A domain restriction placed on a non-invertible function affect its inverse.
Using inverse function concepts, it is found that:
The inverse of the function is [tex]y = \sqrt{x+3}-1[/tex], and the domain of the inverse function is [tex]\left[-3,\infty ][/tex]
A function will have an inverse if for each output, there is only one respective input.
The domain of the inverse is the range of the original function.
The function given is:
[tex]f(x) = (x+1)^{2} -3[/tex]
It's range is [tex]\left[-3, \infty][/tex], which will be the domain of the inverse.
To find the inverse, we exchange x and y, and isolate y, then:
[tex]y = (x+1)^{2} - 3\\ \\x = (y+1)^{2} - 3\\\\(y+1)^{2} = x+3\\ \\\sqrt{((y+1)^{2}} = \sqrt{x+3} \\\\y+1 = \sqrt{x+3}\\\\y = \sqrt{x+3} -1[/tex]
The inverse of the function is [tex]y = \sqrt{x+3} -1[/tex], and the domain of the inverse function is [tex]\left[-3, \infty][/tex].
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Consider the absolute value function
f(x) = x + 21-1.
a. Graph the function.
b. What are the domain and range of the
function?
c. What are the x-intercept(s) and y-intercept of
the function?
d. Describe the symmetry of the graph.
(a) Graph of the function is given below.
(b) The domain of the function is, - ∞ < x < ∞.
The range of the function is, -1 ≤ ∞.
(c) The x - intercepts are, (-3, 0), (-1, 0) and the y - intercept is, (0, 1).
(d) The graph is symmetric about the vertical line y = -2.
What is absolute value function?
The non-negative value of x, regardless of its sign, is referred to in mathematics as the absolute value or modulus of the real number x, symbolized by the symbol |x|. Specifically, |x| = x if x is a positive number, |x| = -x if x is a negative number, and |0| = 0.
Given: f(x) = | x + 2 | - 1.
(a) The graph of the function is attached below.
(b) As the function is absolute function, so the function is defined for all the real numbers.
Hence, the domain is, - ∞ < x < ∞.
The function has all y - values from -1.
Hence, range of the function is, -1 ≤ y.
(c) Now to find the x - intercepts and the y - intercepts.
Let, y = | x + 2| - 1
To find x - intercept plug y = 0
⇒ 0 = |x + 2| - 1
⇒ |x + 2| = 1
⇒ -(x + 2) = 1, (x + 2) = 1
⇒ -x - 2 = 1, x + 2 = 1
⇒ x = -3, x = -1
Therefore, the x - intercepts are (-3, 0) and (-1, 0).
To find y - intercept plug x = 0 in the above equation.
y = |0 + 2| - 1
y = 2 - 1
y = 1
Therefore, the y - intercept is, (0, 1).
(d) From the graph we can see that, the symmetry of the graph is about the vertical line x = -2.
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Help mee someoneeeeee
3. Miranda's jewelry box contains 8 necklaces, 10 pairs of earrings, and 4 bracelets. How many combinations, which contain all 3 kinds of jewelry, can she make?
The number of possible combinations Miranda can make from his box is 240
How to determine the number of possible combinations?The number of jewelry in Miranda box are given as
Necklaces = 8
Earrings = 10 pairs
Bracelets = 3
The number of possible combinations is the product of the above parameters
So, we have
Number of possible combinations = 8 * 10 * 3
Evaluate the products
So, we have
Number of possible combinations = 240
Hence, the number of possible combinations = 240
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find the area of the shape below.
10cm , 27cm, 24cm , 9cm
Answer:
The area of the shape is 396 square cm.
Step-by-step explanation:
A police car drives with a constant speed of
56 miles per hour. How long will it take to
travel a distance of 42 miles?
Answer:
45 minutes
Step by step explanation:
60min ÷ 56miles × 42miles = 45mins
At a butcher hop, Hildabought beef and pork. She left with pound of meat. Expre the number of pound of pork he bought uing a decimal
Using conversion of improper fraction to a decimal, we find that she bought 18.32 pounds of meat, which is a terminating decimal.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
The amount of mean she left, in pounds, was of:We want to convert the improper fraction to decimal, which is made adding the decimal fraction to the integer part, that is:The division of 800 by 25 is exact(32), thus terminating decimal, and she bought 18.32 pounds.learn more about unitary method click here:
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Michael is going to invest in an account paying an interest rate of 6.7% compounded
continuously. how much would michael need to invest, to the nearest dollar, for the
value of the account to reach $100,000 in 14 years?
