The value of P² + Q² + P · Q including elimination of radical denominators is equal to 13.
How to find the value of a expression including elimination of radical in denominators
Herein we have two irrational terms whose denominators are radical expressions, which can be treated by algebraic handling and properties for radical expressions:
P = (√2 + 1) / (√2 - 1)
P = [(√2 + 1) / (√2 - 1)] · [(√2 + 1) / (√2 + 1)]
P = (√2 + 1)² / (2 - 1)
P = (√2 + 1)²
P = 2 + 2√2 + 1
P = 3 + 2√2
Q = (√2 - 1) / (√2 + 1)
Q = [(√2 - 1) / (√2 + 1)] · [(√2 - 1) / (√2 - 1)]
Q = (√2 - 1)²
Q = 2 - 2√2 + 1
Q = 3 - 2√2
Then, the value of P² + Q² + P · Q is:
M = (3 + 2√2)² + (3 - 2√2)² + (3 + 2√2) · (3 - 2√2)
M = 9 + 12√2 + 8 + 9 - 12√2 - 8 + 3 - 8
M = 9 + 8 + 9 - 8 + 3 - 8
M = 21 - 8
M = 13
The value of P² + Q² + P · Q including elimination of radical denominators is equal to 13.
RemarkThe statement is poorly formatted and reports typing mistakes, correct form is presented below:
If P = (√2 + 1) / (√2 - 1) and Q = (√2 - 1) / (√2 + 1), then find P² + Q² + P · Q.
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Joey paints old furniture and sells the pieces at craft fairs. the function f(t) approximates how many pieces of furniture he paints per hour. the function w(h) represents how many hours per week joey spends painting the pieces of furniture. what are the units of measurement for the composite function f(w(h))?
the units of measurement for the composite function f(w(h)) are - furniture/weeks
What are composite functions?function composition is an operation. that takes two functions f and g, and produces a function h = g . f such that h(x) = g. In this operation, the function g is applied to the result of applying the function f to x.
Let as consider the work f(t) approximates how numerous pieces of furniture he paints per hour. It implies unit of this work is furniture/hours. The work w(h) speaks to how numerous hours per week Joey spends portray the pieces of furniture. It implies unit of this work is hours/weeks. We have to be discover the units of estimation for the composite work f(w(h)). It the work f(w(h)), to begin with we ought to apply the work w(h) after that f(t).
[tex]f(w(h)) = \frac{furniture}{hours} (\frac{hours}{week} )\\f(w(h)) = \frac{furniture}{week}[/tex]
The units of measurement for the composite function f(w(h)) is furniture/weeks.
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In the diagram below, if < A = 97 °, < B = 46 °, < D = 97 ° and < F = 37 °, we can say that
The two triangles are similar by AA
There is not enough information to tell
The two triangles are not similar
Answer:
(a) The two triangles are similar by AA
Step-by-step explanation:
Similar triangles have congruent corresponding angles and proportional corresponding side lengths.
Third angleThe third angle in triangle ABC is found using the fact that the sum of angles is 180°.
∠C = 180° -∠A -∠B
∠C = 180° -97° -46° = 37°
Two of the angles, A and C, match the measures of two of the angles in triangle DEF. The matches are ...
∠A = ∠D = 97°
∠C = ∠F = 37°
The two triangles are similar by AA.
__
Additional comment
The similarity statement can be ΔABC ~ ΔDEF.
Our of the four runners: Alex, Ben, Curtis, and Dan, the oldest came in second place. Alex ran the distance faster than Curtis, and Dan ran faster than Ben and Curtis. It is also known, that Ben is older than Alex, and Curtis is older than Dan. In what order did the four runners finish?
Considering the situation described, the classification of the runners is given as follows:
Dan - Ben - Alex - Curtis.
What is the classification of the runners?The oldest came in second place. Ben is older than Alex, and Curtis is older than Dan, hence either Ben or Curtis finished second.
Alex ran the distance faster than Curtis, and Dan ran faster than Ben and Curtis, hence considering the above observation Ben finished second and the classification is:
Dan - Ben - Alex - Curtis.
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A track coach is gathering data on the stride length of each of her 52 team members when running a distance of 500 meters. the population mean is 62.95 inches with a standard deviation of 5.65 inches. what is the standard error of the sample mean? round your answer to the nearest hundredth.
