The answer to the all questions was solved by the methods of factoring:
b. (x+6)(2x+3)c. (x-2)(x-18)a. (2x-3)(x+1)2b. 2(x-2)(4x+1)What is factoring?Factoring is the process of breaking down a mathematical expression or equation into simpler components, such as factors that when multiplied together give the original expression.
In the given questions,
1.Factoring 2x² + 9x + 18:
First, we need to find two numbers that multiply to 2×18=36 and add up to 9.The numbers are 6 and 6, since 6×6=36 and 6+6=12, but we need to adjust them to fit the middle term, which is positive.Therefore, we use 6 and 3: 6×3=18 and 6+3=9.We can write the expression as: 2x²+ 6x + 3x + 18.Now we can factor by grouping: (2x+6)(x+3).The answer is (a) (2x+6)(x+3).2.Factoring x² - 20x + 36:
First, we need to find two numbers that multiply to 36 and add up to -20.The numbers are -2 and -18, since -2×(-18)=36 and -2+(-18)=-20.We can write the expression as: x² - 2x - 18x + 36.Now we can factor by grouping: (x-2)(x-18).The answer is (d) (x-2)(x-18).3.Factoring 2x² - 5x - 3:
We can start by multiplying the first and last coefficients: 2×(-3)=-6.We need to find two numbers that multiply to -6 and add up to -5.The numbers are -6 and 1, since -6×1=-6 and -6+1=-5.We can write the expression as: 2x² - 6x + x - 3.Now we can factor by grouping: (2x-3)(x+1).The answer is (a) (2x-3)(x+1).4.Finding the greatest common factor of 8x² + 18x + 4:
We can start by factoring out any common factors of the coefficients, which is 2.Then we need to find the greatest common factor of the terms with x.The terms are 8x^2 and 18x, and the greatest common factor is 2x.The constant term, 4, is a factor of 2, so we can factor out another 2.The greatest common factor is 2(2x² + 9x + 2).The answer is (d) 4x.5.Factoring 8x² + 18x + 4:
First, we need to factor out any common factors, which is 2.Then, we can follow the steps:STEP 1* - Slide and Multiply the First Number to the Last: (2x+1)(4x+2).STEP 2 - Factor - What Multiplies to get the Last Number and Adds to get the Middle Number? The last number is 2, and the only factors are 1 and 2, which add up to 3, not 9. Therefore, the expression is prime and cannot be factored further.The answer is none of the given options.To know more about factoring expression, visit:
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11 Sabina travels from London to Telford.
A ticket from London to Telford normally costs £65.25
Sabina gets off the cost of the ticket.
Amir travels by train from London to Coventry and then from Coventry to Telford.
The ticket from London to Coventry costs £23.75
The ticket from Coventry to Telford costs £14.95
Work out the difference between the cost of Sabina's journey and the cost of
Amir's journey.
"I have to say a lot of people have been asking this question. No, really. A lot of people come up to me and they ask me. They say, 'What's 2+2?' And I tell them look, we know what 2+2 is. We've had almost eight years of the worst kind of math you can imagine. Oh my god, I can't believe it. Addition and subtraction of the 1s the 2s and the 3s. Its terrible. Its just terrible. Look, if you want to know what 2+2 is, do you want to know what 2+2 is? I'll tell you. First of all the number 2, by the way I love the number 2. It's probably my favorite number, no it is my favorite number. You know what, it's probably more like the number two but with a lot of zeros behind it. A lot. If I'm being honest, I mean, if I'm being honest. I like a lot of zeros. Except for Marco Rubio, now he's a zero that I don't like. Though, I probably shouldn't say that. He's a nice guy but he's like, '10101000101', on and on, like that. He's like a computer! You know what I mean? He's like a computer. I don't know. I mean, you know. So, we have all these numbers and we can add them and subtract them and add them. TIMES them even. Did you know that? We can times them OR divide them, they don't tell you that, and I'll tell you, no one is better at the order of operations than me. You wouldn't believe it. That I can tell you. So, we're gonna be the best on 2+2, believe me. OK? Alright. Thank you." Reporter 1: "But what actually is 2+2?" Trump: "Siddown. No, siddown. I've already answered your question. Haven't I already answered your question. This is what we get from news reporters, folks. Give me a nice question. Yes - you." Reporter 2: "Is your name Donald Trump?" Trump: "Now that's a nice question, folks. That's what I want."
