x³ + y³ = (x + y)(x² - xy + y²)
x³ - y³ = (x - y)(x² + xy + y²).
Proof for 1st Identity :
★ x³ + y³ = x (x² - xy + y²) + y(x² - xy + y²)
⟶ x³ + y³ = x³ - x²y + xy² + x²y - xy² + y³
⟶ x³ + y³ = x³ + y³
Proof for 2nd identity :
★ x³ - y³ = x(x² + xy + y²) - y(x² + xy + y²)
⟶ x³ - y³ = x³ + x²y + xy² - x²y - xy² - y³
⟶ x³ - y³ = x³ - y³
For example,Let us assume that,
x = 1
y = 2
So,
✯ x³ + y³ = 1³ + 2³
⟹ (x + y)(x² - xy + y²) = 1 + 8
⟹ (1 + 2)(1² - (1)(2) + 2²) = 9
⟹ 3 * (1 - 2 + 4) = 9
⟹ 3 * 3 = 9
⟹ 9 = 9
✯ x³ - y³ = 1³ - 2³
⟹ (1 - 2) * (1² + (1)(2) + 2²) = 1 - 8
⟹ ( - 1) * (1 + 2 + 4) = - 7
⟹ ( - 1) * (7) = - 7
⟹ - 7 = - 7
Thus , they can be called as identities/formulae as they are very useful in finding the value of a certain equation or an expression easily.
I hope it will help you.
Regards.
The given measurement of a surface Area of a sphere is 196π.Find it's radius
(thanks in advance)
Answer:
Hope this solution helps you. Sorry for the handwriting .
If AABC = ADEC,
ZB = 2x + 31 and ZE = 7x - 24
A
D
B
E
x = [?]
/_ b = /_ e
2x + 31 = 7x - 24
5x = 55
x = 11
Compare the ratio of miles driven to gallons of gas used for Car A and Car D. Write the ratios as fractions and use a common denominator of 8. The ratio of miles to gallons for Car A is /8. The ratio of miles to gallon for Car D is /8. The ratio for Car A is the ratio for Car D.
Answer:
The ratio of miles to gallons for Car A is
✔ 224
/8.
The ratio of miles to gallon for Car D is
✔ 184
/8.
The ratio for Car A is
✔ greater than
the ratio for Car D.
Step-by-step explanation:
can anyone pls helppppp
Write an expression for the sentence: Kelly has $120 to spend at the fair and spent $15 on food and wants to play games that cost 4$ each
Smart people can answer
Find the distance between each pair of points.
M(-2,5) N(-2,-4)
Answer:
9
Step-by-step explanation:
What is the correct equation to find the value of X?
Answer:
x = 12
Step-by-step explanation:
The 2 angles shown are corresponding angles and congruent, thus
8x - 17 = 5x + 19 ( subtract 5x from both sides )
3x - 17 = 19 ( add 17 to both sides )
3x = 36 ( divide both sides by 3 )
x = 12
What is 4 divided by 3/5
Answer:
20/3 or 6 2/3
Step-by-step explanation: 4/1 times 5/3 multiply and you get 20/3
Answer:
6 2/3
Step-by-step explanation:
Aanya wrote the four equations that are shown below.
A
6 x minus 8 = 4 (x minus 2) + 2 x
B
3 (x minus 1) + 2 x = 3 (x minus 1) + 2
C
7 x + 2 minus x = 6 (x + 2)
D
4 (x + 3) + x = 5 (x + 1) + 7
She examined them, without solving them, to determine which has exactly one solution. Which of Aanya’s equations has exactly one solution?
6 x minus 8 = 4 (x minus 2) + 2 x
3 (x minus 1) + 2 x = 3 (x minus 1) + 2
7 x + 2 minus x = 6 (x + 2)
4 (x + 3) + x = 5 (x + 1) + 7
Answer:
B
Step-by-step explanation:
.' )
Answer:
The answer is B.
Step-by-step explanation:
I just took the test.
Larry is putting a row of rocks around his rectangular pool. Which descriptive model will tell him how many rocks he needs?
[2(pool length) + 2(pool width)] times the width of the rocks
(pool length times pool width) times the width of the rocks
(pool length times pool width) divided by the width of the rocks
[2(pool length) + 2(pool width)] divided by the width of the rocks
Answer:
P = [2( l)+2(w)] / width of the rock
Step-by-step explanation:
row of rocks around his rectangular pool, this tells us we are finding the perimeter
The perimeter of a rectangle is given by
P = 2( l+w)
P = 2( l)+2(w)
But we know that the length takes into account the width of the rock so divide each side by the width of the rock
P = [2( l)+2(w)] / width of the rock
The regular price of a baseball hat is $15.65. If Julio buys the baseball hat on sale for 20% off the regular price, how much change will he receive after paying with $20?
PLEASE HELPPP I DONT UNDERSTAND
Step-by-step explanation:
You need to do the distributive property to answer this question.
Everything in the outside of the parenthesis needs to be multiplied by each number inside the parenthesis.
Hope this helps you!
Answer:
(3 ^2 x 2x^ 4 y^2 )
Step-by-step explanation:
WHAT IS THE LAST SENTANCE FOR DESPASITO IN ENGLISH!!!!!!!!!!!!!!11
From 9:00 p.m. to 6:00 a.m., the temperature dropped 1.6 degrees Fahrenheit per hour.
What was the total change in temperature, in degrees Fahrenheit, between 9:00 p.m. and 6:00 a.m.?
Answer: help plz
Step-by-step explanation:
Answer: 16
Step-by-step explanation:
Which two ratios form a proportion?
