Answer:
[tex]\frac{x+4}{8x+8}[/tex]
Answer: 1/(x+2)
Step-by-step explanation:
[tex]\frac{x+4}{x^2+6x+8}\\[/tex]
[tex]\frac{x+4}{(x+2)(x+4)}[/tex]
the x+4 cancel each other so we are left with 1/(x+2)
if the main question was how to foil the denominator x2 + 6x + 8, i can quickly explain that.
x2 + 6x + 8
a2 + bx + c
first step is to multiply the first variable with that last or a * c which in this case would give 1 * 8 = 8
the next step would be to look at the middle number which is b, in our case 6.
so then you look for two number that can multiply to to give 8 as well as add up to 6. With easy guessing one will come up with 4 and 2.
with this values you can impute them directly into the equation as
x^2 +4x +2x+ 8
split the equation then factor
(x^2 +4x) (2x+ 8)
x(x+4) 2(x+4) note that the factored equation must always be the same in the bracket. If they are not the same then you have made a mistake somewhere across the line.
with the results giving (x+2)(x+4)
The graph of f(x) = |x| is reflected across the y-axis and translated to the left 5 units. Which statement about the domain and range of each function is correct? Both the domain and range of the transformed function are the same as those of the parent function. Neither the domain nor the range of the transformed function are the same as those of the parent function. The range of the transformed function is the same as the parent function, but the domains of the functions are different. The domain of the transformed function is the same as the parent function, but the ranges of the functions are different.
Both the domain and range of the transformed function are the same as those of the parent function. So option A is correct.
What is domain and range ?
All the values that go into a function is called domain . The output values are called the range.
Main body:
We have,
The function f(x) = |x| is reflected across y-axis, which gives |-x| = |x|
And then the function is translated to the left by 5 units.
So, the transformed function is translated to 5 units left.
Thus, from the graph below, we get, g(x) =|x+5|
domain of both functions is the set of all real numbers.
Range of both functions is the set = {y, y≥0}
Hence Both the domain and range of the transformed function are the same as those of the parent function.
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Answer: A on Edge 2023
Step-by-step explanation:
7, 5, 9, 6, 8, 7
What is the mean of this sample? X =
The mean of the sample is 7 when the sample is number 7,5,9,6,8,7.
Given that,
The numbers are 7,5,9,6,8,7.
We have to find the mean of the numbers.
The mean, or average of the given numbers, is calculated by dividing the sum of the numbers by the total number of numbers. Mean is equal to (Sum of All Observations/Total Observations).
In mathematics and statistics, the concept of mean is crucial. The most typical or average value among a group of numbers is called the mean.
The mean is
(7+5+9+6+8+7)/6
42/6
7
Therefore, The mean of the sample is 7 when the sample is number 7,5,9,6,8,7.
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Based on a poll, 69% of internet users are more careful about personal information when using a public WiFi hotspot. What is the probability that amount 3 randomly selected internet users, at least 1 is more careful when using a public wifi hotspot? How is the result affected by the additional information that the survey subjects volunteered to respond
a) If we don't have enough info we can create bias in the results and that's not the idea. and since the experiment is conducted in public WIFI spot probably we have some information that will be not share with other and that probably will create bias in the results. b) And we can use the complement rule and we have:Step-by-step explanation:Previous conceptsThe binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".Solution to the problemLet X the random variable of interest, on this case we now that:The probability mass function for the Binomial distribution is given as:Where (nCx) means combinatory and it's given by this formula:Part aIf we don't have enough info we can create bias in the results and that's not the idea. and since the experiment is conducted in public WIFI spot probably we have some information that will be not share with other and that probably will create bias in the results. Part bFor this case we want this probability:And we can use the complement rule and we have:
A is the set of cities in a region. B is the set of people who are now mayors of the cities in that region.
a. Are the sets equivalent? Explain.
b. Are the sets equal? Explain.
a. The sets are ? because they
b. The sets are:
Anot equivalent
equivalent
The sets A and B are equivalent but they are not equal.
What are equal sets?We know that a set is a collection of elements. The elements that we can find in a set are arranged in order such that we can easily see what is composed of the set.
Now two sets are said to be equivalent if they have the same cardinality. We can see that the set of the sets A and B are equal but not equivalent because they contain the same elements and also have the same cardinality since the cities must all have mayors.
Thus, the number of cities is equivalent to the number of mayors thus the two sets could have the same cardinality (equivalent) but not the same elements thus they are not equal.
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A line has a slope of 1 and passes through the point (-9,-3). what is its equation in slope-intercept form?
The equation in slope - intercept form is y = x + 6
Given,
In the question:
A line has slope is 1 and passes through the point (-9, -3)
To find the equation in slope - intercept form.
Now, According to the question:
Based on the given conditions:
Slope (m) = 1
and, x = -9 , y = -3
Substitute the values into
y = mx + b
-3 = -9 +b
Calculate the sum or difference
-b = -6
Divide both sides of the equation by the coefficient of variable
b = 6
Substitute m = 1 and b = 6 into y = mx + b
y = x + 6
Rewrite y = x + 6 in slope intercept form.
Hence, The equation in slope - intercept form is y = x + 6.
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CAN SOMEOE HELP ME WITH THESE THREE GEOMETRY QUESTIONS??
The missing lengths, using the Pythagorean Theorem, are given as follows:
First picture: 3.6.Second picture: 10.6.Third picture: 4.6.How to obtain the missing lengths?The missing lengths are obtained using the Pythagorean Theorem, which states that:
The sum of the lengths of the sides between the right angle squared is equals to the length of the hypotenuse squared.
Hence, for the first triangle, the hypotenuse is given as follows:
h² = 2² + 3²
h = sqrt(13)
h = 3.6.
For the second triangle, the missing side is given as follows:
x² + 12² = 16²
x² = 16² - 12²
x = sqrt(16² - 12²)
x = 10.6.
For the third triangle, the missing side is given as follows:
x² + 2² = 5²
x² = 21
x = sqrt(21)
x = 4.6.
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An investor bought 500 shares of stock, some at $4.00 per share and some at $5.00 per share. If the total cost was $2375.00, how many shares of each stock did the investor buy?
The number of shares of $4.00's shares are125 and the number of shares of $5.00's shares are 375.
According to the question,
We have the following information:
An investor bought 500 shares of stock, some at $4.00 per share and some at $5.00 per share. And the total cost was $2375.00.
Let's take the cost of $4.00's share to be x and that of $5.00's share to be y.
x+y = 500
x = 500-y ...(1)
4x+5y = 2375
Putting the value of x from equation 1:
4(500-y) +5y = 2375
2000-4y+5y = 2375
2000+y = 2375
y = 2375-2000
y = 375
Putting the value of y in equation 1:
x = 500-375
x = 125
Hence, the number of shares of $4.00's shares are125 and the number of shares of $5.00's shares are 375.
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What is the slope of the line that passes through the points (-4, 5) and
(-7,8)? Write your answer in simplest form.
The slope of the line passing through (-4,5) and (-7,8) is -1.
What is slope of line?Slope of line is the ratio of change in y-coordinate with the change in x-coordinate. It measures the steepness and direction of the line with x-axis (non vertical line.
Slope of line passing through two points (x₁,y₁) and (x₂,y₂) is given by
Slope of line = (y₂-y₁)/(x₂-x₁)
The given points are (-4,5) and (-7,8).
Here x₁ = -4, y₁ = 5
x₂ = -7, y₂ =8
Hence,
Slope of the line = (8-5)/{-7-(-4)}
= (8-5)/(-7+4)
= 3/(-3)
= -3/3
= -1
The slope of line is given by -1.
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Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.
y = √(x-1), y = 0, x= 5;
about the line y = 3.
Answer:
(1/3)π(5-1)^3
Step-by-step explanation:
The volume of the solid obtained by rotating the region bounded by the given curves about the specified line, y = 3, is
V = ∫5√(x-1) dx
V = ∫5(y-(-1)) dy
V = ∫5(y+1) dy
V = ∫5y dy + ∫5dy
V = ∫5y dy + 5
V = [y^2/2]5 + 5
V = [5^2/2] + 5
V = 5+5
V = 10
There were 44 dogs and cats at the pet store if 75% were cats how many cats were at the pets store?
Answer:
33.
Step-by-step explanation:
75% x
100 44
x = (44 * 75 ) / 100 = 33.
Understanding functions
Using the given graph, the function table that is completed would be:
Input Output
-9 1
-5 1
-2 1
How to Solve Functions Using a Graph?A function is graphed by plotting the input values on the x-axis against the output values on the y-axis. This means all input values are on the x-axis, and their corresponding output values are on the y-axis.
To find the output value when an input value is given as 4, we need to trace the output value that corresponds to x = 4 on the graph.
Using the graph in the diagram, we know the following:
When the input value is x = -9, the output value is y = 1.
When the input value is x = -5, the output value is y = 1.
When the input value is x = -2, the output value is also y = 1.
The complete function table would be:
Input Output
-9 1
-5 1
-2 1
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If [tex]y = { \sin}^{ - 1}x [/tex] then prove that [tex]( {1 - x) }^{2} \frac{ {d}^{2} y}{d {x}^{2} } - x \frac{dy}{dx} = 0[/tex]
[tex]{ \green{ \boxed{ \purple{ \sf{(1 - {x}^{2}) \frac{ {d}^{2}y }{d {x}^{2} } - x \frac{dy}{dx} = 0}}}}}[/tex]
Step-by-step explanation:
Given,
[tex]{ \blue{ \sf{y = { \sin}^{ - 1}x}}}[/tex]
differentiate with respect to x
[tex]{ \purple{ \sf{ \frac{dy}{dx} = \frac{1}{ \sqrt{1 - {x}^{2} } } }}}[/tex]
[tex]{ \purple{ \sf{ \sqrt{1 - {x}^{2} } \frac{dy}{dx} = 1}}} \: { \to} \: { \tt{ {eq}^{n} (1)}}[/tex]
This is in the form of uv method
uv = uv' + vu' = 0
[tex]{ \tt{ \sqrt{1 - {x}^{2} } = u}}[/tex]
[tex]{ \tt{ \frac{dy}{dx} = v}}[/tex]
u' = differentiation of u
v' = differentiation of v
Apply uv method to Eqⁿ (1) then,
[tex]{ \purple{ \sf{ \sqrt{1 - {x}^{2} } = \frac{ {d}^{2} y}{d {x}^{2} } + \frac{dy}{dx} \frac{1}{ \cancel2 \sqrt{1 - {x}^{2} } } (0 { \cancel{- 2}}x) = 0}}}[/tex]
Multiply by [tex]{ \red{ \sf{ \sqrt{1 - {x}^{2}}}}} [/tex] then,
[tex]{ \boxed{ \purple{ \sf{(1 - {x}^{2}) \frac{ {d}^{2}y }{d {x}^{2} } - x \frac{dy}{dx} = 0}}}}[/tex]
I need to simplify:
24h + 3d - 10h + 8d
Answer: 14h + 11d
That's it
This function has two zeros.
Using your definition from earlier, what are the TWO zeros of this function?
The zeroes of the function will be negative 2 and 1.
How to get polynomials with zeroes?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
Let a, b, c, and d are the zeroes of the polynomial.
Then the polynomial is given as,
⇒ (x - a)(x - b)(x - c)(x - d)
The degree of the polynomial will be greater than or equal to the number of zeroes.
The intersection of the curve with the x-axis will be (-2, 0), and (1, 0).
Thus, the zeroes of the function will be negative 2 and 1.
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Please help me ( THIS IS THE LAST QUESTION AND IM DONE PLEASE ILL APPRECIATE
Answer: The correct answer = 4
Step-by-step explanation:
(8^2)(4^−3)/(2^4)(8^−2)
=64(4^−3)/(2^4)(8^−2)
=1/(2^4)(8^−2)
=1/16(8−2)
=1/16(1/64)
=1/(1/4)
=4
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5a. find the value of a.
The logarithmic function f(x) = a·log₃(x - 4), passing through the points (13, 7), has the values;
5 a. The value of a is 3.5
b. Please find attached the graph of the function, f(x) = 3.5·log₃(x - 4), created with MS Excel
What is a logarithmic function?A logarithmic function is a function that contain and involves logarithm operation and it is the inverse of an exponential function
The function is f(x) = a·log₃(x - 4),
x > 4 and a > 0
The coordinates of a point on the graph of the function, f is A(13, 7)
5 a. The value of a can be found by plugging in the value of (13, 7) = (x, f(x)), as follows
f(13) = 7 = a·log₃(13 - 4) = a·log₃9 = a·log₃3²
7 = a·log₃3²
7 = 2·a·log₃3 = 2·a·1 = 2·a
2·a = 7
a = 7 ÷ 2 = 3.5
a = 3.5
5 b. The coordinates of the x-intercept of the graph = (5, 0)
The equation of the function is;
f(x) = 3.5·log₃(x - 4)
A third point on the graph is given when f(x) = 14 as follows;
f(x) = 14 = 3.5·log₃(x - 4)
log₃(x - 4) = 14 ÷ 3.5 = 4
3⁴ = x - 4
x = 3⁴ + 4 = 85
Which gives the point, (85, 14)
Similarly, we have the point (31, 10.5), (7, 3.5)
Please find attached the graph of f(x) created with MS Excel
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7. Suppose we are interested in comparing the average years of service accountants have between males and females to see if there is a significant difference between the genders and how long they have stayed in their current job. The following data is provided:
The 99% confidence interval for the difference between the average years of service between men and women would be = 3.43.
What is confidence intervals?Confidence interval is defined as the statistical parameter that is used to know if a set of values would fall within a certain range of population or not.
Using the statistical table, the value of 99% or 0.99 confidence interval has a z-score = 2.576
The standard error that exists between the bothe value = SD/Ö
Where SD = difference between the standard deviations = 8.39 - 4.39 = 4
Where ñ = different between the average years of service = 9.62
Standard error= 4/√9.62 = 4/3.01 = 1.33
The confidence interval = 2.576 × 1.33 = 3.43.
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Give both values of that satisfy the quadratic
equation
5x + 2 = x² + 9x
Give each value as a decimal to 2 d.p.
Answer: [tex]-4.45, 0.45[/tex]
Step-by-step explanation:
[tex]5x+2=x^2 +9x\\\\x^2 +4x-2=0\\\\x=\frac{-4 \pm \sqrt{4^2 -4(1)(-2)}}{2}\\\\x=-2 \pm \sqrt{6}\\\\x \approx -4.45, 0.45[/tex]
What is 1/2 / 2/3 in simplest form
Answer:
5/6
Step-by-step explanation:
1/2 / 2/3 = 0.5/0.6
= 5/6
Find the value of x in the figure below. (only type the numerical value, do not include the degree sign)
By using the fact that the angles are supplementary, we can write and solve a linear equation to find that x equal to 90
How to find the value of x?In the image, we can see two supplementary angles, where by definition, two angles are supplementary if their addition is equal to a plane angle (an angle of 180°).
With that in mind, we can write the linear equation:
x + 2x = 180
So we just need to isolate x in that simple linear equation.
If we subtract 2x in both sides, we will get:
x + 2x = 180
x =180/2x
x= 180/2
90
So the unknown angle has a measure of 90°.
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Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
The rise and the run of the line is shown in the diagram below.
The slope = rise/run = 1/4.
How to Find the Slope of a Line Using the Rise and the Run?The rise of a line is the vertical distance along the line, which is equal to the number if units you move up or down from one point to another, while the run is the horizontal distance along the line, which is the number of units you move from left or right from a point to another.
The slope of any line (m) = rise of the line/run of the line.
Given the graph shown above:
Red line = rise of the line = 1 unit
Blue line = run of the line = 4 units
Slope of the line = 1/4
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Write in point-slope form the equation of the line passing through (-6,-2) and
(-3,-23).
The point-slope form the equation of the line passing through (-6,-2) and (-3,-23) is 7x + y +44=0
What is point-slope form the equation of line?
The point-slope form of the equation of line passing through two points (x₁,y₁) and (x₂,y₂) is given by:
(y-y₁) = m(x-x₁)
Where m is slope and m =(y₂-y₁)/(x₂-x₁)
Here, given points are (-6,-2) and (-3,-23).
So, x₁ = -6, y₁ = -2
x₂ = -3, y₂ = -23
So,
Slope of line of line (m) = {-23-(-2)}/{-3-(-6)}
= (-23+2)/(-3+6)
= -21/3
m= -7
Now,
Equation of line passing through the given points is given by-
y-(-2)= -7{x-(-6)}
y +2 = -7(x+6)
y+2 = -7x - 42
7x + y +42 +2=0
7x + y +44=0
Hence, the equation of line passing through the given points is 7x + y +44=0
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Express each fraction as a percent 7/8 6/50
Answer:
87.5%
12%
Step-by-step explanation:
7 divided by 8 equals 0.875
Multiply that by 100 to get percent to get 87.5%
6 divided by 50 equals .12
Multiplied by 10p to get percent is 12%
Hopes this helps please mark brainliest
Answer:
87.5%
12%
Step-by-step explanation:
Use a calculator to divide the numerator by the denominator. Then multiply the decimal by 100.
7/8 = 0.875 = 87.5%
6/50 = 0.12 = 12%
Write start fraction 39 over 9 end fraction as a whole or a mixed number in simplest form. A. 4 and one-third B. 3 start fraction 9 over 39 end fraction C. 9 and one-third D. 5 and one-fourth
The answer is a because all the other ones are wrong
At best buy they have a 42" TV that sells for $1250 and is on sale for 15% and sales
tax is 6.5%. What is the final cost? (Hint: Calculate the discount first and then the
tax).
