Rationalize the denominator 2/root 3 - 1
Answers
Answer:
Step-by-step explanation:
[tex] \frac{2}{ \sqrt{3} - 1 } \\ \frac{2}{ \sqrt{3 } - 1} \times \frac{ \sqrt{3} + 1}{ \sqrt{3} + 1} \\ \frac{2 \times ( \sqrt{3} + 1)}{( \sqrt{3} - 1)( \sqrt{3 } + 1) } = \frac{2 \sqrt{3} + 2}{( \sqrt{3} )^{2} - {1}^{2} } \\ \frac{2 \sqrt{3} + 2 }{3 - 1} = \frac{2 \sqrt{3} + 2 }{2} = \frac{2( \sqrt{3} + 1)}{2} \\ \sqrt{3 } + 1 = 1.732 +1 = 2.732[/tex]
Or[tex] \frac{2}{ \sqrt{3 - 1} } \\ \frac{2}{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } = \frac{2 \sqrt{2} }{( \sqrt{2} ) ^{2} } = \frac{2 \sqrt{2} }{2} \\ \sqrt{2} = 1.4142[/tex]
I hope I helped you^_^
Related Questions
please help me with this question 17t 200kg divided by 8
Answers
Answer:
1 ton = 1000 kg
So, 17 ton = 17 × 1000
= 17000 kg
17000 + 200 kg = 17200 kg
[tex] \frac{17200}{8} = 2150kg[/tex]
what’s the value of n?
Answers
Answer:
n=1
Step-by-step explanation:
(√5^5)^5 =5^n
5^1/5×5=5^n
1/5×5=n
5/5=n
n=1
Hermione is collecting Chocolate
Frog Cards. She starts with a
collection of 20 cards and gets 2 more
per week. After how many weeks will
she have 64 cards?
Answers
Answer: 22
Step-by-step explanation: 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64
quicker example: 64-20= 44 also 22x2=44 + 20 = 64
The straight line ax+by=1passes through the points (1,4)and (3,1).Find the values of a and b?
Answers
Answer:
a= 3/11
b = 2/11
Step-by-step explanation:
a(1) + b(4) = 1
a + 4b = 1
a(3) + b(1) = 1
3a + b = 1
b = 1-3a
a + 4(1-3a) = 1
a+ 4-12a = 1
-11a = -3
a = 3/11
b = 1-3(3/11)
b= 2/11
The value of a and b are 3/11 and 2/11 respectively.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
We have been given that the straight line ax+by=1 passes through the points (1,4)and (3,1).
Thus, the equation of the straight line passing through the point ( 3,1 )
a(3) + b(1) = 1
3a + b = 1
b = 1-3a
Thus, the equation of the straight line passing through the point(1,4)
a(1) + b(4) = 1
a + 4b = 1
Now substitute the value of b;
a + 4(1-3a) = 1
a+ 4-12a = 1
-11a = -3
a = 3/11
Then b = 1-3(3/11)
b= 2/11
Hence, the value of a and b are 3/11 and 2/11 respectively.
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Kristy’s cellphone company charges a monthly rate of $45 plus $0.05 per text message sent, and $0.58 per video messages sent. Kristy’s sent 8 video messages in October and receive a bill for $55.29. How many text messages did she sent?
Answers
Answer:
About 113.
Step-by-step explanation:
45 + 0.05t +0.58v = 55.29
v = 8
t is 113 text messages.
Kristy’s sent About 113 text messages..
What does it mean to solve an equation?An equation represents equality of two or more mathematical expression.
When someone asks you to solve an equation, then they usually mean to find the values of the unknowns for which that equation would be true (the equality between expressions should hold true for those values).
Solutions to an equation are those values of the variables involved in that equation for which the equation is true.
It is given that Kristy’s cellphone company charges a monthly rate of $45 plus $0.05 per text message sent and $0.58 per video messages sent.
Also Kristy’s sent 8 video messages in October and receive a bill for $55.29.
The equation form as;
45 + 0.05t +0.58v = 55.29
Solve for t when v = 8;
45 + 0.05t +0.58(8) = 55.29
t = 113
Therefore, she sent 113 text messages.
