=========================================================
Work Shown:
A = 1+sqrt(2)
B = 1-sqrt(2)
-------------------
Using A and B, let's add and subtract those values
A+B = (1+sqrt(2))+(1-sqrt(2))
A+B = 1+sqrt(2)+1-sqrt(2)
A+B = 1+1+sqrt(2)-sqrt(2)
A+B = 2
and
A-B = (1+sqrt(2))-(1-sqrt(2))
A-B = 1+sqrt(2)-1+sqrt(2)
A-B = 1-1+sqrt(2)+sqrt(2)
A-B = 2sqrt(2)
-------------------
Next, square both sides of the A equation
A^2 = (1+sqrt(2))^2
A^2 = (1+sqrt(2))(1+sqrt(2))
A^2 = 1(1+sqrt(2))+sqrt(2)(1+sqrt(2))
A^2 = 1+sqrt(2)+sqrt(2)+sqrt(2)*sqrt(2)
A^2 = 1+2sqrt(2)+2
A^2 = 3+2sqrt(2)
-------------------
Do the same for B
B^2 = (1-sqrt(2))^2
B^2 = (1-sqrt(2))(1-sqrt(2))
B^2 = 1(1-sqrt(2))-sqrt(2)(1-sqrt(2))
B^2 = 1-sqrt(2)-sqrt(2)-sqrt(2)*(-sqrt(2))
B^2 = 1-2sqrt(2)+2
B^2 = 3-2sqrt(2)
There's a bit of nice symmetry going on with A^2 and B^2, due to A and B having similar symmetric structures themselves.
-------------------
Lets add A^2 to B^2
A^2+B^2 = (3+2sqrt(2)) + (3-2sqrt(2))
A^2+B^2 = 3+2sqrt(2) + 3-2sqrt(2)
A^2+B^2 = 3+3+2sqrt(2)-2sqrt(2)
A^2+B^2 = 6
-------------------
Now onto the final event
We'll use the difference of squares rule twice
Afterward, apply substitution using the previous sections above.
A^4 - B^4 = (A^2)^2 - (B^2)^2
A^4 - B^4 = (A^2-B^2)(A^2+B^2)
A^4 - B^4 = (A-B)(A+B)(A^2+B^2)
A^4 - B^4 = (2sqrt(2))(2)(6)
A^4 - B^4 = 2*6*2*sqrt(2)
A^4 - B^4 = 24*sqrt(2)
(1+sqrt(2))^4 - (1-sqrt(2))^4 = 24*sqrt(2)
-------------------
To check this with your calculator, you can type in the following
(1+sqrt(2))^4 - (1-sqrt(2))^4 - 24*sqrt(2)
The result you should get should be 0, or very close to it
I'm using the property that if x = y, then x-y = 0.
12. A worker can pack 72 boxes of oranges in 2 hours. At this rate, how many boxes of oranges can she pack
in 8 hours?
Help please, I need this done as soon as possible
Answer:
b
Step-by-step explanation:
A math class is having a discussion on how to determine if the expressions 4x-x+ 5 and 8-3x-3 are equivalent using
substitution.
The class has suggested four different methods.
Which describes the correct method?
O Both expressions should be evaluated with one value. If the final values of the expressions are both positive, then the
two expressions must be equivalent.
OBoth expressions should be evaluated with one value. If the final values of the expressions are the same, then the
two expressions must be equivalent.
O Both expressions should be evaluated with two different values. If for each substituted value, the final values of the
expressions are positive, then the two expressions must be equivalent.
O Both expressions should be evaluated with two different values. If for each substituted value, the final values of the
expressions are the same, then the two expressions must be equivalent.
Answer:
the correct answer is the second one
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
When you are trying to find if they are equivalent, you only want to use one value. If they are both positive, it doesn't mean that they are quivalent. They would have to be the same.
Which equation shows the relationship between the
number of poles ordered, n, and the total cost, c?
A. c = 3n + 120
B. c = 4n + 180
C. c = 20n + 60
D. c = 40n
(NEED HELP ITS DUE TODAY)
Plz Help Ill give brainliest
What is the midpoint of the line segment with the given endpoints?
(−7, 3) and (13, −9)
Answer:
3, -3
Step-by-step explanation:
Solve.
3(x-4) = -3
How do i slove this
Answer:
[tex]3(x - 4) = - 3 \\ 3x + 12 = - 3 \\ 3x = - 15 \\ x = - 5[/tex]
Firstly, multiply the number and variable in the perenthesis. Then move the variable on it's own side of the equation. The simplify.
Answer:
You need to do the Distributive Property. This means multiplying the number outside the parenthesis to each number inside.
Step-by-step explanation:
3(x)=3x
3(-4)=-12
3x+-12=-3
then evaluate using inverse operations to get x=3
5a+12 = 9A-12
Can anybody help me ?
Answer:
a=6
Step-by-step explanation:
5x+12=9x-12
5x+12-12=9x-12-12
5x=9x-24
5x-9x=9x-24-9x
-4x=-24
-24/-4
x=6
Answer: 12 + 5a = 9a + -12
Reorder the terms:
12 + 5a = -12 + 9a
Solving
12 + 5a = -12 + 9a
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-9a' to each side of the equation.
12 + 5a + -9a = -12 + 9a + -9a
Combine like terms: 5a + -9a = -4a
12 + -4a = -12 + 9a + -9a
Combine like terms: 9a + -9a = 0
12 + -4a = -12 + 0
12 + -4a = -12
Add '-12' to each side of the equation.
12 + -12 + -4a = -12 + -12
Combine like terms: 12 + -12 = 0
0 + -4a = -12 + -12
-4a = -12 + -12
Combine like terms: -12 + -12 = -24
-4a = -24
Divide each side by '-4'.
a = 6
Simplifying
a = 6
Step-by-step explanation: found it off of google
R(5. -4) reflect it across the y-axis.
Answer:
(-5,-4)
Step-by-step explanation:
reflection over y-axis makes (x,y) become (-x,y)
PLZ HELP!! ALGEBRA! WILL GIVE U BRAINLIEST!
Answer:
a. -21 b. 14
Step-by-step explanation:
For a, -3x4=-12, and then -12-9=-21. For b, -1/3x-3=1, and then 1+13=14. Hope it helps!
Answer: A.) -21
B.) 14
Step-by-step explanation:
f(-3)=x
A.) f(-3) = 4(-3) - 9
= -12-9
= - 21
B.) f(-3) = -1/3(-3) + 13
= 1 + 13
= 14
Have a nice day good night
3 consecutive even integers that add up to 36
Answer:
10, 12, 14
Step-by-step explanation:
Answer:
10,12 and 14
Step-by-step explanation:
Hope that helps <3
HELP ASAP
Jason has $2.25 worth of dimes and quarters. He has twice as many dimes as quarters. Determine the number of dimes and the number of quarters that Jason has.
Answer:
Step-by-step explanation:
let the number of dimes=x
and number of quarters=y
x=2y
0.10 x+0.25 y=2.25
or 10x+25y=225
divide by 5
2x+5y=45
2 ×2y+5y=45
4y+5y=45
9y=45
y=45/9=5
x=2y=2×5=10
Hence dimes=10
quarters=5
WILL GIVE BRAINLIEST, COMMENT, LIKE, AND 7 POINTS TO BEST ANSWER
If you and a friend walked the same difference at different time, how can you tell who walked faster?
Answer:
By the amount of time it took you guys to get there
Step-by-step explanation:
For example, if I start walking at 8:55 and arrive by 9:10, then it took me about 15 minutes to get there.
If you start walking at 9:10 and arrive by 9:20, it took you 10 minutes to get there meaning you walked faster.
Hope I helped.
Eight rolls of paper towels cost $4.80. At the same unit rate, how much will six rolls of paper towels cost? Describe the steps that you took to determine your answer.Eight rolls of paper towels cost $4.80. At the same unit rate, how much will six rolls of paper towels cost? Describe the steps that you took to determine your answer.
