilistic model, compute:
The probability of the flight being overbooked is 0.38742 or 38.7%.
To calculate the probability of the flight being overbooked, we need to use a probability formula. In this case, we can use the binomial probability formula. The formula is as follows:
[tex]P(x) = ^nC_x * p^x * q^{(n-x)}[/tex]
Where:
P(x) is the probability of x number of events occurring.
n is the total number of trials.
p is the probability of success.
q is the probability of failure.
nCx is the number of ways to choose x items from a set of n items.
Let's say a plane has 8 seats. The airline sells 10 tickets for this flight. The probability of all ten passengers showing up for the flight is quite low. Based on past experience, the airline knows that only 90% of ticketed passengers usually show up for a flight. This percentage is also known as the "show-up rate."
In our case:
n = 10 (total number of passengers)
p = 0.9 (probability of a passenger showing up)
q = 0.1 (probability of a passenger not showing up)
We want to find the probability of having more than 8 passengers show up, which would mean the flight is overbooked. To do that, we need to calculate the probability of having 9 or 10 passengers show up. We can use the formula to calculate this:
P(9 or 10) = P(9) + P(10)
P(9 or 10) = ¹⁰C₉ x 0.9⁹ x 0.1¹ + ¹⁰C₁₀ x 0.9¹⁰ x 0.1⁰
P(9 or 10) = 0.38742 or 38.7%
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Complete Question:
Airlines usually overbook for a flight (sell more tickets than the numbers of available seats). They do this because they know from past experience that only 90% of ticketed passengers actually show up for the flight.
A plane has 8 seats. If the airline sells 10 tickets for this flight, what is the probability that the flight will be overbooked?
Which equation correctly represents the statement shown?
The value of t is 41 more than 24.
A.
t = 41 + 24
B.
t = 41 × 24
C.
24 = t ÷ 24
D.
41 = t − 24
Answer:
option A is the correct answer.
helppppppppppppppppppppppppppp
Answer: x = 6 (look at the image for the solution)
Step-by-step explanation:
Answer: the answer is 35
Step-by-step explanation:
find the pythageoran theorem of the thing and then solve
the area of a rectangular rug is 49x^2-25y^2 in. Use factoring to find possible dimensions of the rug. How are the side lengths related? what value would you need to subtract from the longer side and add to the shorter side for the rug to be a square.
Answer:
Step-by-step explanation:
We can write the area of the rug as:
Area = 49x^2 - 25y^2
To find possible dimensions of the rug, we need to factor the expression on the right side. We can factor out 49 and 25 to get:
Area = 49 * x^2 - 25 * y^2
Area = 7 * 7 * x^2 - 5 * 5 * y^2
So, the area of the rug can be written as the product of two binomials, each of which represents one of the side lengths.
Therefore, one possible set of dimensions for the rug is 7x and 5y, and another possible set is -7x and -5y. Note that the dimensions are related in that the width of the rug is proportional to 7x, and the length is proportional to 5y.
To make the rug a square, the sides must be equal in length. To find the value that would need to be subtracted from the longer side and added to the shorter side, we take the difference between the two possible side lengths:
7x - 5y = (7x + 5y) - 2 * 5y = (7x + 5y) - 10y
So, to make the rug a square, you would need to subtract 10y from the longer side (7x) and add 10y to the shorter side (5y). This would result in both sides being equal to (7x + 5y)/2, making the rug a square.
I will mark BRAINLIEST. Can someone please answer these two questions for me please.
The height of the plane is 1023 meters and the height of the tree is 307 feet.
What are the solutions to the trigonometric questions?Given the data in question 9, this forms a right-triangle.
Angle θ = 12°Opposite to angle θ = xAdjacent to angle θ = 4812mValue of height x = ?To determine the height of the plane x, we use trigonometric ratio
Tangent = Opposite / Adjacent
tan( 12 ) = x / 4812m
x = tan( 12 ) × 4812m
x = 1023m
Therefore, the height of the plane is 1023 meters.
Option A) 1023 meters is the correct answer.
Given the data in question (10)
Angle θ = 62°Adjacent to angle θ = 160ftOpposite to angle θ = xHeight of tool = 6ftSolve for x using trigonometric ratio,
Tangent = Opposite / Adjacent
tan( 62 ) = x / 160ft
x = tan( 62 ) × 160ft
x = 301ft
Now, height of the tree will be;
Height = x + height of tool
Height = 301ft + 6ft
Height = 307 ft
Therefore, the height of the tree is 307 feet.
Option D) 307 feet is the correct answer.
Learn more about trigonometric ratio here: brainly.com/question/28016662
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