[tex]Solution, \mathrm{Expand}\::\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}\right)\left(x+y\right)\left(x^2+y^2\right):\quad :x^4-:y^4[/tex]
[tex]Steps:[/tex]
[tex]\mathrm{Expand}\:\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}\right):\quad x-y, =\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)[/tex]
[tex]\mathrm{Expand}\:\left(x-y\right)\left(x+y\right):\quad x^2-y^2, =:\left(x^2-y^2\right)\left(x^2+y^2\right)[/tex]
[tex]\mathrm{Expand}\:\left(x^2-y^2\right)\left(x^2+y^2\right):\quad x^4-y^4, =:\left(x^4-y^4\right)[/tex]
[tex]\mathrm{Expand}\::\left(x^4-y^4\right):\quad :x^4-:y^4, =:x^4-:y^4[/tex]
The correct answer is [tex]x^4-y^4[/tex]
Hope this helps!!!
The simplification involves the use of the difference of squares identity on the first two terms, yielding (x - y). There's no further simplification possible for the remaining terms (x + y)(x^2 + y^2) under general conditions, resulting in the expression (x - y)(x + y)(x^2 + y^2).
The question involves the simplification of the given expression (
oot{x} + oot{y})(oot{x} - oot{y})(x + y)(x^2 + y^2). To simplify it, we will use the properties of square roots and algebraic identities.
Firstly, we use the difference of squares identity on the first two terms: (
oot{x} + oot{y})(oot{x} - oot{y}) = x - y.
Now, we look at the second pair of terms and realize that we can reshape the given expression using the properties of exponents: (x + y)(x^2 + y^2). Since both (x + y) and (x^2 + y^2) represent sums of powers of x and y, there is no direct simplification possible without additional constraints on x and y.
Therefore, the multiplication of these expressions gives us (x - y)(x + y)(x^2 + y^2) without further simplification under general conditions.
whats the difference between a proper fraction and an improper fraction 10 POINTS
the difference between a proper fraction and an improper fraction is an improper fraction is a fraction that is bigger then the denominator for example 3/4 is a fraction and 7/4 is an improper fraction
Explanation is provided in the image attached.
What is the current value of a future sum of money called?
A.
current value
B.
present value
C.
future value
Your question:
What is the current value of a future sum of money called?
Answer:
B) Present Value
Although current is a synonym of present, present is the correct meaning. The current value of a future sum of money is called Present Value.
Best Of Luck,
- I.A -
Answer:
The current value of a future sum of money is:
Option: B
B. Present Value.
Step-by-step explanation:
Present value--
In terms of finance the present value is the value in the present of a sum of money or stream of cash flows , in contrast to some future value it will have when it has been invested at compound interest.
Future cash flows are discounted at some rate called as discount rate.
Higher the discount rate lower is the present value of future cash flow.
At midnight, the temperature was 30 degrees F. By 6:00 a.m., it had dropped 5 degrees and by noon, it had increased by 11 degrees. What was the temperature at noon?
Answer: 36 degrees
Step-by-step explanation:
subtract 5 from 30=25
add 11 to 25
25+11=36
Considering the temperature changes throughout the day, the temperature at noon was 36 degrees F.
Explanation:If the temperature started at 30 degrees F at midnight, and it dropped 5 degrees by 6:00 a.m, the temperature at 6:00 a.m. was 30 - 5 = 25 degrees F. Then, if the temperature increased by 11 degrees F by noon, we just add this increase to the temperature at 6:00 a.m. This results in 25 + 11 = 36 degrees F. So, the temperature at noon was 36 degrees F.
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Here's the question: You have an electrical circuit with various components, all of which are in series. The current (I) through the system is (5.772 - 5.323i) milliamperes (mA). The impedance (Z) in that same system is (3.342 + 4.176i) kilohms (kΩ). Please tell me the magnitude of the voltage in the circuit.
Answer:
41.99 or 42.0 volts.
Step-by-step explanation:
We have been given the impedance (Z) of the circuit which is:
[tex]Z=3.342+4.176i[/tex]
and the current through the circuit is:
[tex](5.772-5.323i)[/tex]
The voltage across the circuit is given by:
[tex]V= I\times Z=IZ[/tex], where 'V' is the voltage, 'I' is the current, and 'Z' is the impedance.
Plugging the values of 'I' and 'Z' we get:
[tex]V=(5.772-5.323i)\times 10^{-3}\times (3.342+4.176i)\times 10^3[/tex]
[tex]V=(5.772-5.323i)\times(3.342+4.176i)[/tex]
[tex]V= (41.51+6.31i)[/tex]
Now that we have the voltage, we can find the magnitude of the voltage as follows:
[tex]V= \sqrt{(41.51)^2+(6.31)^2}=\sqrt{1723.08+39.81}=\sqrt{1762.89}=41.98 \approx 42.0[/tex]
So the magnitude of the voltage across the circuit is 42.0 Volts.
Convert the following Celsius degrees to Fahrenheit. a. 35° C b. 500° C c. 10° C d. 55° C
A: 95
B: 932
C:50
D:131
John Thunderhawk is making furniture. He finds that to design a particular cabinet and set up his shop to produce it costs $1,800. Then the labor and supplies to build each one are $400. So his cost, y, for x items is represented by y=1,800 + 400x. He can sell the cabinets for $600. So his revenue, y, is represented by y=600x. The solution to this system of equations is his break-even point, the point beyond which he starts making a profit. How many cabinets must he sell to break-even?
The number of cabinets he must sell to breakeven is 9.
How many cabinets must he sell?
Breakeven is when the total cost and the revenue is zero. At the breakeven point, profit is zero.
Breakeven : total cost = revenue
1800 + 400x = 600x
In order to determine the value of x, take the following steps:
Combine similar terms:
1800 = 600x - 400x
Add similar terms together
1800 = 200x
Divide both sides of the equation by 200
x = 1800 / 200
x = 9
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To break-even, John Thunderhawk must sell 9 cabinets. After selling 9 cabinets, his revenue will start exceeding his costs, allowing him to make a profit.
The break-even point occurs when the total cost is equal to the total revenue.
We can find this point by setting the cost equation and the revenue equation equal to each other and solving for x :
Set the cost and revenue equations equal :
Given that the cost equation is y = 1,800 + 400x, and the revenue equation is y = 600x , set these two equations equal to find the break-even point:
[tex]\[ 1,800 + 400x = 600x. \][/tex]
Rearrange the equation :
Subtract 400x from each side:
[tex]\[ 1,800 = 200x. \][/tex]
Solve for x :
Divide by 200 to isolate x :
[tex]\[ x = \frac{1,800}{200} = 9. \][/tex]
Therefore, to break-even, John Thunderhawk must sell 9 cabinets. After selling 9 cabinets, his revenue will start exceeding his costs, allowing him to make a profit.
Question :
John Thunderhawk is making furniture. He finds that to design a particular cabinet and set up his shop to produce it costs $1,800. Then the labor and supplies to build each one are $400. So his cost, y, for x items is represented by y=1,800 + 400x. He can sell the cabinets for $600. So his revenue, y, is represented by y=600x. The solution to this system of equations is his break-even point, the point beyond which he starts making a profit. How many cabinets must he sell to break-even?
A ceiling fan has five equally spaced blades find the angle of rotation the Maps one blade on to the adjacent blade
Answer:
A rotation of 72 degrees will map one blade of ceiling fan to its adjacent blade.
Step-by-step explanation:
We are told that a ceiling fan has 5 equally spaced blades. It will work as a regular pentagon.
We can find angle of rotation to map one blade on adjacent blade dividing 360 by 5 as sum of angles of regular pentagon equals to 360 degrees.
[tex]\text{ Angle of rotation}=\frac{360}{5}[/tex]
Upon dividing 360 by 5 we will get,
[tex]\frac{360}{5} =72[/tex]
Therefore, a rotation of 72 degrees will map one blade of ceiling fan to its adjacent blade.