Answer:
$3.6Step-by-step explanation:
Given that 8 rolls cost $4.80
let us compute how much 1 roll will cost (that is the unit cost of a roll)
so 8 rolls cost $4.80
1 roll will cost x
x= 4.8/8
x=$0.6
so the paper tower cost $0.6 per roll (this is the rate)
therefore 6 rolls will cost
=6*0.6
=$3.6
I need to match each equation with the right answers and I need to show my work for each one
Convert 1/12 ft. To inches.
Answer:
1 inch
Step-by-step explanation:
There are 12 inches in 1 foot so 1/12 is 1 inch
1 foot = 12 inches
1/12 feet = 1 inch
Hallie has 10 times as many pages to read for her homework assignments as Janet. Altogether, they have to read 264 pages. How many pages does each girl have to read?
Answer: 24 pages
Step-by-step explanation:
10 times 24 equals 240
Answer:
Janet has to read 24 pages.
Hallie has to read 240 pages.
Step-by-step explanation:
If Janet has to read n pages, then Hallie has to read 10×n.
Together they have to read 11 × n = 264 pages, so: n=264÷11=24.
Hope this helps
What is the slope of the graph of 3x - 3y = 6?
Answer:
pls help
Step-by-step explanation:
1. Half of a number is at most 5 units from 14.
Answer:
18≤n≤38
Step-by-step explanation:
James bought a car and paid for it in equal payments of $854. After making 41 payments, he still had to pay $16,331.
the temperature in Chicago is 38 digresses it is 40 colder in north Dakota what is the temperature in north Dakota
Answer:
It would -2 degrees in North Dakota.
Step-by-step explanation:
Subtract 40 from 38 to get to -2.
b) Simplify the expression (V7 + 3) square 2
Answer:
[tex]49v^{2} +42v+9[/tex]
Step-by-step explanation:
First, let me say, I'm not sure what exactly the equation is because it's worded weirdly, but I'm assuming it's [tex](7v+3)^{2}[/tex].
(7v+3)(7v+3) [[tex]7v+3^{2}[/tex] is the same as (7v+3)(7v+3).]
[tex]49v^{2} +42v+9[/tex] [When you multiply them, this is the product.]
This is as far as you can simplify without knowing the value of v as far as I know.
helpgchjsghjcvbxnvbsvjdgasghgbhdvbahgvgbd
Answer:
yeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeet
Step-by-step explanation:
Find ABC, Please help!
Answer:
50°
Step-by-step explanation:
Angle A = AngleB (Corresponding angles)
x=2x-50
x=50°
Hope it helps
Answer:
∠ ABC = 50°
Step-by-step explanation:
2x - 50 and x are corresponding angles and congruent, thus
2x - 50 = x ( subtract x from both sides )
x - 50 = 0 ( add 50 to both sides )
x = 50
Thus
∠ ABC = x = 50°
Factor the expression completely.
40x + 32
Answer:
8(5x+4)
Step-by-step explanation:
divide by the GCF 8
Answer:
8(5x + 4)
I hope this helps!
Which equation in standard form has a graph that passes
through the point (-5,11) and -2.5 is the slope.
What is the rate of change from 2
gallons to 4 gallons? Pls I need help!!
Answer:
2 gallons
Step-by-step explanation:
PLSS HELP DUE IN 4 MINS
Answer:
The inverse is 1/2x -1/2
Step-by-step explanation:
f(x) = 2x+1
y = 2x+1
Exchange x and y
x = 2y+1
Solve for y
Subtract 1
x-1 = 2y+1-1
x-1 =2y
Divide by 2
x/2 -1/2 = 2y/2
1/2x -1/2 = y
The inverse is 1/2x -1/2
PLEASE HELP ASAP DUE SOON
the answer is
C. neither
Which equation represents the graphed function?
A. -3x+2=y
B. -2/3x+2=y
C. 3/2x-3=y
D. 2x-3=y
Plz help me I am taking the unit test on edge
Answer:
try c, i took the test as well its either that or b
Step-by-step explanation:
Answer:
I'm pretty sure the answer is D
what is the domain of the function represented by the graph?
Answer: x is equal to or bigger than -3
Step-by-step explanation: