Answers
The inverse and domain of the inverse of the function are attached below.
Inverse of a FunctionIn mathematics, an inverse is a function that serves to “undo” another function. That is, if y produces y, then putting y into the inverse of produces the output x. A function y that has an inverse is called invertible and the inverse is denoted by inverse of y.
The inverse of the given function is
[tex]y = (x+2)^2, y-^1(x) = \sqrt{x} - 2, -\sqrt{x} - 2[/tex]
The domain of the function is
[tex]domain= [0, \infty)[/tex]
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Related Questions
Simplify the following polynomial expression.
Answers
The simplified form of the polynomial expression is 5x⁴ - 37x³ - 6x² + 41x - 6
How to simplify polynomial?The polynomial can be simplified as follows:
Therefore,
(5x⁴ - 9x³ + 7x - 1) + (- 8x⁴ + 4x² - 3x + 2) - (-4x³ + 5x - 1) (2x - 7)
Therefore, we have multiply first
(-4x³ + 5x - 1) (2x - 7) = -4 (2x - 7)x³ + 5x(2x - 7) - 1(2x - 7)
Hence,
(-4x³ + 5x - 1) (2x - 7) = - 8x⁴ + 28x³ + 10x² - 37x + 7
Therefore,
5x⁴ - 9x³ + 7x - 1 - 8x⁴ + 4x² - 3x + 2 + 8x⁴ - 28x³ - 10x² + 37x - 7
Combine like terms
Therefore,
5x⁴ - 8x⁴ + 8x⁴ - 9x³ - 28x³ + 4x² - 10x² + 7x - 3x + 37x - 1 + 2 - 7
5x⁴ - 37x³ - 6x² + 41x - 6
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Find the horizontal asymptote of the graph of the rational function. y = x^2 + 6 ———— 4^2 - 7 Identify the horizontal asymptote for the graph of the function.
Answers
Given:
[tex]y\text{ = }\frac{x^2\text{ + 6}}{4x^2\text{ -7}}[/tex]The rule for horizontal asymptote is shown below:
For the given rational function, the degree of the numerator is equal to the degree of the denominator.
Hence, the horizontal asymptote is:
[tex]\begin{gathered} y\text{ = }\frac{1}{4} \\ \\ 1\text{ is the leading coefficient of the numerator} \\ and\text{ 4 is the leading coefficient of the denominator} \end{gathered}[/tex]Answer:
[tex]y\text{ = }\frac{1}{4}\text{ \lparen Option A\rparen}[/tex]Can someone help explain this to me? Please and thank you!
Answers
Given the points on the line:
[tex]\mleft(-5,-2\mright),\mleft(3,-4\mright)[/tex]You can find the slope of the line using this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where these two points are on the line:
[tex](x_1,y_1),(x_2,y_2)[/tex]In this case, you can set up that:
[tex]\begin{gathered} y_2=-2 \\ y_1=-4 \\ x_2=-5 \\ x_1=3 \end{gathered}[/tex]Then, substituting values into the formula and evaluating, you get:
[tex]m=\frac{-2-(-4)}{-5-3}=\frac{-2+4}{-8}=-\frac{2}{8}=-0.25[/tex]• By definition, the Point-Slope Form of the equation of a line is:
[tex]y-y_1=m\mleft(x-x_1\mright)[/tex]Where "m" is the slope and this is a point on the line:
[tex](x_1,y_1)[/tex]In this case, having the two points on the line shown in the exercise, you can substitute their coordinates into the equation and simplify, in order to get two equations for the line in Point-Slope Form:
- Using the point:
[tex]\mleft(-5,-2\mright)[/tex]You get:
[tex]\begin{gathered} y-(-2)=-0.25(x-(-5)_{}) \\ \\ y+2=-0.25(x+5) \end{gathered}[/tex]- Using the point:
[tex]\mleft(3,-4\mright)[/tex]You get:
[tex]\begin{gathered} y-(-4)=-0.25(x-3_{}) \\ \\ y+4=-0.25(x-3_{}) \end{gathered}[/tex]• By definition the Slope-Intercept Form of the equation of a line is:
[tex]undefined[/tex]what is a inital value.Context: exponential functions.
