The domain at which the function f(x) = x² - 4•x + 2, and the inverse of the function, f(x), is given by the option;
x > 2; [tex] f^{-1}(x) = 2 + \sqrt{x + 2} [/tex]How can the inverse function and the domain of the inverse function be found?The given function is f(x) = x² - 4•x + 2.
The points through which the parabola passes are;
(0, 2)(2, -2), which is the vertex(4, 2)The inverse of the function is found as follows;
f(x) = x² - 4•x + 2
The standard form of a quadratic equation is f(x) = a•(x - h)² + k
Where;
(h, k) = The coordinates of the vertex
a = The coefficient of x²
Comparing, we have;
(h, k) = (2, -2)
a = 1
Which gives;
f(x) = x² - 4•x + 2 = (x - 2)² - 2
f(x) = (x - 2)² - 2
Let f(x) = y
y = (x - 2)² - 2
y + 2 = (x - 2)²
x - 2 = √(y + 2)
x = √(y + 2) + 2 = 2 + √(y + 2)
x = 2 + √(y + 2)
Therefore, f(x) has an inverse when y > -2, which gives;
The domain where f(x) has an inverse is x > 2, given that the expression, 2 + √(y + 2), is always positive.
The inverse of the function is obtained by changing x to [tex] f^{-1}(x) [/tex] and y to x in the equation, x = 2 + √(y + 2), to give;
[tex] f^{-1}(x) = \mathbf{2 + \sqrt{x + 2}} [/tex]The correct option is therefore;
x > 2, f superscript negative 1 Baseline (x) = 2 + StartRoot x + 2 EndRoot
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Answer:
Its D.x > 2; f Superscript negative 1 Baseline (x) = 2 + StartRoot x + 2 EndRoot
Step-by-step explanation:
How many ounces of a 12% alcohol solution must be mixed with 9 ounces of a 20% alcohol solution to make a 16% alcohol solution?
Answer:
9 ounces
Step-by-step explanation:
Let x = number of ounces of 12% solution.
0.12x + 0.2 × 9 = 0.16(x + 9)
0.12x + 1.8 = 0.16x + 1.44
-0.04x = -0.36
x = 9
Answer: 9 ounces
**WITH STEPS ASAP
1. If you know that limx→−1 f(x)=−3 and limx→0 g(x)=3, then evaluate the following limit:
limx→0 f(x−1)g(x)=
2. If you know that limx→4 f(x)=3 and limx→0 g(x)=−5, then evaluate the following limit:
limx→0 f(x+4)+g(x)=
Applying it's properties, the limits of the functions are given as follows:
1. 9.
2. -2.
What is a limit?A limit is given by the value of function f(x) as x tends to a value. Algebraically, for continuous functions, we have that:
[tex]\lim_{x \rightarrow a} f(x) = f(a)[/tex].
Hence, applying the property above, for item 1, we have that:
limx→0 f(x−1)g(x) = f(0 - 1)g(0) = f(-1)g(0) = -3 x 3 = 9.
For item 2, we have that:
limx→0 f(x+4)+g(x) = limx→4 f(x) + limx→0 g(x) = 3 - 5 = -2.
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What is this expression in simplified form?
Any help?
Answer Im thinking 7 but i don't know for sure
Step-by-step explanation:
What do you get if you cross a chicken with a cow?
Yes, I know how these sound.
Answer:
roost beef
Step-by-step explanation:
At a school, the average of the number of boys, girls, male teachers, and female teachers is 117. The average of the number of boys, girls, and male teachers is 151At a school, the average of the number of boys, girls, male teachers, and female teachers is 117. The average of the number of boys, girls, and male teachers is 151. There are 6 fewer male teachers than there are female teachers. The number of female teachers is 1/16 the number of girls. How many boys are there at the school? boys
Using a system of equations, it is found that there are 204 boys at the school.
What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.
For this problem, the variables are given as follows, considering the situation described:
Variable x: number of boys in the school.Variable y: number of girls in the school.Variable z: number of male teachers in the school.Variable w: number of female teachers in the school.The average of the number of boys, girls, male teachers, and female teachers is 117, hence:
(x + y + z + w)/4 = 117
x + y + z + w = 468.
The average of the number of boys, girls, and male teachers is 151, hence:
(x + y + z)/3 = 151
x + y + z = 453.
Then:
x + y + z + w = 468.
453 + w = 468
w = 15.
There are 6 fewer male teachers than there are female teachers, hence:
z = w - 6 = 15 - 6 = 9.
So:
x + y + z = 453.
x + y = 444.
The number of female teachers is 1/16 the number of girls, hence:
y = 16w = 16 x 15 = 240.x = 444 - y = 444 - 240 = 204.There are 204 boys at the school.
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The endpoints of AB are A(-8,-6) and B(-3,-1). Point C lies on Ab and is 3/5 of the way from A to B. What are the coordinates of point C?
Answer: C(-6.125,-4.125)
Step-by-step explanation:
[tex]\displaystyle\\A(-8,-6)\ \ \ \ B(-3,-1)\\Let\ \frac{3}{5}=\lambda \\Hence,\\\boxed {x_C=\frac{x_1+x_2\lambda}{1+\lambda} }\ \ \ \ \ \ \boxed {y_C=\frac{y_1+y_2\lambda}{1+\lambda} }\\\\x_1=-8\ \ \ \ x_2=-3\\\lambda=\frac{3}{5} \\\\\lambda=\frac{0.6*5}{5}\\\\\lambda=0.6\\\\x_C=\frac{-8+(-3)*0.6}{1+0.6} \\\\x_C=\frac{-8-1.8}{1.6} \\\\x_C=\frac{-9.8}{1.6} \\\\x_C=-\frac{9.8*10}{1.6*10} \\\\x_C=-\frac{98}{16} \\\\x_C=-6.125\\\\\\[/tex]
[tex]\displaystyle\\y_1=-6\ \ \ \ y_2=-1\ \ \ \ \lambda=0.6\\\\y_C=\frac{-6+(-1)*0.6}{1+0.6} \\\\y_C=\frac{-6-0.6}{1.6}\\\\y_C=\frac{-6.6}{1.6} \\\\y_C=-\frac{6.6*10}{1.6*10} \\\\y_C=-\frac{66}{16} \\\\y_C=-4.125[/tex]
[tex]Thus,\ C(-6.125,-4.125)[/tex]
HELPP I AM STUCK IN THIS PROBLEM AND NEED IT BY TMR!!
Answer: 100 scores
Step-by-step explanation:
Let the number of points on your fifth test be x
Hence,
[tex]\displaystyle\\\frac{59+80+65+96+x}{5}=80\\[/tex]
Multiply both parts of the equation by 5:
300+x=80*5
300+x-300=400-300
x=100
what is the fraction form of 10.0833333... repeating
What is 10.0833333 as a fraction?
To write 10.0833333 as a fraction you have to write 10.0833333 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.
10.0833333 = 10.0833333/1 = 100.833333/10 = 1008.33333/100 = 10083.3333/1000 = 100833.333/10000 = 1008333.33/100000 = 10083333.3/1000000 = 100833333/10000000
And finally we have:
10.0833333 as a fraction equals 100833333/10000000
Simplify the quantity 12 minus three fifths times the square root of 25 end quantity squared plus the quantity 2 minus 4 end quantity squared.
1,804
814
85
18
The value of the expression (12 - 3/5√25)^2 + (2 - 4)^2 is 85
How to evaluate the expression?The expression is given as
(12 - 3/5√25)^2 + (2 - 4)^2
Evaluate the square root of 25
So, we have
(12 - 3/5√25)^2 + (2 - 4)^2 = (12 - 3/5 * 5)^2 + (2 - 4)^2
Evaluate the product
So, we have
(12 - 3/5√25)^2 + (2 - 4)^2 = (12 - 3)^2 + (2 - 4)^2
Evaluate the difference
So, we have
(12 - 3/5√25)^2 + (2 - 4)^2 = 9^2 + (2 - 4)^2
Evaluate the exponent and the sum
So, we have
(12 - 3/5√25)^2 + (2 - 4)^2 = 85
Hence, the value of the expression (12 - 3/5√25)^2 + (2 - 4)^2 is 85
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In a track meet, Team A won 3 more medals than two times the medals won by Team B. Team A won 9 more medals than Team B, Find the number of medals for each team. Show all set-up, work, and write a complete sentence for your answer.
The number of medals won by team A is 15 medals while the number of medals won by Team B is 9 medals.
How to solve Algebra Word Problems?
Team A won 3 more medals than two times the medals won by Team B.
If the number of medals won by team B is x, than;
Number of medals won by team A = 3 + 2x
Number of medals won by team B = x
Also, we are told that Team A won 9 more medals than Team B.
Thus;
(3 + 2x) = x + 9
2x - x = 9 - 3
x = 6
3 + 2x = 3 + 2(6) = 15 medals
Thus, we conclude that the number of medals won by team A is 15 medals while the number of medals won by Team B is 9 medals.
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6ab, 8ba, (-2ab) and (-3 bc)
Answer:
4ab = 5bc is the answer
Step-by-step explanation:
Answer:
12ab - 3bc.
Step-by-step explanation:
I am assuming you want to add these.
6ab + 8ba + (-2ab) + (-3bc)
= 6ab + 8ab - 2ab - 3bc
= 14ab - 2ab - 3bc
= 12ab - 3bc.
6. The value of a car is gradually declining in such a way that at the end of each year it is worth in January 2002 6 of its value at the beginning .it was worth 36000,000 in January 2000. What was its worth in January 2002?
Answer:
the value of a car is gradually declining in such a way that at the end
Step-by-step explanation:
I don't know what to say
Please help this is due tomorrow
Answer: 150, 4/2, 0.5/2
Step-by-step explanation:
A taxi driver's total income is AED 100 per day, less AED 600. Her expenses are AED 35 per day, plus
AED 450.
Which of the following statements is true?
Let x represent the number of days and y represent the total income or expenses.
Answer:
the AED450
Step-by-step explanation:
I don't know what to say about my answer but I think it's just the best way to anwers
The heights of young women are approximately normal with mean 64.5 inches and standard deviation 2.5 inches. what are the deciles of this distribution?
Deciles are 61.3 and 67.7
What are deciles?
Deciles are measures of position calculated on a set of data. The deciles are the values that separate a distribution into ten equal parts, where each part contains the same number of observations). The decile is a member of the wider family of quantiles.
Given:
Normal distribution =64.5 inches
Standard deviation=σ =2.5 inches
So, here the z- score for left decile= -1.28
and for right decile= +1.28
we know,
z= x-[tex]\mu[/tex]/σ
x= zσ + [tex]\mu[/tex]
x=-1.28*2.5 + 64.5
x= 61.3 and,
x= 1.28*2.5 + 64.5
x=67.7
hence, the deciles are 61.3 and 67.7
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what is the perimeter of the vertices (1,4),(-1,-2),(2,0),(4,0) to the nearest hundredth
The Perimeter of the quadrilateral = 16.93 units
How to Find the Perimeter of a Quadrilateral?The perimeter of the quadrilateral with the given vertices is the sum of the distance between every vertices.
Calculate the distance between the vertices using the distance formula, d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].
Name the vertices as shown below:
A(1,4)
B(-1,-2)
C(2,0)
D(4,0)
Distance between A and B:
AB = √[(−1−1)² + (−2−4)²]
AB = √(4 +36)
AB = 6.32 units
Distance between B and C:
BC = √[(−1−2)² + (−2−0)²]
BC = 3.61 units
Distance between C and D:
CD = √[(4−2)² + (0−0)²]
CD = 2 units
Distance between A and D:
AD = √[(4−1)² + (0−4)²]
AD = 5 units.
Perimeter of the quadrilateral = AB + BC + CD + AD = 6.32 + 3.61 + 2 + 5
Perimeter of the quadrilateral = 16.93 units
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can you please help me with this?
thanks!
The answer is 18 : -2/3 : 15
Step-by-step explanation:
10 + 8 : (-1/3) - 1/3 : 8 + 7
18 : -2/3 : 15
I need help with this ASAP please
Answer:
c between 30 and 40 mins
Step-by-step explanation:
if you look at the graph that's the only line going down.
determine a skier's velocity in km/h, if it takes her 1.7 min to ski down a 1.67 km slope
Answer:58.8km/h
Step-by-step explanation: V= 1.67/1.7= 0.98 km/min
0.98*60min=58.8
One pipe can fill a tank in 8 minutes, a second can fill it in 12 minutes and a third can fill it
in 24 minutes. If the tank is empty how long will it take the three pipes, operating together,
to fill it?
The sum of two numbers is 72. The difference of the two numbers is 40. What are the two numbers.
Let
x
be the larger number and
y
be the smaller number.
Write an equation that expresses the information in the sentence "The sum of two numbers is 72."
Step-by-step explanation:
x + y = 72
x - y = 40
x = y + 40
so, the first equation is then
y + 40 + y = 72
2y + 40 = 72
2y = 32
y = 16
x = y + 40 = 16 + 40 = 56
What is the slope of the line that passes through the points (4, -6) and (-2, 3)?
Write your answer in simplest form.
Answer:
-3/2
Step-by-step explanation:
slope = (y_2 - y_1)/(x_2 - x_1)
slope = (3 - (-6))/(-2 - 4)
slope = (3 + 6)/(-6) = 9/(-6)
slope = -3/2
Answer:
Step-by-step explanation: 3/-2
Which relation is also a function? 25pts!!!!!!!!
Which of the following is an equivalent expression of 15x2 +12x + 8?
Answer:
15 (x + 2\/5)^2 + 28\/5
Step-by-step explanation:
47.
48.
3m-4+2
m+5
j³-64
j-4
49.
-5p+4p² +4
p-2
50. (4p + 3p²-1) ÷ (p + 4)
51. (20x² 13x + 2) = (5x - 2)
52. (12x² - 6x³ - 3-9x) ÷ (3x − 3)
53. (8x² - 2x - 3) + (2x + 1)
54.(-3x² + 6x³ - 4 - x) ÷ (2x + 1)
-
Please solve this
Answer:
29282829939999999 and yea
Say that you own property with a market price of $74,000. the state tax assessors have given it an assessed value of 48% of that amount. if your state’s property tax rate is 0.031, how much do you owe in property tax, to the nearest dollar? a. $1,101 b. $2,294 c. $35,520 d. $1,193 please select the best answer from the choices provided a b c d
Option a. $1101 is the amount one owes in property tax
The market price of the property = $74000
The assessed value of the property as per the state tax assessors= 48%
So, assessed value in terms of dollars = (48/100)*74000 = $35520
Property tax is calculated on the assessed value of the property. Therefore we will calculate the property tax as follows:
Property tax rate in the state= 3.1%
So, property tax on the owned property will be = (3.1/100)*35520 = 1101.12 or 1101
Therefore, option a. $1101 is the correct answer for the given question
Hence, one needs to pay $1101 in property tax to the state
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pls help me 3 i beg of you (IM2)
The polynomial representing the area of the is 49n² - 25
How to determine the polynomialThe formula for area of a square is expressed as;
Area = a²
Where a is the side length
From the image shown, we can see that the side length takes the value (7n - 5)
Substitute the value into the formula
Area = a²
Area = (7n - 5)²
Area = (7n - 5) ( 7n + 5); this is so because of the difference of two squares
Expand the bracket
Area = 49n² + 35n - 35n - 25
collect like terms
Area = 49n² - 25
Thus, the polynomial representing the area of the cube is 49n² - 25
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Write the equation of the line through (3,-5) and perpendicular to -3x + 2y = 12 in slope-intercept form.
The equation of the line through (3,-5) and perpendicular to -3x + 2y = 12 in slope-intercept form is y = -2/3x + 1
Equation of a lineThe equation of a line is expressed as;
y = mx + b
m is the slope
b is the y-intercept
Given the equation -3x + 2y = 12
2y = 3x + 12
y = 3/2x + 6
From the equation, the slope that is perpendicular to the slope is -2/3
Determine the equation
y-(-5) = -2/3(x-3)
y+5 = -2/3x + 6
y = -2/3x + 6 - 5
y = -2/3x + 1
Hence the equation of the line through (3,-5) and perpendicular to -3x + 2y = 12 in slope-intercept form is y = -2/3x + 1
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Z is a standard normal random variable. what is the value of z if the area to the right of z is 0.0122?
The value of z = 2.25
Given that z is a standard normal random variable.
Now the area under a standard normal curve between two z -values gives the probability of z lying between these two z-values.
Given that the area to the right of z = 0.0122
That is probability that the standard normal random variable lies after z = 0.0122
Total probability = 1
Therefore half the area under the standard normal curve = 0.5
Therefore, 0.5 - 0.0122 = 0.4878
We will find the corresponding z-value for this probability value from the normal tables. This is because normal tables gives area between two standard normal variables.
The table value corresponding to 0.4878 = 2.25
Therefore, z -value = 2.25
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1) 6х - 4 = 5х - 11 ; ??
2) 0,3( х -2) = 0,6 + 0,2(х+4) ; ??
[tex] \bf\longrightarrow \: 6x - 4 = 5x - 11 \\ \bf\longrightarrow \: 6x - 5x = - 11 + 4 \\ \bf\longrightarrow \: x = - 7[/tex]
2) 0.3(x-2) = 0.6 + 0.2(x+4) ↓[tex] \bf\longrightarrow \: 0.3(x - 2) = 0.6 + 0.2(x + 4) \\ \bf\longrightarrow \: 0.3x - 0.6 = 0.2x + 1.4 \\ \bf\longrightarrow \: 0.3x - 0.2x = 1.4 + 0.6 \\ \bf\longrightarrow \: 0.1x = 2 \\ \bf\longrightarrow \: x = \frac{ \cancel2}{ \cancel0.1} \\ \bf \longrightarrow \: x = 20[/tex]
