Answers
Answer: The equation is not an identity
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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
Please help meeee! Need the answer for the first box, no phony answers please! Thanks for your help, and happy holidays!
Answers
Answer:
y=2(x+5)^2-4.
Step-by-step explanation:
By solving a little bit, we get the vertex to be (-5, -4). Plugging the info given and the vertex into the vertex form, we get y=2(x+5)^2-4. You have a happy holiday season, too!
Triangle J K L is shown. Point M is the midpoint of side K L and point J is the midpoint of side J L. The length of K J is 12.8 meters, the lengths of J N and N L are 3.7 meters, and the lengths of K M and M L are 5.9 meters. Which statements about triangle JKL are true? Select two options. M is the midpoint of line segment KJ. N is the midpoint of line segment JL. MN = One-halfKJ MN = 4.4m MN = ML
Answers
Answer:
1 and 3
Step-by-step explanation:
Answer:
B) N is the midpoint of line segment JL.
D) MN = 1/2 KJ
Step-by-step explanation:
edgeeee
Combine the like terms to create an equivalent expression.
\large{9y+y}9y+y
Answers
Answer:
20y
Step-by-step explanation:
Which is an example of nonverbal communication?
O A. Test questions
O B. An outline
O C. Words like please
O D. Body posture
Answers
Hope this helps. Pls give me the brainliest if it does.
Choose the point-slope form of the equation below that
epresents the line that passes through the points (-6, 4) and (2,
0). (2 points)
•y -4= - 1/2 (x+6)
•y-4= 2(x+6)
•y+6= - 1/2(x-4)
•y+6= 2(x-4)
Answers
Answer:
A) y-4=-1/2(x+6)
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(0-4)/(2-(-6))
m=-4/(2+6)
m=-4/8
simplify
m=-1/2
y-y1=m(x-x1)
y-4=-1/2(x-(-6))
y-4=-1/2(x+6)
This is my last question I need help please
Answers
Answer:
.11
Step-by-step explanation:
it is correct
Answer:
A) $.11
Step-by-step explanation:
A dozen = 12
To find unit cost you divide cost of items by # of items
In this case we have 12 eggs that cost 1.35
So unit cost = 1.35 / 12 = .11
The sales tax on a surfboard is $12 what is the percent of sales tax?
Answers
Help me pleaseeeeeeeeeeeeeee
Answers
The formula to find the volume of a cube is:
volume= a^3
OR
volume= a*a*a
(a stands for the side length)
The way you would write it is:
V=2.8^3
Then you solve.
You would get 21.952
But since you need to round to the tenth place it would be:
22
Hope this helps! :)
What is the value of (225 ÷ 0.25) – 11.875 written to two decimal places.(2d.p.)
Answers
888.125 is the answer just use your calculator
Answer:
Step-by-step explanation:
888.13
What is the mass of a litter of 9 baby opossums?
Answers
Answer:
It is approximately 0.13 grams.
what percent increase is 1/3 to 1/6
Answers
Answer:
50% increase
Step-by-step explanation:
half of 6 is 3 thus 50%, and vise versa.
1 point
#8. What is the slope of a graph that passes through (5,5) and (5, -7)? *
0
-12
- 12/0
Undefined
12
Answers
Answer:
The answer is undefined
Because it passes through x
Check all that apply F(x) = 3/x(x-5)(x+1)
Answers
Answer:
Options A, D, and E (0, 5, -1)
Step-by-step explanation:
A vertical asymptote is located where the denominator is equal to 0. Therefore, x=0, x=5, and x=-1 are all vertical asymptotes.
Please help in this!
Answers
Step-by-step explanation:
Correct option is C)
41−
21+
19−
9
=
41−
21+
19−3
=
41−
21+
16
=
41−
21+4
=
41−
25
=
41−5
=
36
=6
[tex] \sqrt{41 - \sqrt{21 + \sqrt{19 - \sqrt{9} } } } \\ = \sqrt{41 - \sqrt{21 + \sqrt{19 - 3} } } \\ = \sqrt{41 - \sqrt{21 + \sqrt{16} } } \\ = \sqrt{41 - \sqrt{21 + 4 } } \\ = \sqrt{41 - \sqrt{25} } \\ = \sqrt{41 - 5} \\ = \sqrt{36} \\ = 6[/tex]
Answer:
a) 6
Hope you could get an idea from here.
Doubt clarification - use comment section.
Lee's Leather Store marked down leather jackets 10 percent. What is the sale price of a
leather jacket regularly priced at $130?
O $103
O $113
O $123
O $117
Answers
please help i will give brainliest
Answers
Answer:
because AB//DE
so DÊC=BÂC ( 2 straight lines are parallel and have the same internal angle)
because ACD is the outer angle of the triangle ABC so ACD= ABC+BÂC
because DÊC=BÂC
so ACD= ABC+ DÊC
a number cube is rolled.what is the probability of rolling a number greater than 4
Answers
Answer: 2/6
Step-by-step explanation:
There’s only 2 numbers greater than 4 on a die, so two would be the numerator and the denominator would be the number of possibilities you could roll, which is 1-6.