The difference between the cost of Sabina's journey and the cost of Amir's journey is -£38.70.
We have,
The cost of Sabina's journey is £65.25.
Since she gets off the cost of the ticket, her journey is free, so the cost is £0.
Amir's journey consists of two segments:
London to Coventry and Coventry to Telford.
The cost of the London to Coventry ticket is £23.75, and the cost of the Coventry to Telford ticket is £14.95.
Difference = Sabina's Journey Cost - Amir's Journey Cost
Difference = £0 - (£23.75 + £14.95)
Difference = £0 - £38.70
Difference = -£38.70
This means that Amir's journey is £38.70 more expensive than Sabina's journey.
Therefore,
The difference between the cost of Sabina's journey and the cost of Amir's journey is -£38.70.
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PLEASE HELP FAST!
QUESTION: Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Complete the proof
We can now prove that ∆GFE≈∆GCD by using the Transitive Property of Equality and Substitution. Since GF=EF and GC=DC, then ∆GFE≈∆GCD.
What is Transitive Property of Equality?The transitive property of equality states that if two numbers are equal to the same number, then they are equal to each other. This property is written mathematically as a = b and b = c, then a = c. This property is based on the idea of transitivity, which is the concept that if a thing is true of a first element, and the same thing is true of a second element, then it must be true of the combination of the two elements.
We will use the Transitive Property of Equality and Substitution to prove that ∆GFE≈∆GCD.
Step 1: Transitive Property of Equality
GF/GC=GE/GD (Given)
GE/GD=EF/DC (Given)
GF/GC=EF/DC
Step 2: Substitution
GF=1/2GC (Given)
GE=1/2GD (Given)
EF=1/2DC (Given)
GF=EF (Substituting the given values)
GC=DC (Substituting the given values)
Step 3: Prove
We can now prove that ∆GFE≈∆GCD by using the Transitive Property of Equality and Substitution.
Since GF=EF and GC=DC, then ∆GFE≈∆GCD.
Therefore, ∆GFE≈∆GCD is true.
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please help me find the area
The calculated area of the composite figure is 129 square units
Calculating the area of the composite figureGiven that we have
A composite figure
To find the area of a composite figure, you can break it down into smaller, simpler shapes whose areas you can calculate. Then you can add up the areas of these shapes to get the total area of the composite figure.
The area is then calculated as
Area = Trapezoid + Rectangle + Parallelogram + Triangle
Using the dimensions from the graph, we have
Area = 1/2 * (12 + 6) * 4 + 6 * 10 + 3 * 7 + 1/2 * 6 * 4
Evaluate
Area = 129
Hence, the area is 129 square units
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Given f(x)=5-3x, if f(x)=-19, find x.
please hep me with these 4 questions in math!!
for the first question, the simplest way I solve reflections is by making negatives positive and positives negative.
question 2:
pi is the irrational number as it does not end
question 3:
Slope is equal to -1/2 or -0.5
as it takes 2 units right to go down by 1 unit
Question 4:
C: $11
Write an equation in slope intercept form of the line that passes through the given points
The slope (m) is the change in y divided by the change in x, which represents the rate at which the line is rising or falling.the equation of the line in slope-intercept form is: [tex]y= -\frac{5}{2}x[/tex]
What is the slope-intercept form?To find the equation of a line in slope-intercept form, we need to determine the slope (m) and the y-intercept (b) of the line.
We can use the two given points to find the slope of the line using the slope formula:
[tex]m= \frac{y_2- y_1}{m_2 - m_1}[/tex]
Let's use the first two points $(-4,9)$ and $(-2,4)$:
[tex]m= \frac{4- 9}{-2 - (-4)}[/tex]
Now that we have the slope, we can use the point-slope form of the equation of a line to find the equation of the line:
[tex]y-y_1 = m (x-x_1)[/tex]
Let's use the point (-4,9)
[tex]y-9 = \frac{-5}{2} (x- (-4))[/tex]
simplifying
[tex]y - 9= \frac{-5}{2} (x+4)[/tex]
Multiplying both sides by 2:
[tex]2y- 18 = -5(x+4)[/tex]
Expanding the right side:
[tex]2y- 18 = -5x- 20[/tex]
Adding 20 to both sides:
[tex]2y + 2 = - 5x +2[/tex]
Subtracting 2 from both sides:
[tex]2y=-5x[/tex]
Dividing both sides by 2:
[tex]y= -\frac{5}{2}x[/tex]
Therefore, the equation of the line in slope-intercept form is: [tex]y= -\frac{5}{2}x[/tex]
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Hey guys I need help with this last one
Area of shaded region of the cuboid is 15cm², based on the given volume.