Answers
Exponential functions have the form:
[tex]f(x)=a\cdot x^b.[/tex]The initial value of the function f(x) is given by the value of f(x) when x = 0:
[tex]\text{ initial value }=f(0)=a\cdot x^0=a\cdot1=a.[/tex]AnswerFor an exponential function:
[tex]f(x)=a\cdot x^b,[/tex]we have:
[tex]\text{ initial value }=f(0)=a[/tex]a wheelchair ramp is 4.2 meters long. It rises of 0.7 meter. What is the angle of elevation to the nearest tenth of a degree
Answers
Given :
A wheelchair ramp is 4.2 meters long.
It rises 0.7 meters
So, let the angle of elevation = x
so,
[tex]\begin{gathered} \tan x=\frac{0.7}{4.2}=\frac{1}{6} \\ \\ x=\tan ^{-1}\frac{1}{6}=9.462 \end{gathered}[/tex]Rounding the answer to the nearest tenth
So, the answer is : the angle = 9.5
4. Rangers in Montana wanted to estimate the number of elk in a certain area. They tagged 20
elk one Saturday and sent them back to mix with the other elk in the area. The rangers went back
once a month for the next three months and recorded the following.
Month 1 Month 2 Month 3
4
6
12
Tagged elk in sample
Total elk in sample
7
10
18
a. Estimate the size of the elk population for each month.
Month 1:
Month 2 =
Month 3
Answers
Based on the information in the provided table, the elk population for the first month is 11, the second month is 16, and the third month is 30.
In mathematics, what is a data table?Tables are a good way to organize data by using rows and columns. Tables are a versatile organizational tool that can be used to communicate information on their own or in conjunction with another type of data representation (like a graph).Using the information in the give table, we need to calculate the elk population size for each month.
For first month,
elk population = tagged elk + total elk
= 4 + 7
= 11
For second month,
elk population = tagged elk + total elk
= 6 + 10
= 16
For third month,
elk population = tagged elk + total elk
= 12 + 18
= 30
Therefore, the elk population for first month is 11, second month is 16 and third month is 30 which is calculated from the given table data.
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Classify the expression by the number of terms.5y?-8+62%O not a polynomialO binomial
Answers
Given:
[tex]5y^2-8+6y^4[/tex]There are three terms in the given equation.
trinomial is the final answer.
A bike shop sells you a bicycle for $63 and
a helmet for $21. The total cost is 150% of
what the shop spent originally.
a. How much did the shop spend originally?
b. How much profit did the bike shop earn
by selling the bicycle and helmet to you?
Answers
(a) The initial cost that the shop spend is $56 and;
(b) The profit that the bike shop earned by selling the bicycle and helmet to you is $28.
The price of the bicycle is $63 in a shop.
The price of a helmet is $21.
The total price is 150% more than what the shop originally paid for these times:
The total cost, C = $63 + $21 = $84
The cost is 150% of the initial cost let's say K;
C = 150% of K
C = 150/100 × K
C = 1.5K
Hence, the initial cost will be:
K = C/1.5 = $84/1.5
K = $56
The difference between the two costs will be the profit:
P = C - K
P = $84 - $56 = $28
Hence, the amount the shop spend is $56 and the profit the bike shop earns by selling the bicycle and helmet is $28.
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Several people were asked to report the number of hours of sleep they average per night. The results are shown in thehistogram below. How many of those people average greater than 4.5 and less than 6.5 hours of sleep per night?
Answers
EXPLANATION
We can get the solution by calculating the frequency on the Histogram as shown as follows:
Hours Frequency
4.5-5.5 7
5.5-6.5 4
------------
Total Frequency ----------------------> 11
The number of people that average greater than 4.5 and less than 6.5 hours of sleep per night are 11 persons.
The tallest person who ever lived was approximately 8 feet 11 inches tall.
Write an inequality that represents the heights h (in inches) of every other person who has ever lived.
Answers
Answer: [tex]0 < h \le 107[/tex]
This is the same as writing [tex]h \le 107[/tex] where h is positive
======================================================
Work Shown:
1 foot = 12 inches
8*(1 foot) = 8*(12 inches)
8 feet = 96 inches
8 feet + 11 inches = 96 inches + 11 inches
8 feet + 11 inches = 107 inches
The tallest person is 107 inches tall.