The angle between adjacent blades in a five-blade ceiling fan is b. 72°.
Step 1 :**Understanding the Situation**:
We have a ceiling fan with five equally spaced blades. We need to find the angle of rotation that maps one blade onto the adjacent blade.
Step 2 :**Identifying the Angle between Blades**: Since the blades are equally spaced, we can find the angle between adjacent blades by dividing the full circle (360°) by the number of blades, which is 5.
[tex]\[ \text{Angle between adjacent blades} = \frac{360°}{5} = 72° \][/tex]
Step 3 :**Checking the Options**:
- (a) 144° is twice the angle between adjacent blades. This would correspond to skipping one blade and landing on the third blade, which is not adjacent.
- (b) 72° is the same as the angle between adjacent blades. This seems promising.
- (c) 90° is not consistent with the division of the circle by the number of blades.
- (d) 36° is half the angle between adjacent blades. This would correspond to a situation where we skip two blades, which is not adjacent.
Complete Question :
Ceiling fan has five equally spaced blades. Find the angle of rotation that maps one blade onto the adjacent blad a 144° b 72° c 90° d 36°
What is 220 x 19 in Distributive property
Hello there!
This question is so easy to me.
Explanation:
↓↓↓↓↓
First you had to multiply by the numbers.
[tex]220*19=4180[/tex]
[tex]=4180[/tex]
Answer⇒⇒⇒⇒⇒4180
Hope this helps!
Thank you for posting your question at here on Brainly.
Have a great day!
-Charlie
Many rules concerning two-dimensional geometry have three-dimensional analogues. A. True B. False
The statement is true.
We have given that,
Many rules concerning two-dimensional geometry have three-dimensional analogs.
What are the two-dimensional?Two-dimensional Euclidean space or simply two-dimensional space is a geometric setting in which two values are required to determine the position of an element on the plane.
We have to determine whether the statement is true or false.
The statement is true.
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A veterinarian needs to know an animals weight in kilograms.If 20 pounds is about 9 kilograms and a dog weighs 30 pounds,use a ratio table to find the dogs weight in kilograms.
Answer:
13.5 kgs.
Step-by-step explanation:
Here we have to find conversion factor of lbs into kg.
For this we use the given information.
Given that the weight of a dog is 20 lbs and also 9 kg.
Hence we have conversion factor as
20 lbs = 9 kg
Or 1 lb =9/20 = 0.45 kg.
Using this, we find the 30 lb converted into kg.
For 1 lb, equivalent kg = 0.45
Hence for 30 lbs equivalent kg= 30(0.45) = 13.5 kg.
Write 2.7 as a fraction or mixed number
Answer: [tex]2 \frac{7}{10}[/tex]
Step-by-step explanation: Using the place value chart we can see that 2.7 means two and seven-tenths which can be written as the mixed number
[tex]2 \frac{7}{10}[/tex].
Cameron is playing 9 holes of golf. He needs to score a total of at most 13 over par on the last four holes to beat his best golf score. On the last four holes, he scores 7 over par, 3 under par, 8 over par, and 3 under par.
Cameron does beat his best score. He scores 7 and 8 over par, as well as 3 under par twice. This makes him have 7 + 8 or 15 over par and 3 + 3 or 6 under par. 15 - 6 = 9, which is under 13, his current best score.
Tony wants to buy a new collar for each of his 4 dogs. The collars come in a choice of 9 different colors.
Step 2 of 2 : How many selections of collars are possible if repetitions of colors are not allowed?
There are 126 possible selections of collars for Tony's 4 dogs if repetitions of colors are not allowed.
What is permutation?The number of selections of collars possible if repetitions of colors are not allowed, we can use the concept of permutations.
Using the formula for permutations without repetition, we can calculate this as:
9P4 = 9! / (9 - 4)!
= 9! / 5!
= (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1)
= 3024 / 24
= 126
This shows that 126 possible selections of collars for Tony's 4 dogs if repetitions of colors are not allowed.
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The physician orders Xanax 0.5mg you have on hand 0.25mg tablets how many will you give
Which of the sums below can be expressed as 8(2 + 7)?
2 + 56
10 + 15
16 + 7
16 + 56
The answer to 8(2 + 7) would be 72 so 16 + 56 = 72 as well which means the answer is D) 16 + 56.
Hello there!
The answer should be the last option D.
Explanation:
↓↓↓↓↓↓↓↓↓↓↓↓↓
First you had to calculate with parenthesis
(2+7)=9
8*9
Then multiply and divide from left to right
8*9=72
[tex]8*2=16[/tex]
[tex]8*7=56[/tex]
Answer⇒⇒⇒16+56
Hope this helps!
Thank you for posting your question at here on Brainly.
Have a great day!
-Charlie
how do you write 40% as a fraction or mixed number in simplest form
Which of the following are equivalent to -7?
What is the prime factorization of 135?
135 is a composite number.
135 = 1 x 135, 3 x 45, 5 x 27, or 9 x 15.
Factors of 135: 1, 3, 5, 9, 15, 27, 45, 135.
Prime factorization: 135 = 3 x 3 x 3 x 5, which can also be written 135 = 3³ x 5
The prime factorization of 135 is 3^3 × 5.
How did we get the value?
The prime factorization of 135 is obtained by finding the prime numbers that divide 135 evenly, repeatedly dividing until the quotient is no longer divisible by any prime numbers.
Starting with the number 135, we can see that it is divisible by 3, so we divide 135 by 3:
135 ÷ 3 = 45
Now, we repeat the process with 45. It is also divisible by 3:
45 ÷ 3 = 15
Continuing, we divide 15 by 3:
15 ÷ 3 = 5
Now we have reached a quotient of 5, which is a prime number. We cannot divide it any further, so we have obtained the prime factorization of 135 as follows:
135 = 3 × 3 × 3 × 5
Therefore, the prime factorization of 135 is 3³ × 5.
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In 1 hour how many more times does a rabbits heart beat than a dogs rabbits heart beat per 1 minute 212 dogs heart beat per 1 minute
Answer: In 1 hour, 12720 more times rabbit's heart beat than a dog's rabbits heart beat
Step-by-step explanation:
Since we have given that
Rabbit's heart beat in 1 min 212 times more than dog's heart beat in 1 min.
So, in 1 hour , we get,
[tex]1\text{ hour }= 60\text{ minutes}\\so, heartbeat = 212\times 60=12720[/tex]
So, in 1 hour, 12720 more times rabbit's heart beat than a dog's rabbits heart beat .
To determine how many more times a rabbit's heart beats than a dog's in an hour, multiply the rabbit's beats per minute by 60 to get the hourly beat total, and do the same for the dog. Subtract the dog's total from the rabbit's to find the difference. Assuming a dog's heart rate of 70 beats per minute, a rabbit's heart beats 8,520 more times per hour than a dog's.
To calculate how many more times a rabbit's heart beats than a dog's in one hour, we first need to establish the number of beats per hour for both animals. Since the rabbit's heart beat is 212 times per minute, we multiply this number by 60 (the number of minutes in an hour) to find out the total heartbeats in one hour for a rabbit:
Rabbit heartbeats per hour = 212 beats per minute x 60 minutes = 12720 beats per hour.
Next, we need the same figure for the dog. Without the specific heart rate for the dog, we'll assume a generic heart rate for calculation purposes. For example, if a dog's heart beats 70 times per minute (a common rate for dogs), we multiply by 60:
Dog heartbeats per hour = 70 beats per minute x 60 minutes = 4200 beats per hour.
Now, to find out how many more times the rabbit's heart beats than the dog's, we subtract the dog's heartbeats per hour from the rabbit's:
Rabbit's additional heartbeats = 12720 beats per hour - 4200 beats per hour = 8520 more beats per hour.
How many weeks until all 350 rhinos disappear?
A very simple way to solve this specific problem is acknowledging the fact that the left hand side (L.H.S) is being multiplied by a factor of 10 to get the equation on the right hand side (R.H.S). So, if we multiply the denominator by 10, we'll get the answer, which would be 1 × 10 = 10 weeks.
Hope I could help! :)
Find the area of the quadrilateral EFGH
That's a trap ezoid , lower base b = 4 - -4 = 8, upper base B = 3 - -3 = 6 and height h = 2 - -2 = 4.
[tex]A = \frac 1 2 (b+B) h = \frac 1 2 (8 + 6)(4) = 28[/tex]
Answer: 28
The developing economies' share of the global gross domestic product (GDP) from 2003 to 2017 is shown in the following table. Year Share (% of GDP) Year Share (% of GDP) 2003 20 2011 35 2004 22 2012 38 2005 23 2013 39 2006 27 2014 40 2007 28 2015 41 2008 31 2016 42 2009 31 2017 43 2010 33 (a) Find the quadratic function that best models the developing economies' share of the global GDP as a function of the number of years after 2000. (Round all numerical values to four decimal places.) y(x) = ? (b) The model predicts that in the year 2027 , developing economies reach their maximum share, what %, of the GDP.
Solution-
Quadratic regression equation,
[tex]y =ax^2+bx+c[/tex]
taking x = input/independent variable = year - 2000
and y = output/dependent variable = share of the global GDP
To plot a quadratic equation for the data points, we need to calculate all the constants a,b and c , then putting all the values in the general equation we can get the best fit curve for the data set.
Using, the graphing calculator, we can calculate the values of a, b, and c. The values were found to be,
a = -0.0471
b = 2.6366
c = 12.1001
Putting all the values,
[tex]y =-0.0471x^2+2.6366x+12.1001[/tex]
This is the best fit quadratic function that models the share of the global GDP.
For calculating the share of GDP in the year 2027, we can put the value of x to get the value of y.
x = year-2000=2027-2000=27,
[tex]y=-0.0471(27)^2+2.6366(27)+12.1001=-0.0471(729)+2.6366(27)+12.1001=48.95[/tex]
∴ In the year 2027, the maximum share will be 48.95% of total GDP.
The detailed answer explains how to find the quadratic function that models the data and calculates the predicted share of the GDP in 2027 using the quadratic function.
Quadratic Function Model:
Using the given data points, we can find the quadratic function that best models the developing economies' share of global GDP. This can be achieved by fitting a quadratic equation to the data.
The quadratic function that best models the data is: y(x) = 0.7386x^2 - 28.4235x + 276.0976
Predicted Share of GDP in 2027:
To find the predicted share of the GDP in 2027, substitute x = 27 (since 2027 is 27 years after 2000) into the quadratic function.
By calculating, the predicted share of the GDP in 2027 is approximately 44.5233%.
The Six members of the homecoming decorating committee want to make 525 people flowers for the homecoming dance each flower takes 4 1/2 minutes to make about how long will each member of the committee have to spend making flowers
the answer is 2362 1/2 minutes
To find out how long each member of the committee will have to spend making flowers, we need to divide the total time needed to make the flowers by the number of committee members.
Explanation:To find out how long each member of the committee will have to spend making flowers, we need to divide the total time needed to make the flowers by the number of committee members.
Each flower takes 4 1/2 minutes to make, so the total time needed is 525 * 4 1/2 minutes. We can convert 4 1/2 minutes to 4.5 minutes, and then multiply it by 525 to get the total time needed.
Finally, we can divide the total time by the number of committee members (6) to find out how long each member will have to spend making flowers.
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Can someone please explain this? Brainliest to the correct answer
Hey there!!
This question is based on "direct variation".
Direct variation says :-
... y = kx ( Where k is the constant ).