The standard error of the sample mean to the nearest hundredth is mathematically given as
S.E=0.784
What is the standard error?The amount by which the population means deviates from a sample mean is represented by the standard error of the mean, which is more often referred to as simply the standard error.
It informs you how much the sample means would change if you were to perform an experiment using fresh samples from the same population but this time uses different samples.
The standard error is obtained by calculating the standard deviation and then dividing that number by the square root of the sample size. It determines the accuracy of a sample mean by factoring in the variation in sample means that exists from one set of data to the next.
Generally, The population's mean height is 62.95 inches, so let's use that.
Taking into account that the population has a standard deviation of 5.65 inches
The sample mean is used to calculate the standard error of the mean.
[tex]SE=\frac{SD}{\sqrt{n}}[/tex]
Therefore
[tex]SE=\frac{5.65}{ \sqrt{52}}[/tex]
S.E=0.7835
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Amanda is building a soft triangular kennel for her dog. she has four wooden planks of lengths 2 feet, 3 feet, 5 feet, and 6 feet. determine which planks amanda should use to build the triangular-shaped kennel. enter the lengths from least to greatest. a triangular kennel made of carpet-covered planks
Amanda would use 3 planks of lengths 3 feet, 5 feet, and 6 feet.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.To determine which planks Amanda should use to build the triangular-shaped kennel:
To build a kennel for dog, we would try to make it the largest possible with what we have.So, we would go with the 3 longest planks: 3ft, 5ft, and 6ft.By looking at the length, we see that we could make something very close to a right triangle since we could use the 6ft as a hypotenuse, and have the two other sides as 3ft and 5 ft (6² is almost 3²+5², which equals 34).That means our corner angle would be slightly over 90 degrees.Therefore, Amanda would use 3 planks of lengths 3 feet, 5 feet, and 6 feet.
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Find the radius of convergence of the power series. (if you need to use or –, enter infinity or –infinity, respectively. ) [infinity] (−1)n xn 2n n = 0
For given power series [tex]\sum_{n=0}^{\infty} \frac{(-1)^nx^n}{2^n}[/tex] the radius of convergence is 2.
For given question,
We have been given a power series [tex]\sum_{n=0}^{\infty} \frac{(-1)^nx^n}{2^n}[/tex]
We need to find the radius of convergence of the power series.
We use ratio test to find the radius of convergence of the power series.
Let [tex]a_n=\frac{(-1)^nx^n}{2^n}[/tex]
[tex]\Rightarrow a_{n+1}=\frac{(-1)^{n+1}x^{n+1}}{2^{n+1}}[/tex]
Consider,
[tex]\lim_{n \to \infty}|\frac{a_{n+1}}{a_n} |\\\\= \lim_{n \to \infty} |\frac{\frac{(-1)^{n+1}x^{n+1}}{2^{n+1}}}{ \frac{(-1)^nx^n}{2^n} } |\\\\=\lim_{n \to \infty} |\frac{(-1)^{n+1}x^{n+1}}{2^{n+1}}\times \frac{2^n}{(-1)^nx^n} |\\\\=\lim_{n \to \infty} |\frac{(-1)x}{2} |\\\\=\lim_{n \to \infty}|\frac{-x}{2} |\\\\=\frac{x}{2}[/tex]
By Ratio test, given power series converges at [tex]|\frac{x}{2} | < 1[/tex]
⇒ |x| < 2
So, the radius of convergence is 2.
Therefore, for given power series [tex]\sum_{n=0}^{\infty} \frac{(-1)^nx^n}{2^n}[/tex] the radius of convergence is 2.
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Write and solve an equation based on the following question.
8 is the product of 4 and what number?
A 4 = 8x 2
B. 8 = 4x: 4
C 8=4x 2
D. 4 = 8x 1/2
Answer:
D
Step-by-step explanation:
hihihihihuiuiijihihihihihihih
what are the minimum and maximum temperatures in the house ?
Answer:
I mean, I think it varies by house and by location but a general range would be:
Min: 64 *F
Max: 74 *F
Given g of x equals cube root of the quantity x minus 3, on what interval is the function positive? (–[infinity], –3) (–[infinity], 3) (–3, [infinity]) (3, [infinity])
the interval in which g(x) is positive is [3, ∞].
On what interval is the function positive?Here we have the function:
g(x) = ∛(x - 3)
The interval in which the function is positive is defined by:
g(x) > 0.
Then we have:
∛(x - 3) > 0.
We need to solve that inequality for x.
∛(x - 3) > 0
The cube root respects the sign of the argument, then:
x - 3 > 0
x > 3
Then the interval in which g(x) is positive is [3, ∞].
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Can anyone help me with this!
Answer:
The answer is B.
[tex] \frac{1025}{4} [/tex]
Step-by-step explanation:
Greetings ![tex] \frac{x {}^{6} - x}{4y} ...substitute \: x = - 4 \: and \: y = 4 \\ \frac{( - 4) {}^{6} - (- 4) }{4(4)} ...apply \: exponent \: rule \\ \frac{4096 + 4}{16} = \frac{4100}{16} = \frac{1025}{4} [/tex]
(-4)^6 - - 4 / 4 x 4
4096 + 4 / 16
4100/16
= 1025/4
So, answer is B. 1025/4
Hope this helps!
Could someone explain how to get the correct answer when trying to find the f(X) and g(X) on a graph like this? Thanks!
Answer:
f(3) = g (3)
Step-by-step explanation:
graphically, we notice that the graphs of f and g intersect
at the point of coordinates (3 , 0)
Then
f(3) = 6 = g(3)
Then
f(3) = g (3)
Divide $4800 between Kofi and Kweku so that Kofi gets three times what Kweku gets
Answer:
see explanation
Step-by-step explanation:
let x be the amount Kweku gets then Kofi gets 3x , so
x + 3x = 4800
4x = 4800 ( divide both sides by 4 )
x = 1200
that is
Kweku gets $1200
Kofi gets 3 × $1200 = $3600
If you flipped two coins simultaneously, for a total of 24 times, how many times, on average, would you expect to get a head and a tail?
When two coins are flipped simultaneously 24 times, on average 12 times we will get a head and a tail.
For given question,
When two coins are tossed simultaneously, the sample space is as follows:
S = { HH, HT, TH, TT} where H denotes Head and T denotes tail.
Using the formula of probability,
P = Number of favorable outcomes/total number of outcomes,
we get,
P(HT) = 1/4
and
P(TH) = 1/4
We know that the occurrence of two mutually exclusive events is the sum of their individual probabilities.
So, P(Head on one and Tail on other)
= P(HT) + P(TH)
= 1/4 + 1/4
= 2/4
= 1/2
= 0.5
So, when two coins flipped simultaneously, the probability of flipping 2 coins and getting a head and a tail is 0.5
In this question, we need to find the number of times getting a head and a tail when two coins are flipped simultaneously 24 times
= 0.5 × 24
= 12
Therefore, When two coins are flipped simultaneously 24 times, on average 12 times we will get a head and a tail.
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Convert 2 ounces into grams. Round your answer to the nearest whole number
Answer: 57
I'm pretty sure that's what it is
Step-by-step explanation:
5107465
State the value of digit in figures ?
Place value of 5 in 5107465 is equal to 5,000,000.
According to the statement
we have given that the a value and we have find the place value of a digit 5 in this numbers.
So, For this purpose,
The given digit is 5107465
And we have find the value of digit 5 in it so,
we know that,
A Place value is the position or place of a digit in a given number .
As we can see that, in given number 5107465:-
5 is at one million place = 5 * 1,000,000 = 5,000,000
1 is at hundred thousand place = 1 * 100000 = 100000
0 is at ten thousand place = 0 * 10000 = 0
7 is at thousand place = 7 * 1000 = 7000
4 is at hundred place = 4 * 100 = 400
6 is at tens place = 6 * 10 = 60
5 is at unit place = 5 * 1 = 5
Therefore,
Place value of 5 in 5107465 is equal to 5,000,000.
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Lexi needs to hire a carpenter to redo her bathroom. Charlie and Sons charges $1000 for the design fee and $75 per
hour for labor. Home Dreams charges $800 for the design fee plus $80 per hour for the labor.
Find the cost of each service assuming the job will take 100 hours.
Which contractor is more expensive? How do you know?