2/6, 1/3, or approx. 33.3%
A number cube will have six sides and two out of six will be greater than four, therefore, there is around a 33.3% chance you will roll a number greater than 4. :)
Find the circumference of a circle with a radius of 2.4 m
Answers
Answer:
here,
circumference of circle (c)=2πr
=2×22÷7×2.4
15.0857143.
the other two options are…
c. Function A and function B both have two real solutions.
d.The vertex of function A is lower on the graph than the vertex of function B.
GIVING BRAINLIEST IF FAST
Answers
Explanation: use desmos or trust me lol
Estimation Rita goes to the mall. If x is the number of items she bought, the expression 18.54x+23 gives the amount she spent in dollars at one store. Then she spent 25 dollars at another store. Find the expression which represents the amount Rita spent at the mall. Then estimate how much Rita spent if she bought 2 items.
Answers
Answer:
18.54x +48$85Step-by-step explanation:
The total amount Rita spent is ...
(18.54x +23) +(25) = 18.54x +48 . . . total spent
__
When x=2, that is approximately ...
(18.5)(2) + 48 = 37 +48 = (40 -3) +(50 -2) = (40 +50) -(3 +2) = 90 -5 = 85
Rita spent about $85 if she bought 2 items.
_____
Additional comment
Estimation is often done using 1 significant figure. In this case, that would mean rounding the equation to 20x+50, so it would give a value of 90 when x=2.
An additional task when estimating is to estimate the error in the estimate. Here, using 20x+50 has an error of approximately 1.5x+2 (too high), so the error for 2 items will be about (1.5(2)+2) = 5. That is, the estimate of 90 is approximately 5 too high. Even this estimate has a remaining small error of 0.04x (too low).
х2 + 2x, 3х + 5, x2 + 1, 6x - 4
Answers
Answess
Step-by-step explanation:
-3(3 - 10x) please help, distributive property.
Answers
Answer:
-9 +30x
Step-by-step explanation:
-3(3) = -9
-3(-10x) = 30x
-9 +30x
Hope that helps
Please someone help meee! It’s advanced algebra
Answers
Answer: I think it would be 80 feet I hole I’m correct.
Step-by-step explanation: So to explain 20 + 50 is 80 and that’s how I got the answer I am not 100% sure but I wanted to help you :-)
Find the size of unknown angles
Answers
Answer:
hope it helps.
plzz give me brainliest
Write the inequality represented by the graph below. (0,-2) (0,1)
Answers
Our answer is y > (with the line at the bottom) 2x - 2.
5x/2 - 3x/4 = 10 1/2
how to solve this?
Answers
[tex] \frac{5x}{2} - \frac{3x}{4} = 10 \frac{1}{2} \\ [/tex]
[tex] \frac{5x}{2} - \frac{3x}{4} = \frac{21}{2} \\ [/tex]
Multiply both sides by 4
[tex]4 \times ( \frac{5x}{2} - \frac{3x}{4} ) = 4 \times \frac{21}{2} \\ [/tex]
[tex]10x - 3x = 42[/tex]
[tex]7x = 42[/tex]
Divide both sides by 7
[tex] \frac{7x}{7} = \frac{42}{7} \\ [/tex]
[tex]x = 6[/tex]
If someone has a cylindrical container filled to the top with water and pours the water in a cone with the same diameter, d= 6in, and height, h=14 in, into the cone, what is the volume of water left in the cylinder?
Answers
Answer:
6.2
Step-by-step explanation: TOOK THE TEST
Sam paid $50 for her new skateboard. In addition, she paid $3.50 in taxes. What was the tax rate on Sam's purchase?
Answers
Answer: $53.50 ?
Step-by-step explanation:
Maria earns $12/hour as a store clerk. This week she worked 49 hours. Estimate her
gross wage for her 2 week pay period, assuming she worked 40 hours last week?
Answers
Answer:
a= $1,068 without overtime pay
b= $1,122 with overtime pay
Step-by-step explanation:
[tex]a = (12 \times 49) + (12 \times 40) \\ = 1068[/tex]
[tex]b = (9(12 \times 1.5) + (12 \times 40)) + (12 \times 40)\\ = 1122[/tex]
PLEASE ANSWER AS SOON AS YOU SEE THIS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Which expression is equivalent to 5 (2 + 7)? 2 (5 + 7) 2 + 7 (5) 5 (2) + 7 5 (2) + 5 (7)
Answers
Answer:
D. 5 (2) + 5 (7)Step-by-step explanation:
Given expression:
5(2 + 7)Distribute this to get:
a(b + c) = ab + ac5(2 + 7) = 5(2) + 5(7)Correct choice is D
Answer:
D. 5 (2) + 5 (7)
Step-by-step explanation:
Given expression:
• 5(2 + 7)
Distribute this to get:
• a(b + c) = ab + ac
• 5(2 + 7) = 5(2) + 5(7)
correct choice is D