Answer:
P≈39141 ENTER 39141
Step-bystep explanation:
Source TRUST ME BRO
Help would be much appreciated
Answer:
[tex]r(t)=\dfrac{1}{t}\ln \left(\dfrac{A}{P}\right)[/tex]
Step-by-step explanation:
Given function:
[tex]A(t)=Pe^{rt}[/tex]
Divide both sides by P:
[tex]\implies \dfrac{A}{P}=e^{rt}[/tex]
Take natural logs of both sides of the equation:
[tex]\implies \ln \left(\dfrac{A}{P}\right)=\ln e^{rt}[/tex]
[tex]\textsf{Apply the power law}: \quad \ln x^n=n \ln x[/tex]
[tex]\implies \ln \left(\dfrac{A}{P}\right)=rt\ln e[/tex]
Apply the natural log law: ln (e) = 1
[tex]\implies \ln \left(\dfrac{A}{P}\right)=rt[/tex]
Divide both sides by t:
[tex]\implies r=\dfrac{1}{t}\ln \left(\dfrac{A}{P}\right)[/tex]
Can someone help me ?
Answer:
2
Step-by-step explanation:
2 [tex]\frac{3}{5}[/tex] ÷ 1 [tex]\frac{3}{10}[/tex]
[tex]\frac{13}{5}[/tex] ÷ [tex]\frac{13}{10}[/tex]
[tex]\frac{13}{5}[/tex] x [tex]\frac{10}{13}[/tex] = 2
Adaim ha a goal to reach 70 mile. If he hike 8 mile per day, how long will it take him to hike all 70 mile?
It will take at least 9 days for adaim to reach his goal of 70 miles.
Given that,
The 70-mile mark is Adaim's objective. He can hike 8 miles every day.
To find : How long will he need to hike the entire 70 miles?
Therefore, your main task will be to find X.
X times 8 equals 70.
Dividing both sides by 8 yields X on its own.
X therefore equals 70/8.
In the event that your teacher prefers a decimal, you would convert that to 8.75 and round to 9 because it is a day.
Therefore, It will take atleast 9 days for adaim to reach his goal of 70 miles.
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what is the probability that when drawing 2 cards without replacement from a standard 52 card deck that the second is an ace given that the first is a 10
The probability is 1/3 of the given event .
What is probability ?Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.
CalculationThere are 52×51 outcomes when you draw 2 cards one after another without returning the first drawn card to the deck.
There are 48×4 outcomes when the first card is not Ace and the second card is Ace. There are 4×3 outcomes when both cards are Ace. The total outcomes are 48×4+4×3=51×4.
The probability is 51×452×51=51/52×4/51=4/52=1/3.
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(03.02 LC)
A turtle is 6 feet below the surface of the sea. If his position can be recorded as −6 feet, what would the position of 0 represent?
Group of answer choices
A.) 6 feet in the sea
B.) 6 feet above the water
C.) At the bottom of the sea
D.) On the surface of the sea
Option (D) is the correct option and
The position of 0 represents on the surface of the sea.
Given, a turtle is 6 feet below the surface of the sea.
And his position can be recorded as −6 feet.
Now, if his position is recorded as -6 feet, then
according to the cartesian plane
0 represents the origin i.e. the surface of the sea.
Hence, Option (D) is the correct option and
The position of 0 represents on the surface of the sea.
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Anita works 31 hours next week, What is her gross
pay, total amount of deductions, and net pay,
assuming the same percentage is taken out for each
of her deductions during the next pay period?
What formula will we use to calculate her gross pay:
Answer:
In order to answer this question, the amount she makes must be provided.
Factor completely 3x4 – 30x³ +75x². (1 point)
O3(x - 5)²
3x²(x - 5)²
3x²(x²-10x+25)
3x²(x + 5)(x - 5)
Answer: 3x²(x - 5)²
Step-by-step explanation:
Factoring out 3x² of each term leaves you with 3x²(x² - 10x +25)
We can still factor out (x² - 10x +25) to (x-5)(x-5), which is simply (x-5)².
This will leave you with 3x²(x - 5)².
