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
Monica makes tomato sauce with the plants she grows in her garden. She uses 3 basil leaves in her sauce for every 8 tomatoes. She is making a big batch of sauce with 32 tomatoes from her garden.
Answers
Answer: 12 Basil leaves
Step-by-step explanation:
Given
Monica uses 3 basil leaves for every 8 tomatoes
For 32 tomatoes she needs
[tex]\Rightarrow 3\ \text{basil leaves}\equiv8\ \text{Tomatoes}\\\\\Rightarrow 4\times 3\ \text{basil leaves}\equiv4\times 8\ \text{Tomatoes}\\\\\Rightarrow 12\ \text{basil leaves}\equiv 32\ \text{Tomatoes}[/tex]
Thus, she needs 12 basil leaves.
Can someone help pls? :)
Answers
Answer:
209/50 is the improper fraction of 4.18
mixed no. is 4 9/50
Instructions: Find the measure of the indicated angle to the nearest degree.
Answers
Answer:
A = 79°
Step-by-step explanation:
CosA = adjacent ÷ hypoteneous
A = Cos^-1(6÷32)
A. =. 79.19°
A= 79°
Write an algebraic model based off this numerical model
Answers
Step-by-step explanation:
T0 = a³+4
T1 = a⁴x a¹ +4
T2= a³ + a³ + 4
T3= a⁴ + a⁴* a² + 4
T4= a⁴ + a⁴ x a¹ + 4
T5= a³ + a³ + a⁴+4
Answer:
hello,
Step-by-step explanation:
c(1)=5
c(2)=9
c(2)-c(1)=9-5=4
c(2)=9
c(3)=13
c(3)-c(2)=13-9=4
c(3)=13
c(4)=17
c(4)-c(3)=17-13=4
c(4)=17
c(5)=21
c(5)-c(4)=21-17=4
for n=1,2,...,k :
c(n+1)-c(n)=4 and c(n+1)=4*(n+1)+1=4n+5
c(1)=1
Ya and Yb represent continuous linear relations. Some values from the relations are shown in the
table below. Graphically solve the linear system.
Answers
The solution to the continuous linear relation is: (2,-7)
The data on the table can be presented as:
Relation A
[tex](x_1,y_1) = (-8,-5)[/tex]
[tex](x_2,y_2) = (-3,-6)[/tex]
Relation B
[tex](x_1,y_1) = (-8,-15)[/tex]
[tex](x_2,y_2) = (-3,-11)[/tex]
Plot the points of each relation and draw a line through the points (see attachment)
Write out the point of intersection of the two lines.
[tex](x,y) = (2,-7)[/tex]
Hence, the solution to the continuous linear relation is: (2,-7)
Read more at:
https://brainly.com/question/20291958
Does anyone know what math topic this is?
Answers
Answer:
Comparing quantities
profit loss
cost price selling price.....
Graph the image of each figure under the given translation
Answers
Answer:
zzzzzZzzzzzzzzzzzzzzzzz zzz-zzzZzzzzzzzz
Step-by-step explanation:
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz
After 10 years, Hamid's account earned $900 in interest. If the interest rate (in decimal form) is 0.08, how much did Hamid initially invest? Without substitution, solve the formula chosen in the previous step for the unknown variable in terms of the known variable(s).
Answers
Answer:
Hamid initially invested $1,125.
Step-by-step explanation:
This is a simple interest problem.
The simple interest formula is given by:
[tex]E = P*I*t[/tex]
In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.
After 10 years, Hamid's account earned $900 in interest.
This means that [tex]t = 10, E = 900[/tex]
Interest rate of 0.08:
This means that [tex]I = 0.08[/tex]
How much did Hamid initially invest?
We have to find P. So
[tex]E = P*I*t[/tex]
[tex]900 = P*0.08*10[/tex]
[tex]P = \frac{900}{0.8}[/tex]
[tex]P = 1125[/tex]
Hamid initially invested $1,125.
I don't understand need help?
Answers
9514 1404 393
Answer:
2. (only)
Step-by-step explanation:
The Pythagorean theorem tells you the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. To determine if these are right triangles, determine if that condition is met.
1. 3^2 +5^2 = 9 + 25 = 34 ≠ (√35)^2 . . . . not a right triangle
2. 5^2 +4^2 = 25 +16 = 41 = (√41)^2 . . . a right triangle
3. 6^2 +8^2 = 36 +64 = 100 ≠ (√10)^2 . . . . not a right triangle
4. 3^2 +3^2 = 9 +9 = 18 ≠ (3√3)^2 = 27 . . . . not a right triangle
ZA and ZB are complementary angles. If m A = (x – 21)° and m
ZB = (2x – 15)°, then find the measure of ZA.
Answers
Answer:
A = 21
Step-by-step explanation:
Complementary angles add to 90
x-21 + 2x-15 = 90
Combine like terms
3x -36 = 90
3x-36+36 = 90+36
3x = 126
Divide by 3
3x/3 =126/3
x = 42
We want to find ZA = x-21
A = 42-21
A = 21
If the sum of the measures of two angles is 90° they are known as complementary angles.
