Answers
Answer:
the answer is 10•57(approximated as 10•6)
Answer: [tex]\sqrt{3}+\sqrt{5}[/tex]
On a keyboard, we could type this as sqrt(3) + sqrt(5)
==============================================================
Explanation:
The given expression is considered a nested radical because one radical, the [tex]\sqrt{15}[/tex], is buried inside another radical.
Let's assume that nested radical is of the form [tex]\sqrt{a}+\sqrt{b}[/tex] where a & b are positive real numbers.
Set the given expression equal to [tex]\sqrt{a}+\sqrt{b}[/tex] and square both sides to see what happens. We'll do a bit of algebra to simplify and rearrange things a bit as well. See the steps below.
[tex]\sqrt{8+2\sqrt{15}} = \sqrt{a}+\sqrt{b}\\\\\left(\sqrt{8+2\sqrt{15}}\right)^2 = \left(\sqrt{a}+\sqrt{b}\right)^2\\\\8+2\sqrt{15} = \left(\sqrt{a}\right)^2 + 2\sqrt{a}\sqrt{b} + \left(\sqrt{b}\right)^2\\\\8+2\sqrt{15} = a + 2\sqrt{ab} + b\\\\8+2\sqrt{15} = (a+b) + 2\sqrt{ab}\\\\[/tex]
If we equate terms, we get this system of equations
[tex]\begin{cases}8 = a+b\\2\sqrt{15} = 2\sqrt{ab}\\\end{cases}[/tex]
Solve the first equation for 'a' to get a = 8-b
------------------------------
Let's plug a = 8-b into the second equation and solve for 'b'
[tex]2\sqrt{15} = 2\sqrt{ab}\\\\\sqrt{15} = \sqrt{ab}\\\\15 = ab\\\\15 = (8-b)b \ \ \text{ .... replace a with 8-b}\\\\15 = 8b-b^2\\\\b^2-8b+15 = 0\\\\(b-3)(b-5) = 0\\\\b-3 = 0 \ \text{ or } \ b-5 = 0\\\\b = 3 \ \text{ or } \ b = 5\\\\[/tex]
If b = 3, then a = 8-b = 8-3 = 5
If b = 5, then a = 8-b = 8-5 = 3
We have this symmetry going on with 'a' and b. If one value is 3, then the other is 5, and vice versa. The order doesn't matter.
That means the equation
[tex]\sqrt{8+2\sqrt{15}} = \sqrt{a}+\sqrt{b}\\\\[/tex]
updates to
[tex]\sqrt{8+2\sqrt{15}} = \sqrt{3}+\sqrt{5}\\\\[/tex]
The order doesn't matter on the right side since we can add two numbers in any order.
---------
You can use your calculator to confirm the answer.
Note that
[tex]\sqrt{8+2\sqrt{15}} \approx 3.968118785[/tex]
and
[tex]\sqrt{3}+\sqrt{5} \approx 3.968118785[/tex]
both result in the same decimal approximation to help show the two sides are equal.
Related Questions
Find all values of the variable x for which the rational expression is undefined.
8x+9/x^2-13x+42
The expression is undefined when x=
Answers
Answer:
Step-by-step explanation:
8x+9/x^2-13x+42
Write 8 x as a fraction with denominator 1
8x+9/x^2-13x+42
then we multipuly 8x/1 by x^2/x^2
Gemma graph this set of points (0,5), (6,3), (6,-2), (0, -2) then connects them to create
a polygon. What shape did she draw?
A. Rectangle
B. Square
C. Parallelogram
D. Trapezoid
.
Answers
Answer:
D trapezoid
Step-by-step explanation:
i used the graphing demos
Use linear regression to find an equation that would best predict a fair home price based on the
comps given below. Round each variable to 4 decimal places.
Answers
Answer:
y = 0.0807x - 3.4286
Step-by-step explanation:
Given the data above :
X :
1400
1700
1500
Y:
108
133
120
Using a linear regression calculator, the regression equation obtained is :
y = 0.0807x - 3.4286
Slope = 0.0807
Intercept = - 3.4286
x = predictor variable
y = predicted variable
find the area of the figure
Answers
Answer:
Not enough information
Step-by-step explanation:
Unless this is a square, you don't have enough information to answer this question. It would be 14 * 14 if it was a square which would be 196.
ending on your answer
What percent of the large square is shaded?
O 56%
O 5%
06%
44 %
Answers
What kind of triangles are these?