Determine if the two functions f and g are inverses of each other
algebraically. If not, why not?
Answer:
Step-by-step explanation:
(x + 2)(x - 1)(x - 2) = 0
polynomial equations
Answer:
∴ (x + 2)(x - 1)(x - 2) = x³- x² - 4x + 4
Step-by-step explanation:
(x + 2)(x - 1)(x - 2) = (x² + 2x - x - 2)(x - 2)
= (x² + x - 2)(x - 2)
= (x³ + x² - 2x - 2x² - 2x + 4)
= x³ - x² - 4x + 4
Tamira is making trail mix. She has $80 to spend on a mixture of almonds and cashews. Almonds cost $8 per pound and Cashews cost $10 per pound. Let "x" represent the pounds of almonds and "y" represent the pounds of cashews. Write an equation to model this scenario.
The equation that models the scenario is:
80 = 8x + 10y
Where x is the number of pounds of almonds and y is the number of pounds of cashews.
Which equation models the scenario?
We know that almonds cost $8 per pound and Cashews cost $10 per pound, so if you buy x pounds of almonds and y pounds of cashews, the total cost is:
c(x, y) = x*$8 + y*$10
Now we know that Tamira has $80 to spend, so the total cost will be equal to $80, then the equation that models this scenario is:
$80 = x*$8 + y*$10
Or, removing the units:
80 = 8x + 10y
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identify a quadratic function in standard form with zeros 5 and -1
Step-by-step explanation:
Using Vieta's formula
x²-(sum of roots)x+(product of roots)=0
x²-(5+-1)x+(5×-1)=0
x²-4x-5=0
Alternatively,
if the zeros are 5 and -1 then the quadratic factorizes to (x-5)(x+1) Now expand it
x²+x-5x-5=0
x²-4x-5=0
Identify a quadratic function in standard form with zeros 5 and -1
x (2) + (2)x - 15 = 0
X=3 and x= -5
(x - 3) = 0 and (x + 5) = 0
Solving inequalities
Solve -2x-6>x+9.
The solution for the given inequality is x < -5.
What is inequality in mathematics?
An inequality in mathematics is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line.
The given inequality is -2x - 6 > x + 9
Subtract x from both sides.
-2x -6 -x > x + 9 -x
-3x - 6 > 9
Add 6 to both sides, and we get
-3x - 6 + 6 > 9 + 6
-3x > 15
Divide both sides by -3
⇒ x < -5
Hence, the solution for the given inequality is x < -5.
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please answer these two algebra 2/trig questions. please show work.
a. The vertical height is y = 100tSinθ - (1/2)9.8t².
b. Time of flight is t = 200sin(theta)/9.8.
What is projectile motion?A projectile motion is a type of motion that an object or particle experiences when it is launched into a gravitational field, such as from the surface of the Earth, and proceeds along a curved route only under the influence of gravity.
We know At any time t, a projectile's horizontal and vertical displacement are x = V₀tCos θ where V is the initial velocity, θ is the launch angle
y = V₀tSinθ - (1/2)gt².
Given ball was hit with an initial velocity of 100 feet per second
∴ Height in feet is
y = 100tSinθ - (1/2)9.8t².
The time for which the ball will stay in the air is a time of flight which is given by the formula t = 2v₀sin(theta)/g.
t = 200sin(theta)/9.8.
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The radius of a circle is 1. What is the measure, in radians, of the angle subtended by an arc 13 18 long?
The measure of the arc 13cm long with a radius = 1 is 13rad
What is an arc of a circle?The arc of a circle is defined as the part or segment of the circumference of a circle. A straight line that could be drawn by connecting the two ends of the arc is known as a chord of a circle. If the length of an arc is exactly half of the circle, it is known as a semicircular arc.
Length of an arc = ∅/360 x 2πr
where ∅ = subtended angle in degree
r = 1 = radius of the complete circle
length = 13
13 = ∅ /360 x 2 x π x 1
but 2π rad = 360 degrees
substitute 2π rad for 360 into the equation
13 = ∅/2π rad x 2 x π x 1
By cross multiplying
∅ = 13 x 2π rad / 2 x π
∅ = 13 rad
In conclusion, the angle subtended by the arc in radians is 13 rad.
