Answer:
[tex]\frac{5-\sqrt{2}}{27}[/tex]
Step-by-step explanation:
This kind of problem uses a sort of algebra trick.
To rationalize [tex]\frac{1}{5+\sqrt{2}}[/tex], multiply both numerator and denominator by what is called the conjugate radical -- the same expression but with opposite sign.
Note: this is really a clever name for 1, and multiplying by 1 does not change the value of an expression, it changes the way the expression looks.
Here goes:
[tex]\frac{1}{5+\sqrt{2}} \cdot \frac{5-\sqrt{2}}{5-\sqrt{2}}=\frac{5-\sqrt{2}}{25+5\sqrt{2}-5\sqrt{2}+2}\\=\frac{5-\sqrt{2}}{25+2}\\=\frac{5-\sqrt{2}}{27}[/tex]
See how the radical disappears from the denominator?
Step-by-step explanation:
Answer:
\frac{5-\sqrt{2}}{27}
27
5−
2
Step-by-step explanation:
This kind of problem uses a sort of algebra trick.
To rationalize \frac{1}{5+\sqrt{2}}
5+
2
1
, multiply both numerator and denominator by what is called the conjugate radical -- the same expression but with opposite sign.
Note: this is really a clever name for 1, and multiplying by 1 does not change the value of an expression, it changes the way the expression looks.
Here goes:
\begin{gathered}\frac{1}{5+\sqrt{2}} \cdot \frac{5-\sqrt{2}}{5-\sqrt{2}}=\frac{5-\sqrt{2}}{25+5\sqrt{2}-5\sqrt{2}+2}\\=\frac{5-\sqrt{2}}{25+2}\\=\frac{5-\sqrt{2}}{27}\end{gathered}
5+
2
1
⋅
5−
2
5−
2
=
25+5
2
−5
2
+2
5−
2
=
25+2
5−
2
=
27
5−
2
See how the radical disappears from the denominator?
I want some Mathematics questions about ratio and proportion
Answer:
Mel fills his gas tank up with 6 gallons of premium unleaded gas for a cost of $26.58. How much would it cost to full an 18 gallon tank?
or
Jacob ran 10 miles in 80 minutes. At that rate how far would he run in 2.5 hours?
37 1/2% into a fraction
Answer:
37/200
Step-by-step explanation:
[tex] 37\frac{1}{2} \% \\ equal \: to \: \frac{37}{200} [/tex]
Describe the transformation in words only for 4 please :)
Answer:
a rotation of 45° , this could be it
I need help on this pre-calculus function about domain and range.
Answer:
7
Step-by-step explanation:
Think you guys and help a fellow master out? Ill give brain list and 50 points.
Select the correct answer.
Mark transferred songs from his computer onto his portable music player. He transferred songs in minutes. How many songs did he transfer per minute?
A.
song per minute
B.
songs per minute
C.
songs per minute
D.
songs per minute
Answer:
He transferred 2 6/7 songs in 1 2/3 minutes.
Answer:
songs per minute. the answer is B
Trina ran 2 1/2 miles of Friday, 2 3/4 miles on Saturday and 3 mies on SUnday. The next week she ran the same amount. How far in miles did she run in two weeks?
Answer:
16 [tex]\frac{1}{2}[/tex] miles
Step-by-step explanation:
2 [tex]\frac{2}{4}[/tex] + 2 [tex]\frac{3}{4}[/tex] = 4 [tex]\frac{5}{4}[/tex] which equals 4 + 1 [tex]\frac{1}{4}[/tex] or 5 [tex]\frac{1}{4}[/tex]
5 [tex]\frac{1}{4}[/tex] + 3 = 8 [tex]\frac{1}{4}[/tex]
she ran 8 and one-quarter miles in the first week and if she ran the same amount the second week then we can add to get the answer:
8 [tex]\frac{1}{4}[/tex] + 8 [tex]\frac{1}{4}[/tex] = 16 [tex]\frac{2}{4}[/tex] or 16 [tex]\frac{1}{2}[/tex]
Help pls I really need this
Answer:
{2 , 4} is the answer of this question.
solve for x…..…………………
Answer:
x = 11
Step-by-step explanation:
From the diagram, we find,
(2x - 16) + (x - 8) = 9
=> 2x - 16 + x - 8 = 9
=> 2x + x - 16 - 8 = 9
=> 3x - 24 = 9
=> 3x = 9 + 24
=> 3x = 33
=> x = 33/3
=> x = 11
It rained 12 days out of 30 days. Which
ratio compares the number of rainy days to
the number of dry days?