What is a cuboid?A cuboid is a solid form or a three-dimensional shape in geometry. A cuboid is a convex polyhedron that has six rectangular sides, eight vertices, and twelve edges. Another name for a cuboid is a rectangle prism. A cube is a cuboid with six square sides. A rectangular cube is a real-world illustration of a cuboid.
What is Volume?Each object in three dimensions takes up some room. The volume of this area is what is being evaluated. The area occupied within an object's boundaries in three dimensions is referred to as its volume. It is also referred to as the object's potential.
Finding an object's volume can help us calculate the quantity needed to fill it, such as the volume of water needed to fill a container, aquarium, or water tank.
Given volume of cuboid=75cm³
volume of cuboid is given by = lbh=75
where
l-length
b=breadth
h=height
h= 5cm
lbh=75
lb(5)=75
lb=75/5=15
we know that area of shaded region is given by l×b.
therefore the area=lb=15cm²
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Find the sum. -
3/4 + 1/2 =
Answer:
Is the problem -3/4 + 1/2 or 3/4 + 1/2?
I'll just do both then.
-3/4 + 1/2 = -1/4
3/4 + 1/2 = 5/4 or 1 1/4
Step-by-step explanation:
You're welcome.
Answer:
[tex] \frac{3}{4 } + \frac{1}{2} [/tex]
take lcm of denominators i.e. 4and 2
so, the lcm of 4 and 2 is 4.
[tex] \frac{3}{4} + \frac{2}{4} [/tex]
[tex] \frac{3 + 2}{4} [/tex]
[tex] \frac{5}{4} [/tex]
Step-by-step explanation:
hope this will be helpful:)
CAN SOMEONE HELP WITH THIS QUESTION?
The answer of the given question based on the logarithmic differentiation to solve with the respect to x the answer is the derivative of y = (6 + 6x)ˣ with respect to x is:
dy/dx = (6 + 6x)ˣ * [ln(6 + 6x) + x/(1 + x)].
What is Derivative?In calculus, derivative of function represents rate at which function is changing with respect to its input variable. It is fundamental concept in calculus and is used to study many physical, economic, and scientific phenomena.
To find the derivative of y = (6 + 6x)ˣ using logarithmic differentiation, we take the natural logarithm of both sides of the equation and then differentiate implicitly with respect to x.
Taking the natural logarithm of both sides of the equation gives:
ln(y) = x ln(6 + 6x)
we differentiate both sides of the equation with respect to x, using the chain rule on the right-hand side:
1/y * dy/dx = ln(6 + 6x) + x * 1/(6 + 6x) * 6
Simplifying the right-hand side gives:
1/y * dy/dx = ln(6 + 6x) + x/(1 + x)
Multiplying both sides by y gives:
dy/dx = y * [ln(6 + 6x) + x/(1 + x)]
Substituting y = (6 + 6x)ˣ gives:
dy/dx = (6 + 6x)ˣ * [ln(6 + 6x) + x/(1 + x)]
Therefore, the derivative of y = (6 + 6x)ˣ with respect to x is:
dy/dx = (6 + 6x)ˣ * [ln(6 + 6x) + x/(1 + x)]
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Dan is training for a bike race. He wants to bike 300 miles over the next couples of weeks. Dan biked 29 miles a day for 3 days. Then, he biked 32 miles a day for 4 days. How many more miles does he still have to bike to get to his goal of 300 miles?
A. Sara estimated that Dan would need to bike about 80 more miles to get to his goal of 300 miles. Is this a reasonable estimate? Why or why not?
B. Write an equation for this problem with a letter standing for the unknown quantity.
C. Solve the problem. Show your work.
Answer:
Step-by-step explanation:
a. Sara's estimate is reasonable because:
Dan has biked for 7 days so far, 29 miles for 3 days and 32 miles for 4 days.