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8.76 11.9 11.73 15.9 in order please help me
Answers
Answer:
Least to greatest: 8.76,11.73,11.9,15.9
Greatest to least: 15.9,11.9,11.73,8.76
Step-by-step explanation:
plz give me brainliest
Answer:
Step-by-step explanation:
Use the number on the left of the decimal first. Smallest to largest gives
8
11
11
15
8 and 15 have their positions fixed. Where they are now, that is where they will stay.
So let's mark them
8.76
11
11
15,8
Now all we need do is figure out the 11s.
11.90
11.73
I added the 0 so you could think about money. You see a great looking scarf. Which would you rather pay: 11.73 or 11.90. Never mind that you really like it and the difference isn't worth squabbling about. Which is better to pay? You should answer 11.73. It's smaller than 11.90. So what's the answer
8.76
11.73
11.90
15.9
Solve for b.
2(b − 8) + –11 = 3
b =
Answers
Answer:
b = 15
Step-by-step explanation:
2 (b - 8) + -11 = 3
2b - 16 + -11 = 3
2b - 16 + -11 = 3
2b - 27 = 3
2b = 3 + 27
2b = 30
b = 30 ÷ 2
b = 15
Answer:
[tex] = > 2(b - 8) + - 11 = 3[/tex]
[tex] = > 2b - 16 + - 11 = 3[/tex]
[tex] = > 2b - 27= 3[/tex]
[tex] = > 2b = 27 + 3[/tex]
[tex] = > 2b = 30[/tex]
[tex] = > b = \frac{30}{2} [/tex]
[tex]=>b=15[/tex]
can someone answer this please
Answers
Answer:
DE = 1/2 AC -> AC = 4
EF = 1/2 AB -> AB = 6
DF = 1/2 BC -> BC = 8
Step-by-step explanation:
hope it help u
11. Write y = 2x² +12x+14 in vertex form.
Please show work if possible so I know how to do it
Answers
Answer:
y = 2(x + 3)² - 4
Step-by-step explanation:
y = 2x² + 1 2x + 14
Move the constant (14) to the left side
y - 14 = 2x² + 12x
Now factor out 'a' , the coefficient of x² term
y - 14= 2(x² + 6x)
Divide the coefficient of 'x' by 2 ⇒ 6/2 = 3
Find the square of '3' and add it to x² + 6x ⇒ x² + 6x + 9
Multiply the square of 3 and add it to y - 14; 9*2 = 18
y- 14 = 2(x² + 6x + 9)
y - 14 + 18 = 2(x² + 6x + 9)
y + 4 = 2(x² + 6x +9)
y + 4 = 2(x + 3)²
y = 2(x + 3)² - 4
Vertex ( -3 , -4)
Can someone please solve this?
Answers
Answer: x = 3
Step-by-step explanation:
[tex]2x-7=\frac{1}{3}x-2\\\\6x-21=x-6\\\\5x-21=-6\\\\5x=15\\\\x=3[/tex]
Solve for x: two thirds(x − 2) = 4x
Answers
Answer:
-2/5 =x
Step-by-step explanation:
2/3 ( x-2) = 4x
Multiply each side by 3/2
3/2 * 2/3 (x-2) = 3/2 *4x
x-2 = 6x
Subtract x from each side
x-2-x = 6x-x
-2 = 5x
Divide each side by 5
-2/5 = 5x/5
-2/5 =x
x=− 2/5=−0.4 is the answer please mark brainliest
ATTENDING TO PRECISION The diagram shows an insect called a walking stick Use the ruler to estimate the length of the abdomen and the length of the thorax to the nearest inch. How much longer is the walking stick's abdomen than its thorax? How many times longer is its abdomen than its thorax?
Answers
Estimation and precision are used when the actual value cannot be easily determined or calculated.
The length of the abdomen is [tex]2\frac 14[/tex] inchesThe length of the thorax is [tex]1\frac 34[/tex] inchesThe abdomen is longer than the thorax [tex]1\frac 27[/tex] timesGiven that, the length is to be measured to the nearest [tex]\frac 14\ inch[/tex], we have the following observations
The length of the abdomen starts at the 0 mark and ends after the 2-mark. The length ends before [tex]2\frac{1}{2}[/tex]. So, the length of the abdomen can be estimated to [tex]2\frac{1}{4}[/tex] --- to the nearest [tex]\frac{1}{4}[/tex].Similarly, the length of the thorax starts at the [tex]2\frac{1}{4}[/tex] mark and ends before [tex]4\frac{1}{4}[/tex]. The end of the thorax length can be estimated to: [tex]4[/tex] --- to the nearest [tex]\frac{1}{4}[/tex].So, we have:
[tex]L_1 = 2\frac 14[/tex] --- the length of the abdomen
[tex]L_2 = 4 - 2\frac 14[/tex]
Express as improper fraction
[tex]L_2 = 4 - \frac{9}{4}[/tex]
Take LCM
[tex]L_2 = \frac{16 - 9}{4}[/tex]
[tex]L_2 = \frac{7}{4}[/tex]
Express as proper fraction
[tex]L_2 = 1\frac{3}{4}[/tex] --- the length of the thorax
The number of times (n) the abdomen is longer than the thorax is calculated as follows:
[tex]n = L_1 \div L_2[/tex]
So, we have:
[tex]n = 2\frac 14 \div 1\frac 34[/tex]
Express as improper fractions
[tex]n = \frac 94 \div \frac 74[/tex]
Rewrite as:
[tex]n = \frac 94 \times \frac 47[/tex]
[tex]n = \frac 97[/tex]
Express as proper fractions
[tex]n = 1\frac 27[/tex]
Hence, the abdomen is [tex]1\frac 27[/tex] times longer than the thorax
Read more about estimation and precision at:
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Gabbar watched 650 movies in the last 5 years. Every year he watched 10 movies less than the previous year. How many movies did he watch in the 1st year?
Answers
Answer:
he watched 2movie in 1st year
Sum = n/2[2a + (n - 1)d]
5/2(2a + 4 x -10) = 650
2a - 40 = 650 x 2/5 = 260
2a = 260 + 40 = 300
a = 150
He watched 150 movies in the first year.
The series is 150 + 140 + 130 + 120 + 110 = 650
2out of 5 people own a bike if there are 2500 people in the neighborhood about how many people own a bike
Answers
Find the decimal for 2 out of 5 by dividing 2 by 5:
2 out of 5 = 2/5 = 0.40
Multiply total people by 0.40:
2500 x 0.40 = 1,000
Answer: 1,000
How to evaluate a2 + b - c2
Answers
Quadrilateral PQRS is a rectangle. What is the length of PQ?
Select the best answer from the choices provided.
А.7
B.19.799
C.24.249
D.28
Answers
Answer:
C
Step-by-step explanation:
remember SOHCAHTOA
SOH is for sin
CAH is for cosin
TOA is for tan
line PS=14 so line QR=14
line PQ is your x value. so to solve, write out tan30=14/x
rewrite it so it now says x= 14/tan. type that in to your calculator and you get your answer
Can someone please help me use a protractor on this question since I don’t have one?
Answers
Answer:
If you don't have a protractor handy, you can determine the size of an angle using the basic geometric principles of triangles. You'll need a scientific calculator to solve the equations. Most smartphones are equipped with them, but you can also download a free app or access a free calculator online.
Sofia's batting average is 0.022 higher than Joud's batting average. Joud has a batting average of 0.169
What is Sofia's batting average?
Answers
Answer:
0.191
Step-by-step explanation:
S = Sofia's batting average
J = Joud's batting average
S=?
J=0.169
S = 0.022 + 0.169
S = 0.191
Answer:
0.191
Step-by-step explanation:
S = Sofia's batting average
J = Joud's batting average
S=?
J=0.169
S = 0.022 + 0.169
S = 0.191
Hope this helps <3
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The function y = f(x) is graphed below. What is the average rate of change of the function f(x) on the interval 1 < x < 2?
Answers
Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels at a rate of 45 miles per hour. The westbound train travels at a rate of 55 miles per hour. How long will it take for the two trains to be 280 miles apart
Answers
Answer: 2.8 hours
Step-by-step explanation:
Train A: time= t, v=45mi/hr, d= d
Train B: time t, v= 55mi/hr, d=280-d
Distance = v times t (d=vt)
t = d/v (time for both trains is the same, so t=t)
Train A: t=d/45
Train B: t=(280-d)/55
d/45 = (280-d)/55 (cross multiplication)
55d = 15400-45d
55d+45d = 15400
100d = 15400
d = 154 miles (280miles - 154miles = 126 miles)
Train A travel 154 mi and train B travel 126 mi
Train A travel 154 miles in 2.8 hrs.
Train B travel 126 miles in 2.8 hrs.
154 miles at a rate of 55mi/h = 2.8 hours and
126 miles at a rate of 45mi/h = 2.8 hr.
f(x)= 2/3x +3; Find when f(x)=-5
Answers
Hi ;-)
f(x) = ²/₃x + 3 ∧ f(x) = -5
²/₃x + 3 = -5
²/₃x = -5 - 3
²/₃x = -8 / * ³/₂
x = -12
The price of an item has been reduced by $2.18. The new sale price is $16.55. What was the original price?
Answers
Answer:
$18.73
Step-by-step explanation:
$16.55 + $2.18
(sorry if I'm wrong)
x3+y3+z3=k, what replaces k?
Answers
Find x, y, and z such that x³+y³+z³=k, for each k from 1 to 100.
On the surface, it seems easy. Can you think of the integers for x, y, and z so that x³+y³+z³=8? Sure. One answer is x = 1, y = -1, and z = 2. But what about the integers for x, y, and z so that x³+y³+z³=42? … I hope it helps you
The greater of two numbers is 6 more than 4 times the smaller. Their sum is 41. FInd the numbers.
Answers
Answer:
7 and 34
Step-by-step explanation:
let x and y be the 2 numbers with x > y
The 2 equations to solve are
x = 4y + 6 → (1)
x + y = 41 → (2)
Substitute x = 4y + 6 into (2)
4y + 6 + y = 41 , that is
5y + 6 = 41 ( subtract 6 from both sides )
5y = 35 ( divide both sides by 5 )
y = 7
Substitute y = 7 into (1)
x = 4(7) + 6 = 28 + 6 = 34
The 2 numbers are 7 and 34
please help meh its midpoint
Answers
Step-by-step explanation:
[tex]mid \: point \: of \: x = \frac{x1 + x2}{2} \\ x = \frac{8 + - 12}{2} \\ = \frac{ - 4}{2} = - 2 \\ mid \: pont \: of \: y = \frac{y1 + y2}{2} \\ y = \frac{ - 5 + - 1}{2} \\ = \frac{ - 6}{2} \\ = - 3 \\ the \: coordinates =( xy) = ( - 2 \: - 3) \\ thank \: you[/tex]
This is midpoint please help.
Answers
Step-by-step explanation:
[tex]thank \: you[/tex]
Answer:
(1, 13)
Step-by-step explanation:
it is above in the photo.
The sum of 1/4 and 1/8 times the difference between 2/3 and 5/6.
What is the numerical expression for the phrase?
Answers
Answer: (1/4 + 1/8) x (2/3-5/6)
Step-by-step explanation:
The sum of 1/4 and 1/8 times the difference between 2/3 and 5/6
If Gabby wants to buy a t-shirt for $35.99 but she has a discount for 10% off, how much is her final cost?
Answers
Answer:
It's $32.39.
Step-by-step explanation:
35.99 - 35.99*10% =
=35.99 - 35.99*0.1
=35.99 - 3.599
=32.391
32.391 is close to 32.39 so we will round it to that number.
The answer is $32.39.
If a tortoise is time traveling an average of 1/3 miles per hour, how long would it take the tortoise to travel 6 miles ?
Answers
Answer:
18
Step-by-step explanation:
6 ÷ 1⁄3 = 18
7+4c=7c+6
-----------------
Answers
Answer:
Solution given:
7+4c=7c+6
subtracting both side by 4c
7+4c-4c=7c-4c+6
solve like terms
7=3c+6
subtracting both side by 6
7-6=3c+6-6
3c=1
c=1/3
Answer:
c = -1/3
Step-by-step explanation:
7 + 4c = 7c + 6
7 - 8 + 4c = 7c
-1 + 4c = 7c
-1 = 7c - 4c
-1 = 3c
-1/3 = c