Answer:
WHEN THE SUM of two numbers multiplies their difference --
(a + b)(a − b)
-- then the product is the difference of their squares:
(a + b)(a − b) = a2 − b2
For, the like terms will cancel.
Symmetrically, the difference of two squares can be factored:
x2 − 25 = (x + 5)(x − 5)
x2 is the square of x. 25 is the square of 5.
The sum of two squares -- a2 + b2 -- cannot be factored. See Section 2.
Example 1. Multiply (x3 + 2)(x3 − 2).
Solution. Recognize the form:
(a + b)(a − b)
The product will be the difference of two squares:
(x3 + 2)(x3 − 2) = x6 − 4.
x6 is the square of x3. 4 is the square of 2.
Upon seeing the form (a + b)(a − b), the student should not do the FOIL method. The student should recognize immediately that the product will be a2 − b2.
That is skill in algebra.
And the order of factors never matters:
(a + b)(a − b) = (a − b)(a + b) = a2 − b2.
Step-by-step explanation:
(a+b)(a-b)
use a and b in the first bracket to multiply the next bracket ; a(a-b)+b(a-b)
a square-ab+ab-bsquare
How do you write 1 2 as a power of 2?
Answer:
12² = 144
12 to the power of 2 us equal to 144
Talia attended a 5-day math camp that lasted 5/6 of an hour each day. How many total hours did Talia spend at math camp?
Answer:
Total hour Talia spend at math camp = 100 hour
Step-by-step explanation:
Given:
Number of days = 5 days
Per hour attended = 5/6 per hour
Find:
Total hour Talia spend at math camp
Computation:
Total number of hour per day = 24 hour
Total hour Talia spend at math camp = Number of days x Per hour attended x
Total number of hour per day
Total hour Talia spend at math camp = 5 x 5/6 x 24
Total hour Talia spend at math camp = 5 x 5 x 4
Total hour Talia spend at math camp = 25 x 4
Total hour Talia spend at math camp = 100 hour
What happens when you log an e?
When you log an e, you are essentially taking the natural logarithm of the number. This means that you are taking the logarithm of a number to the base e, which is about 2.718. The result of this calculation is the number of times the number must be multiplied by itself to get the original number.
For example, if you were to log an e, it would be equal to 1, since e x e = e. If you log a number bigger than e, such as 8, the result would be equal to 2.079, which means that 8 must be multiplied by itself twice (2.079 times) to get the original 8.
In general, when you log a number, you can think of it as a way of seeing how many times that number needs to be multiplied by itself to get the original number. This can be useful in many fields, from mathematics to engineering to physics, to find the mathematical relationship between two numbers.
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Mike jogged 6 laps around a 0.25 mile track on Tuesday and 7 laps on Thursday. How many miles did he job on Tuesday and Thursday?
Answer: 3.25 miles
Step-by-step explanation:
Given
Mike Jogged 6 laps around a 0.25-mile track on Tuesday
7 laps on Thursday
Miles jogged on Tuesday is [tex]6\times 0.25=1.5\ \text{mile}[/tex]
Miles jogged on Thursday is [tex]7\times 0.25=1.75\ \text{miles}[/tex]
Total miles Jogged is [tex]1.75+1.5=3.25\ \text{miles}[/tex]
HELP ME ASAP AND I MEAN ASAP
Answer:
9miles
Step-by-step explanation:
Answer:
Step-by-step explanation:
The width of a rectangle measures (8p+5) centimeters, and its length measures (4p + 4) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle
Answer:
Perimeter = 24p + 18 cm
Step-by-step explanation:
Perimeter = 2[(8p+5)+(4p+4)]
simplify:
Perimeter = 16p + 10 + 8p +8
combine like terms:
Perimeter = 24p + 18
Select the correct answer. which expression is equivalent to this quotient?
An expression which is equivalent to given [tex]\frac{\frac{1}{z+5} }{\frac{z+3}{5z+15} }[/tex] is 5 / (z + 5)
The correct answer is an option (B)
Consider given quotient.
[tex]\frac{\frac{1}{z+5} }{\frac{z+3}{5z+15} }[/tex]
Consider expression 5z + 15
We can write this expression as 5(z + 3) by taking out the common factor 5.
So given quotient would be,
[tex]\frac{\frac{1}{z+5} }{\frac{z+3}{5(z+3)} }[/tex]
As we know a fraction is put in lowest terms by cancelling out the common factors of the numerator and the denominator.
For fraction [tex]\frac{z+3}{5(z+3)}[/tex] , the common term is z + 3.