If you round 29 and 32 up and down respectively to 30, then Dan will of have ridden about 30 * 7, or 120 miles so far. 300-120 is 80, so that is a good estimate.
b. If x stands for the miles Dan still needs to bike, then:
(29*3) + (32*4) + x = 300
c. 87 + 128 + x = 300
x = 85
Find the area of one stretcher course of 18 concrete blocks if the blocks are 6 3/8 in long and 4 in high, and if the mortar joints are 1/8 in thick. (Hint: 18 blocks require 17 mortar joints.)
The area of one stretcher course of 18 concrete blocks is 467 1/2 square inches.
What is Area of stretcher course ?
To find the area of a stretcher course, you need to know the dimensions of the bricks or blocks, the number of bricks or blocks in the course, and the thickness of the mortar joints between them. The formula for the area of a stretcher course is:
Area of stretcher course = (Number of bricks or blocks) x (Length + Width) x Height
where Length is the length of each brick or block, Width is the width of each brick or block, and Height is the height of each brick or block.
According to the question :
To find the area of one stretcher course of 18 concrete blocks, we first need to calculate the total length and height of the course, taking into account the thickness of the mortar joints.
Length of the course = 18 blocks x 6 3/8 inches per block = 114 3/4 inches
Total width of the course = 17 mortar joints x 1/8 inch per joint = 2 1/8 inches
Height of the course = 4 inches
To calculate the area of the stretcher course, we need to multiply the length, width, and height of the course:
Area of stretcher course = Length x Width x Height
Area of stretcher course = (114 3/4 + 2 1/8) x 4
Area of stretcher course = (116 7/8) x 4
Area of stretcher course = 467 1/2 square inches
Therefore, the area of one stretcher course of 18 concrete blocks is 467 1/2 square inches.
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88.128 x 0.5 Multiplication question
Answer:
44.064x
Step-by-step explanation:
Answer: when you time 88.128 by 0.5, it gives you an answer of 44.064
Hope this helps :)
True or false a triangle with no congruent sides is a scalene triangle
Answer:
true
Step-by-step explanation:
bcoz in iso triangle 2 sides are equal
and in equilateral all sides are equal
what led to the development of the aviation industry
a. the development of texas’ wwII aircraft training facilities
b. the placement of the johnson space center
c. the petrochemicals industry
d. texas’ location and climate
Texas' location and climate led to the development of the aviation industry.
What is the significance of Texas in the development of the aviation industry?
The development of the aviation industry in Texas can be attributed to its favorable geographical location and climate. Texas is located in the southern part of the United States, making it a strategic location for air travel between the east and west coasts of the country. Additionally, its warm and dry climate provided ideal conditions for flight testing and training.
Reason what led to the development of the aviation industry :
Texas has a long history of aviation, with the Wright brothers conducting one of their earliest flight demonstrations in the state in 1910. The establishment of military bases during World War II and the subsequent development of aircraft training facilities in Texas further fueled the growth of the aviation industry in the state. Additionally, the placement of the Johnson Space Center in Houston helped to establish Texas as a hub for aerospace research and development. However, it is Texas' favorable location and climate that truly made it a prime location for the aviation industry. Its central location made it a strategic location for air travel and logistics, while its warm and dry climate provided ideal conditions for flight testing and training. Today, Texas remains one of the top states for aviation and aerospace industries, with major airports, aircraft manufacturers, and research institutions located throughout the state.
Therefore, option (d) is correct.
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If Big Bun won 5 out of 25 matches, what percent did he win? A 25% B 20% C 15% D 10%
Answer:20%
Step-by-step explanation:
5(100)/25=20
Samir and Kylie are making fruit salads for a picnic. Samir mixes 1 cup of melon and 3 cups of apple and Kylie mixes 2 cups of melon and 9 cups of apple. Use Samir and Kylie’s percent of melon to determine whose fruit salad will taste more melony.
Answer:
Step-by-step explanation:
Samir total cups = 1 + 3 = 4
% melon = 1/4 x 100 = 25%
Kylie total cups = 2 + 9 = 11
% melon = 2/11 x 100 = 18%
Samir's is more melony. 25% > 18%
Regines father is given a yearly increase in salary of 15%. How much is he receiving now if he's salary 2 years ago was 25250
Regine's father is currently receiving a salary of 29037.50.