F is a function that maps 6-bit binary strings to 4-bit binary strings. for x∈{0,1}6, f(x) is the string x with the last two bits removed. which property best describes the function f?
The property best describes the Function f IP 4- to- 1 Correspondance.
f is Nat Bijective since Not one-one.
x1= 010101 = 010111
then 2 and 7 2 maps to 0101
So f is mat one-one.
fip Mat 2 - to- 1 correspondance
Since
2 , = 0101 vo , 212 = 0101 01 , 23 = 010 / 1 1
One point 0101
go,
f is Not 2 - to- 1 correspondance.
7 12) is the storing a with the last two
bits mold so we have only $ possibility
of 4 strings going to a single storing.
f can not be 16 - to - 1 correspondance.
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Let f(x) = xe−x if x ≥ 0 and f(x) = 0 if x < 0
Is f a probability density function?
Yes. [tex]f(x)[/tex] is a PDF if
• [tex]f(x) \ge 0[/tex] for all [tex]x[/tex] in the support; this is true, since [tex]e^{-x}>0[/tex] for all [tex]x[/tex], and multiplying a positive number [tex]x[/tex] doesn't change this fact;
• the integral of [tex]f(x)[/tex] over its support is 1; this is also true, since
[tex]\displaystyle \int_{-\infty}^\infty f(x) \, dx = \int_0^\infty xe^{-x} \, dx = 1[/tex]
which can be computed by parts.
Help is needed!!!!! im bad at math :,)
Answer:
Step-by-step explanation:
A= π(5)²
= 3.14(5)²
= 3.14(25)
= 78.5 ans
Which of the following graphs represents the inequality? 4 ⪰ b
The solution to the inequality 4 ≥ b is represented in the graph
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
Inequality shows the non equal comparison between two or more numbers and variables.
Given the inequality:
4 ≥ b
Rearranging gives:
b ≤ 4
The solution to the inequality 4 ≥ b is represented in the graph
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Write an equation for the nth term of the arithmetic sequence.
Step-by-step explanation:
Given [tex] \sf \: first \: term \: (a) = \dfrac{1}{4} \\ [/tex][tex] \small{\sf \: Common \: difference \: (d) = \dfrac{1}{2} - \dfrac{1}{4} = \bold{\dfrac{1}{4}}}[/tex]To findnth termSolution[tex] \sf \: T_n = a+(n-1)d[/tex]
[tex] \sf \: T_n = \frac{1}{4} +(n-1) \frac{1}{4} [/tex]
[tex]\sf \: T_n = \frac{1}{4} + \frac{n}{4} - \frac{1}{4} [/tex]
[tex]\sf \: T_n = \frac{n}{4}[/tex]
an equation for the nth term of the arithmetic sequence. is n/4
Step-by-step explanation:
TN=n/4 is the nth term of arithmetic sequence.
Find the volume of the cylinder.
Either enter an exact answer in terms of pi or use 3.14 for pi
4
6
Answer:
144π or 452.16 units³
Step-by-step explanation:
The formula for volume of a cylinder is [tex]\pi r^2 h[/tex]. We can use the given values for radius and height to find the volume of the cylinder.
Finding the Volume[tex]V=\pi r^2 h\\V=\pi6^2(4)\\V=\pi36(4)\\V=144\pi \ OR\ 452.16[/tex]
The volume of the cylinder is 144π or 452.16 units³.
Sloane kicked a soccer ball off the ground at a speed of 36 feet per second. the height of the ball can be represented by the function h(t) = −16t2 36t where t is the time in seconds. . how many seconds did the ball travel before returning the ground? t = 0.44 seconds t = 2.25 seconds t = 16 seconds t = 36 seconds
The total time in seconds the ball will take to travel before returning the ground is 2.25 seconds.
What is factorisation?The breaking or breakdown of an entity (such as an integer, a matrices, or a polynomials) into a products of another unit, or factors, whose multiplication results in the original number, matrix, etc., is known as factorisation or factoring in mathematics.
Calculation for the time;
Let 't' be the time in second the ball will travel.
Let H(t) be the total height travelled by the ball.
The equation of the height is given as
[tex]H(t)=-16 t^{2}+36 t[/tex]
As soon as the ball will return to the ground the total height will become zero.
So, put equation of height equal to zero.
[tex]-16 t^{2}+36 t=0[/tex]
Factorise the above equation;
[tex]-16 t\left(t-\frac{9}{4}\right)=0[/tex]
Put each value equals to zero to get the value of time.
[tex]\begin{aligned}&t=0 \mathrm{sec} \\&t=9 / 4=2.25 \mathrm{sec}\end{aligned}[/tex]
As, time can not be zero
Therefore, the total time taken by the ball to return to the ground is 2.25 sec.
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please i need help FAST
someone please help i will give brainliest
From the two functions function 2 has the highest maximum value.
Given two functions,one is y=-[tex]x^{2} -2x-2[/tex] and f(-2)=1,f(-1)=6,f(0)=9,f(1)=10,f(2)=9,f(3)=6.
We ae required to choose a function which is having highest maximum possible value.
Function is like a relationship between two or more variables expressed in equal to form. Each value of x of a function has some value of y.
The highest value in the second function is 10 which is at x=1. Put the value of x=1 in y=-[tex]x^{2} -2x-2[/tex].
y=-1-2-2
y=-5
So it might not be highest value of this function.So the second function has highest maximum value of 10 at x=1.
Hence the second function has highest value.
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The area of a square is 400 square units. If the length of each side of the
square increased by one unit, would its area be a rational number? Explain.
yes it will be a rational number.
square having area 400 sq units will have a length of 20 on each side by increasing the length of each side by 1 we get 21 then the area will be
21 ^ 2=441
Then we will have a rational number.
A ladder resting against a wall makes an
angle of 63° with the ground. The foot of
the ladder is 4.7 m from the wall.
Calculate the height of the top of the
ladder above the ground
Answer:
9.224
Step-by-step explanation:
In the xy-plane, the line y = 2x + b intersects the parabola y = x² + bx + 5 at the point (3, k). If b is a
constant, what is the value of k?
By algebraic handling, the value of k of the system of equations is equal to 2.
What are the values of two constants such that a system of equations has a single solution?
Herein we find a system formed by two equations, a linear function and a quadratic equation with the following characteristics:
y = x² + b · x + 5 (1)
y = 2 · x + b (2)
If we eliminate y in (1) and (2), then we have this expression:
x² + b · 3 + 5 = 2 · x + b
3² + b · x + 5 = 2 · 3 + b
3 · b + 14 = 6 + b
14 = 6 - 2 · b
8 = - 2 · b
b = - 4
By (2), y = k, x = 3 and b = - 4, we find the value of k:
k = 2 · 3 - 4
k = 6 - 4
k = 2
By algebraic handling, the value of k of the system of equations is equal to 2.
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The manager of spiffy lube auto lubrication shop is trying to revise his policy on ordering grease gun cartridges. currently he orders 110 cartridges per week, but he runs out of cartridges 1 out of 4 weeks. he knows that, on average, the shop uses 95 cartridges per week. he was also willing to assume that the demand for cartridges is normally distributed. a. compute the standard deviation of the distribution?
Using the normal distribution, it is found that the standard deviation is of 26.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.For this problem, we have that the mean is of [tex]\mu = 95[/tex], while X = 110 has a p-value of 0.75, hence X = 110, Z = 0.575, and then we solve for [tex]\sigma[/tex] to find the standard deviation.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.575 = \frac{110 - 95}{\sigma}[/tex]
[tex]0.575\sigma = 15[/tex]
[tex]\sigma = \frac{15}{0.575}[/tex]
[tex]\sigma = 26[/tex]
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Given MTS and SQP, find sq
From the given similar triangles we can conclude that the length of Side SQ is; 4
How to solve similar triangles?
We are given that;
PQ is parallel and congruent to MT.
Now, from the concept of similar triangles , we can say that;
PS/TS = QS/MS
From the given triangle we see that;
PS = 3 - 2x
QS = 6x - 1
MS = 30
TS = 10
Thus;
(3 - 2x)/10 = (6x - 1)/30
Cross multiply to get;
3(3 - 2x) = 6x - 1
9 - 6x = 6x - 1
Rearranging gives;
6x + 6x = 9 + 1
12x = 10
x = 10/12
x = 5/6
Thus;
SQ = 6(5/6) - 1
SQ = 4
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