If h is someone's height in inches only, then [tex]0 < h \le 107[/tex] is the inequality that describes all possible values of h.
We can simplify that into writing [tex]h \le 107[/tex] and write off to the side somewhere that h must be positive.
Answer: 0 < h < 107 inches
Step-by-step explanation:
First, we see this question asks us to represent in inches, so we will convert 8'11" into inches.
8 feet * 12 inches in a foot = 96 inches
96 inches + 11 inches = 107 inches
Next, we will write our inequality. If this person was the tallest, then everyone else will be less tall. We assume that nobody will be less than 0 inches tall, so that is the left side of our inequality.
0 < h < 107 inches
Since this question asks about every other person who has ever lived, we do not use ≤ (greater than or equal to) since the tallest person is the only height equivalent to 107 inches.
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Graph the parabola.y=x2 - 10x + 23Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click onthe graph-a-function button.12-110х5?42-1010-
Answers
Answer:
• Vertex: (5,-2)
,• Points to the left of the vertex: (3,2) and (4,-1)
,• Points to the right of the vertex: (7,2) and (6, -1)
Explanation:
Given the equation of the parabola:
[tex]y=x^2-10x+23[/tex]First, determine the vertex:
[tex]\begin{gathered} \text{Axis of symmetry: }x=-\frac{b}{2a} \\ x=-\frac{-10}{2\times1} \\ x=5 \\ \text{When x=5} \\ y=5^2-10(5)+23=-2 \\ \implies\text{Vertex}=(5,-2) \end{gathered}[/tex]A table of values for the function is given below with the vertex identified:
Thus, we have the graph below:
• Vertex: (5,-2)
• Points to the left of the vertex: (3,2) and (4,-1)
,• Points to the right of the vertex: (7,2) and (6, -1)
What is 3/8×3/8×3/8 written as a power
Answers
if f(x) and f1(x) are inverse functions of each other and f(x)=2x+5 what is f1(8)?-13/241/823
Answers
we have the following:
[tex]undefined[/tex]R is perpendicular to U. S is parallel to T. m <1 = 39° . Find the remaining angles.
Answers
First, notice that angle 1 and angle 4 are vertical angles, therefore:
[tex]\measuredangle1=39\text{ = }\measuredangle4[/tex]then, we have that angle 1 and angle 2 are supplemetary angles, then:
[tex]\begin{gathered} \measuredangle1+\measuredangle2=180 \\ \Rightarrow\measuredangle2=180-\measuredangle1=180-39=141 \\ \measuredangle2=141 \end{gathered}[/tex]Since angle 3 and angle 2 are vertical, we have the first measures of the diagram:
[tex]\begin{gathered} \measuredangle1=39 \\ \measuredangle2=141 \\ \measuredangle3=141 \\ \measuredangle4=39 \end{gathered}[/tex]Then, angle 1 and angle 5 are corresponding angles, then, we have the following:
[tex]\measuredangle1=39=\measuredangle5[/tex]Now, angle 5 and angle 6 are complementary angles, therefore:
[tex]\begin{gathered} \measuredangle5+\measuredangle6=90 \\ \Rightarrow\measuredangle6=90-\measuredangle5=90-39=51 \\ \measuredangle6=51 \end{gathered}[/tex]Angle 5 is vertical with angle 7, and angle 6 is vertical with angle 8. Also, we can see that angle 9 is a right angle, then, we have the next measures:
[tex]\begin{gathered} \measuredangle5=39 \\ \measuredangle6=51 \\ \measuredangle7=39 \\ \measuredangle8=51 \\ \measuredangle9=90 \end{gathered}[/tex]Finally, notice that angles 4, 9 and 10 are the angles of a right triangle, then, we would have the following:
[tex]\begin{gathered} \measuredangle4+\measuredangle9+\measuredangle10=180 \\ \Rightarrow\measuredangle10=180-\measuredangle9-\measuredangle4=180-90-39=51 \\ \measuredangle10=51 \end{gathered}[/tex]then, angle 10 and angle 11 are supplemetary, then:
[tex]\begin{gathered} \measuredangle10+\measuredangle11=180 \\ \Rightarrow\measuredangle11=180-\measuredangle10=180-51=129 \\ \measuredangle11=129 \end{gathered}[/tex]angle 10 is vertical with angle 13 and angle 11 is vertical with angle 12, then:
[tex]\begin{gathered} \measuredangle10=51 \\ \measuredangle11=129 \\ \measuredangle12=129 \\ \measuredangle13=51 \end{gathered}[/tex]Solve the equation 2x2 - x - 5 = 1 using the quadratic formula.
Answers
For a general quadratic polynomial of the form:
[tex]ax^2+bx+c=0[/tex]the solution is
[tex]x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]this formula is called "the quadratic formula". There are 2 solutions indicated by the subindex 1 and 2 in x.
In our case, by comparing polynomials, we can see that
[tex]\begin{gathered} a=2 \\ b=-1 \\ c=-6 \end{gathered}[/tex]becuase our polynomial is
[tex]2x^2-x-6=0[/tex]in which we moved 1 to the left hand side as -1.
Then, by applying the quadratic formula, we have
[tex]x_{1,2}=\frac{-(-1)\pm\sqrt[]{(-1)^2-4(2)(-6)}}{2(2)}[/tex]Then ,the first solution is
[tex]x_1=\frac{-(-1)+\sqrt[]{(-1)^2-4(2)(-6)}}{2(2)}[/tex]and the
One side of a triangle is 4 times longer than the shortest side and the third side is 3 centimeters less than twice the length of the shortest side. The perimeter of the triangle is 46.How long is the shortest side of the triangle?
Answers
Let's use the variable x to represent the shortest side of the triangle.
If one side is 4 times longer than the shortest side, it measures "4x".
If the third side is 3 cm less than twice the length of the shortest side, it measures "2x - 3".
So, if the perimeter is 46 cm, we have:
[tex]\begin{gathered} x+4x+2x-3=46 \\ 7x-3=46 \\ 7x=49 \\ x=\frac{49}{7}=7 \end{gathered}[/tex]So the shortest side measures 7 cm.
I NEED HELP PLSSSSSS THIS IS NOT EASY FOR ME AND THIS IS DUE TMR!
Answers
The plus sign is a composite of rectangles . The shape is comprised of:
1. 4 congruent rectangles with sides 20 in and 12 in
2. A square at the center with sides 20 in by 20in
The total area of Demi's Tester ca be found using the formula:
[tex]Total\text{ area = 4 }\times\text{ l}\times\text{ b +}l^2[/tex]Substituting the given side lengths:
[tex]\begin{gathered} Total\text{ area = 4 }\times\text{ 20 }\times\text{ 12 + 20}\times\text{ 20} \\ =\text{ 1360 in}^2 \end{gathered}[/tex]Hence, the total area of Demi's poster is 1360 square in
I have a 93% in my ELAR grade, but today we took a CBA and I got a 72% on it. how much will that drop my grade in skyward. please help
Answers
we have the following:
[tex]\frac{93+72}{2}=\frac{165}{2}=82.5[/tex]therefore, the answer is 82.5%
19. Sally has $35 and earns $15 for each batch of cake balls she sells. Kristen has $52 and earns $12 for each batch of cookies she sells. How many batches of cake balls does Sally need to sell to have more money than Kristen?
Answers
ANSWER
6 batches
EXPLANATION
Let the number of batches of cake balls or batches of cookies be x.
Sally has $35 and earns $15 for every batch of cake she sells.
This means that the total amount of money that she has after selling x batches of cake balls is:
35 + 15x
Kristen has $52 and earns $12 for every batch of cookies she sells.
This means that the total amount of money that she has after selling x batches of cookies is:
52 + 12x
To find the number of batches of cake balls that Sandy must sell to have more money than Kristen, we have to write the inequality:
35 + 15x > 52 + 12x
Now, collect like terms:
15x - 12x > 52 - 35
3x > 17
Divide through by 3:
x > 17/3
x > 5.7
We have to round up to whole number since batches of cake balls must be whole.
So, Sandy must sell 6 batches of cake balls to have more money than Kristen.
How do I solve and what would the answer be?
Answers
SOLUTION
Given the question in the image, the following are the solution steps to get the inverse of the function
STEP 1: Write the given function
[tex]f(x)=\frac{2}{x-5}[/tex]STEP 2: Define an inverse of a function
[tex]\mathrm{A\: function\: g\: is\: the\: inverse\: of\: function\: f\: if\: for}\: y=f\mleft(x\mright),\: \: x=g\mleft(y\mright)\: [/tex]STEP 3: Find the inverse of the given function
[tex]\begin{gathered} f(x)=\frac{2}{x-5} \\ \text{Set the function f(x) to y} \\ y=f(x)=\frac{2}{x-5} \\ y=\frac{2}{x-5} \\ \text{Swap x with y} \\ x=\frac{2}{y-5} \\ \text{solve for y} \\ By\text{ cross multiplication,} \\ x(y-5)=2 \\ xy-5x=2 \\ \text{Add 5x to both sides} \\ xy-5x+5x_{}=2+5x \\ xy=2+5x \\ \text{Divide both sides by x} \\ \frac{xy}{x}=\frac{2+5x}{x} \\ y=\frac{2+5x}{x}=\frac{2}{x}+\frac{5x}{x} \\ y=\frac{2}{x}+5 \\ \text{Set the inverse to y} \\ f^{-1}(x)=_{}\frac{2}{x}+5 \end{gathered}[/tex]Hence, the inverse of the function is;
[tex]\frac{2}{x}+5[/tex]Let z(t)= 2t^2 +7t -4, find z(-1) and z(2).
Answers
Let z(t) be the function:
[tex]z(t)=2t^2+7t-4[/tex]Then, to find z(-1), we evaluate directly into the function like this:
[tex]z(-1)=2(-1)^2+7(-1)-4=2(1)-7-4=2-11=-9[/tex]and we do the same thing for z(2):
[tex]z(2)=2(2)^2+7(2)-4=8+14-4=18[/tex]therefore, z(-1)=-9 and z(2)=18
Fill in the table given the visual pattern for the first 5 steps
Answers
The pattern consists of adding a new square on the right, and then adding a new square below previous squares.
Directions: Answer the following questions using the figure below.
3. Name two right angles.
a. NOK, JOK
b. NOJ, NOL
C. NOJ, JOL
Answers
(C.) The two right angles in the diagram are NOJ and JOL.
What is right angle?
A right angle is formed when two straight lines intersect each other at 90˚ or are perpendicular to each other at the intersection.
A right angle is denoted by angle 90 degrees.
The symbol between NOJ indicates right angle because the measure of the angle is 90 degrees.
Since the sum of angles on a straight line is 180 degrees, and we know angle NOJ, angle JOL can be calculated as follows;
NOJ + JOL = 180
JOL = 180 - NOJ
JOL = 180 - 90
JOL = 90
Thus, the two right angles in the diagram are NOJ and JOL.
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Antonio buys persian rugs and then resells them for 150%
of his cost. If he bought a 4' by 9' rug $120, for how much
will he resell it?
Answers
Answer:
$180
Step-by-step explanation:
So first we need to know that 100% would be $120 because that was 100% of the price. Selling it for half the price is the same as selling it for 50%. So what we will be doing is we are going to sell the whole carpet - we are just going to sell it for half of $120. Now we need to thinking what would half the price be because half the price is the same as 50%. So 120/2 = $60 so if we have 100 percent (so $120) plus 50% (which is $60) the total we sold it for would be $180. Therefore our final answer would be $180.
Find the sum. Enter your answer in the box below as a fraction, using theslash mark (/) for the fraction bar.2 413 13+Answer here
Answers
SOLUTION
We want to solve the fraction
[tex]\begin{gathered} \frac{2}{13}+\frac{4}{13} \\ \text{the two fractions has the same denominator, which is 13} \\ so\text{ we write the 13 and add the numerators 2 and 4} \\ we\text{ have } \\ \frac{2+4}{13} \\ =\frac{6}{13} \end{gathered}[/tex]Hence, the answer is 6/13
what is the solution set?
Answers
Answer:
the answer is either 20 or 4 ..
Try to solve for x and y
Answers
Answer:
x = 7
y = 8
Step-by-step explanation:
Create two equations.
