The simplest form of the expression [tex]\frac{5+\sqrt{3} }{2-\sqrt{3} }[/tex] is [tex]13+7\sqrt{3}[/tex].
The simplest form of a fraction is one with a reasonably prime denominator and numerator. It indicates that, except for 1, there is no common factor between the fraction's numerator (upper portion or top) and denominator (lower part or bottom).
In elementary algebra, the procedure of rationalization is performed to get rid of the irrational number in the denominator. There are several methods for rationalizing the denominator.
An expression comprises a variable, a number, or a combination of a number, a variable, and operation symbols. An equation is created by joining two expressions with an equal sign.
Consider the expression,
[tex]\frac{5+\sqrt{3} }{2-\sqrt{3} }[/tex]
Rationalizing the denominator,
[tex]\frac{5+\sqrt{3} }{2-\sqrt{3} } = \frac{5+\sqrt{3} }{2-\sqrt{3} } \times \frac{2+\sqrt{3} }{2+\sqrt{3}}[/tex]
[tex]\frac{5+\sqrt{3}}{2-\sqrt{3}} =\frac{(5+\sqrt{3})(2+\sqrt{3})}{(2-\sqrt{3})(2+\sqrt{3})}[/tex]
Using the identity,
( a + b )( a - b ) = a² - b²
Therefore,
[tex]\frac{5+\sqrt{3}}{2-\sqrt{3}} =\frac{5 \times 2 + 5 \times \sqrt{3} + \sqrt{3} \times 2 + (\sqrt{3} )^{2}}{(2)^{2}-(\sqrt{3} )^{2}}[/tex]
[tex]\frac{5+\sqrt{3}}{2-\sqrt{3}} = \frac{10+7\sqrt{3}+3}{4-3}[/tex]
[tex]\frac{5+\sqrt{3}}{2-\sqrt{3}} = \frac{13+7\sqrt{3}}{1}[/tex]
[tex]\frac{5+\sqrt{3}}{2-\sqrt{3}} = 13+7\sqrt{3}[/tex]
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whats the formula for finding the area
Answer:
square = width*height,
circle=pi*r^2
triangle = w * h * 0.5
Step-by-step explanation:
square = width*height,
circle=pi*r^2
triangle = w * h * 0.5
Polygon AVC’s slides 4 units left and 3 units up on the coordinate plane. If the original measure of angle A was 75 degrees, what I’d the measure of angle A’?
The angle of A when the polygon slides 4 units left and 3 units up on the coordinate plane is 75°.
How to calculate the angle?From the information, Polygon AVC’s slides 4 units left and 3 units up on the coordinate plane. If the original measure of angle A was 75 degrees.
It should be noted that translation doesn't change the angle. Therefore, the number will be the same as the translation is stationary.
Therefore, the angle of A when the polygon slides 4 units left and 3 units up on the coordinate plane is 75°
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A wet bicycle tire leaves a trace of water on the floor. The tire has a radius of 30 \text{ cm}30 cm30, start text, space, c, m, end text, and the bicycle wheel makes 333 full rotations before stopping.
How long is the trace of water left on the floor?
Round your answer to the nearest \text{cm}cmstart text, c, m, end text
The trace of water left on the floor is the circumference of 565.2 cm.
Water traces are seen on the floor from a wet bicycle tire.
The bicycle wheel makes three complete rotations before coming to a stop, circumference and the tire has a radius of 30 cm.
The circle of the cycle is indicated by the water stain left on the floor.
Given the radius = 30 cm
So,
C = 2 × 3.14 × 30
C = 188.4
Given that a bicycle wheel turns three times before pausing to pick up a trace of water, the answer is,
3 x 188.4 = 565.2 cm
the floor has a 565.2 centimeter trace of water.
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PLEASE HELP!! 20 points
The transformations needed to sketch the graph of [tex]h(x) = \sqrt[3]{1 - x}[/tex] are described as follows:
Starting with the graph of the basic function [tex]y = \sqrt[3]{x}[/tex], horizontally shift the graph right one unit, and then reflected the graph about the x-axis.
What is a transformation in a function?A transformation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x).
Examples are shift left, shift right, shift down, shift up, vertical stretching, horizontal stretching, vertical compression, horizontal compression, reflection over the x-axis, reflection over the y-axis, and rotations by a determined amount(in degrees). All these translations have predetermined rules that we apply to the figures.
