inverse of f(x)=2 1/2-3 1/3x and what is its x intercept
Answers
Find appropriate f(x) first
2 1/2=5/23 1/3=10/3Now
y=-10/3x+5/2So
InterchAnge x and y
x=-10/3y+5/2Find y which is the inverse
x-5/2=-10/3yy=-3/10x+5/2×3/10y=-3/10x+3/4x intercept
10/3x+3/4=0x=-3/4×3/10x=-9/40Graph attached
Answer:
\(\textsf{Inverse function}: \quad f^{-1}(x)=\dfrac{3}{4}-\dfrac{3}{10}x\)
\(x\textsf{-intercept}:\quad\left(\dfrac{5}{2},0\right)\)
Step-by-step explanation:
Given:
\(f(x)=2\frac{1}{2}-3\frac{1}{3}x\)
Rewrite the function so it is a rational function
Convert the mixed numbers to improper fractions:
\(\implies f(x)=\dfrac{5}{2}-\dfrac{10x}{3}\)
Make the denominators the same:
\(\implies f(x)=\dfrac{3 \cdot 5}{3\cdot 2}-\dfrac{2 \cdot 10x}{2 \cdot 3}\)
\(\implies f(x)=\dfrac{15}{6}-\dfrac{20x}{6}\)
Combine:
\(\implies f(x)=\dfrac{15-20x}{6}\)
The inverse of a function is its reflection in the line y = x
To find the inverse, make x the subject
Replace f(x) with y:
\(\implies y=\dfrac{15-20x}{6}\)
\(\implies 6y=15-20x\)
\(\implies 6y-15=-20x\)
\(\implies x=\dfrac{-6y+15}{20}\)
\(\implies x=\dfrac{15-6y}{20}\)
Replace x with \(f^{-1}(x)\) and y with x:
\(\implies f^{-1}(x)=\dfrac{15-6x}{20}\)
If necessary, convert back into the same format as the original function:
\(\implies f^{-1}(x)=\dfrac{15}{20}-\dfrac{6x}{20}\)
\(\implies f^{-1}(x)=\dfrac{3}{4}-\dfrac{3}{10}x\)
The x-intercept of the inverse function is the point at which it crosses the x-axis, so when \(f^{-1}(x)=0\)
\(\implies \dfrac{15-6x}{20}=0\)
\(\implies 15-6x=0\)
\(\implies 6x=15\)
\(\implies x=\dfrac{15}{6}=\dfrac{5}{2}\)
Therefore, the x-intercept is:
\(\left(\dfrac{5}{2},0\right)\)
Related Questions
Factor the expression
7c+49
Answers
Which equation matches the table?
Answers
An equation that matches the table include the following: y = x + 5.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
m represent the slope.x and y represent the points.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (6 - 5)/(1 - 0)
Slope (m) = 1/1
Slope (m) = 1.
At data point (0, 5) and a slope of 1/, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 5 = 1(x - 0)
y - 5 = x
y = x + 5
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mr. Krabs saw some rickety chairs on sale they were 89.5% off the normal price was $15 each mr. crab four chairs how much did he spend
Answers
The normal price of each chair is
\(=\text{ \$15}\)The percentage off the normal price is
\(=89.5\text{ \%}\)The percentage of the present price of each chair will be
\(\begin{gathered} 100\text{ \% - 89.5 \%} \\ =10.5\text{ \%} \end{gathered}\)To calculate the present value of one chair, we will use the formula below
\(=\text{percentag of the normal price}\times normal\text{ price}\)By substituting the values, we will have
\(\begin{gathered} \text{new price of each chair will be=}\frac{10.5}{100}\times15 \\ \text{new price of each chair will be}=\frac{157.5}{100} \\ \text{new price of each chair will be}=\text{ \$1.575} \end{gathered}\)Since Mr .Krabs bought 4 chairs, the amount he spent will be
\(\text{Amount spent = price of each chair}\times Number\text{ of chairs}\)By substituting the values, we will have
\(\begin{gathered} \text{Amount spent = price of each chair}\times Number\text{ of chairs} \\ \text{Amount spent}=1.575\times4 \\ \text{Amount spent}=\text{ \$6.30} \end{gathered}\)Therefore,
The amount Mr.Krabs spent is = $6.30
with which measurement procedure is the target behavior recorded if it occurs at any point within the scoring interval?