Equation 1
Both triangles are isosceles triangles since two of their sides are congruent. Therefore, the base angles of the top triangle are equal:
[tex]\implies y^2-8=x^2+x[/tex]
Equation 2
According to the Vertical Angles Theorem, when two straight lines intersect, the opposite vertical angles are congruent. Therefore, the apexes of the triangles are equal. This means the sum of the base angles are equal:
[tex]\implies (y^2-8)+(x^2+x)=8x+8x[/tex]
[tex]\implies y^2-8+x^2+x=16x[/tex]
[tex]\implies y^2-8+x^2+x-x^2=-x^2+16x[/tex]
[tex]\implies y^2-8+x=-x^2+16x[/tex]
[tex]\implies y^2-8+x-x=-x^2+16x-x[/tex]
[tex]\implies y^2-8=-x^2+15x[/tex]
Substitute the first equation into the second equation and solve for x:
[tex]\implies x^2+x=-x^2+15x[/tex]
[tex]\implies x^2+x+x^2=-x^2+15x+x^2[/tex]
[tex]\implies 2x^2+x=15x[/tex]
[tex]\implies 2x^2+x-15x=15x-15x[/tex]
[tex]\implies 2x^2-14x=0[/tex]
[tex]\implies 2(x^2-7x)=0[/tex]
[tex]\implies x^2-7x=0[/tex]
[tex]\implies x(x-7)=0[/tex]
Therefore:
[tex]\implies x=0, \quad x=7[/tex]
If x was zero, some of the angles would be zero, which is impossible.
Therefore, the only valid solution is x = 7.
Substitute the found value of x into the first equation and solve for y:
[tex]\implies y^2-8=(7)^2+7[/tex]
[tex]\implies y^2-8=49+7[/tex]
[tex]\implies y^2-8=56[/tex]
[tex]\implies y^2=64[/tex]
[tex]\implies y=8[/tex]
Solution
x = 7y = 8Find the product of (3 x 109) and (2 x 109). Write the final answer in scientific notation.
6 x 10^81
6 x 100^18
6 x 10^18
6 x 10^9
pls help
Answers
Answer:
C. 6 x 10^18
Step-by-step explanation:
This is the correct answer
What is 9^p/9^5= 9^3. What is p in tbe equation?
Answers
The value of "p" in the given equation 9^p/9^5= 9^3 is p = 8 using the concept of exponents and powers.
As per the question statement, we are given an equation which is as follows : 9^p/9^5= 9^3 and we are supposed to find the value of "p" in the given equation,
We will be using the concept of exponents and powers.
We know, a^m*a^n = a^(m+n)
and, a^m/a^n = a^(m-n)
Hence using the same formula, we get
9^p/9^5= 9^3
Left Hand side(LHS): 9^p/9^5 = 9^(p-5)
Right hand side(RHS): 9^3
As LHS = RHS
We get 9^(p-5) = 9^3
Now equating the powers, as the base is same, we get
p-5=3
p = 8
Hence, the value of "p" in the given equation 9^p/9^5= 9^3 is p = 8 using the concept of exponents and powers.
Equation: The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.Exponents and powers: In mathematics, a base number raised to an exponent is referred to as a power. The base number is the factor that is multiplied by itself, and the exponent indicates how many times the base number has been multiplied.
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Jake and Mia sold muffins at the bake sale. Jake collected $38 for selling a number of chocolate and blueberry muffins, while Mia collected $20 for selling
the same type of muffins. The following system of equations represents the scenario where is the price of a chocolate muffin and y is the price of a
blueberry muffin. What does the coefficient 3 represent?
(No Calculator)
8x+3y=38
2x+6y=20
Answers
The coefficient 3 represents that the numbers of blueberry muffins sold by Jake is 3.
What is defined as the system of equations?In algebra, a system of equations is two or more equations that must be solved simultaneously (i.e., the solution must fulfill all equations in the system). The quantity of equations must match the total of unknowns for a system to produce a unique solution.For the given question;
Total amount = chocolate muffins's amount + blueberry muffins's amount
Jake's total sell = $38.
Mia's total sell = $20.
Let 'x' be the price of each chocolate muffins.
Let 'y' be the price of each blueberry muffins.
The system of linear equation is;
8x + 3y = 38
2x + 6y = 20
Thus, the coefficient 3 represents that the numbers of blueberry muffins sold by Jake is 3.
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