The parent cube root function is given by:
[tex]y = \sqrt[3]{x}[/tex]
To have x -> x - 1, we reflect the function over the y-axis, hence:
[tex]y = \sqrt[3]{-x}[/tex]
To have -x -> 1 - x, we shift it one unit right, hence:
[tex]h(x) = \sqrt[3]{1 - x}[/tex]
The order of the transformations can be reversed, i. e., shift right then reflection.
Thus the correct statement to sketch the graph is given by:
Starting with the graph of the basic function [tex]y = \sqrt[3]{x}[/tex], horizontally shift the graph right one unit, and then reflected the graph about the x-axis.
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What is the value of the expression 5(2to the power of 3 -)?. Show your work
The value of the expression, 5([tex]2^{-3}[/tex]) is expressed as: 5/8.
How to Find the Value of an Expression?We are given the expression, 5([tex]2^{-3}[/tex]), to find the value of the expression, the steps explained below should be taken.
5([tex]2^{-3}[/tex]) [given expression]
Apply the negative exponents rule to evaluate the exponent in the expression
5([tex]2^{-3}[/tex]) = 5(1/2³)
5([tex]2^{-3}[/tex]) = 5/2³
Solve the exponent to eliminate the power of minus 3
5([tex]2^{-3}[/tex]) = 5/(2 × 2 × 2)
5([tex]2^{-3}[/tex]) = 5/8
Thus, the value of the expression, 5([tex]2^{-3}[/tex]) is expressed as: 5/8.
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Let g(x)=3 x+2 and f(x)=x-2 / 3 . Find each value.
(f⁰f)(0)
A composite function exists as a function that depends on another function. The value for (f⁰f)(0) = - 4/3
What is meant by composition function?In mathematics, function composition exists as an operation ∘ that takes two functions f and g, and has a function h = g ∘ f such that h(x) = g. In this operation, the function g exists used to the result of applying the function f to x.
Function composition is a mathematical procedure where two functions, f, and g, are taken and a function, h = g ∘ f, is produced such that h(x) = g(f(x)). The function g exists used in this operation on the outcome of applying the function f to x.
Let the two functions be g(x) = 3x + 2 and f(x) = x - 2/3
Now, (f⁰f)(x) = f[f(x)]
f(x) = x - 2/3
(f⁰f)(x) = f( x - 2/3)
simplifying the above equation, we get
(f⁰f)(x) = (x - 2/3) - 2/3
(f⁰f)(0) = - 2/3 - 2/3
(f⁰f)(0) = - 4/3
Therefore, the value of (f⁰f)(0) = - 4/3.
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Can someone just solve pls
Answer:
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Point Form:
(10,8)
Equation Form:
x=10,y=8
Step-by-step explanation:
GIVING BRAINLIEST :D
Answer:
(5,6)
The x axis is 5 and the y axis is 6.
I really hope this will help you. Good luck! Have a great day!!!! :)
What is an equation in point slope form that passes through (8,2) and has a slope of -5
Answer:
y-2 = -5(x-8)
Step-by-step explanation:
y-y₁=m(x-x₁)
5. The sequence of numbers below is missing the
fourth value. Which of the following is the form
of the missing value in its lowest terms?
3/11, 6/16,9/21,__, 15/31, 18/36
a. 12/25
b. 4/13
c 6/13
d. 1/2
E.7/26
Answer:
C
6/13
Step-by-step explanation:
Comment
This is not a true sequence. It just has the same things done to the numerator as to the denominator.
The numerator (top part of the fraction).
Add 3 to the previous numerator's top
So 3 + 3 = 6 which is the numerator of the second term.
15 + 3 = 18 which is the numerator of the seventh term.
So the numerator of the 4th term is 9 + 3 = 12
The Denominator
The difference there is 5
So 21 + 5 = 26
The answer is
12/26
This reduces down to 6/13
Ryan and Aqil had 352 stickers altogether. After Ryan lost 25% of his stickers, the ratio of Ryan's stickers to Aqil's stickers was 9:4. How many stickers did Aqil have?
Aqil have 88 stickers.
Let Ryan have x stickers initially. Then Aqil will have (352-x) stickers. Ryan lost 25% of his stickers i.e., x-(25% of x)
= x- 25x/100
= x-x/4
= 3x/4
After Ryan lost 25% of his stickers, the ratio of Ryan's stickers to Aqil's stickers was 9:4 i.e.,
3x/4 : (352-x) = 9 : 4
⇒ 3x/4/(352-x) = 9/4
⇒3x/4 x 4 = 9 x (352-x)
⇒3x = 3168-9x
⇒3x+9x = 3168
⇒12x = 3168
⇒x = 3168/12
⇒x = 264
∴ Ryan have 264 stickers of the total 352 stickers and Aqil will have (352-x) i.e., 88 stickers.
Hence, Aqil have 88 stickers out of the 352 stickers.
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A business owner made a survey where he ask his customers150 what do they like the most between a fish and meat and he got this data 85 like meat 125 like fish 70 like both fish and meat 1 what is the probability for a customer to pick at least one item?
Taking into account the definition of probability, the probability for a customer to pick at least one item is 14/15.
Definition of ProbabitityProbability is the possibility that a phenomenon or an event will happen, given certain circumstances and it is expressed as a percentage.
The probability of any event A is defined as the ratio between the number of cases in which event A may or may not occur and the total number of possible cases. This is called Laplace's Law:
P(A)= number of favorable cases÷ total number of posible cases
Union of eventsThe union of events, AUB, is the event formed by all the elements of A and B. That is, the event is verified when one of the two, A or B, or both occurs and it is read as "A or B".
The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:
P(A∪B)= P(A) + P(B) -P(A∩B)
where the intersection of events, A∩B, is the event formed by all the elements that are, at the same time, from A and B.
Probability for a customer to pick at least one itemIn first place, let's define the following events:
M: The event that a customer like meat.F: The event that a customer like fish.So you know:
P(M)= 85÷150= 17/30P(F)= 125÷150= 5/6P(F and R)= P(F∩R)= 70÷150= 7/15In this case, considering the definition of union of events, the probability for a customer to pick at least one item is calculated as:
P(M∪F)= P(M) + P(F) -P(M∩F)
P(M∪F)= 17/30 + 5/6 -7/15
P(M∪F)= 14/15
Finally, the probability for a customer to pick at least one item is 14/15.
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Pls help I’ll mark u brainlest asap and extra points for the correct answer
Answer:
Step-by-step explanation: the five was never in bracket and -2 times 2 = -4
(5)^2 -2(5-3)
=(5)^2 -2(2)
=25 -2(2)
25 (-4)
-100
The average number of times Americans dine out in a week fell from 4. 0 in 2008 to 3. 8 in 2012 (Zagat. Com, April 1, 2012). The number of times a sample of 20 families dined out last week provides the following data.
6 1 5 3 7 3 0 3 1 3
4 1 2 4 1 0 5 6 3 1
a. Compute the mean and median
b. Compute the first and third quartiles
c. Compute the range and interquartile range
d. Compute the variance and standard deviation
e. The skewness measure for these data is 0. 34. Comment on the shape of this distribution. Is it the shape you would expect? Why or why not?
f. Do the data contain outliers?
a. Mean and Median is 2.95 and 3 respectively
b. The first and third quartiles5.25 and 15.75 respectively
c. Range and interquartile range is 7 and 4 respectively
d. Variance and Standard Deviation is 4.201 and 2.049 respectively
e. The skewness is not expected as it largely differs from the mean.
Rearranging the data.
0, 0, 1, 1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 4, 4, 5, 5, 6, 6,7
Mean = ∑▒(x/N)
Mean = (6+1+ 5 +3+ 7+ 3 +0+ 3+ 1+ 3 +4 +1+ 2+ 4 +1+ 0 +5 +6 +3+ 1)/20
= 59/20
=2.95
Median = Sum of (10th and 11th number) /2
(3 +3)/ 2
=6/2
=3
Quartile = 0, 0, 1, 1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 4, 4, 5, 5, 6, 6,7
Q1=Value of (((n+1))/4)
Q1=Value of ((1(20+1))/4)
Q1=Value of ((21))/4)
Q1= (5.25)
observation=Value of (5th)
observation= 1
Q3=Value of (((n+1))/4)
Q3=Value of ((3(20+1))/4)
Q3=Value of (((63))/4)
Q3= (15.75)
observation=Value of (16th)
observation = 5
Range = highest value - lowest value
= 7-0
= 7
Interquartile range = q3 – q1
=5 – 1
= 4
Variance = Σ(Xi-¯X)2/N
x (x-xi) (x-xi)2
0 (0-2.95) -2.95
0 (0-2.95) -2.95
1 (1-2.95) -1.95
1 (1-2.95) -1.95
1 (1-2.95) -1.95
1 (1-2.95) -1.95
1 (1-2.95) -1.95
2 (2-2.95) 0.95
3 (3-2.95) 1.95
3 (3-2.95) 1.95
3 (3-2.95) 1.95
3 (3-2.95) 1.95
3 (3-2.95) 1.95
4 (4-2.95) 2.95
4 (4-2.95) 2.95
5 (5-2.95) 3.95
5 (5-2.95) 3.95
6 (6-2.95) 4.95
6 (6-2.95) 4.95
7 (7-2.95) 5.95
Σ=(84.0125)
Variance = 84.0125/20
Variance = 4.201
Standard deviation = √variance
S.D = √4.201
S.D = 2.049
e. the skewness is not expected as it largely differs from the mean.
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simplify the expression: 3a+4a
Answer: 7a
Step-by-step explanation:
Step-by-step explanation:
do sum of 3a and 4a your answer will be 7a
Solve for the indicated variable. Include all of your work in your answer. Submit your solution. A = 1 + prt ; for r
Multiply by 2: Divide by (a+b)
Answer:
r=(a-1)/pt
Step-by-step explanation:
a=1+prt
a-1=prt
a-1/pt=r
r=a-1/pt
In a bake sale, you recorded the number of muffins sold and the amount of sales in a table as shown.
a. What is a function that relates the sales and the number of muffins?
The function that relates the sales and the number of muffins is :
S = 2.5 m
What is the sales amount ?The sales amount can be find by the total sales. That is , if there are n products to sell and selling amount is x rs. then we can easily find the total sales by multiplying them and by this total sales we can easily find the number of items sold per units and vice versa.
In the question given,
amount (A) = $ 250.00
Now take any of two values from table ,
Choose any two points and calculate the slope:
slope = [tex]\frac{50 - 20}{20 - 8}[/tex] = 2.5
thus, y = 2.5x
Hence we can say the function that relates the sales and the number of muffins is :
S = 2.5 m
where, S = sales amount
m = number of muffins to be sell
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The complete question is:
In a bake sale, you recorded the number of muffins sold and the amount of sales in a table as shown.
a. What is a function that relates the sales and the number of muffins?
b. How many muffins would you have to sell to make at least $ 250.00 in sales?
A hand held music player was marked down by 1/4 of the original price. If the sales price is $128.00, what is the original price?
Answer:
A) The original price of music player is $170.66
B) If the item was marked up by 1/2 before it was placed on the sales floor, what was that the store paid for the digital player.?
Step-by-step explanation:
A)you would divide $128 by 4, getting $32. then add that to the original price, being $160.
B) you would divide $160 by 2, getting $80, then add those two together in order to find what it was marked up to, being $240. hopefully this helps
Simplify each expression. Rationalize all denominators. (3+2 √5)(1-√20)
All denominators are [tex]= -17-4\sqrt{5}[/tex].
The phrase simplifies manner to make something simpler to do or recognize. So, by decreasing or simplifying the fractions method we make the fraction as simple as feasible. We do this by dividing the numerator and the denominator with the aid of the most important range that could divide into both numbers precisely.
The only form is likewise known as the decreased form of a fraction. for instance, ¾ is the most effective shape of a fraction that has a not unusual thing equal to 1. but 2/4 is not the most effective form, because 2/four can in addition be simplified and written as ½.
Step one is to perceive a common issue between the denominator and numerator. The denominator and numerator are each divided by the commonplace thing. The department operation is repeated until there are not any extra elements. The fraction is said to be simplified if no greater factors go out.
Apply FOIL method : (a+b)(c+d)= ac+ad+bc+bd
[tex](3+2\sqrt{5} )(1-2\sqrt{5} =3.1.3(-2\sqrt{5} )+2\sqrt{5}.1+2\sqrt{5} (-2\sqrt{5} )[/tex]
[tex]= 3.1+3(-2\sqrt{5} )+2\sqrt{5} .1+2\sqrt{5} (-2\sqrt{5} )[/tex]
[tex]= -17-4\sqrt{5}[/tex]
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Please help me I need help
Answer: 2
Step-by-step explanation:
8+14-5-7+3-7-4
add first.
8+14+3=25
25-5-7-7-4
now subtraction, set aside the added solution, 25.
-5-7-7-4=-23
25-23=2
Answer:
2
Step-by-step explanation:
Parentheses
Exponents
Multiply
Divide
Addition
Subtraction
8+14-5-7+3-7-4
Do addition and subtraction what ever comes first from left to right.
22-5-7+3-7-4
17-7+3-7-4
10+3-7-4
13-7-4
6-4
2
which option?
pls help giving brainliest answers!! :)
Answer: D y=4x 3=4y+x
Step-by-step explanation:
[tex]y=4x\ \ \ \ m=4\\\\3=4y+x\\3-x=4y+x-x\\3-x=4y\\-x+3=4y[/tex]
Divide both parts of the equation by 4:
[tex]\displaystyle\\-\frac{x}{4} +\frac{3}{4}=y \\\\-\frac{1}{4} x+0.75=y\\\\y=-\frac{1}{4} x+0.75\ \ \ \ m_{\perp}=-\frac{1}{m}=-\frac{1}{4}[/tex]
Hi... im stuck on this question. can anyone help?
Step-by-step explanation:
or, y° + 40° + y + 30° = 180 [Sum of angle of a triangle]
or, 2y°+ 70° = 180°
or, 2y° = 180° - 70°
or, y = 110°/2°
or. y = 55°
Therefore the value of y is 55°
A=P(1+in)
P=900
i=0.03
n=2
A=?
The value of A is 954
According to the question we have been given that
The equation to be used is : A = P(1+in)
The values we have been given are ;
P = 900
i = 0.03
n = 2
We need to find the value of A. So to find the value of A we have to put the required values in the equation given to us. Thus,
A = 900(1+0.03*2)
We will solve according to the BODMAS rule that is we have to first solve the bracket terms.
A = 900(1 + 0.06)
A = 900*1.06
A = 954
Hence the value of A is 954.
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Multiply. (√3+√5)(√3-√5)
On multiplying (√3+√5)(√3-√5), we get answer as -2
How can square roots be multiplied?1. Split the radicands in half. A number known as a radicand appears underneath the radical symbol.
2. To multiple radicands, multiply the integers as if they were whole numbers. Always keep the item beneath a single radical sign.
3. Use factoring to exclude any perfect squares from the radicand. To achieve this, check whether any perfect squares have the radicand as a factor.
4. Position the square root of the ideal square before the radical sign. Don't change the second component of the radical symbol.
5. Square the square's root. Sometimes it is necessary to multiply a square root by itself.
We are given,
(√3+√5)(√3-√5)
⇒ (√3)² - (√5)²
⇒ 3 - 5
⇒ -2
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Convert 9 feet to meters
Round your answer to the nearest tenth.
(……..) meters
Answer:
2.7432 meters ≈ 2.7 meters.Step-by-step explanation:
Convert 9 feet into meters:
9 feet= 2.7432 metersRound 2.7432 meters:
2.7432 ≈ 2.7.answer is 2.7 meters.What is -27 divided by 23 multiplied by 18?
Answer:
Step-by-step explanation:
Answer:
-21 3/23
Step-by-step explanation:
-27 / 23 is -1 4/13, -1 4/23 *18 is -21.13 or -21 3/23
alex wrote checks on tuesday for 30$ and 35$. He also made a deposit in his checking account of 185 . Find the overall change in the amount in his checking account
Answer:
He would have $100 in his bank account from the information provided
Step-by-step explanation:
Which equation is equivalent to the formula below?
good luck buddy rip if you dont get the question
Interest Suppose you deposit $ 2000 in a savings account that pays interest at an annual rate of 4 % . If no money is added or withdrawn from the account, answer the following questions.
b. How much will be in the account after 18 years?
$4051.63 will be in the account after 18 years.
The formula to be used is given as follows :
A(t) = a ( 1 + r )^t (1)
where, A(t) = future value
a = principal amount or amount initially deposited.
r = annual interest rate
t = time
According to the question we have been given that
a = $2000
r = 0.04
t = 18 years
putting the required values in equation (1) we get
A(t) = 2000 (1+0.04)^18
A(t) = 2000 (1.04)^18
A(t) = 2000*2.03
A(t) = $4051.63
Thus $4051.63 will be in the account after 18 years.
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Select all possible combinations of swimming and biking times that meet both the distance and the time constraints in this situation.
0.2 hours of swimming and 1.3 hours of biking
1.5 hours of swimming and 0.5 hours of biking
0.5 hours of swimming and 1.5 hours of biking
1 hour of swimming and 1 hour of biking
0 hours of swimming and 2 hours of biking
Answer:
Step-by-step explanation:
It’s the 3rd and last one 0.5 swim and 1.5 bike and 0 hours swim and 2 bike
I’ve done the test