Answer:
69.06
Step-by-step:
1 ) Calculate the discount.
15% of 1250 is...
187.5
2 ) Subtract 187.5 from 1250...
1062.5
3 ) Calculate the sales tax.
6.5% of 1062.5 is...
69.06
4 ) Add 69.06 to 1062.5 to get the final answer...
$1131.56
Hope this helps! :)
Answer:
69.06
Step-by-step explanation:
15% of R1250
= R187, 5
R1250 - R187 ,5
= R1062,5
Once in a classroom, teacher gave 4 square tiles to Samriddhi and Surav each. Then ask them to arrange them in rectangular or square form. Samriddhi arranged the tiles in square form and Saurav arranged in the rectangular form, whose perimeter is more and by how much?
Answer: hm
Step-by-step explanation: yes.
Express the radical using the imaginary unit, i.
+-v-77=+-
The radical expressed using the imaginary unit i is ±(√77)*i .
The iota(i) is an imaginary unit number that is denoted by i and the value of iota(i) is √-1 , that is √-1 = i .
In the question,
it is given that
the the radical expression is ±√-77 , we have to express it using the imaginary unit (i) .
So , ±√-77 can be written as
= ±√(-1 × 77)
= ±√-1 × √77
Substituting the value of i that is √-1 = i ,
we get
= ± i * √77
= ±(√77)*i
Therefore ,The radical expressed using the imaginary number i is ±(√77)*i .
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Test II Solve the given equations using the method of Extracting the square roots. Show your solution(5 points each)
1. x²=16
2. (x-4)²=169
3. 4 x²-225=0
The quadratic functions x² = 16, (x - 4)² = 169 and 4x² - 225 = 0 have solutions 4, (17 or -9) and (7.5 or -7.5) respectively.
Quadratic EquationsA quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term. The first condition for an equation to be a quadratic equation is the coefficient of x² is a non-zero term(a ≠ 0). For writing a quadratic equation in standard form, the x² term is written first, followed by the x term, and finally, the constant term is written. The numeric values of a, b, c are generally not written as fractions or decimals but are written as integral values.
In the first function;
1. x² = 16
take the square roots of both sides;
x = √16
x = 4
2. (x - 4)² = 169
Open the bracket
x² - 8x + 16 = 169
Solving for x
x = 17 or x = - 9
3. 4x² - 225 = 0
4x² = 225
x = 7.5 or x = -7.5
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Given the equation( shown below in the pic attached) which graph best represents f^-1(x)?
The graph best represents f^-1(x) is Option A so A is correct.
Given function:
f(x) = [tex]5\sqrt{x+3} -2[/tex]
Inverse of f(x) is:
[tex]= 5\sqrt{y+3}-2=x= 5\sqrt{y+3}=x+2= \sqrt{y+3}=(x+2)/5= y+3=((x+2)^2)/25= y=((x+2)^2)/25-3= y=(x^2)/25+(4x)/25+4/25-3= y=(x^2)/25+(4x)/25-71/25[/tex]
f^-1(x) = 1/25([tex]x^{2} +4x-71[/tex]).
Using graphing calculator:
The inverse of f(x) represents the graph Option A so A is correct.
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Plutonium–238 has a yearly decay constant of 7.9 × 10-3. If an original sample has a mass of 15 grams, how long will it take to decay to 12 grams?
It will take approximately 28 years to decay 15 gram sample to 12 gram.
Given,
The yearly decaying of Plutonium-238 = 7.9 × 10⁻³
The mass of original sample = 15 grams
We have to calculate the time taken to decay to 12 grams.
Here,
At = A0 × e^(-k × t)
At = 12 g
A0 = 15 g
k = 7.9 × 10⁻³ = 0.0079
We have to find t.
That is,
At = A0 × e^(-k × t)
12 = 15 × e^(-0.0079 × t)
12/15 = e^(-0.0079 × t)
0.8 = e^(-0.0079 × t)
Now,
Logarithm both sides (because ln(e) = 1:
ln(0.8) = ln(e^(-0.0079 × t))
ln(0.8) = (-0.0079 × t) × ln(e)
-0.223 = -0.0079 × t
t = -0.223 / -0.0079
t = 28.23
t ≈ 28 years
Therefore,
It will take approximately 28 years to decay 15 gram sample to 12 gram.
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