Answers
Answer:
5)isosceles triangle 6)scalene triangle 7)equilateral triangle
plzzzzzzz mark me brainliest plzzzzzzzark request to you
For the purpose of determining the value of its end-of-year inventory, a clothing store creates a list at the end of the year of every item currently in stock along with each iter's wholesale price. Which of the
following is the best description of the end-of-the-year activity?
Answers
Answer:
A census, because the wholesale prices of all items are listed.
Step-by-step explanation:
If z is a standard normal variable, find the probability.
The probability that z is greater than -1 82
Answers
Answer:
.
Step-by-step explanation:
5x=525010 solve for x
Answers
Answer:
x =105002
Step-by-step explanation:
5x=525010
Divide each side by 5
5x/5=525010/5
x =105002
Which of the following situations could be described by the equation y = 120 - 25x?
Answers
Answer:
Is there any other information?
Step-by-step explanation:
Solve the following addition problems. Remember to carry as necessary.
995lb6oz+1,004lb11oz =
24T1,507lb 12oz + 7T938lb6oz =
6T14oz11T1,949lb8oz + 5T49lb15oz =
Answers
2. 31T2445LB18OZ
3. 22T1998LB37OZ
i think those are correct
ASAP ppppoopoooooooopppp
Answers
Answer:
The area of the figure is 36 [tex]in^2[/tex].
Step-by-step explanation:
You can cut the composite shapes into two shapes to make the calculation process easier: a triangle and a rectangle. The area of the triangle is [tex]\frac{1}{2} * 9*2=\frac{1}{2} *18=9[/tex] [tex]in^2[/tex], and the area of the rectangle is 9 * 3 = 27 [tex]in^2[/tex], so the area of the composite shape is 27 + 9 = 36 [tex]in^2[/tex].
Answer:
36in²
Step-by-step explanation:
In order to find the area of a composite shape, we must split the shape up into two regular shapes.
Thus, area of composite shape = area of triangle + area of rectangle
The area of a rectangle can simply be found my multiplying the width by the length
The rectangle shown has a length of 9 in and a width of 3 in
Hence, A = 9 * 3
9 * 3 = 27
Therefore the area of the rectangle is 27in²
The area of a triangle can be calculated by multiplying the base length by the height and then dividing the product by 2
The triangle shown has a given height of 2 in and a base length of 9 in
Thus, [tex]A=\frac{2*9}{2}[/tex]
2 * 9 = 18
18 / 2 = 9
Hence, the area of the triangle is 9 in²
Finally we add the two areas together
9 + 27 = 36
Hence, the area of the composite figure is 36in²
Your friend has two standard decks of 52 playing cards and asks you to randomly draw one card from each deck. What is the probability that you will draw two spades?
Answers
Answer:
If you have 2 decks of 52, it would be 1/52 chance per card, so since there are two, add it up, its 2/104
Step-by-step explanation:
Answer:
1/16
Step-by-step explanation:
:))
Select the correct answer.
Consider function g.
g(x)= 5/x-1 +2
What is the average rate of change of function gover the interval [-4,3]?
ОА. -7/2
OB. 1/2
OC. -1/2
OD. 2
Answers
Answer:
Option B
Step-by-step explanation:
Average rate of change of a function 'f' in the interval x = a and x = b is given by,
Average rate of change of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
Given function is,
g(x) = [tex]\frac{5}{x-1}+2[/tex]
We have to calculate the rate of change in the interval [-4, 3],
Average rate of change = [tex]\frac{g(3)-g(-4)}{3-(-4)}[/tex]
g(3) = [tex]\frac{5}{3-1}+1[/tex]
= 2.5 + 1
= 3.5
g(-4) = [tex]\frac{5}{-4-1}+1[/tex]
= -1 + 1
= 0
Average rate of change = [tex]\frac{3.5-0}{3+4}[/tex]
= [tex]\frac{3.5}{7}[/tex]
= [tex]\frac{1}{2}[/tex]
Therefore, Option B will be the answer.
Answer:
B
Step-by-step explanation:
Edmentum
Choose the function that shows the correct transformation of the quadratic function shifted two units to the right one
unit up.
o f(x) = (x - 2)2 - 1
O f() = (x - 2)2 + 1
o f() = (x + 2)2 - 1
o f(x) = (x + 2)2 + 1
Answers
The last one f(x)=(x+2)2+1 because two units to the right is positive and going up is also positive
ASAP pleeeease ASAP ASAP
You are given the results of measurement of resistors. We are testing the
measurement tool. It will pass the technical control if the mean value will be
in the range [198-202] with standard deviation less than 3 Ohms. Will the tool
pass the technical control?
Answers
Answer:
As both the standard deviation and the mean have the desired values, the tool passes the technical control.
Step-by-step explanation:
Mean:
The mean is the sum of all values divided by the number of values.
[tex]M = \frac{199+204+201+197+195+204+200}{7} = 200[/tex]
The mean is in the desired range.
Standard deviation:
The standard deviation is the square root of the sum of the difference squared between each value and the mean, divided by the number of values.
[tex]S = \sqrt{\frac{(199-200)^2+(204-200)^2+(201-200)^2+(197-200)^2+(195-200)^2+(204-200)^2+(200-200)^2}{7}} = 1.18[/tex]
As both the standard deviation and the mean have the desired values, the tool passes the technical control.
appreciation on fixed assets jornal entry
Answers
Answer:
APPRECIATION ON FIXED ASSETS
The value of asset increases due to inflation. Increase value of assets is added with related asset. It is also recorded in credit side of profit and loss account.
A certain coin is a circle with diameter 18 mm. What is the exact area of either face of the coin? The exact årea of either face of the coin is mm2. (Simplify your answer. Type an exact answer in terms of re.)
Answers
I don't understand it sorry
5c+4c+2 and 5c+2(2c+1)
Answers
Answer:
11 c12 cyfiddiddjkssjksajusaahogsyi of
ME LO RESUELVEN PORFAAAAAAAAAAAA
Answers
Answer:
A = arcTan(8/15) = 0.4900 radians = 28.07°
Step-by-step explanation:
Tan(A) = 8/15
A = arcTan(8/15) = 0.4900 radians = 28.07°
Plz help need help help
Answers
Answer:
8,560
Step-by-step explanation:
8000 x .02 interest/year x 3.5years=560 interest earned
8000+560=8,560 investment worth after 3.5 years
help please mathematics!!!
Answers
Answer:
answer: 16
because 16/20 is an equivalent fraction to 4/5 hope that helps!
Find the value of x for which m||n.
A. Can't be determined.
B. 21
C. 8
D. 19
Answers
The two given values add up to 180. From there you can use this equation to solve
8x - 26 + 38 = 180
Answer:
The answer is B. 21Step-by-step explanation:
what is the diameter of 16
Answers
Answer:
d=32
Step-by-step explanation:
Solution
d=2r=2·16=32
12.5g of a medicine cost 1075 naira. what is the cost of 1g medicine
Answers
Please help is for now
Answers
A new batching plant has been constructed and of the first 50 batches, three are found to not meet specification. a. Construct a 98% Score confidence interval for the population proportion of batches that do not meet specification for the new batching plant. b. Construct a 98% traditional confidence interval.c. Comment on the difference.
Answers
Answer:
The responses to these question can be defined as follows:
Step-by-step explanation:
[tex]x=3 \\\\n=50\\\\\hat{p}=\frac{x}{n}=0.06\\\\\hat{q}=1-\hat{p}=0.94[/tex]
In point a:
[tex]98\%[/tex] confidence interval for population proportion (p):
[tex]c=98\%=0.98\\\\\alpha=1-c=0.02\\\\\frac{\alpha}{2}=\frac{0.02}{2}=0.01\\\\z_{\frac{\alpha}{2}}=2.326\\\\[/tex]
For point b:
[tex]98\% \ confidence\ interval =\hat{p} \pm z_{\frac{\alpha}{2}} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\\\[/tex]
[tex]=0.06 \pm 2.326 \sqrt{\frac{0.06\times 0.94}{50}}\\\\ =0.06 \pm 2.326 (0.0336)\\\\=0.06 \pm 0.078\\\\98\% \ CI =(-0.018, 0.138)[/tex]
For point c:
[tex]The\ difference\ between \ 98\% \ CI\ is \ -0.018\ to\ 0.138[/tex]
Multiply.
(-3+2i)(-4+4i)
Write your answer as a complex number in standard form.
Answers
Answer:
4 - 20 i
Step-by-step explanation:
you do stuff and you get 4 - 20 i
if you spend $20 each week and give your brother $5 each week, how much would you have then
Answers
Answer:
$25
Step-by-step explanation:
actually you would be spending $25 every week
Can anyone answer this
Answers
Answer:
108ft²
Step-by-step explanation:
6×6=36
12×12=144
144-36=108ft for the shaded part
Answer:
108 ft²
Step-by-step explanation:
12 ft × 12 ft
144 ft²
6 ft × 6 ft
36 ft²
144 ft² - 36 ft²
108 ft²