3:4 and 6:12
3:4 and 9:15
3:4 and 12:18
3:4 and 15:20
Answer:
3:4 and 15:20
Step-by-step explanation:
The answer is the fourth one because 3:4 and 15:20 are equivalent, so there's your answer. Hope it helps!
The total cost after tax to repair Deborah's computer is represented by 0.09(60h)+60h, where h represents the number of hours it takes to repair Deborah's computer. What part of the expression represents the amount of tax Deborah has to pay? Explain.
Answer:
0.09(60h)
Step-by-step explanation:
The part that represents the tax is 0.09.
This is because, we can rewrite the sum as;
Amount of tax + Total cost for the number of hours
Now, the amount of tax can only be a percentage of the total
We can write 0.09 as 9/100
This can be interpreted as 9% of the total amount
So therefore we can rewrite the amount as;
9% of 60h + 60h
So the part that represents the amount of tax Deborah has to pay is 0.09(60h)
A student solved the equation below using the steps shown, rounding to two decimal places if necessary.
which step contains the first mistake ?
A. step 2
B. step 1
C. step 3
D. step 4
Answer:
Step 1
Step-by-step explanation:
please help me? im desperate!
Answer:
The same sign
Step-by-step explanation:
What is the slope of a line that is perpendicular to the line shown on the graph?
Which function has exactly three distinct real zeros? A. h(x) = (x − 9)2(x − 4)2 B. h(x) = x(x + 7)2 C. h(x) = (x − 3)(x + 1)(x + 3)(x + 8) D. h(x) = (x − 2)2(x + 4)(x − 1)
Answer: D is the correct answer .
D. h(x)= (x-2)^2(x+4)(x-1)
Step-by-step explanation: For Plato users the correct answer is D .
The function which has three distinct zeroes is h(x) = (x − 2)²(x + 4)(x − 1), the correct option is D.
What is a Function?A function is a law that relates a dependent and an independent variable.
The zeroes of the function are the point at which the function value becomes 0.
The function which have three distinct real zeroes is
h(x) = (x − 2)²(x + 4)(x − 1)
(x-2)² = 0
x = 2
(x+4) = 0
x = -4
x-1 = 0
x = 1
To know more about Function
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*EXTRA PTS PLS ANSWER* Find the equation of a line that has a slope of 1/2 and a y-intercept = 1. (Don't leave any spaces in between characters) *
Answer:
y = [tex]\frac{1}{2}[/tex] x + 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = [tex]\frac{1}{2}[/tex] and c = 1 , thus
y = [tex]\frac{1}{2}[/tex] x + 1 ← equation of line
there are 48 newborn girls in a hospital nursery. For every 3 girls, there are 2 boys. How many newborn babies are in the nursery?
Hi! I believe your answer is 80 newborn babies. To find the number of boys, divide 48 by 3 (since it is for every 3 girls) and you'll get 16. Next, multiply 16 and 2 (for every 2 boys) and you'll get 32. Lastly, add 48 and 32 and you'll get the number of newborn babies in the nursery (80). I hope this helps you! Good luck and have a great day. ❤️✨
Number of total newborn babies = 80
What is ratio?A ratio can be defined as the relationship or comparison between two numbers of the same unit to check how bigger is one number than the other one.
Given,
Total number of girls = 48
For every 3 girls, there are 2 boys.
Ratio of girls to boy = 3/2
Let there are x boys,
then,
48/x = 3/2
3x = 96
x = 32
Number of boys = 32
Total newborn babies = Number of girls + number of boys
= 48 + 32 = 80
Hence, 80 newborn babies are in nursery.
Learn more about ratio here:
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A person invests 1000 dollars in a bank. The bank pays 6% interest compounded
monthly. To the nearest tenth of a year, how long must the person
leave the money
in the bank until it reaches 3300 dollars?
Answer:
t=19.94841\approx 19.9 \text{ years}
t=19.94841≈19.9 years
Step-by-step explanation:
Someone please help only answer if your 100 percent sure
Answer:
90
Step-by-step explanation:
please help me with this
CAN SOMEONE HELP ME PLEASE ?!
Answer:
A. XY
Step-by-step explanation:
The answer is XY because it is the same length as XZ. I didn't determine this by guessing, but by eliminating the wrong answer choices. The tick marks indicate what lines are congruent to each other. The answer can't be C because AY is congruent to YC since they both have 3 tick marks, indicating that they are congruent to each other. Same goes for the others.
Kainoa collects trading cards. He has 1,032 baseball cards, 709 basketball cards, and 833 football cards. He wants to put all of them in albums. Each page in the albums holds 18 cards. How many pages will he need to hold all of his cards? He will need pages
Answer:
143 pages
Step-by-step explanation:
Kainoa has:
1,032 baseball cards, 709 basketball cards, and 833 football cards.
Totally number of cards =
(1032 + 709 + 833)cards = 2574 cards
We are told that:
Each page in the albums holds 18 cards
The pages he will need to hold all of his cards is calculated as:
2574 cards ÷ 18 cards = 143 pages.
Simplify the following - (32)²
Answer:
=-1024
Step-by-step explanation:
Hope this helps (:
20 POINTS!! HELP ME PLZZ I NEED HELP WITH THIS!!
Answer:
0.22222222
Step-by-step explanation:
Hope this helps!!!
Answer:
0.22222222
Step-by-step explanation:
you have to divide 2 by 9.
Landon is going to use a computer at an internet cafe. The cafe has an initial charge of $10 to use a computer and an additional charge of $0.80 for every minute of use. Write an equation for C , C, in terms of t , t, representing the total cost of using a computer for t t minutes at the internet cafe.
Answer:0.80t+10
Step-by-step explanation: