Answers
Answer: The equation is not an identity
==========================================================
Explanation:
We'll expand out the right hand side to see if we can simplify it to the left hand side. The stuff on the left will stay the same for each step.
I'll use c = a+b as a way to help distribute.
[tex]a^4 + b^4 = (a+b)(a^3 - a^2b-ab^2 + b^3)\\\\a^4 + b^4 = c(a^3 - a^2b-ab^2 + b^3)\\\\a^4 + b^4 = a^3c - a^2bc-ab^2c + b^3c\\\\a^4 + b^4 = a^3(c) - a^2b(c)-ab^2(c) + b^3(c)\\\\a^4 + b^4 = a^3(a+b) - a^2b(a+b)-ab^2(a+b) + b^3(a+b)\\\\a^4 + b^4 = a^4+a^3b - a^3b-a^2b^2-a^2b^2-ab^3 + ab^3+b^4\\\\a^4 + b^4 = a^4+(a^3b - a^3b)+(-a^2b^2-a^2b^2)+(-ab^3 + ab^3)+b^4\\\\a^4 + b^4 = a^4-2a^2b^2+b^4\\\\[/tex]
Unfortunately, we can't go any further. We have a^4 and b^4 on the right hand side, but we also have the term -2a^2b^2 that didn't cancel out. Therefore, the original equation is not an identity.
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Here's another way you can see that we don't have an identity.
Let's say we fixed 'a' to be equal to 1.
That means the equation
[tex]a^4 + b^4 = (a+b)(a^3 - a^2b-ab^2 + b^3)[/tex]
would turn into
[tex]1^4 + b^4 = (1+b)(1^3 - 1^2b-1b^2 + b^3)[/tex]
and simplify to
[tex]1 + b^4 = (1+b)(1 - b-b^2 + b^3)[/tex]
Now replace b with x and you'll have the two equations to represent the left and right hand sides
[tex]y = 1+x^4\\y = (1+x)(1-x-x^2+x^3)[/tex]
which you can graph on the same xy axis. You should note that the two equations produce different curves. The curves would need to be identical if we wanted an identity to happen.
Side note: you can pick other values for 'a' instead of just 1.
Related Questions
help pls please PLEASE
Answers
Answer:
c
Step-by-step explanation:
it's really product of power
Simplify. √25a^2.
40 points but reported if troll.
Answers
The square root of 25 is 5 and the square root of a^2 is a.
Hope this helps and if possible could I please have the brainliest answer?
Evaluate (35 = x)
2 when x = 7
O A. 3
O B. 7
O c. 5
O D. 26
I will give brainiest points
Answers
Answer:
the answer : a
equation : 35 = x
35 = 7
35/7 = 5
5-2 = 3
Hey there!
(35 ÷ x) - 2
= (35 ÷ 7) - 2
= (5) - 2
= 5 - 2
= 3
Therefore, your answer is: Option A. 3
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Please help me out
Fill in the blanks for this graph
1. This graph crosses the y-axis at______
2. The graph increases in the interval_____
3. The graph decreases in the interval____
Answers
Answer:
1 -5
don't know the answer of q2 and q3
Max can run 10 miles in 2 hours. At this rate, how long will it take him to run 25 miles
Answers
Answer:
Step-by-step explanation: 10 miles per 2 hours is the First step. Knowing this helps a lot. Next you need to understand your solving for 25 miles. 10 goes into 25 2.5 times. This means you need to multiply the time by 2.5 as well. That would be 5 hours.
There were 264 pieces of broccoli and 60% of them were covered in cheese how many of them were covered in cheese
Answers
Answer:
158.4 pieces of brocoli were covered in cheese
Step-by-step explanation:
AYO math
3.14159 x the fraction 3 and 2 divided by 96
Answers
Answer:
hey
Step-by-step explanation:
how r u?
wyd?
u from?
u r girl or boy??
Answer:
7.
Step-by-step explanation:
If a coordinate point is at (4, 2) and is translated down 3 units and right 1 unit, what is its new coordinate point? *
Answers
Answer:
1,3
Step-by-step explanation:
If a coordinate point is at (4, 2) and is translated down 3 units and right 1 unit, what is its new coordinate point?
4-3=1
2+1=3
(1,3)
Answer: (-1,5)
Step-by-step explanation:
Mateo wants to buy a BMX bike to compete in his town's extreme sports contest. He set up a lemonade and cookie stand to raise the money. Mateo sold lemonade for $1 per cup and cookies for $3 each. He sold 40 cups of lemonade and 20 cookies. How much money did he make?
Answers
Answer:100$
Step-by-step explanation: you multiply 40x1 and 20x3
Use the properties of operations to write an expression equivalent to 4x+1/2+2x-3. Please include explanations. Thanks!
Answers
Answer:
[tex]6x -2\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]4x + \frac{1}{2} + 2x - 3[/tex] Addition of like terms
[tex]6x + \frac{1}{2} - 3[/tex] Addition of content terms
[tex]6x -2\frac{1}{2}[/tex]
Please help with this !
Answers
Answer:
16 m
Step-by-step explanation:
12² + b² = 20²
I hope this helps!
Answer:
b = 16 m
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is
b² + 12² = 20²
b² + 144 = 400 ( subtract 144 from both sides )
b² = 256 ( take square root of both sides )
b = [tex]\sqrt{256}[/tex] = 16 m
a local company uses 13 1/2 tons of paper in one week. It recycles about 1/3 of its waste. how many tons of paper does the company recycle in one week?
Answers
Answer:
4 1/2 tons of recycled paper
Step-by-step explanation:
13.5/3 = 4.5 or 4 1/2
Determine if the graph represents a linear function, quadratic function, or exponential function.
Group of answer choices
Exponential
Linear
Quadratic
Answers
Answer:
Step-by-step explanation:
Answer:
quadratic function
Step-by-step explanation:
y=(x-1)²-3
Multiply (5.6 x 10") (6.1 x 10* )and write the
answer in scientific notation.
Answers
Answer:
3.416 x 10^(" + * + 1)
Step-by-step explanation:
The exponents of (5.6 x 10") (6.1 x 10* ) seem incorrect. Whatever they are, do the following:
1) multiply 5.6 times 6.1. Result = 34.16
Add the two exponents: (" + *)
The result is 34.16 x 10^(" + *)
Then move the decimal point one to the left and add 1 to the 10 exponent:
3.416 x 10^(" + * + 1)
Terre Haute to Indianapolis to Bloomington measure 3 cm on the map. What is the actual distance?
a) 100 km
b) 150 km
c) 200 km
d) 250 km
Answers
From the information given, it can be deduced that the actual distance from Terre Haute to Indianapolis to Bloomington is 150km.
From the complete information, we are told that on the map of Indiana, 1cm = 50km.
Therefore, since Terre Haute to Indianapolis to Bloomington measures 3 cm on the map, the actual distance will be:
= 3 × 50 = 150km
Learn more about distance on:
https://brainly.com/question/2166162
Answer:
if you are from connexus 8th grd 02051 pre-algebra A unit 5 lesson 6
then here are the correct answers
Step-by-step explanation:
1. B. 150 km
2. A. 300 km
3. D. 7.5 cm
4. B. 30 yd ^ 2
5. A. 90 x 45
i hope this helps please coment if you can! = ) <3
Can I get a simple answer
Answers
Answer:
The y-intercept of Function A is greater the Function B's.
Step-by-step explanation:
Function B's y-intercept is -5.
Function A's y-intercept is 5.
Ryan went for a drive in his new car. He drove at a speed of 62 miles per hour for 99.2 miles. For how many hours did he drive?
Answers
Answer: well you should take notes go review what your teacher has taught you and take notes then go back to that question and you should know hope this helps
Step-by-step explanation:
A bird flies down from a higher elevation to a lower elevation at a rate of 3 meters per second. Which equation models the bird's change in elevation, in meters, after 120 seconds?
O A. (-120)(-3) = -360
O B. 120. 3 = 360
O C. 120(-3) = 360
O D. 120(-3) = -360
No links please
Answers
Answer:
D
Step-by-step explanation:
Answer: The answer is 120(-3)= -360
Step-by-step explanation:
A. P. E. X.
Hassan picked 5 pounds of strawberries. That afternoon, Hassan's sister ate 1/4 of the strawberries. How many pounds of strawberries did Hassan's sister eat? Write your answer as a fraction or as a whole or mixed number.PLZZZZZZZ HELP
Answers
Answer:
Hassan's sister ate 5/4 pounds of strawberries.