Answers
If the target behavior is recorded whenever it occurs at any point within the scoring interval, the measurement procedure used is called continuous recording or event recording. This method involves observing and recording each instance of the behavior without considering its duration or intensity.
Continuous recording is typically used when the target behavior is discrete and occurs relatively infrequently or has a short duration. With this measurement procedure, each occurrence of the behavior is recorded as a separate event, regardless of when it starts or ends within the scoring interval. Examples of behaviors that can be measured using continuous recording include vocalizations, hand clapping, or instances of aggression.
Continuous recording provides a comprehensive account of the frequency or rate at which the behavior occurs, allowing for a detailed analysis of its occurrence patterns. This method is particularly useful when a precise count of behavior instances is needed and when the duration or intensity of the behavior is not a focus of measurement.
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I WILL GIVE 100COINS
Answers
#1
10,7.5,9,12,7.5,8\(\\ \rm\Rrightarrow Mean=\dfrac{10+7.5+7.5+9+12+8}{6}=\dfrac{54}{6}=9\)
#2
12,12,11.5,11.5,12.5,13\(\\ \rm\Rrightarrow Mean=\dfrac{12+12+11.5+11.5+12.5+13}{6}=72.5/6\approx 12\)
The variables y and x have a proportional relationship, and y = 5 when x = 4.
What is the value of x when y = 8?
Answers
Answer:
\(\boxed{a = 6.4}\)
Step-by-step explanation:
Given:
\(x:y = (4):(5)\)
Let the value of "x" be known as "a".
\(x:y = a:8\)
Setting up the proportion:
\(\rightarrow 4:5 = a :8\)
Multiplying the middles and the extremes:
\(\rightarrow 5a = 4 \times 8\)
Simplifying the RHS:
\(\rightarrow a = \dfrac{4 \times 8}{5}\)
\(\rightarrow \boxed{a = 6.4}\)
Thus, the value of x is 6.4 when y is 8.
Answer:
\(\sf x=\dfrac{32}{5}\)
(or x = 6.4 if you want it in decimal form)
Step-by-step explanation:
If y and x have a proportional relationship, then:
y = kx (for some constant k)Given:
x = 4y = 5Substitute the given values into the equation to find k:
⇒ 5 = k(4)
⇒ k = 5/4
Therefore, \(\sf y=\dfrac54x\)
When y = 8, substitute y = 8 into the equation and solve for x:
\(\sf \implies \dfrac54x=8\)
\(\sf \implies x=8 \cdot \dfrac45\)
\(\sf \implies x=\dfrac{32}{5}\)
Determine which car i traveling fater. Car A: 110 ft per econd
Car B: 60 mile per hour
Answers
The total time since automobile A's departure is five hours.
You must create an expression for distance as a function of time in order to solve this. Since you are required to locate the location at which their respective distances are equal and to describe the result in terms of time, you are aware that you require that statement in those terms.
Distance = 60 km/h*(1+x) for automobile A.
Distance traveled by Car B at 75 km/h (x)
x is the time expressed in hours.
When one of those two equations surpasses the other, they are equal.
so:
60 +60x = 75x
60=15x
x=4, however, my statement is formatted to start counting when car B started moving. Therefore, the total time since automobile A's departure is five hours.
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Full question:
Two cars A and B travel along the same road in the same direction from the same starting point. Car A maintains a speed of 60 km/h and car B is at 75 km/h. But car B started one hour later. How many hours will B take to overtake A?
Kelly sold digital cameras on her web site. She bought the cameras for $56 each and included a 65% price increase to get the selling price.To the nearest dollar, what was the selling price for one camera?
Answers
Kelly bought digital cameras for $56 each and applied a 65% price increase to determine the selling price. To find the selling price of one camera, we need to calculate the price increase and add it to the original purchase price.
To calculate the price increase, we first find 65% of the original purchase price ($56) by multiplying it by 0.65:
Price increase = 0.65 * $56 = $36.40
Next, we add the price increase to the original purchase price to find the selling price:
Selling price = $56 + $36.40 = $92.40
Rounded to the nearest dollar, the selling price for one camera is $92.
Therefore, the selling price for one camera, after a 65% price increase, is approximately $92.
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the drawing is composed of a rectangle and a semicircle. find the area of the figure to the nearest unit. not drawn to scale
a. 41 cm2
b. 220 cm2
c. 410 cm2
d. 820 cm2
Answers
Answer:
c
Step-by-step explanation:
Members of a baseball team raised $1592.50 to go to a tournament. They rented a bus for $844.50 and budgeted $68 per player for meals. Determine the number of players the team can bring to the tournament.
Answers
Answer: Assume p to be the number of players, then, the equation which describes this problem is,
844.50+ 68 p = 1592.50844.50+68p=1592.50
68 p = 74868p=748
p = 11p=11.
The number of players, the team can bring to the tournament are 11.
Step-by-step explanation:
Answer: They can bring 11 players to the tournament.
Step-by-step explanation:
$1592.50 - $844.50= $748
Divide $748 by $68, then you will get 11. And 11 will be the answer.
I need help, anyone know how to do the quadratic formula to solve this question?
Answers
Answer:
(2x - 3) (x + 3)
Step-by-step explanation:
What is the surface area of this shape?
Answers
(3x2)2 + (2x1)2 + (3x1)2
Answer:
A=2(wl+hl+hw)=2·(3·2+1·2+1·3)=22
Step-by-step explanation:
I reported the other answer HAHAHA here is the correct one
What is the equation of the vertical asymptote for the graph of the rational function g(x)=6x−1
Answers
Solution n(x), where n(x) is the denominator of the function (notice that this only works if t(x) is not zero for the same value of x).When the denominator is equal to zero, you can solve for x to determine the vertical asymptotes.
How can you locate the graphing formula for a vertical asymptote?By finding the solution to the equation n(x) = 0, where n(x) is the denominator of the function (note that this only works if the numerator t(x) is not zero for the same x value), vertical asymptotes can be obtained. For the function, locate its asymptotes. With the equation x = 1, the graph has a vertical asymptote.When the denominator is equal to zero, you can solve for x to determine the vertical asymptotes. This has previously been factored, therefore reduce each component to zero and get the solution. Since the asymptotes are lines, they are represented mathematically by line equations. X = 3 and X = 1 are the vertical asymptotes.To learn more about Vertical asymptotes refer to:
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make x the subject of
h= 4(x+3y)+2
Answers
Answer:
5x+7y+2
Step-by-step explanation:
Which expression is equivalent to 12.8-3s+15.5+8s?
A. -2+5s
B. 5s+28.3
C. 33.3s
D. 27.3+5s
Answers
Answer:
5s + 28.3
Step-by-step explanation:
12.8 + 15.5 = 28.3.
-3s + 8s = 5s.
so 12.8-3s+15.5+8s = 5s + 28.3
Determine if the subset of R^2 consisting of vectors of the form [a b], where a + b = 1 is a subspace. Select true or false for each statement. This set is closed under scalar multiplications This set is a subspace This set is closed under vector addition The set contains the zero vector
Answers
If the subset of R^2 consisting of vectors of the form [a b], where a + b = 1 is a subspace. The statement: This set is closed under scalar multiplications This set is a subspace .This set is closed under vector addition The set contains the zero vector is False.
Vector:A vector is a quantity or phenomenon that has two independent properties: magnitude and direction. The term also denotes the mathematical or geometrical representation of such a quantity.