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What is 23a 76b - 17a 42b
if there are 20 apples and 40 bananas for a fruit basket, fill out all of the possible ratios of apples to bananas that could be made.
Answer:
Step-by-step explanation:
Ian is bisecting line segment cd. First, ian places the compass on point d and opens it to a width larger than half of the segment. What is the next step?.
The next step to bisect the line segment CD is to make an arc above the line as well as an arc below the line.
How to cut a line segment in half is as follows:
• Place the compass at point D.
• Set the compass to be just a little bit longer than half the length of the line segment.
• Draw arcs above and below the line.
• Do the same thing by keeping the compass at C point while maintaining the same compass width.
• Draw the line segment that passes through the points where both arcs crosses each other.
Hence, after keeping compass on point D, the next step will be to draw an arc above and below the line segment.
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Why is the formula for a triangle 1 2BH?.
By using the rectangle, we proved that area of triangle is half the area of rectangle that is 1/2 (base×height).
Some properties of rectangle are ?The opposite sides are parallel and equally spaced apart, and each internal angle is 90 degrees.360 degrees are equal to the total of all internal angles.Both of the diagonals are identical in length and parallel to one another.A rectangle's perimeter is equal to 2a+2b units if its sides are of lengths a and b.A rectangle with sides that are a and b long has an area that is equal to ab sin 90 square units.Diagonally is the diameter of the circumference of a rectangle.To Prove:- Area of a triangle= 1/2 (base×height)
Diagonals of a rectangle divide it into two parts of equal parts that is area
.
Let ABCD be a rectangle.
In ΔABC and ΔADC,
AC=AC
By Alternate Interior Angles:
∠BAC=∠CAD
∠BCA=∠CDA
Hence, ΔABC≅ΔACD
∴ar(ΔABC) =ar(ΔACD)
Let ΔABC,
We draw a line AD perpendicular to BC, line EF parallel to BC passing through A and lines BE and CF , perpendicular to BC passing through B and C respectively.
In rectangle ADBE,
we get,
ar(ΔABE)=ar(ΔADB)
Similarly, in rectangle ADCF,
ar(ΔADC)=ar(ΔACF)
Now, area of rectangle BCFE, from axiom,
=(length)⋅(breadth)
=AB⋅BC
=AD⋅BC
Also,
ar(BCFE)
=ar(ADBE)+ar(ADCF)
=2⋅ar(ΔADC)+2⋅ar(ΔADB)
=2(ar(ΔADC)+ar(ΔADC)
=2(ar(ΔABC))
From (1) and (2),
2(ar(ΔABC))=AD⋅BC
ar(ΔABC)=1/2AD⋅BC
ar(ΔABC)=1/2(base)⋅(height)
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Please help due tonight.
Answer:
A
Step-by-step explanation:
Mr. Brian is planning a staff party. Plates come in packs of 8 and napkins come in packs of 12. Mr. Brian wants to buy the same number of napkins and plates. What is the smallest number of plates Mr. Brian can buy?
pls help will give brainly
The percentage error of Bob’s measurement is 3.87%
The percentage error is The difference between the estimated value and the actual value in relation to the actual value is given as a percentage. Analyst use this formula to determine how big is the error in a relation to true value.
Percentage error can be calculated by the given formula
percentage error=((Exprimental value-Actual value))/(Actual value)∙100
Here, given that
The experimental volume of liquid is 18.8 ml, and the actual volume of liquid is 18.1 ml
i.e. exprimental volume=18.8 mL
and, actual volume=18.1 mL
Now, we will calculate the percentage error
So,
percntage error=((18.8-18.1))/18.1∙100
percentage error=0.7/18.1∙100
percentage error=0.0387∙100
percentage error=3.87%
Hence,
We got percentage error of 3.87% in measurement
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Jaida worked 21.5 hours last week. She earned $11.60 per hour of work.
How much money did Jaida earn last week?
$9.90
$249.40
$1.85
$33.10
Answer:
249.40 Option b
Step-by-step explanation:
When multiplying 21.5 x 11.60 you get $249.40
Identify the type of transformation.
The type of transformation is translation
How to determine the type of transformation?The figures represent the given parameters
On the figure, we can see that:
Both shapes have the same size
This means that none of the shapes is dilated
Also, the orientation of the shapes are the same
This implies that the shapes are not rotated or reflected
So, the closest transformation is translation
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