Given :-
... y = 5 and x = -45
Now, we will have to find the constant
... 5 = -45k
... -5 / 45 = k
... 1 / 9 = k
Now, find the value y and x value given is -24.
... y = -24k
... y = -24 * 1/9
... y = -8 * 1/3
... y = -8/3
Hope my answer helps!!
There is a total of 1,500 people in the town of Markston. Only 55% of them voted during the town's elections this year. How many people voted?
Answer:
In total 825 people in the town voted.
Step-by-step explanation:
55% = 0.55
1,500 * 0.55 = 825
Answer:
825
Step-by-step explanation:
55% = 55/100 = 0.55; this means that
0.55(1500) = 825 people voted.
Plz help can’t find the answer
multiply the 2/8 x 4/9 first
then add the 7/9
you'll get 6/9
simplify to get the answer: 2/3
[tex]\frac{7}{9} -\frac{2}{8} \times \frac{4}{9}[/tex]
Start by multiplying the fractions together. When multiplying fractions they don't need to have a common denominator, so multiply 2/8 and 4/9 from left to right.
[tex]\frac{2}{8} \times \frac{4}{9} = \frac{8}{72}[/tex]
Now your new problem looks like: 7/9 - 8/72. When subtracting fractions they have to have common denominators so multiply 7/9 by 8/8.
[tex]\frac{7}{9} \times \frac{8}{8}= \frac{56}{72}[/tex]
You can now subtract 56/72 and 8/72 to get your final answer.
[tex]\frac{56}{72} -\frac{8}{72} = \frac{48}{72}[/tex]
This fraction can be simplified by dividing both sides by 8 because the numerator and denominator of this fraction are multiples of 8 and can be divided evenly by 8.
[tex]\frac{48}{72} \div \frac{8}{8} = \frac{6}{9}[/tex]
6/9 can be simplified even further by dividing both sides by 3 because both 6 and 9 can be divided evenly by 3.
[tex]\frac{6}{9} \div \frac{3}{3} = \frac{2}{3}[/tex]
D) 2/3 is your final answer.
A baker bought some flour. He used 2/5 of the flour to make bread and used the rest to make batches of muffins. If he used 16 lb. of flour making bread and 2/3 lb. for each batch of muffins, how many batches of muffins did he make?
Let’s start out by what we already know. He used 2/5 of flour to make bread and he used 16 Ibs to make bread. This implies that the amount is (2/5)x=16.
2/5x=16
X= 5 x 16/2
X= 40
Since he used 16 Ibs of flour for bread, the rest are for the muffins, which is around 24 Ibs.
We know that each thing of muffins will use 2/3 Ibs of flour.
24/2/3
24/1/2/3
24/1 x 3/2 = 36
36 is the answer to your question. :)
Help!!!!!!!!!!!!!!!!!!!!????
when multiplying exponents with the same base, add exponents.
true or false?
Don't know if this will help but here :)
Answer:
True
Step-by-step explanation:
We are given that when two variables with same base are multiplied then the exponents will be add.
We have to find that given statement is true or false.
Rule:[tex]a^b\times a^d=a^{b+d}[/tex]
Suppose we have x and [tex]x^2[/tex]
[tex]x\times x^2=x^{1+2}=x^3[/tex]
There are two variable with same base x therefore, the power will be added.
Hence, the statement is true.
Answer:True
numbers between 590 and 610 divisible by 2 3 5 and 10
The only number between 590 and 610 that is divisible by 2, 3, 5, and 10 is 600.
Explanation:The question asks for numbers between 590 and 610 that are divisible by 2, 3, 5, and 10. To solve the problem, we need to find the numbers that can be divided evenly (without remainder) by all of these numbers.
After calculating, we can see that the only number that fits all these conditions is 600.
The number 600 is divisible by 2, 3, 5, and 10 which means it can be divided by these numbers without leaving a remainder. For example, 600 divided by 2 equals '300', 600 divided by 3 equals '200', 600 divided by 5 equals '120', and 600 divided by 10 equals '60'.
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