Examples of vectors in nature are velocity, momentum, force, electromagnetic fields, and weight. A quantity or phenomenon that exhibits magnitude only, with no specific direction, is called a Scalar . Examples of scalars include speed, mass, electrical resistance, and hard-drive storage capacity.
Scalar Multiplication:Scalar multiplication is the multiplication of a vector by a scalar (where the product is a vector), and is to be distinguished from inner product of two vectors (where the product is a scalar).
For quaternion scalars and matrices:
λ = 2 A = \(\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right]\)
2A = 2\(\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right]\)
= \(\left[\begin{array}{ccc}2a&2b\\2c&2d\\\end{array}\right]\) = \(\left[\begin{array}{ccc}a.2&b.2\\c.2&d.2\\\end{array}\right]\)
= \(\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right]\) × 2 = A2
Subspace:In mathematics, and more specifically in linear algebra, a linear subspace, also known as a vector subspace is a vector space that is a subset of some larger vector space. A linear subspace is usually simply called a subspace when the context serves to distinguish it from other types of subspaces.
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A farmer is building a fence to enclose a rectangular area against an existing wall, shown in the figure below.
Three of the sides will require fencing and the fourth wall already exists.
If the farmer has 152 feet of fencing, what are the dimensions of the region with the largest area?
Answers
Answer:
where is the figure?? thanks
Lindsey wants to figure out her final math grade scores are 88.5% 90% 82% 94.5% and 80% what is Lindsey‘s final average?
Answers
Answer:
87%
Step-by-step explanation:
88.5% + 90% + 82% + 94.5% + 80% = 435%435% ÷ 5 = 87%So, Lindsey's final average is 87%I hope this helps!
Find the equation of the line that passes through (-5,3) and (1,1)
Answers
The equation of the line that passes through (-5,3) and (1,1) is y = (-1/3)x + 3.
To find the equation of the line that passes through the given points, we need to use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope of the line and b is the y-intercept.
First, we need to find the slope of the line. The slope formula is:
m = (y₂ - y₁) / (x₂ - x₁)
Plugging in the given points, we get:
m = (1 - 3) / (1 - (-5))
m = (-2) / (6)
m = -1/3
Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line. The point-slope form is:
y - y₁ = m(x - x₁)
Plugging in the slope and one of the given points, we get:
y - 3 = (-1/3)(x - (-5))
y - 3 = (-1/3)(x + 5)
y - 3 = (-1/3)x - (5/3)
y = (-1/3)x + (9/3)
y = (-1/3)x + 3
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if a fair die is rolled 5 times, what is the probability, rounded to the nearest thousandth, of getting at least 2 fours?
Answers
So the probability, rounded to the nearest thousandth, of getting at least 2 fours in 5 rolls of a fair die is 0.194.
What is the simple definition of probability?A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
According to the given information:The probability of getting at least 2 fours is the sum of the probabilities of getting exactly 2, 3, 4, or 5 fours:
P(X ≥ 2) = P(X=2) + P(X=3) + P(X=4) + P(X=5)
Using the binomial formula, we can calculate each of these probabilities:
P(X=k) = (n choose k) p^k (1-p)^(n-k)
where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from n distinct items.
P(X=2) = (5 choose 2) (1/6)² (5/6)³ = 0.1608
P(X=3) = (5 choose 3) (1/6)³ (5/6)² = 0.0322
P(X=4) = (5 choose 4) (1/6)⁴ (5/6)¹ = 0.0013
P(X=5) = (5 choose 5) (1/6)⁵ (5/6)⁰ = 0.00003
Therefore,
P(X ≥ 2) = 0.1608 + 0.0322 + 0.0013 + 0.00003 = 0.1943
So the probability, rounded to the nearest thousandth, of getting at least 2 fours in 5 rolls of a fair die is 0.194.
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I need help please
Answers
First we add 0.3 to 3.7, that way we will have an integer and it would be more easy to make the operations. Then we have 4.
Then we can substract the 4 to the 9.4, getting 5.4.
Finally we add once again 0.3 (because in the difference we have an extra .3) to the 5.4, getting 5.7.
Then Tamela swims 5.7 more than Blake every day.
PLEASE HELPPPPPPPPP:(
Answers
Answer: The first one, y = 3x - 4
Hope this helps :)
Answer:
Option 1, which is y= 3x - 4
Which is a better buy? 3 candy bars for $0.30 each or 3 candy bars for $1.50?
Answers
Answer:
3 candy bars for 0.30
Step-by-step explanation:
The same amount of bars for less is the better buy
Answer:
3 candy bars for $0.30 each is the better buy
Step-by-step explanation:
We must do the math to find out how much 3 candy bars will cost for 30 cents each.
0.30 x 3 = 0.90
Therefore, three candy bars cost 90 cents. 90 cents is less than a dollar and 50 cents. Therefore, the 3 candy bars for $0.30 each is the better deal.
-3(3p-1)<7p+51 help plssss
Answers
Answer:
p > -3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtract Property of EqualityStep-by-step explanation:
Step 1: Define
-3(3p - 1) < 7p + 51
Step 2: Solve for p
Distribute -3: -9p + 3 < 7p + 51Add 9p to both sides: 3 < 16p + 51Subtract 51 on both sides: -48 < 16pDivide 16 on both sides: -3 < pRewrite: p > -3Here we see that any value p greater than -3 would work as a solution to the inequality.
A lenght of wire is bent to make a square of side 3.2 cm a: what is the length of wire in the square B: if the wire is silver costing 50 naira per centimetre what is the cost of the square C: 20 of the squares are linked together to make a necklace what does it cost to make the necklace
Answers
Answer:
12.8cm
640 naira
12,800 naira
Step-by-step explanation:
length of the wire is equal to the perimeter of a square
perimeter of a square = 4 x length
4 x 3.2 = 12.8 inches
cost of the square = length of the wire x 50
12,8 x 50 = 640
20 x 640 = 12800
Jasmine has 8 packs of candle wax to make scented candles. Each pack contains 14 oz of wax. Jasmine uses 7 oz to make one candle. How many candles can she make?
Answers
Deon rented a truck for one day. There was a base fee of $18.95, and there was an additional charge of 87 cents for each mile driven. Decon had to pay $244,28 when he returned the truck. For how many miles did he drive the truck?
Answers
Deon drove the truck for 259 miles.
Let the number of miles driven by Deon be represented by m. Deon rented a truck for one day. There was a base fee of $18.95, and there was an additional charge of 87 cents for each mile driven. Deon had to pay $244,28 when he returned the truck. We need to determine how many miles he traveled in the truck. From the statement above, we can form an equation to represent the given information: Cost of renting truck = base fee + additional charge = $18.95 + $0.87m = $244.28We solve for m: First, we subtract $18.95 from both sides to isolate the term $0.87m:$0.87m = $244.28 - $18.95 = $225.33Then, we divide both sides by $0.87 to isolate the variable m: $$0.87m/0.87 = $225.33/0.87m = 259.00m = 259. Therefore, Deon drove the truck for 259 miles. Answer: \boxed{259}.
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Find the area of the figure below
77.25 cm^2 154.5 cm^2 87.55 cm^2 175.1 cm^2
Answers
The area of the given triangle is 87.55 square centimeter.
From the given triangle, base=17 cm and height=10.3 cm.
The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.
Here, area of a triangle = 1/2 ×17×10.3
= 87.55 square centimeter
Therefore, area of the given triangle is 87.55 square centimeter.
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The total length of these planks is 92 metres. Work out the number of planks of length 2 metres in Ben workshop.
Answers
Answer: 13
Step-by-step explanation:
I need sum help please and thanks :)
Answers
Answer:
6/16n is your answer I think