What is percentage increase?A percentage increase in mathematics is the proportion by which a quantity or value has grown in comparison to its initial value. It is computed by subtracting the original value from the new value, multiplying the result by 100, and then subtracting the difference between the two values. The percentage increase formula is:
(new value - original value) / 100% of the original value is the percentage increase.
The yearly increase is 15%, thus:
salary increase = 25250 x 0.15 = 3787.50
The current salary is:
current salary = salary from two years ago + salary increase
current salary = 25250 + 3787.50
current salary = 29037.50
Hence, Regine's father is currently receiving a salary of 29037.50.
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the area of a rectangle is 14 square units. it has the side length of x and y. given each value for x, find y.
1. x = 4 and 1/5
2. x = 2 and 1/3
3. x = 7/6
Answer:
1. y = 3 1/3
2. y = 6
3. y = 12
Step-by-step explanation:
A = xy => xy = 14 => y = 14/x
1. x = 4 1/5 = 21/5
y = 14/x = 14/(21/5) = (5 x 14)/21 = 10/3 = 3 1/3
2. x = 2 1/3 = 7/3
y = 14/x = 14/(7/3) = (3 x 14)/7 = 6
3. x = 7/6
y = 14/x = 14/(7/6) = (6 x 14)/7 = 12
You want to create a simulation of the following scenario:
In country x 50% of people have blood type O, 25% have blood type A, 12.5% have blood type B, and 12.5% have blood type AB.
In country y, 60% have blood type O, 20% have type A, 10% have type B and 10% have type AB.
What is the best way to assign values for a simulation using random digits table?
Choose answer from photo below! A, B, C, or D : this is the answer I want, not just an explanation please, thank you so much! 100 points!
Thank you :)
Answer: click thanks if you like my answer. have a good day <:
The best way to assign values for a simulation using a random digits table is to first identify the possible outcomes and assign a number or range of numbers to each outcome. Then, using the random digits table, randomly select digits and match them to the assigned outcomes.
For example, in the given scenarios for blood types in different countries, each blood type is assigned a specific number or range of numbers. Using the random digits table, the assigned numbers can be matched to the digits in the table to simulate the occurrence of each blood type in the population.
To answer the questions:
1.What is the purpose of assigning values for a simulation using a random digits table?
The purpose of assigning values for a simulation using a random digits table is to create a simulated scenario that reflects the likelihood of different outcomes based on assigned probabilities. This can help in making predictions and decisions in various fields such as medicine, finance, and social sciences.
2.In which scenario are blood types represented with the fewest number of digits?
Blood types are represented with the fewest number of digits in the third scenario for both Country X and Country Y. Blood type O is represented with 0, blood type A with 1, blood type B with 3, and blood type AB with 4, while all other digits are ignored.
3.In which scenario are blood types represented with the most number of digits?
Blood types are represented with the most number of digits in the first scenario for Country X, where blood type O is represented with 0, 1, 2, 3, 4, and 5, blood type A with 6 and 7, blood type B with 8, and blood type AB with 9. The same applies to Country Y in the first scenario.
Step-by-step explanation:
hope its help <:
what should target charge for a package of paper plates if they want to make a 75% profit on the plates that originally cost $9.00
Answer:
$15.75
Step-by-step explanation:
Ava is going on holiday with Fly Away airlines. The maximum weight her suitcase can be is 2020 kg.
When empty her suitcase weighs 33 kg.
The clothes she plans on taking have a combined weight of 55 kg.
Her electrical accessories have a combined weight of 44 kg.
She is also taking 55 hardback books, which each weigh 720720 g.
Finally, the toiletries she is taking have a combined weight of 46004600 g.
How much over the maximum weight will Ava's suitcase be? Give your answer in grams.
As a result, Ava's luggage will weigh 123622200 grams more than the permitted maximum.
What exactly is weight?Weight is the force of gravity that pulls objects toward the core of the Earth. The resulting force that pulls a substance toward Earth is known as gravity. In contrast to gravity force, which occurs among any two masses, this only occurs between Earth as well as a mass.
First, we need to convert all the weights to grams, since the weight limit is given in kilograms and the weights of clothes, electrical accessories, and toiletries are given in grams.