According to the question[tex] \bf \large \longrightarrow \: \:( x \: - \: 21) \: + \: (2x \: - \: 15) \: = \: 90 \degree[/tex]
Now , Opening brackets and simplifying
[tex] \bf \large \longrightarrow \: \: x \: - \: 21 \: + \: 2x \: - \: 15\: = \: 90 \degree[/tex]
[tex]\bf \large \longrightarrow \: \:3x \: - \: 36 \: = \: 90 \degree[/tex]
[tex]\bf \large \longrightarrow \: \:3x \: = \: 90 \: + \: 36[/tex]
[tex]\bf \large \longrightarrow \: \:3x \: = \: 126[/tex]
[tex]\bf \large \longrightarrow \: \:x \: = \: \frac{126}{3} \\ [/tex]
[tex]\bf \large \longrightarrow \: \:x \: = \: \cancel\frac{126}{3} \: \: \large \: ^{42} \\ [/tex]
[tex]\bf \large \longrightarrow \: \: x \: = \: 42[/tex]
Now , we have to find ZA .
ZA = x - 21[tex]\bf \large \implies \: \:A \: = \: 42 \: - \: 21[/tex]
[tex]\bf \large \implies \: \:A \: = \: 21[/tex]
The measure of angle ZA is 21°
Your teacher gave you 1/2 of a bag of candy, but she only gave your friend 1/3 of a bag. How much more of the bag did your teacher give you than your friend?
Answers
Answer:
We can convert the 2/3 bag of candy that we got to 16/24, by multiplying both the top and bottom by 8. Similarly, we multipy the 1/8 bag of candy that our friend got by 3 on the top and bottom to get 3/24.
We find the difference between these two:
(16/24) - (3/24) = (16-3)/24 = 13/24
So we get 13/24 more of the bag of candy than our friend did.
Answer:
1/6
Step-by-step explanation:
you’re being asked the difference between the amounts of your candy and your friend’s candy.
So you must subtract 1/3 from 1/2.
=> 1/2 - 1/3
=> 3*1 - 2*1/3*2. ( You criss-cross and you multiply the denominators)
=>. 3 - 2 /6
=> 1/6
So you got 1/6 more candies in your bag than your friend.
Debt is a result of spending more than you make.
True
False
Answers
the unknown side of a trapezium.
Answers
Answer:
11 mm
Step-by-step explanation:
121=area of a rectangle and area of triangle
121=x*8+(0.5)*x*(14-8), 11x=121, x=11
Answer:
[tex]11mm[/tex]
Step-by-step explanation:
Let the unknown side be x
[tex]Area \: \: \: of \: \: the \: \: trapezium = \frac{1}{2} \times (sum \: \: of \: \: \: the \: \: parallel \: sides) \times height \\ 121= \frac{1}{2} \times (8 + 14) \times x \\ 121 \times 2 = 22x \\ 242 = 22x \\ \frac{242}{22} = \frac{22x}{22} \\ 11 = x[/tex]
Please answer this question.
Answers
Answer:
B) 14%
Step-by-step explanation:
principal = 220000
First two years 10% paid.
.10 x 220000 = 22000
220000-22000 = 198000
x = percent
x = [tex]\frac{New -Old}{Old}[/tex]
x = [tex]\frac{170000-198000}{198000}[/tex]
x = -.1414
Round to .14
14% is the difference in amounts.
The principal (198000) will need to be reduced 14% to equal 170000
What’s is the product of
1/15 X 1/3 =?
Answers
Answer:
[tex] \frac{1}{45} [/tex]Step-by-step explanation:
[tex] \frac{1}{15} \times \frac{1}{3} [/tex]
[tex] = \frac{1}{15 \times 3} [/tex]
[tex] = \frac{1}{45} (ans)[/tex]
ASAP!! can i get some help on this question, and a step by step explanation please, it would help
a lot thanks.
Answers
Answer:
[tex]{ \tt{ {3x}^{2}(5 {x}^{3} ) = 15 {x}^{5} }}[/tex]
Step-by-step explanation:
[tex]{ \sf{3 {x}^{2}(5 {x}^{3} )}} \\ = { \sf{ {x}^{5} (3 \times 5)}} \\ = { \sf{15 {x}^{5} }}[/tex]
pls help asap no wrong answers------------
Answers
Answer:
0.75, 1.25
Step-by-step explanation:
first we bring the line equation into the same format as the parabola equation (y = ...)
3x - y = 1
=>
y = 3x - 1
now we can say for the intersection points both equations must have the same result.
4x² - 1 = 3x - 1
4x² - 3x = 0
x(4x - 3) = 0
there are only 2 possible cases to make this true :
x = 0
and 4x - 3 = 0
4x = 3
x = 3/4 = 0.75
for the y value let's use the easier equation (line) :
y = 3×3/4 - 1 = 9/4 - 4/4 = 5/4 = 1.25
This one is giving me trouble, I need help on it
What is the domain of the function graphed below?
Answers
Answer:
x≤7
Step-by-step explanation:
i hope it will help
===============================================
Explanation:
The drawing is fairly faint, but it appears there's an arrow pointing to the left at the location (-6,3). If this is the case, then the function curve continues on forever in that direction.
The domain is the set of allowed x values. If we were to place the pencil on the blue curve and shade the x axis directly above or below that pencil point, then we would effectively shade everything to the left of x = 7.
In other words, we would shade x < 7 on the number line. The value x = 7 itself is left out due to the open hole.
Again, this all assumes that there is an arrow at (-6,3) that points to the left.
By visual inspection, determine the best-fitting model of the three types of regression for the data plot below.
A. Quadratic
B. Exponential
C. Linear
D. None of the above
Answers
Answer:
B. exponential
Step-by-step explanation:
The graph is clearly decreasing exponentially, shown by the downward curve. Therefore, the answer should be B.
Please help me fast
Answers
Answer:
864
Step-by-step explanation:
A=6a^2=6·12^2=864
Answer:
864 in^2
Step-by-step explanation:
2(144+144+144) = 2(432) = 864 in^2.
Hope this helped!
I have been having a lot of trouble with this assignment and I don't really understand some of the graph so if anyone can a little help would be great
Answers
Answer:
1. The graph represents the inequality y > 2x + 1
2. The y-intercept (where a line meets the y-axis) is at point (0,1). This line rises by 2 for every point it moves to the right (this is called the slope). A dotted line means that point on the line are not included in the solution set, thus you use the > symbol.
1 point Write the equation of the line that is parallel to the line given and through the given point. Do not use spaces in your equation y=-x-3 (-3,4)
Answers
Answer:
y=3x+9......(i)
y=-4x-12...(ii)
these are the equation
What is the equation of the following line? Be sure to scroll down first to see
all answer options.
(0,0)
(-1/2, -3)
O A. y = 2x
O B. y=*
O C. y = 3x
ООО
OD. y = -6x
E. y=-*
OF. y = 6x
Answers
Answer:
I think the correct answer is F. y = 6x
We will see that the line equation is y = 6*x
How to find a linear equation?
A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we know that the line passes through two points (x₁, y₁) and (x₂, y₂) then we can write the slope as:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
In this case, the line passes through the points: (0, 0) and (-1/2, -3)
Then the slope is:
[tex]a = \frac{0 - (-3)}{0 - (-1/2)} = 6[/tex]
Then the line is of the form y = 6*x + b
To find the value of b, we use the fact that the line passes through the point (0, 0), then we have:
0 = 6*0 + b
0 = b
We can conclude that the line is y = 6*x
If you want to learn more about linear equations, you can read:
https://brainly.com/question/4074386
Minnie bought 6 postcards during 3 days of vacation. After 8 days of vacation, how many total postcards will Minnie have bought?
Answers
Explanation: 6/3 = 2 postcards per day
2x8 = 16 postcards
Answer:
16 post cards
Step-by-step explanation:
bcos (6postcards÷3days)=2. so 2postcards in a day. So the 2 postcards per day u multiply it by 8. (2postcards ×8 days)= 16 post cards
In circle O, the length of OB is 6 inches, and the measure of ∠AOB is 120°. What is the length of arc AB, in inches (show your answer in terms of π)? *
Answers
Answer:
4π inches
Step-by-step explanation:
Formula for finding length of arc AB = θ/360*2πr
Where,
Central angle (θ) = 120°
Radius (r) = 6 inches
Length of arc AB = 120/360*2*π*6
Length for arc AB = ⅓*12π
= 4π inches
please answer correctly and i will give 10 extra points
Answers
Answer:
I believe the answer would be 48.6 milliliters
Step-by-step explanation:
54 * 0.9 = 48.6
Solve 2x + 3y = C, for y
Answers
Answer:
y= [tex]\frac{c-2x}{3}[/tex]
Step-by-step explanation:
2x+3y=C
isolate y
3y=C-2x
y= [tex]\frac{c-2x}{3}[/tex]
if u can help be fast please
Answers
A) 5 sides = 72.00
interior =108.00
B) 9 sides = 40.00
interior = 140.00
C) 15 sides = 24.00
interior = 156.00
D) 19 sides = 18.95
interior = 161.05
These are exterior angles right? y'know what I'll just put both
Find the x and the y.
2x+y+79-x+4y=180
Answers
x = − 5 y + 101
A video store charges $12 for used games and $25 for new games. Jonathan has saved $300 to spend on video games. This scenario is represented by a linear equation.
12x + 25y = 300
x = number of used games
y = number of new games
How many games can Jonathan buy if he spends all his money on used games?
Answers
Answer:
25 used games
Step-by-step explanation:
Divide his money by the price for one used game
300/12
25
Answer:
y=0
12x=300
X=300/12
X=25
he can buy 25 used games .
Step-by-step explanation:
