The value of the expression [tex]\frac{2+\sqrt{5} }{\sqrt{5} }[/tex] after rationalizing the denominator is [tex]\frac{2\sqrt{5}+5 }{5}[/tex].
A finite collection of symbols that is well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.
Rationalizing the denominator is the process of shifting a root, such as a square root or a cube root, from the fraction's denominator to its numerator (numerator).
The numerator is the part of a fraction that comes before the vinculum.
The denominator of a fraction is the phrase that comes before the vinculum.
Consider the expression,
[tex]\frac{2+\sqrt{5} }{\sqrt{5} }[/tex]
Now, let [tex]y=\frac{2+\sqrt{5} }{\sqrt{5} }[/tex]
To rationalize the denominator we multiply and divide the expression by √5.
[tex]y=\frac{2+\sqrt{5} }{\sqrt{5} } \times \frac{\sqrt{5} }{\sqrt{5} }[/tex]
[tex]y=\frac{2\sqrt{5}+(\sqrt{5} )^{2} }{(\sqrt{5} )^{2}}[/tex]
[tex]y=\frac{2\sqrt{5}+5 }{5}[/tex]
The value of the expression when rationalized [tex]\frac{2+\sqrt{5} }{\sqrt{5} }[/tex] is [tex]\frac{2\sqrt{5}+5 }{5}[/tex].
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f(x)=b x and g(x)=logbx are inverse functions. Explain why each of the following is true.
a. The translation f₁(x)=b x-h of f is equivalent to a vertical stretch or compression of f .
The function f₁(x) can be either vertical stretch or vertical compress: TRUE
What do we mean by Logarithmic Function?The following is the formula for basic logarithmic functions: Where b > 0, f(x) = logbx(r), y = logbx.It is the reciprocal of the exponential function x=b∧y.Log functions are denoted by natural logarithm (ln) and common logarithm (log).Here are a few examples of logarithmic functions:
f(x) = ln (x - 2)g(x) = log2(x + 5)-2h(x) = 2 log x, etc.So,
Given function:
f(x) = bˣg(x) = logbxThen,
f₁(x)=b^(x-h)f₁(x)=b^x/b^hNow, Put bˣ=f(x):
f₁(x)=f(x)/b^hf₁(x)=b^(-h)f(x)f₁(x)=c f(x)We discovered that:
c=b^(-h)So, depending on the values of b and h, c can be greater than or less than one.
Therefore, the statement "the function f₁(x) can be either vertical stretch or vertical compress" is TRUE.
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Brett is joining a new gym. He can join Power Plus or Heavy Hulk. At Power Plus, it will cost $34.04 per month, plus a sign-up fee of $24.00. At Heavy Hulk, it will cost $34.29, plus a sign-up fee of $36.50. Right now, Heavy Hulk is cutting their sign-up fee in half for new members. If Brett signs up at a gym today, after how many months will the cost of the memberships be the same?
If Heavy Hulk is cutting their sign-up fee in half for new members. If Brett signs up at a gym today, the number of months that the cost of the memberships be the same is: 23 months.
Number of monthsLet x represent the number of months
Hence,
Formulate
$34.04x+24= $34.29x+(36.50/2)
Collect like terms
($34.04x -34.29x)= 24-(36.50/2)
0.25x=24-18.25
0.25x=5.75
Divide both side by 0.25x
x=5.75/0.25
x=23 months
Therefore If Heavy Hulk is cutting their sign-up fee in half for new members. If Brett signs up at a gym today, the number of months that the cost of the memberships be the same is: 23 months.
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Can someone please help
And explain why correct
If your gonna be immature just go on with your day
Answer:
AD
Step-by-step explanation:
It is the only segment that meets a side of triangle ABC at a right angle.
23% of a snack mix is almonds. How much snack mix would you need to get 230 g of almonds?
Answer:
23 times 10 is
230 so your answer is 2 times 10
help meeeeeeeeeeeee.
Answer:
4:1, 20:5
Step-by-step explanation:
You can determine if a ratio is equivalent by dividing each term with the respective term in the other ratio. If you come out with 1, the ratios are equivalent.
Answer:
4:1 & 20:5
Step-by-step explanation:
These two ratios are equal and true to 12:3!
Hopefully this helps have a great day! :D
You pay $10 to play the following game of chance. There is a bag containing 12 balls, five are red,
three are green and the rest are yellow. You are to draw one ball from the bag. You will win $14 if
you draw a red ball and you will win $12 is you draw a yellow ball. How much do you expect to
win or loss if you play this game 100 times?
After playing 100 times the player will loose $-16.67.
Given the outcomes and the probability is:
Outcome Probability
-$10 1 (cost to play)
$14 draw red 5/12
$12 draw yellow 4/12
therefore, expected probability = ∑x.p(x)
x is no of trials and
p(x) is probability of the results.
E(x) = (14)5/12 + (12)4/12 + (0)3/12 - 10
E(x) = -2/12
E(x) = -10.1667
For 100 games the expected value E(100x) =
E(100x) = E(x) × 100
E(100x) = -10.1667 × 100
E(100x) = -16.67 i.e loss after game.
Hence the player lose $-16.67 after 100 games.
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A 3-quart container of disinfectant costs $13.56. What is the price per cup?
Answer: The answer is $1.13.
Step-by-step explanation:
There are 12 cups inside a 3-quart container.
SOMEONE PLEASE HELPPPP MEEEEEEE
Answer:
Step-by-step explanation:
h
Answer: Corresponding Angles
Step-by-step explanation:
9square rooted x 3square rooted x 2square rooted as single surd
Answer: [tex]3\sqrt{6}[/tex]
Step-by-step explanation:
[tex]\sqrt{9}[/tex] × [tex]\sqrt{3}[/tex] × [tex]\sqrt{2}[/tex] = [tex]\sqrt{54}[/tex]
= [tex]3\sqrt{6}[/tex]
Convert 1/27 to a decimal. Write the decimal using an ellipsis, then write the decimal using an overbar
1/27 to a decimal is .0370
Given,
1/27
Divide 1 by 27 so we get
.0370
Decimal, Integers or whole numbers are numbers to the left of the decimal point, while decimal numbers are numbers to the right of the decimal point. It is critical to understand place value when comparing decimals, doing operations on decimals, and so on. This is how a decimal number's place value chart appears. Chart of Place Values
In the case of decimals, the place value system for the whole number component is the same as the full number. However, following the decimal point, a new realm of numbers emerges in which we employ decimal fractions.
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Answer:
yes
Step-by-step explanation:
so yea
y = – 3
y = x – 0.8
A coordinate grid with 2 lines. The first line passes through the points (0, negative 0.1) and (0.8, 0). The second line is horizontal passes through the point (0, negative 3). The lines intersect at a point with a coordinate of slightly to the left of negative 2 and negative 3.
What is the best approximation for the solution to this system of equations?
(–3.2, –3)
(–2.9, –3)
(–2.2, –3)
(–1.9, –3)
The best approximation for the solution to the system of equation is option C) (-2.2 , -3)
According to the question we have been given two system of linear equation which are:
y = -3 (1)
and y = x - 0.8 (2)
Now solving these two equation and find the value of x
Substituting the value of y from equation (1) to the equation (2) we get
-3 = x - 0.8
-3 + 0.8 = x
x = -2.2
Thus the best approximation for the solution to the system of equation is option C) (-2.2 , -3)
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A florist is arranging a bouquet of daisies and tulips. He wants twice as many daisies as tulips in the bouquet. If the bouquet contains 24 flowers, how many daisies are in the bouquet?
(A) 8 daisies (B) 12 daisies (C) 16 daisies (D) 24 daisies
The correct option is (c) 16 daisies
If the bouquet contains 24 flowers then total 16 daisies are in the bouquet.
What are polynomial functions ?In mathematics, polynomial function can be defined as the equation which consist of coefficient, variables and exponents. All the equations such as quadratic equation, cubic equation which has non negative number as their powers are part of polynomial equation.
Some examples of polynomial equation are :
2x+53x = 93x² + 5x+19(x-3)³Now, for the given question,
let d = number of daisies
t = number of tulips
according to statement polynomial equation is,
d + t = 24 , say equation (i)
Twice as many daisies as tulips:
d=2t
Put the value of d in equation (i)
2t + t = 24
3t = 24
t = 8
As, number of daisies = 2 (number of tulips)
Therefore, d = 2t = 2 (8) = 16
Thus, total 16 daisies are in the bouquet.
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m∠W=73°. Find the measure of the complement of ∠W.
115°
15°
17°
107°
The measure of the angle that complements m∠W is 17°. Option C
What are complementary angles?Complementary angles are defined as angles that sum up to 90 degrees.
They are also called angles at right angle.
Example:
If x and y are termed complementary angles, then
x + y = 90°
From the information given, we have that;
m∠W is complementary to another unknown angle x
This is represented as;
x + m∠W = 90°
But m∠W = 73°
Substitute the value into the equation
x + 73° = 90°
collect like terms
x = 90 - 73
x = 17°
Thus, the measure of the angle that complements m∠W is 17°. Option C
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the city council of anytown, u.s.a., is reviewing the funding for local sports-related activities. to be better informed, the council commissions a study. place the sample groups in order from best to worst, based on how well they would represent the population of anytown residents with an active interest in sports.
The correct order from best to worst of the sample groups is b→ a→ c.
The study conducted by the City Council of USA incorporates the reviewing for the funding for local sports-related activities.
There are 3 sample groups selected from the population of Anytown residents with an active interest in sports. They are:
a. High-school students at three different schools.
b. People randomly approached at a softball tournament, a swim meet, an athletic supply store, and a sports bar.
c. People randomly approached at a department store and at a shopping mall
All these groups are selected randomly.
But for (b), the people are obviously interested in sports activities, as they are selected from softball tournament, a swim meet, an athletic supply store, and a sports bar.
Next would be (a), because the students being younger is probably more interested in sports than elder ones.
The last would be the (c), people selected from the department store since they would be less aware of local- sports related activities.
So the order of samples from best to worst is b→ a→ c.
The question is incomplete. Find the complete question below:
The city council of Anytown, U.S.A., is reviewing the funding for local sports-related activities. To be better informed, it commissions a study. Order the sample groups, best to worst, based on how well they would represent the population of Anytown residents with an active interest in sports.
a. high-school students at three different schools
b. people randomly approached at a softball tournament, a swim meet, an athletic supply store, and a sports bar
c. people randomly approached at a department store and at a shopping mall
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I NEED HELP ASAP!!!
Which of the following expressions represents “the difference between a number and eleven”?
11 – n
-11 n
n + 11
n – 11
All of the following represent the same concept except _____.
a number minus five
five more than a number
the sum of a number and five
a number increased by five
thank you!!
The difference between a number (n) and eleven is written as;
⇒ 11 - n
The exception statement is;
''a number minus five''
What is Number system?
A system of writing to express the number is called number system.
Now, Let a number is 'n'
Then, The difference between a number (n) and eleven is,
11 - n
And, Find the mathematical expression of all the statement as;
Let x is a number.
1. a number minus five = x - 5
2. five more than a number = x + 5
3. the sum of a number and five = x + 5
4. a number increased by five = x + 5
So, Clearly the exception statement is;
''a number minus five''
Therefore, The difference between a number (n) and eleven is written as;
⇒ 11 - n
The exception statement is;
''a number minus five''
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What values of x and y satisfy the system of equations {2x+12y=−173x+2y=7?
Enter your answer as an ordered pair, like this: (42, 53)
If your answer includes one or more fractions, use the / symbol to separate numerators and denominators. For example, if your answer is (4253,6475), enter it like this: (42/53, 64/75)
If there is no solution, enter "no"; if there are infinitely many solutions, enter "inf."
The solution to the system where the system contains linear equations is (59/16, -65/32)
What are linear equations?Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the solution to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
2x + 12y = −17
3x + 2y = 7
Multiply through 3x + 2y = 7 by 6
So, we have
18x + 12y = 42
Subtract the equation 2x + 12y = −17 from 18x + 12y = 42
So, we have
18x - 2x + 12y - 12y = 42 + 17
Evaluate the like terms
So, we have
16x = 59
Divide both sides by 16
So, we have
x = 59/16
Substitute x = 59/16 in 3x + 2y = 7
3 x 59/16 + 2y = 7
This gives
177/16 + 2y = 7
So, we have
2y = 7 - 177/16
Evaluate the difference
2y = -65/16
Divide by 2
y = -65/32
Hence, the solution to the system where the system contains linear equations is (59/16, -65/32)
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In the following figure, BA≅CA, and D is on BC
If BD = 3, then it means that CD is also equal to 3 by definition of Isosceles triangle.
What is the missing length of the triangle?
We are given a triangle with the condition that BA ≅ CA. This means that side BA has a length equal to that of side CA.
Now, an Isosceles triangle is defined as a triangle that has at least two sides of equal length. This means that the given triangle ABC is an Isosceles triangle.
Now, since Triangle ABC is an Isosceles triangle, it means that when we draw a perpendicular line through the point joining the two equal sides, it bisects the third side of the triangle.
Thus, it means that BD is congruent to CD.
If BD = 3, then it means that CD is also equal to 3 by definition of Isosceles triangle.
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if f(x) = 6x - 4, what is f(x) when x = 8?
Answer:
Step-by-step explanation: 44.
f(x)=6x-4
x=8
f(8)=6(8)-4
f(8)= 48-4
f(8)=44
I am a 4-digit number larger than 2,500. No two of my digits are the same. The product of the thousands digit and the hundreds digit is equal to the ones digit. The sum of my digit is 16.
Read the clues. Find the number
Step-by-step explanation:
4-digit number abcd
a >= 2
a×b = d
so, 2 <= b <= 4 to allow a single digit result of a×b, and if b would be 1 or 0, the result would be either a copy of a or of b violating the rule that no 2 digits are the same.
that means a >= 3, because with a = 2 and b <= 4 the number can't be larger than 2500.
and that again means 2 <= b <= 3 and 3 <= a <= 4 to allow a single digit result of a×b.
the sum of "my digit" ? I guess you mean the sum of all digits is 16.
a + b + c + d = 16
so, my first guess :
a = 3
b = 2
therefore
d = 3×2 = 6
that means we have already 11 as sum of the digits, that leaves 5 for c.
so, the number would be
3256
the only alternative would start with a = 4 and then b = 2.
but that would make d = a×b = 8. abd 8 + 4 + 2 = 14, and that leaves for c only 2 to sum up to 16, and that would duplicate b.
so, 3256 is the only solution.
Please help me out please please please
Answer:
I think the first
Step-by-step explanation:
A local construction company has been asked to increase the pitch of a client’s roof so that it is steeper. Currently, the roof is pitched at about 30%. In other words, the roof rises 6 feet for every 20 feet of horizontal distance. The pitch of the roof would increase if the roof rose:
Answer:
more than 6 feet for 20 feet horizontal
Step-by-step explanation:
Increasing the rise increases the pitch
I need help with this problem, I have been stuck on it for awhile.
After 4 stops both buses will have the same amount of riders that is 27.
What are mathematical operations, exactly?An operation is a function in mathematics that converts zero or more input values (also known as "operands" or "arguments") to a good output value.The operation's arity is determined by the number of operands.So, Bus A: 15 people ( +3 at every stop)
Bus B: 35 people ( -2 at every stop)
Then,
Stop 1: Bus A (15 + 3) = 18; Bus B (35 - 2) = 33Stop 2: Bus A (18 + 3) = 21; Bus B (33 - 2) = 31Stop 3: Bus A (21 + 3) = 24; Bus B (31 - 2) = 29Stop 4: Bus A (24 + 3) = 27; Bus B (29 - 2) = 27Therefore, after 4 stops both buses will have the same amount of riders that is 27.
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MARKING BRAINLEIST AND 100 POINTS JUST PLS EXPLAIN HOW TO SOLVE!!
What is the length of segment AB when A(-2,2) and
B(5,2)?
Answer:
7
Step-by-step explanation:
You have to do the square root of: (5-(-2)) squared pluse (2-2) squared
Now you have the square root of 7 squared
7 squared is 49, so you have the square root of 49
that equals 7
*Don't forget to mark brainliest
PLEASE HELP ME ASAP
Answer:
x≤−9/2 or x>7/4
Step-by-step explanation:
I NEED HELP MARKING BRAINLIEST
Answer:
15/36
Step-by-step explanation:
Multiply the top and bottom factors together, i.e.,
3 x 5
4 x 9
this ends up with the answer 15/36.
Answer:
5/12 = 0.416666667
Factor:
5/2^2.3 = 0.416666667
The graph shows the height of a football after being thrown. Use the graph to estimate the x- and y-intercepts of the function, where the function is positive and negative, and interpret the meanings in the context of the situation.
From the graphed function, it is found that:
The x-intercept is of 5. This means that the football will hit the ground after 5 seconds.The y-intercept is of 6. This means that at time 0, the football was at a height of 6 feet.The function is always positive, which means that the ball is in the air for 6 seconds.The graph shows that the function is never negative.What are the intercepts of a function f(x)?The x-intercept of a function f(x) is the value of x when the f(x) = 0, that is, the value of x when the function crosses the x-axis.The y-intercept of a function f(x) is the value of y when the x = 0, that is, the value of y when the function crosses the y-axis.From this graph, it is found that:
The x-intercept is of 5. This means that the football will hit the ground after 5 seconds.The y-intercept is of 6. This means that at time 0, the football was at a height of 6 feet.When a function is positive and when it is negative?A function is positive when it is above the x-axis.A function is negative when it is below the x-axis.Hence:
The function is always positive, which means that the ball is in the air for 6 seconds.The graph shows that the function is never negative.More can be learned about functions at https://brainly.com/question/24808124
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Four friends race their bikes down the street. Evan finishes in 6.2 seconds, Devon in 6.0999 seconds, Liza in 6.188 seconds, and Tasha in 6.168 seconds. Which order shows the friends’ times from fastest to slowest?
Answer:
Evan, Liza, Tasha, Devon
Step-by-step explanation:
For each pair of functions, find f(g(x)) and g(f(x)) .
f(x)=x-3/2, g(x)=2 x-3
A composite function exists as a function that depends on another function. A composite function exists formed when one function exists substituted into another function.
The value of f(g(x)) = (2x-6)/2 and g(f(x)) = x - 6.
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 given functions be f(x) = x-3/2 and g(x) = 2x - 3
f(g(x)) = f(2x-3)
simplifying the above equation, we get
f(g(x)) = f(2x-3) = ((2x-3) - 3)/2
f(g(x)) = f(2x-3) = (2x-6)/2
f(g(x)) = (2x-6)/2
g(f(x)) = g(x-3/2)
simplifying the above equation, we get
g(f(x)) = g(x-3/2) = 2((x-3)/2) - 3
g(f(x)) = g(x-3/2) = x - 6
g(f(x)) = x - 6
Therefore, the value of f(g(x)) = (2x-6)/2 and g(f(x)) = x - 6.
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Suppose you know the measures of all three angles of a triangle. Can you use the Law of Sines to find the lengths of the sides? Explain.
Answer:
No
Step-by-step explanation:
Without any side lengths, the most three angles can determine is similarity, not congruency. This means you can determine the ratio of the lengths of the sides, but not any of the sides individually.
A customer is ordering brick pavers to cover a rectangular walkway that is 3 feet by 15 feet and a square sitting area
that is 6 feet on a side. If one box of pavers covers 5.28 square feet, what is the minimum number of boxes of pavers
the customer should buy?
07
10
O 11
O 16
A customer should buy minimum 16 boxes of pavers.
In this question, a customer is ordering brick pavers to cover a rectangular walkway that is 3 feet by 15 feet and a square sitting area that is 6 feet on a side.
First we find the total area that will be covered by pavers.
Area of rectangle = length × width
Area of rectangle = 15 × 3
Area of rectangle = 45
And the area of square = side²
area of square = 6²
area of square = 36
So, the total area would be,
Total area = area of rectangle + area of square
Total area = 45 + 36
Total area = 81
So, the total area is 81 square feet.
one box of pavers covers 5.28 square feet.
So using unitary method,
81 / 5.28
= 15.534
≈ 16 boxes
This means, approximately 16 boxes will require to cover the above area.
Therefore, the customer should buy minimum 16 boxes of pavers.
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