Maximum weight limit = 2020 kg = 2020000 g
Weight of empty suitcase = 33 kg = 33000 g
Weight of clothes = 55 kg = 55000 g
Weight of electrical accessories = 44 kg = 44000 g
Weight of 55 hardback books = 55 x 720720 g = 39639600 g
Weight of toiletries = 46004600 g
Total weight of suitcase and contents = 33000 + 55000 + 44000 + 39639600 + 46004600 = 125642200 g
Amount over maximum weight limit = total weight - maximum weight limit = 125642200 - 2020000 = 123622200 g
Therefore, Ava's suitcase will be over the maximum weight limit by 123622200 grams.
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What is the meaning of "concatenation is associative"?
The term "concatenation is associative" means that if we concatenating sequences or strings, the order in which it is performed does not matter.
What is the meaning of "concatenation is associative"?Basically, in mathematics, concatenation is the operation of joining two or more sequences or strings together. The meaning of "concatenation is associative" is that when concatenating three or more sequences or strings, the order in which the concatenation is performed does not matter.
This means that we can group the concatenation of any number of sequences or strings in any way we like, and the result will always be the same.
For example, given three strings A, B, and C, the following expressions would give the same result:
(A + B) + C
A + (B + C)
All these is because the order of concatenation does not affect the final outcome. The property of associativity is important in many areas of mathematics and computer science, such as algebra, programming, and database design.
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Bria is a customer who would like to display her collection of soap carvings on top of her bookcase. The collection needs an area of 300 square inches. What should b equal for the top of the bookcase to have the correct area? Round your answer to the nearest tenth of an inch.
(1 point) help me pls D;
please D:
b equal for the top of the bookcase to have the correct area= 5 cm2
What is surface area?A solid object's surface area is a measurement of the total area that the surface of the object takes up.
The definition of arc length for one-dimensional curves and the definition of surface area for polyhedra (i.e., objects with flat polygonal faces), where the surface area is the sum of the areas of its faces, are both much simpler mathematical concepts than the definition of surface area when there are curved surfaces.
A smooth surface's surface area is determined using its representation as a parametric surface, such as a sphere.
This definition of surface area uses partial derivatives and double integration and is based on techniques used in infinitesimal calculus.
Henri Lebesgue and Hermann Minkowski at the turn of the century sought a general definition of surface area.
L × b = 300
b = 300 / L
b = 300 / 60 = 5
Hence, b equal for the top of the bookcase to have the correct area= 5 cm2.
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Let the region R be the area enclosed by the function f(x) = ln (x) + 1 and
g(x)=x-1. If the region R is the base of a solid such that each cross section
perpendicular to the a-axis is a semi-circle with diameters extending through the
region R, find the volume of the solid. You may use a calculator and round to the
nearest thousandth.
The volume of the solid is 7.58 thousandths when rounded to the nearest thousandth.
What is area?Area is a measure of the size of a given space or the amount of a given surface. It can be measured in square feet, square meters, acres, hectares, and other units. Area can be used to describe the size of a two-dimensional shape or the surface area of a three-dimensional object. Area can also be used to calculate the amount of material needed to cover a given space, such as for a roof, carpet, or other covering.
To find the volume of the solid, we will use the following formula:
V=∫baπ(y2−(x−1)2)dx
Where b is the upper bound of the integral, a is the lower bound of the integral and y is the height of the solid.
Since the region R is the base of the solid, we can set a = 0 and b = 2, since this is the x-value at which the two functions intersect. Additionally, we can set y = ln(x) + 1 since this is the height of the solid.
Therefore, the volume of the solid is:
V = ∫02π(ln(x)2 + 12 − (x−1)2)dx
Calculating the integral, we get:
V = [π(xln(x)2 + x − 2xln(x) − x + 1)]02
Substituting the bounds of the integral, we get:
V = [π(22ln(2)2 + 2 − 4ln(2) − 2 + 1)] − [π(02ln(0)2 + 0 − 2ln(0) − 0 + 1)]
Simplifying the equation, we get:
V = π(ln(2)2 + 1 − 2ln(2))
Finally, substituting the value of ln(2) into the equation, we get:
V = 3.14159 (2.386294 + 1 − 4.772188) ≈ 7.58 thousandths
Therefore, the volume of the solid is 7.58 thousandths when rounded to the nearest thousandth.
In conclusion, the volume of the solid whose base is the region R and each cross section perpendicular to the a-axis is a semicircle is 7.58 thousandths when rounded to the nearest thousandth. This was calculated by integrating the equation V=∫baπ(y2−(x−1)2)dx with the bounds of integration a=0 and b=2 and the height of the solid y=ln(x)+1.
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Round this number to the
nearest tenth.
5.460
Answer:5.5
Step-by-step explanation:
5.46
You rounded to the nearest tenths place. The 4 in the tenths place rounds up to 5 because the digit to the right in the hundredths place is 6.
5.5
When the digit to the right is 5 or greater we round away from 0.
5.46 was rounded up and away from zero to 5.5
Answer:
Step-by-step explanation:
We know that the tenth of a decimal number is the first number after the decimal. In this case the tenth in 5.460 is the 4. 0.46 is all we need to round the number. Since 6 is greater than 5, 4 will round up. Hence the answer is 5.5.
Derrick invested some money at 2.25% simple interest and $1000 less than twice this amount at 1.5%. His total income from the interest was $510. How much was invested at each rate?
Derrick invested $23,306.28 at 2.25% and $462.79 at 1.5%.
What is percentage?
Percentage is a way of expressing a number as a fraction of 100. It is denoted by the symbol "%". For example, 50% means 50 out of 100 or 0.5 as a decimal.
Let's start by assigning variables to the unknown quantities in the problem. Let x be the amount Derrick invested at 2.25% and y be the amount he invested at 1.5%.
According to the problem, Derrick invested "1000 less than twice" the amount he invested at 2.25% at 1.5%. This means:
y = 2(0.0225x - 1000) = 0.045x - 2000
Now we can set up an equation based on the total income from the interest:
0.0225x + 0.015y = 510
Substituting the expression for y from the first equation, we get:
0.0225x + 0.015(0.045x - 2000) = 510
Simplifying and solving for x, we get:
0.0225x + 0.000675x - 30 = 510
0.023175x = 540
x = 23306.28
So Derrick invested approximately $23,306.28 at 2.25%. To find the amount he invested at 1.5%, we can substitute this value for x in the equation for y:
y = 0.045x - 2000 = 0.045(23306.28) - 2000 = 462.7856
So Derrick invested approximately $462.79 at 1.5%.
Therefore, Derrick invested $23,306.28 at 2.25% and $462.79 at 1.5%.
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Tiger Global Management had R6 500 000 in sales last year. The company’s total comprehensive income was R217 000, its total assets turnover was 1,04, and the company’s return on equity (ROE) was 14%. The company is financed entirely with debt and common equity. What is the company’s debt ratio?
Answer:
Step-by-step explanation:
To calculate the company's debt ratio, we need to know its total liabilities and total assets. We can use the total assets turnover ratio to calculate the company's total assets:
Total assets turnover = Sales / Total Assets
1.04 = R6,500,000 / Total Assets
Total Assets = R6,500,000 / 1.04 = R6,250,000
Since the company is financed entirely with debt and common equity, its total liabilities are equal to its total debt. We can use the return on equity (ROE) formula to calculate the company's total equity:
ROE = Net Income / Total Equity
0.14 = R217,000 / Total Equity
Total Equity = R217,000 / 0.14 = R1,550,000
Now, we can calculate the company's debt ratio:
Debt Ratio = Total Debt / Total Assets
Debt Ratio = (Total Assets - Total Equity) / Total Assets
Debt Ratio = (R6,250,000 - R1,550,000) / R6,250,000
Debt Ratio = R4,700,000 / R6,250,000
Debt Ratio = 0.752 or 75.2%
Therefore, the company's debt ratio is 75.2%.
Solve for x for number 6. Find the length indicated for number 8. Find TU
Step-by-step explanation:
hope this will help you
F(x)=5x+1 independent variable
Answer:
Step-by-step explanation:
You roll a number cube labeled 1 through 6, one time.What is the probability that you roll a number that is less than 5?
HURRY!
Answer:
66.67%
Step-by-step explanation:
To find the probability, divide 4 by 6, since there are 4 numbers less than 5, out of 6 in total.
4/6
= 0.6667
So, the probability is approximately 66.67%