The quotient is x³-3x²-3x+9 and the remainder is -33.
What is synthetic division?Synthetic division is a method used to perform the division operation on polynomials when the divisor is a linear factor.
When we divide a polynomial p(x) by a linear factor (x - a) (which is a polynomial of degree 1), Q(x) is the quotient polynomial and R is the remainder.
p(x)/q(x) = p(x)/(x- a) = Quotient + (Remainder/(x - a))
p(x)/(x - a) = Q(x) + (R/(x - a))
Given that, (x⁴-12x²-6)/(x+3)
Here, (x⁴+0x³-12x²+0x-6)/(x+3)
Now,
-3| 1 0 -12 0 -6|
| -3 9 9 -27|
________________
1 -3 -3 9 |-33
So, remainder = -33 and quotient = x³-3x²-3x+9
Therefore, the quotient is x³-3x²-3x+9 and the remainder is -33.
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White Oak is 15 miles from River City. What would its distance be on the map? WHOEVER ANSWERS GETS 30 POINTS
When White Oak is 15 miles from River City and the scale is 1 in.=3 mi, the distance in the map is 5 inches.
How to explain the scale?The ratio that describes the relationship between the actual figure and its model is called the scale. It serves as a representation of the actual figures in smaller units on maps. A scale of 1:5, for instance, means that 1 on the map is equivalent to the size of 5 in the real world.
A scale of 1:5, for instance, means that the size of 1 unit in the drawing corresponds to the size of 5 units in the real world. A scale of 1:5 is evident, for instance, if a giraffe that stands 150 inches tall in real life is depicted on the drawing as 30 inches tall.
In this case, when White Oak is 15 miles from River City and the scale is 1 in.=3 mi, the distance in the map is:
= 15 / 3
= 5 inches.
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Bryson's Dad is 38 years old. If this is four years than three times Bryson's age, how old is Bryson?
The age of Bryson today is 11 1/3 years
How to determine the age of Bryson today?From the question, we have the following mathematical statements:
Bryson's dad age = 38
Bryson's dad age = 4 + 3 * Bryson's age
Represent Bryson's age with x
So, we have the following equation
Bryson's dad age = 38
Bryson's dad age = 4 + 3x
substitute the known values in the above equation, so, we have the following representation
4 + 3x = 38
Evaluatet the like terms
3x = 34
Divide by 3
x = 11 1/3 years
Hence, Bryson's age as per the mathematical statement is 11 1/3 years
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Simplify the expression to a polynomial in standard form:(-x+4)(3x^2+3x+5)
deci nu știi să faci matematică?
if alen eats 7 apples and then 4 oranges 2 bananas how much calsium has he goten
Answer:
So there are 11 mg of calcium in apples.
38 mg of calcium in oranges.
And 6 mg of calcium in bananas.
So if he ate 7 apples, that adds up to:
7 * 11 = 77 mg of calcium.
4 oranges adds up to:
4 * 38 = 152 mg of calcium
2 bananas adds up to:
2 * 6 = 12 mg of calcium.
In total:
77 + 152 + 12 = 241
Alen ate 241 mg of potassium
Step-by-step explanation:
Hope it helps! =D
Jayden needed to get his computer fixed. He took it to the repair store. The technician at the store worked on the computer for 3. 75 hours and charged him $60 for parts. The total was $528. 75. Write and solve an equation which can be used to determine xx, the cost of the labor per hour
The required equation is x × 3 = 528.75 - 60.
The cost of the labor per hour is $156.25
How do equations work?
The definition of an equation is a mathematical statement with at least two terms that contain variables or equal numbers.
Let x be the cost of the labor per hour.
We know that
x × 3 = labor cost
60 + x × 3 = total cost
We also know that the total cost is $528.75
So we can write the equation:
60 + x × 3 = 528.75
Solving for x:
x × 3 = 528.75 - 60
x × 3 = 468.75
x = 468.75/3
x = 156.25
Therefore, the cost of the labor per hour is $156.25
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Davinder earns 4.5% interest per year on the money she has saved in her bank account.