Step-by-step explanation:
=> 5 x 1/4=> 5/4Conclusion:
Therefore, Hassan's sister ate 5/4 pounds of strawberries.
Hoped this helped
[tex]BrainiacUser1357[/tex]
What is the value of the expression
3-4 ?
Answers
Answer:
[tex]3 - 4 = 1[/tex]
✨✨
3-4
you just need to subtract 3 from -4
so , your answer is -1
What is the ninth term of the arithmetic sequence defined by the rule below?
A(n) = -15 + 2(n – 1).
A. 1
B. -1
C. 31
D. -31
Answers
Answer:
A
Step-by-step explanation:
Substitute n = 9 into the nth term rule
A(9) = - 15 + 2(9 - 1) = - 15 + 2(8) = - 15 + 16 = 1 → A
Ethan buys a new phone. It cost 75$. He will pay for this on his 1st bill.
His phone plan charges 0.06 dollars per minute on the phone.
'He has $90 to spend on his 1st bill. How long can he be on his phone to not go over his budget?
Answers
Answer:
250 minutes
Step-by-step explanation:
90-75=15
15/0.06=250
Answer:
x = 250 minutes
Step-by-step explanation:
The equation for this problem can be set up as follows-
Y = 0.06x+75
y = total phone bill
x= number of minutes on his phone
If Ethan can spend a total of $90 maximum, then y = 90
90 = 0.06x +75 solve for X to determine how many minutes he can be on his phone to reach a $90 total.
x = 250 minutes
maria's garden measures 14 feet by 16 feet and has a perimeter of 60 feet. Musharraf's garden measures 10 yards by 4 yards. What is the difference between the two perimeters?
Answers
The difference between the two perimeters is 32 yards.
Maria's garden measures 14 feet by 16 feet and has a perimeter of 60 feet.
Musharraf's garden measures 10 yards by 4 yards. The perimeter will be:
= 2(10 + 4)
= 2 × 14
= 28 yards
The difference will be:
= 60 - 28
= 32 yards.
solve pls brainliest
Answers
Answer:
$30
Step-by-step explanation:
Over 5 years she will have been paid $30 in interest. To find the amount of interest first find the total amount the account has after 5 years. The formula for simple interest is A=P(1+rt). Where A is the total amount, P is the principal (initial amount), r is the rate in decimal form, and t is the time in years.
Plug in the values to solve, A=200(1+0.03*5). Then, simplify to get A=230. Finally, to get only the interest, I, use the formula A-P=I. So, 230-200=30. Therefore, the interest Leila earned was 30 dollars.
Find the area of the shape
Answers
Answer:
400 [tex]ft^{2}[/tex] (Don't forget the square symbol!)
Step-by-step explanation:
For the triangle:
Base times height divided by 2.
8 x 25 = 200
200/2 = 100
For the regtangle:
Width times height.
25 x 12 = 300
Add them together, and you get:
100 + 300 = 400.
Answer:300
Step-by-step explanation:25*12=300
25
x12
50
250+50=300
There are 32 vanilla cupcakes and 40 chocolate cupcakes at a bakery. All of the cupcakes must be placed in boxes with the same number of vanilla cupcakes and the same number of chocolate cupcakes in each box.
Answers
Answer:
5 to 4
Step-by-step explanation:
when it's asking for a ratio it's basically division
chocolate/vanilla = 40/32 = 5/4
5/4 is the same as 5:4 or 5 to 4
Tell whether the ordered pair is a solution to the equation.
(4, 4); y = -x + 8
Answers
Answer:
Yes, it is.
Step-by-step explanation:
(4) = -(4)+8
4=4
True
How many hours is 7:45 to 1:00
Answers
Step-by-step explanation:
There are 17 hours between 7:45 to 1:00
Rectangle has length 8.1 and perimeter 28.5 find the width
Answers
Answer:
6.15
Step-by-step explanation:
perimeter of a rectangle= 2(Length + width)
perimeter=28.5
length=8.1
28.5=2(8.1+ Width)
28.5=16.2+ 2(Width)
28.5-16.2=2(Width)
12.3=2(Width)
12.3/2=Width
6.15=Width
Marking brainliest
What do you thinks this means and why does it matter
Answers
Answer:
You didnt put anything for me to see lol
Step-by-step explanation: