Answer:
We know that:
x = 3 + 2*√2
And we want to find the value of:
[tex]x - \frac{1}{x}[/tex]
First, we can rewrite the above expression as:
[tex]x - \frac{1}{x} = \frac{x^2}{x} - \frac{1}{x} = \frac{x^2 - 1}{x}[/tex]
Now we can replace the value of x by the one above, we will get:
[tex]\frac{x^2 - 1}{x} = \frac{(3 + 2*\sqrt{2})^2 - 1 }{3 + 2*\sqrt{2} } = \frac{3^2 + 2*2*\sqrt{2} + (2*\sqrt{2})^2 - 1 }{3 + 2*\sqrt{2} }[/tex]
Now we can simplify this to get:
[tex]\frac{9 + 4*\sqrt{2} + 4*2 - 1 }{3 + 2*\sqrt{2} } = \frac{16 + 4*\sqrt{2} }{3 + 2*\sqrt{2} }[/tex]
We could finally compute that last equation, to get:
[tex]\frac{9 + 4*\sqrt{2} + 4*2 - 1 }{3 + 2*\sqrt{2} } = \frac{16 + 4*\sqrt{2} }{3 + 2*\sqrt{2} } = 3.716[/tex]
does the following data show direct variation.
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Write the quadratic equation in factored form. Be sure to write the entire equation.
x2 - 5x - 24 = 0
Answer:
2x-5x-24=0
-3x-24=0
-3x=24
x=24/-3
x=-8
Answer:
x=x2-24/5
2 −24
Step-by-step explanation:
x2−5x−24=0
Add 5x to both sides. Anything plus zero gives itself.
x
2
−24=5x
Add 24 to both sides.
x
2
=5x+24
These marbles are placed in a bag and two
of them are randomly drawn.
What is the probability of drawing two yellow
marbles if the first one is NOT placed back into
the bag before the second draw?
Give your answer as a rational number, reduced to
simplest terms.
1
[ ?
Hint: Multiply the probability of the 1st Event by the
probability of the 2nd Event to get your answer.
Answer: 1/45
Step-by-step explanation:
Please answer number 5 I’ll give brainliest thanks
Answer:
Hello! answer: C
Hope that helps!
Answer:
b
Step-by-step explanation:
Experimental - 5 choices, 1 is Q = 1/5
Theoretical - 5 choices, landed on Q 4 times =4/5
guys help meeee im timed
These cones are similar. Find the surface
area of the smaller cone. Round to the
nearest tenth.
2 cm
3 cm
Surface Area = [ ? ) cm2 Surface Area = 75 cm2
Helppppp plssss
Answer:
33.3 cm²
Step-by-step explanation:
Recall: Area Scale Factor = (Linear Scale Factor)²
Area scale factor = surface area of bigger cone/surface area of smaller cone
Let the surface area of the smaller cone be represented as x
Therefore,
Area scale factor = 75/x
Linear scale factor = radius of bigger cone/radius of smaller cone = 3/2
Thus:
75/x = (3/2)²
75/x = 9/4
Cross multiply
x*9 = 75*4
9x = 300
Divide both sides by 9
x = 300/9
x = 33.3 cm² (nearest tenth)
PLssssssssssssss help..
Answer:
141.4
Step-by-step explanation:
i think
Alondra studies 7 hours this week for end-of-year exams. He spends 1 hour on English and an equal number of hours each on math, science and history.
Write an equation and find the solution.
Step-by-step explanation: 5 19 7 36
Alondra studies 7 hours this week for end-of-year exams. He spends 1 hour on English and an equal number of hours each on math, science and history.
Write an equation and find the solution
Total hours = english hours + ( math + science + history ) hours
Total hours = english hours + other subjects hours
7 hours = 1 hours + 3( x ) hours solve for x
(7 - 1) hours = (1 - 1) hours + 3x hours
6 hours / 3 = 3x / 3 hours
2 hours = x hours
Emma buys two bus tickets to Bradford. She pays with a £10 note. How much change will she get?
Hello there I hop you are having a good day :)
So, if she brought 2 tickets an they cost £4.00 you would add £4.00 + £4.00 = £8.00 and then you would take that away from the £10.00 - £8.00 = £2.00 so Emma would get £2.00 change :) hopefully that helps you.
(2/7×8/4)+2/3÷(2/6×3/6+1/6)
Answer:
Answer attached
Step-by-step explanation:
Help!! Can someone explain this to me I’m not getting it.
Answer:
A. 99 sq cm
Step-by-step explanation:
Area of geometric shape
= 2 times the area of one triangle with base a and height c
+ 2 times the area of one triangle with base c and height b
+ Area of rectangle with dimensions a and c.
[tex] = 2 \times \frac{1}{2} ac + 2 \times \frac{1}{2} bc + ac \\ \\ = ac + bc + ac \\ \\ = 2ac + bc \\ \\ = 2(13)(3) + 7(3) \\ \\ = 78 + 21 \\ \\ = 99 \: sq \: cm[/tex]
=============================================================
Explanation:
The rectangular base has area of length*width = a*c = 13*3 = 39 square cm. Let m = 39 since we'll use it later.
The triangles on the left and right sides have an area of base*height/2 = c*b/2 = 3*7/2 = 21/2 = 10.5 sq cm. They combine to an area of 2*10.5 = 21 sq cm. Let n = 21 since we'll use it later.
The triangles in the north and south positions have base 'a' and height 'c', so the area of each is base*height/2 = a*c/2 = 13*3/2 = 39/2 = 19.5 sq cm. That means the two north and south triangles add up to 19.5+19.5 = 39 sq cm. Let p = 39 since we'll use it later.
Overall, we have a total area of m+n+p = 39+21+39 = 99
The area of this flat 2D figure is 99 sq cm. If we folded along the dashed lines, then we'd get a 3D rectangular pyramid that has surface area of 99 sq cm. The surface area is the amount of material along the outside of the 3D figure. Or you can think of it like saying "If we painted all four sides of the 3D pyramid, then we cover 99 cm^2 of area".
A company rents storage sheds shaped like rectangular prisms. Each shed is 13 feet long and 6 feet wide and 12 feet tall the rental cost is 4$ per cubic foot how much does it cost to rent one shed
Answer:
It costs $3,744 to rent one shed.
Step-by-step explanation:
Given that a company rents storage sheds shaped like rectangular prisms, and each shed is 13 feet long and 6 feet wide and 12 feet tall, and the rental cost is 4 $ per cubic foot, to determine how much does it cost to rent one shed The following calculation must be carried out, knowing that the volume of a rectangular prism is obtained by multiplying its length by its width and its height:
(13 x 6 x 12) x 4 = X
(78 x 12) x 4 = X
936 x 4 = X
3.744 = X
Therefore, it costs $ 3,744 to rent one shed.
Five times the sum of 4 and some number is 40.
Answer:
5 × 4 = 20 not 40
Step-by-step explanation:
A multiple choice test contains questions
with four options each: A, B, C, or D. If
Natalie randomly guesses on the last three
questions, what is the probability that she
gets all three correct?
Answer:
Probability of getting all three correct answer = [tex]\frac{1}{64}[/tex]
Step-by-step explanation:
Given - A multiple choice test contains questions with four options each: A, B, C, or D. If Natalie randomly guesses on the last three questions.
To find - what is the probability that she gets all three correct.
Proof -
Given that, question has 4 options.
And 1 option can be correct,
Let
x be that Natalie gives correct answer.
So,
Probability of getting, correct answer, P(x) = [tex]\frac{1}{4}[/tex]
So,
Probability of getting, incorrect answer, P(x') = 1 - [tex]\frac{1}{4}[/tex] = [tex]\frac{3}{4}[/tex]
Now,
Given that, she guess the 3 questions.
All correct means,
first, second, third question answer is correct.
So,
Probability of getting all three correct answer = [tex]\frac{1}{4}[/tex]×[tex]\frac{1}{4}[/tex]×[tex]\frac{1}{4}[/tex] = [tex]\frac{1}{64}[/tex]
Tessellations
Determine whether the following regular polygon tessellates the plane.
Decagon
a. Yes; measure or interior angle = 144
b. no; measure of interior angle = 144
c. yes: measure of interior angle = 36
d. no; measure of interior angle = 36
Please select the best answer from the choices provided
Answer:
B. No; measure of interior angle = 144
Step-by-step explanation:
I calculated it logically
Find the area of the shaded region 29.8, 28, 13
The solution is, The area of the shaded region is 112cm^2.
What is area ?Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
here, we have,
First find the area of the rectangle
A = l*w
= 9*16
= 144
The unshaded area is a trapezoid
A = 1/2 ( b1+b2) *h
= 1/2 ( 5+11) * 4
= 1/2 (16) * 4
=32
The area of the shaded region is
rectangle - trapezoid
144-32
112cm^2
Hence, The solution is, The area of the shaded region is 112cm^2.
To learn more on Area click:
brainly.com/question/20693059
#SPJ3
An average of 40 cars per hour arrive to be painted at a single-server GM painting facility. 95% of the cars require 1 minute to paint; 5% must be painted twice and require 2.5 minutes to paint. Assume that interarrival times are exponential.
a. On the average, how long does a car wait before being painted?
b. If cars never had to be repainted, how would your answer to part (a) change?
Answer:
2.719 minutes
Step-by-step explanation:
Step 1 :
We have to consider using the M/G/I /GD /∞/∞ Queuing system with the rate of arrival λ and the rate of service μ.
Since average of 40 cars arrive every hour at the painting facility, it follows that:
Arrival rate λ = 40cars /hour
= 40/60 cars/hour
=2/3 cars/hour
More, we were told that 95% of the cars require 1 minute to paint, 5% must be painted twice and require 2.5 minutes to paint, therefore, the average time to paint a car is given by
95/100x1 + 5/100 x 2.5 = 19/20 + 1/8 = 43/40min
It follows that:
Service rates μ = 40/43cars/min
to solve an equation with a variable which of the following are done? the value of the variable should be guest first inverse operation are used the variable needs to be isolated addition is always used select all that apply.
9514 1404 393
Answer:
inverse operation are used the variable needs to be isolatedStep-by-step explanation:
A solution is always of the form ...
variable = something
In order to get this form, the variable needs to be isolated (put by itself on one side of the equal sign).
In general, isolating the variable involves using inverse operations to "undo" whatever is done to the variable. These are generally applied in the reverse order of the operations that are done to the variable. The list of operations done and their order can be identified using the Order of Operations to consider how an equation would be evaluated for some value of the variable.
56000009x434383985934863
Answer:
2.43255071E22
Rounding to the nearest tenth: 2.4
Nearest hundredth: 2.43
Step-by-step explanation:
Hope I helped! :)
Answer:
2.43255e16
Step-by-step explanation:
solve the given system of equations 2x + 8y= 5 and 24x - 4y = -15
9514 1404 393
Answer:
(x, y) = (-1/2, 3/4)
Step-by-step explanation:
A graphing calculator does a nice job of finding the solution.
(x, y) = (-1/2, 3/4)
__
You can eliminate y by adding twice the second equation to the first.
(2x +8y) +2(24x -4y) = (5) +2(-15)
50x = -25
x = -1/2 . . . . . . divide by 50
__
24(-1/2) -4y = -15 . . . . .substitute for x in the second equation
-4y = -3 . . . . . . . . . add 12
y = 3/4 . . . . . . . . . divide by the coefficient of y
The solution is (x, y) = (-1/2, 3/4).
choose the correct symbol to compare the fraction 8/10 and 4/5
Answer:
[tex]\frac{8}{10} =\frac{4}{5}[/tex]
Step-by-step explanation:
Both the numerator and denominator of the fraction [tex]\frac{8}{10}[/tex] share a common factor of 2, so you can divide the fraction by [tex]\frac{2}{2}[/tex](1). This leaves you with:
[tex]\frac{8}{10}[/tex] ÷ [tex]\frac{2}{2}[/tex] = [tex]\frac{4}{5}[/tex]
This means that the fraction [tex]\frac{8}{10} =\frac{4}{5}[/tex].
5(x+1)=4(x-1)+x
What is x?
Answer:
There isn't an answer.
Step-by-step explanation:
5(x+1) = 4(x-1) + x
5x + 5 = 4x - 4 + x
5x +5 = 5x -4
0 = -9
no x, so no answer.
Robert spun the fair spinner shown below 1,060 times,
About how many times would Robert expect to spin a 1, 3, or 8?
Answer:
About 400 times
Step-by-step explanation:
Given
[tex]n = 1060[/tex]
See attachment for spinner
Required
Determine the number of times an outcome of 1, 3 or 8 is expected
First, calculate the theoretical probability of 1, 3, or 8
This is calculated as:
[tex]Pr = P(1) + P(3) + P(8)[/tex]
The spinner is divided into 8 equal segments and each outcome appears once.
So, we have:
[tex]Pr = \frac{1}{8}+\frac{1}{8}+\frac{1}{8}[/tex]
Take LCM and add
[tex]Pr = \frac{1+1+1}{8}[/tex]
[tex]Pr = \frac{3}{8}[/tex]
So, the expected number of times (E) is:
[tex]E = Pr * n[/tex]
[tex]E = \frac{3}{8} * 1060[/tex]
[tex]E = \frac{3* 1060}{8}[/tex]
[tex]E = \frac{3180}{8}[/tex]
[tex]E = 397.5[/tex]
Approximate
[tex]E = 398[/tex]
This means about 400 times
Write each rational numbers as a decimal rounded to 4 decimal places.
43/10 = and 4 15/18 =
Answer:
Step-by-step explanation:
3
Given a bag of marbles 3 are red, 5 are black, and 8 are green, what is the
probability that the you do not pull out a red marble?
Answer:
13/15
86.67%
Step-by-step explanation:
non red marbles = 13
total marbles = 15
13/15 = 0.866667
86.67%
Helppp PLEASEEEE!!!!!! !!!
Answer:
-3hf
Step-by-step explanation:
graph your linear equation. y=x÷3
Which equation is true when x =
1
2
?
A.
6
÷
x
=
3
B.
8
x
=
16
C.
x + 2 = 1
D.
10
÷
x
=
20
Answer:
Step-by-step explanation:
NO ONE IS TRUE
6/12=2NOT 3
8*12=96NOT16
12+2=14 NOT 1
10/12=1.2 NOT 20
Use the information for the question below.
Project A Project B Time 0 -$10,000 -$10,000 Time 1 $5,000 $4,000 Time 2 $4,000 $3,000 Time 3 $3,000 $10,000
If WiseGuy Inc. uses payback period rule to choose projects, which of the projects (Project A or Project B) will WiseGuy Inc. prefer?
a. Project A and Project B have the same ranking,
b. Project A
c. Cannot calculate a payback period without a discount rate.
d. Project B
Answer:
The correct option is d. Project B.
Step-by-step explanation:
Note: See the attached excel file for the calculation of the Cumulative Cash Flows of Projects A and B.
Payback period refers to the number of time or period that is needed to recoup the amount of money spent a project. The
payback period rule states that when considering two or more projects, a project with the shortest payback period should be selected.
Payback period can be calculated as follows:
Payback period = Time before full recovery + (Unrecovered cost at start of the time of full recovery / Cash flow during the time of full recovery) ………………. (1)
Using the information in the excel file (in red color), equation (1) can be calculated for Project A and Project B as follows:
Project A payback period = 2 + ($1,000 / $3,000) = 2.33
Project B payback period = 2 + ($3,000 / $10,000) = 2.30
Since the payback period of Project B payback period which is 2.30 is lower than the Project A payback period of 2.33, Project B should be selected.
Therefore, the correct option is d. Project B.
Connor made 16 brownies. He put nuts on 6 brownies. Write
the simplified fraction of the brownies that had nuts.
6/16 = 3/8
hope this helps