She starts off with £200.
How much is in her account after five years?
Just enter the value
The amount of money in Davinder's account after five years is equal to £236.
How to calculate the simple interest and future value?Mathematically, simple interest can be calculated by using this formula:
S.I = PRT or S.I = A - P
Where:
S.I represents the simple interest.P is the principal or starting amount.R is the interest rate.A is the future value.T represents the time measured in years.Substituting the given parameters into the simple interest formula, we have;
S.I = 200 × 4.5/100 × 5
S.I = 200 × 0.045 × 4
S.I = £36.
Next, we would calculate the future value as follows;
Future value, A = S.I + P
Future value, A = £36 + £200
Future value, A = £236.
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How do you find the general solution of an exact differential equation?
The general solution of an exact differential equation can also be found by solving the associated homogenous equation and adding the particular solution obtained from the original equation.
1. Identify the exact differential equation.
2. Find the integrating factor by multiplying the equation by an expression of the form e^(f(x)).
3. Multiply the integrating factor with the equation to make it exact.
4. Integrate both sides of the equation to obtain the general solution.
5. Check the solution by differentiating it to confirm that it satisfies the original equation.
6. Add the particular solution obtained from the original equation to the homogenous solution to get the general solution.
The general solution of an exact differential equation can be found by using an integrating factor. An integrating factor is a function of the independent variable which can be multiplied with the equation in order to make it exact. Once the equation has been made exact, it can be solved using the standard integration techniques. In addition, the general solution can be found by solving the associated homogenous equation and then adding the particular solution obtained from the original equation.
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Iman ate 1/3 of a bag of popcorn.
His 4 friends ate equal shares of the remaining popcorn.
Which expression represents the popcorn that each friend ate?
Answer: 1/3 per friend.
Step-by-step explanation:1/3 1/6*4= 3/3 or 1 whole bag. to find the 1/6, 2/3 multiply by 1/4= 2/12 or 1/6 of popcorn per friend
Ned help PLEASE…………………
Answer:
0.82
Step-by-step explanation:
A： area =2( 0.8*0.6*+0.6*1+0.8*1) =2(0.48+0.6+0.8)=2*1.88 =3.76
B：area = 2(1.4*0.5+0.5*1.2+1.4+1.2) =2(0.7+0.6+1.68)=2*2.98=5.96
total 9.72
cost = $6.79* 9.72/80 =$0.82
What is the answer? What is the answer? What is the answer? What is the answer? What is the answer? What is the answer? What is the answer? What is the answer? What is the answer?
The amount of money Rashon would need to invest is equal to $8,300.46.
How to determine the value of equivalent quarterly interest rate?Mathematically, the compound interest on an investment can be calculated by using this mathematical expression:
A(t) = P(1 + r/n)^{nt}
Where:
A represents the future value.r represents the interest rate.n represents the number of times compounded.P represents the principal.T represents the time measured in years.In this scenario, Rashon's investment is compounded quarterly at an interest rate of 6.9% as follows:
Quarterly interest rate = 0.069/4
Quarterly interest rate = 0.01725%
20,200 = P(1 + 0.01725)^{4 × 13}
20,200 = P(1.01725)^52
20,200 = 2.4336P
Principal, P = 20,200/2.4336
Principal, P = $8,300.46.
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Answer:
In this scenario, Rashon's investment is compounded quarterly at an interest rate of 6.9% as follows:
Quarterly interest rate = 0.069/4
Quarterly interest rate = 0.01725%
20,200 = P(1 + 0.01725)^{4 × 13}
20,200 = P(1.01725)^52
20,200 = 2.4336P
Principal, P = 20,200/2.4336
Principal, P = $8,300.46.
The track team is hosting a bake sale to earn money for new uniforms. They are selling 3 different types of pies:
Apple, Pumpkin, & Key Lime.
They arrange the pies on 2 tables, with all the apple pies on one table and all the pumpkin & key lime pies on the other. Both tables have the exact same number of pies. There are twice as many pumpkin pies as key lime. There are 5 more apple than pumpkin pies.
Write & Solve a System of Equations to determine how many PUMPKIN pies they are selling.
Here is one possible system of equations to represent the information provided:
The system of equationsLet x be the number of apple pies, y be the number of pumpkin pies, and z be the number of key lime pies.
The number of apple pies is the same as the number of pumpkin and key lime pies combined, since both tables have the same number of pies: x = y + z
There are twice as many pumpkin pies as key lime pies: y = 2z
There are 5 more apple pies than pumpkin pies: x = y + 5
Solving for y in the second equation, we have: y = 2z
Substituting that into the first equation we have: x = 2z + z = 3z + 5
Substituting that into the third equation we have: x = y + 5 = 2z + 5
So we have a system of equations:
x = 3z + 5y = 2zNow we can solve for any of the variables. Let's find the number of PUMPKIN pies
y = 2z
We can substitute in any value of z to get y.
For example, if we let z=5, we can find that
y=2(5)=10 pumpkin pies
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James has x quarters. His brother has 4 times as many quarters as James has. How may quarters do they have altogether?
The total number of quarters James and his brother will be 5x
Addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.
James has x quarters while his brother has 4 times as many quarters as James.
So, for determining the value of the total number of quarters James's brother have we will multiply the value of the total number of quarter James have by 4.
So, the value of the total quarter James's brother has = 4*x = 4x
Now for determining the total number of quarters of James and his brother we will add both values.
The total number of quarters James and his brother will be= x+4x = 5x
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On a Cartesian plane sketch the region which represents the set of points for which x<2 and y>or= to 2
The inequality for this problem is defined as follows:
x < 2.y >= 2.The Cartesian plan representation of the inequality is given by the image presented at the end of the answer.
How to graph the inequality?The two conditions for the inequality are given as follows:
x < 2.y >= 2.These conditions are plotted as follows:
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a manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 418 gram setting. is there sufficient evidence at the 0.10 level that the bags are overfilled? based on a 24 bag sample, the manufacturer decides to reject the null hypothesis. what is the conclusion?
There is sufficient evidence at 0.10 level of significance that the machine is overfilling the bags. So the option 1 is correct.
A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 418 gram setting.
For the given question,
The Hypothesis for the test would be:
H(0): μ = 418
H(1): μ > 418
The fact that the null hypothesis is rejected means that there is enough data to conclude that the machine is significantly overfilling the bags at the 0.10 level of significance.
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The complete question is:
A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 418 gram setting. Is there sufficient evidence at the 0.10 level that the bags are overfilled? Based on a 24 bag sample, the manufacturer decides to reject the null hypothesis. What is the conclusion?
1. There is sufficient evidence at the 0.10 level of significance that the machine is overfilling the bags.
2. There is not sufficient evidence at the 0.10 level of significance that the machine is overfilling the bags.
1. Amanda goes to the bookstore and buys 4 comics and 1 novel, which together cost $19. Janelle goes to the same bookstore and buys 1 comic and 2 novels for $17. How much does each comic and each novel cost? adc
Each comic costs $4.71 and each novel costs $7.29.
What is the linear equation?
A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.
Let x be the cost of one comic and y be the cost of one novel.
From Amanda's purchase, we know that:
4x + y = $19
From Janelle's purchase, we know that:
x + 2y = $17
We can use the first equation to solve for y in terms of x:
y = $19 - 4x
We can substitute this expression for y into the second equation:
x + 2($19 - 4x) = $17
x + 2$19 - 8x = $17
-7x = $17 - 2$19
-7x = -$33
x = $33/-7 = $4.71
We can use this value of x to find the value of y:
y = $19 - 4($4.71) = $7.29
Hence, each comic costs $4.71 and each novel costs $7.29.
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The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 9 above 80 to 89, at 9 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Flower Town.
