=========================================================
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.
If 2KL=KL+MN, then KL=MN
Choose the definition, theorem, or postulate that justifies the statement.
A. Subtraction Property of Equality
B. Definition of Midpoint
C. Segment Addition Postulate
D. Symmetric Property (of= or≅)
E. Reflexive Property (of= or≅)
F. Transitive Property (of= or≅)
G. Definition of Congruence
H. Substitution Property
I. Addition Property of Equality
J. Multiplication Property of Equality
K. Division Property of Equality
Answer:
a. subtraction property of equality
Step-by-step explanation:
A rectangle on a coordinate plane is translated 5 units up and 3 units to the left. Which rule describes the translation?
(x, y) → (x + 5, y – 3)
(x, y) → (x + 5, y + 3)
(x, y) → (x – 3, y + 5)
(x, y) → (x + 3, y + 5)
Answer:
The last one (x,y)->(x+3,y+5)
Step-by-step explanation:
Whenever you move the x coordinate it’s the opposite, for example translated 3 units the the left is +3 and translated 3 units to the right is -3.
Whenever you move the y coordinate it’s normal so up 5 units means +5 and down means -5.
Answer:
C
Step-by-step explanation:
simple addition
Which expressions are equivalent to 3x + 3(x + y)?
Choose all answers that apply:
A 6x + 3y
B 3(x + x + y)
C 3ay
Answer:
A and B
Step-by-step explanation:
3x+3(x+y)
3x+3x+3y
6x+3y
B
3(x+x+y)
3x+3x+3y
6x+3y
Best answer gets brainliest 2+2
Answer:
I would say this would be either 4, 22, or fish
5. It is a method of describing a set, in words.
A. Roster Notation
C. Set Builder Notation
B. Listing Method
D. Verbal Description Method
Answer
There are two common ways of describing or specifying the members of a set: roster notation and set builder notation. These are examples of extensional and intensional definitions of sets, respectively
50+ Points!
Solve the equation.
5^-9×325+(-42÷-14)
Answer:
−6347653.25 or 3.0001664, not my style of math but it is definitely one of the two.
Step-by-step explanation:
−1953125 x 325 + 3
−6347656.25 + 3 = −6347653.25
Answer:
3.0001664
Step-by-step explanation:
.
Select the smallest fraction from the following list of fractions.
3/4
2 2/3
3/5
1 1/2
7/8
2/3
Write an equation in slope-intercept form that passes through (2, -3) and slope of -5.
Step-by-step explanation:
Hey there!
The given slope is "-5" and it passes through point (2,-3).
Use one-point formula to find out the equation.
[tex](y - y1) = m(x - x1)[/tex]
Put all values.
[tex](y + 3) = - 5(x - 2)[/tex]
Simplify it.
[tex](y + 3) = - 5x + 10[/tex]
[tex]y = - 5x + 10 - 3[/tex]
[tex]y = - 5x + 7[/tex]
Therefore, the equation is y= -5x+7.
Hope it helps...
A town has a population of 2000 and grows at 3.5% every year. To the nearest year, how long will it be until the population will reach 3900?
Answer:
27 years.
Step-by-step explanation:
2000->100%
?->3.5%
=70 people growth each year
3900-2000=1900[expected growth]
70-per year
1900-?
1900*1/70=27.1
=27.|1
27 years
It will take 9 years for the town's population to reach 3900.
What is an exponential function?"An exponential function is a function of form f (x) = a^(x), where a is the base."
Exponential growth function:f(x) = a×(1+r)^x
where,
f(x) = exponential growth function
a = initial amount
r = growth rate
x = number of time intervals
For given situation,
initial population: a = 2000,
growth rate r = 3.5/100
⇒ r = 0.035
f(x) = 3900
We need to find the nearest year to reach the population 3900.
i.e., to find value of x(years)
Using the exponential growth function,
⇒ 3900 = 2000(1 + 0.035)^x
⇒ 3900/2000 = (1.035)^x
⇒ 1.95 = (1,035)^x
⇒ [tex]x=log_{1.035} 1.95[/tex]
⇒ x = 19.41
⇒ x ≈ 19
Therefore, it will take 19 years to reach 3900.
Learn more about exponential growth here:
https://brainly.com/question/11487261
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Rewrite the expression using a single, positive exponent: 14^-3x14^12
Answer:
14⁹
Step-by-step explanation:
When you're multiplying, you add the exponents. So, -3+12=9.
Please help me I really need it Big points for help.
The three Miller boys were calculating the volume of their new fish tank to determine how many gallons of water the tank can hold. Each brother measured a different dimension of the tank. Their measurements were 1 yard in length, 1 foot in width, and 18 inches in height.
1. There are approximately 7.5 gallons per cubic foot. If you want to know how many gallons of water the tank can hold, what unit of measure would you use to calculate the volume of the fish tank? Explain why
2. Determine how many gallons of water the fish tank can hold. Carefully show your work and include units of measure.
1. Because you know the number of gallons per square foot. You would want to use cubic feet for the measurement of the tank.
2. Convert all dimensions to feet:
1 yard = 3 feet
18 inches = 1.5 feet.
Volume of tank = 3 x 1.5 x 1 = 4.5 cubic feet.
Multiply gallons per cubic foot by cubic feet of tank:
7.5 x 4.5 = 33.75 gallons.
PLS ANSWER HELP
Thanks
Can y’all please help me with my question??
Answer:
p
Step-by-step explanation:
Can y’all please help me with my question??
The data represented by the following stem-and-leaf plot range from
to
2189
3 504
4 127
5 36
A. 29; 53
B. 28; 56
C. 28; 53
D. 29, 56
SUBMIT
Answer:
28;56
Step-by-step explanation:
According to the stem-and-leaf plot, the range of the data represented by the stem-and-leaf plot is 63.
To determine the range of the data represented in stem and leaf plot, we need to look at the smallest and largest values. The smallest value is obtained by taking the smallest leaf in the plot, which is 36, and adding it to its corresponding stem (5). So, the smallest value in the data set is 536.
Next, we look for the largest value, which is found at the bottom of the last stem. In this case, the last stem is 5, and the largest leaf is 9. Therefore, the largest value in the data set is 599.
Now that we have the smallest and largest values, we can calculate the range by subtracting the smallest value from the largest value:
Range = Largest Value - Smallest Value
Range = 599 - 536
Range = 63
So, the answer is Answer: C. 28; 53
To know more about stem and leaf plot here
https://brainly.com/question/32053953
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Please help, due in 6 hrs (will mark brainliest and giving 85 points) will ask seperate question for the 85 points
Answer: If I'm being honest I only know parts A and B.
A. (4, 19) and (7, 7).
B. 4/1 or just 4.
Step-by-step explanation:
B. From point (7, 7) to (6, 11) is up 4 and left 1, rise over run is how you write the slope so it would be written as 4/1. Depending on you're teacher you can just put 4 and it can be correct, so, 4/1 or just 4.
There are 2 out of 5 boxes shaded. What percent is not shaded?
Answer:
i am going to say 3/5 but am not sure
Step-by-step explanation:
in which of these situations do the quantities combine to make 0? A. A dolphin swims 20 feet straight down from the surface. It then rises 20 feet to return to the surface. B. Scott earns $20 at his family's garage sale. He then earns $20 walking dogs for his neighbors. C. Travis receives $10 from a friend to pay for a concert ticket. He then spends $20 on tickets for his friend and himself. D. A scuba diver drops 30 feet below sea level. He then swims 30 feet across the ocean floor.
Answer:
A. A dolphin swims 20 feet straight down from the surface. It then rises 20 feet to return to the surface.
Step-by-step explanation:
It goes down 20 then up 20
-20 + 20 = 0
Answer:
Answer A
Step-by-step explanation:
This is the correct option as you are going feet down and then 20 feet back up. So basically, an equation that would represent this is -20+20=0.
1. How can you tell the difference between the pre-image and image when only given the coordinates or a picture?
Answer:You need To tell them apart, they will usually be defined separately.
Step-by-step explanation:
Finance Application. Tony earned $8.25 per hour at his after school job. Each week he earned $80. Write and solve an equation to show how many hours he worked each week.
Answer:
9.6969 hours
Step-by-step explanation:
8.25x = 80
x = 9.6969 hours
The figure shows three quadrilaterals on a coordinate grid: A coordinate plane is shown. Quadrilateral D has sides measuring 3 units and 1 unit. Quadrilateral F has sides measuring 3 units and 1 unit. Quadrilateral E has sides measuring 2 units and 6 units. Which of the following statements is true about the three quadrilaterals? D and E are similar but not congruent. E and F are similar and congruent. D and E are similar and congruent. F and D are similar but not congruent.
Answer:
A: D and E are similar but not congruent.
Step-by-step explanation:
hope this help
Triangle CDA is the image of triangle ABC after a 180° rotation around the midpoint of segment AC. Triangle ECB is the image of triangle ABC after a 180° rotation around the midpoint of segment BC.
Answer:ABCD and ABEC are parallelograms because they both have a pair of parallel lines.
DCE AND CEB are congruent angels
How can I turn this into a graph in Desmos,
Answer:
in Desmos there should be a plus sign right above the list of your equations on the left side. Click that plus sign and then click "table". then enter your numbers. then your points will be shown on the graph
to turn this into a line long press on the button next "y" on the table you have made, then select "lines"
Answer:
you go to desmos and you go to the left side of the website. choose which graph you want to do. if you want to use a regression line graph, or anything else. lmk if you need help
Step-by-step explanation:
Jacob spent $10 of the $25 in his wallet write a decimal that represents the fraction of the $25 Jacob spent
Solve the inequality:
u^2 > 8u + 33
Answer:
u<−3 or u>11
Step-by-step explanation:
u2=8u+33
u2−(8u+33)=8u+33−(8u+33)(Subtract 8u+33 from both sides)
u2−8u−33=0
(u+3)(u−11)=0(Factor left side of equation)
u+3=0 or u−11=0(Set factors equal to 0)
u=−3 or u=11
drag each item to its correct place es de monomios
Answer:
Step-by-step explanation:
-2x
Grado : 1
Coefficiente : -2
Parte literal : x
x²y⁴:
Grado : 2+4 = 6
Coefficiente : 1
Parte literal : x²y⁴
i need help asap please
Answer:
270mi
Step-by-step explanation:
5.4/2 = 2.7
2.7 * 100 = 270
what equation represents the line that passes through (-2,-1) and has a slope of 5
Answer:
y + 1 = 5 (x+2) in point slope form or y = 5 x + 9 in intercept slope form
Step-by-step explanation:
Answer:
y=5x+9
Step-by-step explanation:
0.93=
please explain how you got the answer.
Please help and explain!! I WILL MARK BRAINLIEST
Answer:
plot a graph and count it
Step-by-step explanation:
midpoint is the middle point of the line. it can be found by dividing the length of the line by 2 then counting inwards by that number.
Identify the number of terms in this polynomial.
5k^5+7k-2
Answer:
cuatro terminos