8, 16, 48, 192, 960,
Step-by-step explanation:
pls mark me as brainliest
A: P = 2L + 2W solve for W
B: C = 5/9(F - 32) solve for F
Answer:
A. P/2 - L = W
B. 9/5C + 32 = F
Step-by-step explanation:
A. P = 2L + 2W
P = 2(L+W)
P/2 = L + W
(P/2)-L = W
B. C = 5/9(F - 32)
9/5C = F - 32
9/5C + 32 = F
what is BE in the figure
Answer:
I honestly don't understand what is being asked
Answer:
25
Step-by-step explanation:
B is second in the English alphabet and E is on the 5th positions on this same English alphabet
someone help me with this
WILL MARK AS BRAINLIST (or whatever you call it)
30 points for it
(Ignore the bottom ones that r hard to see)
Answer:
1) 11/13
2) -7/8
3) -3/9
4) 7/11
7) 5/6
8) 2/3
9) -1
10) -1/7
Step-by-step explanation:
simplifying
7) 10/12 = 5/6
8) 4/6 = 2/3
9) -4/4 = -1
Can't see 5, 6, 11
For the function f defined by f(x) = 3x^2 + 3x + 4, find the following values.
(a) f(-9) =
(Simplify your answer.)
[tex] \large \mathfrak{Solution : }[/tex]
let's solve for f(-9) :
3(-9)² + (3 × -9) + 4(3 × 81) - 27 + 4243 - 23220Step-by-step explanation:
220that's all
thank you
Factor 18p – 36 to identify the equivalent expressions.
Choose 2 answers:
A
3(9p – 12)
B
9(2p – 4p)
2(9p – 18)
18(p - 2)
Answer:
DandC
Step-by-step explanation:
Can somebody help me please #1
Answer:
See below.
Step-by-step explanation:
a. Choose any 3 non-collinear points on the plane. For example, plane R can be described as plane OSQ.
b. "Collinear" means points that lie on the same line. Example: M, N, P (note that the line these points are on does not lie in plane R)
c. [tex]\overrightarrow{NM}[/tex] and [tex]\overrightarrow{NP}[/tex]
d. There are many. Examples: O, N, Q, S. Not M. Not P.
I WILL GIVE CORRECT ANSWER BRAINLIEST!
Each ride at the carnival requires 4 tickets to ride. Kate purchased 20 tickets and has
already ridden some rides.
Kate writes the expression 20 – 4r and Brian writes the expression 4(5 – 1) to
determine how many tickets Kate has left after riding some rides. Both expressions
are correct
Drag each description to explain each part of both expressions.
Step-by-step explanation:
In Kate's equation, 20 is the total number of tickets, 4 is number of tickets per ride, r is number of rides already ridden, and 4r is the number of tickets used
in Brian's equation, 5 is total number of rides Katie can ride and 5 - r is the number of rides left to ride
Answer:
Step-by-step explanation: I just did it
i need help algebra please
Answer:
a ) 2
b) 9
c) y= 2x + 9
are the answerrrrrrrrrr
Matt has a square basketball court in his backyard that has an area of 196 ft². What is the side length of the basketball court?
A) 14 feet
B) 49 feet
C) 56 feet
D) 28 feet
Answer:
fourteen feet
Step-by-step explanation:
The side length is usually much shorter then the overall length
decimal expansion for
1). 10 / 11
2). 1/9
5
3). 1 -
27
Answer:
3
Step-by-step explanation:
1-27!!!!!!!!!!!!!!!!!
Which is equivalent to 1/4?
(equivalent means equal)
04/12
O 4/16
03/15
O 25/90
-1/2 (-3y + 10)
Please, I need help on this one.
Answer:
[tex] - \frac{1}{2} ( - 3y + 10) \\ \\ = \frac{3}{2} y - \frac{10}{2} \\ \\ = { \boxed{ \boxed{ \frac{3}{2} y - 5}}}[/tex]
HELP
To make an international telephone call you need the code for the country you are calling. The codes for country A, country B, and C are three consecutive integers
whose sum is 84. Find the code for each country.
Answer:
27, 28, 29
Step-by-step explanation:
If you divide 84 by 3, the quotient will be in the middle of the three integers. We get 28 from dividing 84 by 3, therefore our string of numbers are 27, 28, and 29.
X=?
Missing angle=?
Answer: 132
X = 180 - 47 +1
x=132
Answer:
x = 67, 133 degrees
Step-by-step explanation:
2x - 1 + 47= 180
2x + 46 = 180
2x (+ 46 - 46) = 180 - 46
2x = 134
2x/2 = 134/2
x = 67
2x - 1
2(67) - 1
134 - 1
133 degrees
Alex has 8 quarters six dimes and four nickels in his pocket what is the probability he will not select a quarter. How to give my the answer like 2/10
Explanation:
There are 8+6+4 = 18 coins, 18-8 = 10 of which aren't quarters.
10/18 = 5/9 is the probability of not selecting a quarter.
Find the volume of a rectangular prism that is 10 cm long, 3 cm wide, and 2 cm high. Please draw and label the prism
Answer:
Volume = Length × Width × Height
Volume = 10 × 3 × 2
Volume = 60 cm
What is 6,940 x 500?
Answer:
3,470,000 pls mark me branilest
Answer:
The answer is 3,470,000
Which term would be combined with the constant +2 in the expression -8x^2 + 3x +2?
Answer:
102(5x+2y)+3x+6y−10
Step-by-step explanation:
Terms is each part of an algebraic expression separated by a plus or minus sign.
As 2(5x +2y ) , 3x , 6y2(5x+2y),3x,6y and 1010 .
Factor is a product of two or more numbers, algebraic variables or algebraic expressions . 2(5x +2y )2(5x+2y) has two factors 22 and (5x +2y )(5x+2y) .
3x3x has two factors 33 and xx .
6y6y has two factors 66 and yy .
-10−10 has one factors
Coefficient is the numerical factor of a term that contains a variable.
2(5x +2y ) the factor is 22 .
3x3x the factor is 33 .
6x6x the factor is 66 .
-10−10 the factor is -10−10 .
Variable is a symbol, usually a letter, used to represent a number.
As xx and yy
Constant is a term without a variable.
As -10−10 .
From the graph of the function, determine the domain and the range.
Domain: (-2, 0) (0,5] Range: (-2,0] [2, 4]
Domain: [-2, 4] Range: (-2, 0] [2, 4]
Domain:(-2, 0) (0, 4) Range: (-2,5]
Domain: (-2, 4] Range: (-2, 0] [2, 4)
Hey there again! :)
This function is a piecewise function and it's different from previous question.
As you may notice, the graphs are separated and some of coordinate points are not a part of domain and range. That's why we have separate domain and range.
First, let's consider that line graph. The one that contains (-2,0) and (0,-2).
Our domain is the set of all x-values. Only (-2,0) is a closed dot. We use [ ] for closed dot and ( ) for opened dot.
Hence, the first domain is [-2,0)
Next, we find the range of line graph or line segment.
Range is the set of all y-values. Hence, the first range is (-2,0]
We are not done yet! We have to find the second domain and range, which is a curve graph.
From the curve graph, our first point starts from (0,4) and ends at (5,4)
Since (0,4) is an opened dot and (5,4) is a closed dot.
Therefore, the second domain is (0,5]
For the range, the minimum point is (3,2) and maximum point is (0,4) and (5,4). Use the y-coordinate to find range.
Hence, the second range is [2,4}
Gathering Both Domain and Range
First Domain is [-2,0)First Range is (-2,0]Second Domain is (0,5]Second Range is [2,4]Combine both domains and ranges.
Hence, the domain is [-2,0] U (0,5] and the range is (-2,0] U [2,4] or The First Choice
Let me know if you have any questions!
Topic: Functions / Domain & Range
The width of a rectangle is 2w and the length is (w + 5). The perimeter is 40 inches. What are the measurements of the rectangle
Answer:
Width = 2w , Length = w+5 , perimeter = 40
Perimeter of rectangle = 2 (Length + Width)
P= 2 (L + w)
40 = 2 [ (w+5) + (2w) ]
40 = 2 ( 3w+5)
40= 6w +10
6w= 40 – 10
6w= 30
w = 30/6
w = 5
Width = 2w = 2(5) = 10
Length = w + 5 = 5+5 = 10
I hope I helped you^_^