So, [tex]\frac{z+3}{5(z+3)} = \frac{1}{5}[/tex]
We know that for fractions a/b and c/d where b ≠ 0, d ≠ 0, if we take quotient of these fraction then that would be,
(a/b) / (c/d) = (a/b) × (d/c)
So, given quotient would be,
[tex]\frac{\frac{1}{z+5} }{\frac{1}{5} }\\\\\\=\frac{1}{z+5} \times \frac{5}{1} \\\\\\=\frac{1\times 5}{(z + 5)\times 1}[/tex]
= 5 / (z + 5)
Therefore, an equivalent expression is: 5 / (z + 5)
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Can you plase answer the question.
Answer:
I don't understand your language
Step-by-step explanation:
During lockdown down period people work very puzzled and their decided to play some game firstly they collect the 17 cards and write the numbers 1 to 17 put them in a box people make a bet from the chance of drawing the number either the prime or even number
etc.
From the universal set; N = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17}
Probability of drawing an even or prime number will be 15/17.
What is Probability?Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event. The probability of all the events in a sample space adds up to 1.
N = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17}
Prime = {1,2,5,7,11,13,17}
Even = {2,4,6,8,10,12,14,16}
Pr(Prime) = 7/17
Pr(Even) = 8/17
Pr(Prime or even) = 7/17 + 8/17
Pr(Prime or even) = 15/17
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Can someone help me with this.
Writing equations from graph
What is the coefficient in this expression?
12 - x + 3
The coefficient is -1
Does parallel programming always improve the performance of an application over sequential programming?
Parallel programming can improve the performance of an application over sequential programming in certain cases, but it is not a guarantee.
Explain about working of Parallel programming?Parallel programming allows for the use of multiple processors or cores to perform tasks simultaneously, which can improve the overall speed of an application. However, parallel programming can also introduce complexity and overhead, which can decrease performance. The potential for improved performance depends on the specific application and the design of the parallel implementation. Some applications may not benefit from parallel programming because they are not computationally intensive or because their data is not easily divided into parallelizable tasks. Additionally, the performance improvement also depends on the number of cores and the communication costs between them.
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Find expressions for the possible dimensions of the rectangular prism.
V = 12y3 + 13y2 + 3y
Answer:
Step-by-step explanation:
The dimensions of a rectangular prism are length, width, and depth.
Volume = length * width * depth
Here, V = 3y3 + 16y2 + 5y. If you can factor that into three terms, those could be the dimensions of the prism.
How do you factor it? Do all three terms have something in common? Sure, they all have a y, so factor a y out of each term.
V = y(3y2 + 16y + 5)
Then, factor what's left.
V = y(3y + 1)(y + 5)
The dimensions of the prism are y, (3y + 1), and (y + 5).
Answer:
The dimensions of a rectangular prism are length, width, and depth.
Volume = length * width * depth
Here, V = 3y3 + 16y2 + 5y. If you can factor that into three terms, those could be the dimensions of the prism.
How do you factor it? Do all three terms have something in common? Sure, they all have a y, so factor a y out of each term.
V = y(3y2 + 16y + 5)
Then, factor what's left.
V = y(3y + 1)(y + 5)
The dimensions of the prism are y, (3y + 1), and (y + 5).
Step-by-step explanation:
it's this write ... comments plz have a nice day
What is a shape called with 1000000000 sides?
Answer:
Regular megagon
Step-by-step explanation:
Regular megagon is a shape called with 1000000000 sides.
Please help with this question if you can
Answer:
5.1
Step-by-step explanation:
so the leaning ladder makes a right angled triangle so we can use pythagoras to calculate the the length (the hypotenuse):
5²+1²=x²
25+1=x²
√26=x
x=5.099...
and now we round to one d.p so it becomes 5.1 (1 d.p) as the hundreths digit is 9 and 9 is rounded up.
Keith Martin is the controller for Daniels Printing Service. Keith has been putting in a lot of overtime; therefore, Mr. Daniels has allowed Keith to hire an assistant. Keith’s assistant is a bright, high school graduate, but he has never taken an accounting class. Keith is trying to decide which accounting activities he should delegate to his assistant. Keith is willing to give the assistant a few simple instructions on how to complete each task, but he doesn’t have time to teach the assistant to be an accountant
The tasks that Keith can delegate to the assistant are List the account balances from the general ledger in the Trial Balance columns of the end-of-period spreadsheet, Add the Debit and Credit columns of the trial balance and Type the formal financial statements using the data from the Income Statement and Balance Sheet columns of the spreadsheet.
List the account balances from the general ledger in the Trial Balance columns of the end-of-period spreadsheet: Keith should delegate this task to his assistant. This is a relatively straightforward task that does not require a deep understanding of accounting principles. The assistant can be provided with clear instructions on how to pull the account balances from the general ledger and list them in the trial balance columns of the spreadsheet.
Add the Debit and Credit columns of the trial balance: Keith should delegate this task to his assistant. This is a simple arithmetic task that the assistant can perform with clear instructions.
Make the adjusting entries on the spreadsheet: Keith should retain this task. Adjusting entries involve more complex accounting knowledge and require a deeper understanding of accounting principles. It would be difficult for the assistant to complete this task without proper training.
Complete the spreadsheet: Keith should retain this task. This task requires a deep understanding of accounting principles and an understanding of how the various accounts and transactions relate to each other. It would be difficult for the assistant to complete this task without proper training.
Type the formal financial statements using the data from the Income Statement and Balance Sheet columns of the spreadsheet: Keith should delegate this task to his assistant. The assistant can be provided with clear instructions on how to organize the data from the spreadsheet into formal financial statements. It does not require a deep understanding of accounting principles.
Journalize and post the adjusting entries: Keith should retain this task. This task requires a deep understanding of accounting principles and an understanding of how the various accounts and transactions relate to each other. It would be difficult for the assistant to complete this task without proper training.
--The question is incomplete, answering to the question below--
"Keith Martin is the controller for Daniels Printing Service. Keith has been putting in a lot of overtime; therefore, Mr. Daniels has allowed Keith to hire an assistant. Keith's assistant is a bright, high school graduate, but he has never taken an accounting class. Keith is trying to decide which accounting activities could be delegated to his assistant. Keith is willing to give the assistant a few simple instructions on how to complete each task, but he doesn't have the time to teach the assistant to be an accountant.
For each task listed, state whether Keith should continue to do the work or delegate the task to his assistant. Explain each answer.
1. List the account balances from the general ledger in the Trial Balance columns of the work sheet.
2. Add the Debit and Credit columns of the trial balance.
3. Make the adjusting entries on the work sheet.
4. Complete the work sheet.
5. Type the formal financial statements using the data from the Income Statement and Balance Sheet columns of the work sheet.
6. Journalize and post the adjusting entries."
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a solid metal sphere of volume 1280cubic centimeters
is melted down and recast into 20 equal solid cubes.fund length of the side of each cube
a solid m or a solid m fear of volume
A container has 2 cups of milk in it. How many 1/4 cups are in the container?
Explain or show your reasoning.
a sum of money is divided among two friends in the ratio 4:11 if the smaller amount is $420, determine the larger amount?
Answer:
1155
Step-by-step explanation:
let the ratio be 4x:11x
4x=420
x=105
11x=11*105
=1155
You work at an oil refinery and are in charge of draining a tank until the
are 635 gallons left inside. The tank starts with 827 gallons, and you c
drain it at a rate of 48 gallons per minute. How many minutes do you
need to drain the tank to the right level?
You need
minutes.
Subtract 4 from 1/6 of 42
Here's link[tex]^{}[/tex] to the answer:
bit.[tex]^{}[/tex]ly/3gVQKw3
Answer:
42/6 = 7
7 - 4 = 3
Step-by-step explanation:
Consider the quadratic equation x? = 4x - 5. How many solutions does the equation have? A The equation has one real solution. The equation has two real solutions. The equation has no real solutions. D The number of solutions cannot be determined
Answer:
{-1, 5} (two real solutions).
Step-by-step explanation:
On the left side we want x^2, not x?
We need to rewrite x? = 4x - 5 in standard form, that is, as a quadratic with x terms in decreasing powers of x:
x^2 - 4x + 5 = 0
This factors easily to (x - 5)(x + 1) = 0.
We let each factor equal zero (0) separately and solve for x:
{-1, 5} (two real solutions).
The game starts at 1830. They play four eight minute quarters, and half-time lasts for thirty minutes. What time should you tell your parents to pick you up? Give your answer in both 12 and 24 hour clock notation
Therefore , the solution to the given problem of time comes out to be the time to pick up by your parents is 7:32.
What is time?the idea that time was the fourth dimension and that space and time were therefore inseparably connected. According to his general theory of relativity (opens in new tab), the mass and momentum of adjacent matter influence how much space-time enlarges and compresses.
Here,
Given : The game starts at 18:30
Thus,
They play for eight minutes quarters and half time last for 30 minutes.
So,
To find the time to pick up by your parents:
=> 8*4 + 30
=> 32 + 30
=> 62
Thus time after 62 minutes is 7:32
Therefore , the solution to the given problem of time comes out to be the time to pick up by your parents is 7:32.
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Q 9-1 Pythagorean Theorem and Trig
A girl is 20 ft. east of her school and her bike is 21 ft. south of the school. How far is she from her bike? Round to the nearest hundredth.
The distance between the girl and her bike is 25.00 ft.
What is distance?Distance is the measure of how far apart two objects, places, or points are. It can be measured in a variety of units, such as miles, kilometers, inches, centimeters, or other units.
The distance between the girl and her bike can be found using the Pythagorean Theorem. The Pythagorean Theorem states that the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse.
In this case, the girl is 20 ft. east of the school and 21 ft. south of the school. Therefore, the two sides of the triangle are 20 ft. and 21 ft. and the hypotenuse is the distance between the girl and her bike.
Using the Pythagorean Theorem, the hypotenuse is equal to the square root of (20^2 + 21^2) = 25.00 ft.
Therefore, the distance between the girl and her bike is 25.00 ft.
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please answer asap!
Answer:
10.2 is the answer not sure
70 years later from 1590
Answer: 1660
Step-by-step explanation: 70 + 1590 = QUICK MATHS
Answer:1660
Step-by-step explanation:
Please hurry it is timed and i need help!
The best option regarding the solutions of the trigonometric equation presented in this problem is given as follows:
A. 60º + n360º, 300º + n360º.
How to solve the trigonometric equation?The trigonometric equation for this problem is defined as follows:
[tex]\cos{x} - \sqrt{1 - 3\cos^2{x}} = 0[/tex]
Then, isolating the cosine, we have that:
[tex]\cos{x} = \sqrt{1 - 3\cos^2{x}}[/tex]
Applying the square for both sides, we have that:
cos²(x) = 1 - 3cos²(x).
4cos²(x) = 1.
cos²(x) = 1/4
cos²(x) = 0.25.
Applying the square root to both sides, we have that:
cos(x) = 0.5.
Meaning that the angle measures of x with the cosine of 0.5 are given as follows:
x = 60º, x = 300º.
(as the cosine is positive on the first and fourth quadrant).
One entire lap over the unit circle is equivalent to 360º, hence adding 360º n times to any of these solutions is also a solution to the trigonometric equation, meaning that option a is correct.
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It is a problem about the systems of equations that do not arise.
It is desired to distribute 420 € among three people, so that the first has €40 more than the second, and the third has half of what they have between the first two.
a) It proposes a system of linear equations to calculate what corresponds to each one. b) It solves, using the Gauss method
The solution to the equations is
The value of first x = € 160
The value of second y = € 120
The value of third z = € 140
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the first , second and third be represented as x , y , and z
The total amount to be distributed = € 420
So , x + y + z = € 420 be equation (1)
Now , first has €40 more than the second
So , x = y + 40 be equation (2)
And , third has half of what they have between the first two
So , z = ( 1/2 ) ( x + y ) be equation (3)
Substituting the value of x in the equation (3) , we get
z = ( 1/2 ) ( 2y + 40 )
z = y + 20 be equation (4)
Substituting the value of z and x in equation (1) , we get
( y + 40 ) + y + ( y + 20 ) = 420
On simplifying the equation , we get
3y + 60 = 420
Subtracting 60 on both sides of the equation , we get
3y = 360
Divide by 3 on both sides of the equation , we get
y = € 120
Therefore , the value of x = € 160
The value of z = € 140
Hence , the solution to the equation is € 160 + € 120 + € 140 = € 420
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Why is triangle always 180 degrees?
Triangle is always 180 degrees because the sum of all angles in a triangle is 180 degrees. This is known as the "Triangle Angle Sum Theorem." The theorem states that the sum of all angles in a triangle is equal to 180 degrees.
1. A triangle is a three-sided polygon with three angles.
2. The sum of the three angles in any triangle must be 180 degrees.
3. This is known as the Triangle Angle Sum Theorem.
4. The Triangle Angle Sum Theorem states that the sum of the angles in a triangle must equal 180 degrees.
5. It does not matter which angles the triangle has, the sum will always equal 180 degrees.
6. This theorem is based on the fact that the sum of the angles in any triangle is equal to two right angles or 180 degrees.
7. The Triangle Angle Sum Theorem can be proven by drawing a triangle, and then measuring and adding the three angles.
8. The sum of the three angles will always equal 180 degrees.
9. Therefore, triangle is always 180 degrees.
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Find the distance between the pair of points.
(−6, 4) and (−9, 4)
Answer:
6
Step-by-step explanation:
6