When comparing the data, which measure of variability should be used for both sets of data to determine the location with the most consistent temperature?
IQR, because Desert Landing is skewed
IQR, because Desert Landing is symmetric
Range, because Flower Town is skewed
Range, because Flower Town is symmetric
Range, because it measures the distinction between the highest and lowest values in a dataset, providing a clear estimate of variability for both sets of data. It is unaffected by skewness or symmetry, making it a useful measure of variability for comparing the temperature consistency of Desert Landing and Flower Town.
What is meant by histogram?A histogram is a rough illustration of how numerical values are distributed. Karl Pearson coined the phrase at the beginning.
A histogram is a visual representation of statistical data that makes use of rectangles to illustrate the frequency of data points over a range of successive numerical intervals of equal width. The independent variable and dependent variable are plotted along the horizontal axis and the vertical axis, respectively, in the most typical type of histogram.
A common tool for graphing is the histogram. It is employed to summarise continuous or discrete data that is measured on an interval scale. It is frequently used to provide a convenient manner of illustration for the main characteristics of the data distribution.
Therefore, the correct answer is both option c) and d) Range, because Flower Town is skewed and symmetric.
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Answer:
The correct answer is:
Range, because Flower Town is symmetric
For a scale drawing bathroom, 1/6 inch represents an actual length of 1 foot. If the bathroom measures 1 1/2 inches by 2 inches in the drawing, what are it's actual dimensions (length and width)?
Answer:
12ft x 9ft
Step-by-step explanation:
1/6" equals 1' actual ==> 1"=6'actual.
1.5" = 9'
2" = 12'
By utilizing the given scale of 1/6 inch equals 1 foot, the actual length of the bathroom is calculated to be 9 feet and width is 12 feet, from the given measurements of the drawing.
Explanation:The mentioned math problem is based on scale conversion, specifically in the realm of measurement. Given that every 1/6 inch on the scale drawing equals 1 foot in reality, the first step to solving this problem is to convert the measurements of the drawing into scale inches. To convert the length of 1 1/2 inches to the actual length, multiply 1.5 by 6 (as 1 inch is 6 times of 1/6 inch). This equals to 9 feet. Similarly, for the width of 2 inches, multiply 2 by 6 to get 12 feet.
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Find two positive numbers satisfying the given requirements.
The product is 154 and the sum is a minimum.
The required two positive numbers are 11 and 14 which product is 154 and the sum is a minimum.
What is the number system?A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9.
The product is 154 and the sum is a minimum.
As per the question, the required solution would be as:
product sum
1 x 154 1 + 154 = 155
2 x 77 2 + 77 = 79
11 x 14 11 + 14 = 25
7 x 22 7 + 22 = 29
Here, we can arrange these numbers as:
25 < 29 < 79 < 155
This means the sum (11 + 14 = 25) is a minimum.
So the minimum value = 11
And the maximum value = 14
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An alligators tail length is proportional to its body length. An alligator with a body length of 2.5 feet has a tail length of 2.8 feet. What is the tail length of an alligator whose body length is 9.2 feet?
Answer:
4.34
Step-by-step explanation:
proportional: 2.8/2.5 =1.12
body + tail = body + 1.12 body = 2.12 body = 9.2.
so body = 9.2/2.12 = 4.34
x≥ 0 in slope intercept form
y>4 in slope intercept form
x≤5 in slope intercept form
Please help quickly!!
The slope intercept form of the expressions are 0 ≤ x, y > 4 and 5 ≥ x
How to determine the inequalities in slope intercept form?From the question, we have the following parameters that can be used in our computation:
x≥ 0 in slope intercept formy>4 in slope intercept formx≤5 in slope intercept formThe slope intercept form of an inequality is represented as
y > mx + c
Note that the symbol > can be replaced by the appropriate inequality symbol
When the given expressions are rewritten, we have
0 ≤ x
y > 4
5 ≥ x
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3 ( � − 2 ) + � − 1 = 3(x−2)+x−1= 5 5
Answer: The equation provided is already solved, on the left side of the equation it shows the step by step solution of the equation:
3(x-2)+x-1 = 3(x-2) + x - 1 = 5
3x - 6 + x - 1 = 5
Combining like terms
4x - 7 = 5
Adding 7 to both sides
4x = 12
Dividing both sides by 4
x = 3
So the value of x that makes the equation true is x = 3
Step-by-step explanation:
A survey found that 12 out of every 15 people in the United States
prefer eating at a restaurant over cooking at home. If 400 people
selected eating at a restaurant on the survey, how many people
took the survey?
If 12 out of every 15 people prefer eating at a restaurant, then 12/15 of the people who took the survey chose that option. We know that 12/15 of the total number of people who took the survey is equal to 400 people, so we can set up the equation:
(12/15)x = 400
To find the total number of people who took the survey, we can solve for x by multiplying both sides of the equation by 15/12:
x = (400)(15/12)
x = 500
So, 500 people took the survey.
Write a function g(x) with a graph that is the reflection of the graph of f across the x-axis.
f(x) = - square root 14x
The function g(x) with a graph that is the reflection of the graph of f(x) = - square root 14x across the x-axis is given as follows:
[tex]g(x) = \sqrt{14x}[/tex]
How to obtain the function g(x)?The parent function f(x) is defined as follows:
[tex]f(x) = -\sqrt{14x}[/tex]
The rule for a reflection over the x-axis is given as follows:
g(x) = -f(x).
Meaning that only the signal of the function is changed.
Removing the negative signal, the function g(x) is then defined as follows:
[tex]g(x) = \sqrt{14x}[/tex]
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What equation should i us
Answer: C
Step-by-step explanation:
The length of the PR would be 82.
Option (A) is correct.
What is an expression?
An expression is a combination of numbers, variables, and mathematical operations that represents a value or a computation. Expressions can be simple or complex and can include constants, variables, and various mathematical operations such as addition, subtraction, multiplication, and division. Expressions are often used to represent mathematical operations in algebraic, trigonometric, and calculus problems. They can be evaluated to find a numerical value or simplified to reveal underlying mathematical relationships.
In the given figure, the length of both line segments is equal, hence
PR = 10x + 842
PQ + QR = 10x + 842
8x + 678 + 12 = 10x + 842
First we can subtract 12 from both sides of the equation:
8x + 678 = 10x + 830
Then we can subtract 8x from both sides of the equation:
678 = 2x + 830
Then we can subtract 830 from both sides of the equation:
-152 = 2x
Then we can divide both sides of the equation by 2:
x = -76
So PR = 8x + 678 + 12
PR = 8(-76) + 678 + 12
PR = -608 + 678 + 12
PR = -608 + 690
PR = 82
Hence, the length of the PR would be 82.
Option (A) is correct.
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Marshall has b buttons. He gives away 13 buttons. Write an expression that shows the number of buttons Marshall
has left.
Answer:
Since Marshall gives away 13 buttons out of b buttons, it means that b is an expression of a number which is greater than 13. Therefore,the answer is b - 13.
a data analyst for a phone company is analyzing the data of 150 of their customers, which accounts for 1% of their total customers. the analyst wants to determine the average number of hours each day a customer uses their phone, for calls and for texts, during a 30-day period. based on the data, the customers averaged 0.25 hours per day per call and 1.75 hours each day for texts. construct an equation in the correct form of y
Total number of a customer uses his phone each day in hour 0.25t + 1.75
Total number of a customer uses his phone each day in hour (e) = the customer spend time in hour on calls + the customer spend time in hour on texts.
total number of a customer uses his phone each day in hour (e) = the customer spend time in hour on calls + the customer spend time in hour on texts.
the customer spend time in hour on calls = the number of calls the customer made per day (t) times the average time spent by customers per day per hour (0.25 hours)
The number of hours the customer spend on texts is given as 1.75 hours each day.
Therefore required equation is:
e = 0.25t + 1.75
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Mrs. Cooper paid more than $22 for a pack of hand towels. Each towel cost $2.85. The hand towels were available in packs of 4, 5, 6, and 8. Use the inequality to find the minimum number of towels, t, in the pack.
Using inequality, the minimum number of towels in the pack is t = 6.
How to Find Minimum Number Using Inequality?We can start by using the inequality 2.85t > 22, where t is the number of towels in the pack.
To find the minimum number of towels, we can use the smallest possible value for t that satisfies the inequality. Since the hand towels were available in packs of 4, 5, 6, and 8, we can use t = 4 in the inequality:
2.85(4) > 22
Simplifying the left side of the inequality gives:
11.4 > 22
This is not true, so t = 4 does not satisfy the inequality.
Next, we can use t = 5:
2.85(5) > 22
Simplifying the left side of the inequality gives:
14.25 > 22
This is also not true, so t = 5 does not satisfy the inequality.
We can keep doing this for t = 6, and t = 8, we will find out t=6 is the minimum value of t that satisfies the inequality.
2.85(6) > 22
Simplifying the left side of the inequality gives:
17.1 > 22
This is true, so t = 6 is the minimum number of towels in the pack.
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96x2let be the inverse function of . take to be an output of the function . that is, and . (a) which statement best describes ?
The output of a function is returned by the inverse function, which also returns the initial value. Consider the inverse relationship between the functions f and g: f(g(x)) is g(f(x)) is x.
How can you determine a function's inverse?Write the function y as a function of x, i.e., y = f(x), and then solve for x as a function of y, to determine the inverse of a function.
steps for determining a function's inverse.
In the equation expressing the function, swap out f(x) with y.
Swap out x and y. To put it another way, swap out every x for a y and vice versa.
Solve for y.
Change y to f-1 (x).
The output of a function is returned by the inverse function, which also returns the initial value. Consider the inverse relationship between the functions f and g: f(g(x)) = g(f(x)) = x.
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Rachel is making a tent. The triangular piece of fabric for the front of her tent has an area of 24 ft. ². Find the height of the fabric if it is 6 feet long at it's base. 
The height of the fabric is 8 ft.
Now, According to the question:
Rachel is making a tent.
The triangular piece of fabric for the front of her tent has an area of 24 [tex]ft^2[/tex]
and, it is 6 feet long at it's base.
We have to find the height of the fabric .
Now, Based on the given condition:
Formulate the problem:
24 × 2 ÷ 6
Cross out the common factor:
4 × 2
Calculate the product or quotient :
= 8
Hence, the height of the fabric is 8 ft.
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A net of a rectangular pyramid is shown. The rectangular base has length 25 ft and width 22 ft. The net of the pyramid has length 74.8 ft and width 70.4 ft. Find the surface area of the pyramid.
The surface area of the pyramid is 1702.8 ft².
What is Surface Area?The area of a three dimensional object on it's outer surface is called the surface area of the object.
Rectangular pyramid has a rectangular base and four triangular faces.
Net of the pyramid is shown below.
Area of the rectangular base = 25 × 22 = 550 ft²
Now we have to find the area of four triangular faces.
Area of a triangle = [tex]\frac{1}{2}[/tex] × base × height
Heights of the triangle BCX and ADZ can be found as below :
Combined height of both triangles = 74.8 - 25 = 49.8
Height of each triangle = 49.8 / 2 = 24.9 ft
Area of triangles BCX and ADZ = 2 × ( [tex]\frac{1}{2}[/tex] × base × height)
= Base × height
= 22 × 24.9
= 547.8 ft²
Similarly,
Combined height of triangles ABW and CDY = 70.4 - 22 = 48.4
Height of each triangle = 48.4 / 2 = 24.2 ft
Area of triangles ABW and CDY = Base × height
= 25 × 24.2
= 605 ft²
Total surface area of the pyramid = 550 ft² + 547.8 ft² + 605 ft²
= 1702.8 ft²
Hence 1702.8 ft² is the total surface area of the pyramid.
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