Answer: The inverse of the function y = 2^x^2 - 4 is not a function because it is not a one-to-one function.
Step-by-step explanation:
The inverse of a function is a reflection of the original function over the line y = x. To find the inverse of the function y = 2^x^2 - 4, we need to switch the variables x and y and then solve for x.
y = 2^x^2 - 4
x^2 = log2(y + 4)
x = sqrt(log2(y + 4))
However, this expression is not the inverse of the original function because it is not a one-to-one function, meaning that the same output can have multiple inputs. For example, log2(10) = 3 and log2(14) = 3.5, so sqrt(log2(10)) = sqrt(3) = sqrt(log2(14)) = sqrt(3.5). This means that for y = 10, x can be either sqrt(3) or sqrt(3.5), which is not allowed in a function.
Therefore, the inverse of the function y = 2^x^2 - 4 is not a function.
What are the answers for this
Doranda was given two paid vacation days by her employer when she started her new job. She will receive an additional three days per year of paid vacation for each year she remains with the company up to a maximum of four work weeks of paid vacation time. Part A
The expression for the number of paid vacation days for x years is
2 + 3x.
What is an expression?An expression contains terms with addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number of paid vacation days = 2
Now,
She will receive an additional three days per year of paid vacation for each year she remains with the company.
This means,
For x years,
Number of paid vacation days = 2 + 3x
Now,
The expression for x years.
= 2 + 3x
Thus,
2 + 3x is the expression for the number of paid vacation days for x years.
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The complete question.
A)
Write an expression for the number of paid vacation days for x years.
Cassandra is knitting a scarf. She increases the length of
the scarf by 25 centimeters each hour she knits. After 3
hours, the scarf is 125 centimeters long.
The initial length of the scarf is 50 centimeters.
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
We can use the given information to find the rate at which Cassandra is knitting the scarf and the initial length of the scarf.
Let L be the initial length of the scarf in centimeters, and let r be the rate at which Cassandra is knitting the scarf in centimeters per hour. Then, we have:
L + 25h = length of scarf after h hours
Substituting h = 3 and the length of the scarf after 3 hours = 125, we get:
L + 25(3) = 125
L + 75 = 125
L = 50
Therefore, the initial length of the scarf is 50 centimeters.
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Cassandra is knitting a scarf. She increases the length of
the scarf by 25 centimeters each hour she knits. After 3
hours, the scarf is 125 centimeters long what is initial length of scarf.
a researcher divided subjects into three groups according to whether or not they have brown, blue or green eyes, and then selected members from each group for her sample. what sampling method was the researcher using? group of answer choices random systematic cluster stratified
If the researcher divided subjects into three groups according to whether or not they have brown, blue or green eyes, then the researcher was using a stratified sampling method.
Here a researcher divided subjects into three groups according to whether or not they have brown, blue, or green eyes.
The selected members from each group for their sample
The stratified sampling method is defined as the sampling method that divides the total population into the smaller group
Here the total population is divided into three groups according to whether they have brown, blue or green eyes.
Therefore, researcher was using stratified sampling method
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From the top of a canyon, the angle of depression to the far side of the river is 52°, and the angle of depression to the near side of the river is 71°. The depth of the canyon is 230 feet. What is the width of the river at the bottom of the canyon? Round to the nearest foot.
Trig question
Answer:
49ft
Step-by-step explanation:
Sketching out the problem, we get something like the diagram below. Assuming the canyon makes a roughly 90° angle with the ground, we can see that we have two right-angled triangles formed.
Focusing on the first triangle: since we have the angle, and we know the height of the canyon is 230ft, we can also find the combined width of the ground and river (let's call this y) using cos:
cos38=230/y
0.7880107536=230/y
y=230/0.7880107536= 291.874189467ft
Focusing now on the first triangle: since we have the angle, and we know the height of the canyon is 230ft, we can find the width of the ground (let's call this x) using cos:
cos19=230/x
0.94551857559=230/x
x=230/0.94551857559= 243.252756673ft
Therefore, the width of the river must be the difference between the combined width of the ground and river, minus the width of the ground:
291.874189467ft - 243.252756673ft = 48.621432794ft ≈ 49ft
The area of an equi
Lateral triangle having height 12 cm is
The area of an equilateral triangle having height 12 cm is 83.136 sq.cm.
An equilateral triangle in geometry is a triangle with equal-length sides on all three sides. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others. It is sometimes referred to as a regular triangle because it is a regular polygon.
if height h is given in equilateral triangle then first we have to find the length of side which can be solve by this formula like a right angle triangle where side of equilateral triangle is a and another side is a/2 and next is height which is given 12 cm.
[tex]a^{2} -(a/2)^{2} = 12^{2}[/tex]
[tex](3/4)a^{2} = 144[/tex]
[tex]a^{2} = 192\\a = \sqrt{192}[/tex]
a = 13.85
area of equilateral triangle = [tex]((\sqrt{3})/ 4 )a^{2}[/tex]
= 1.732*192/4
83.136 sq.cm
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the school swimming pool is 50m long and 21 m wide. The pool is divided lengthwise into six lanes for a swim meet. what is the area of each lane?
Answer:
175m²
Step-by-step explanation:
Total area (of pool):
50 × 21 = 1050
Area of each lane:
1050 ÷ 6 = 175
29. A racket is propelled upward from the top of a building 210 feet tall at an initial velocity of 112 feet per secon
The function that describes the height of the rocket in terms of time t is S(t) = - 16+2 + 112t + 210.
Determine the time at which the rocket reaches its maximum height.
a. 2.8 seconds
b. 3.5 seconds
C. 7 seconds
d. 5.6 secands
The time at which the rocket reaches its maximum height is 3.5 seconds. Therefore, b. is the correct answer.
What is function f(x)?An equation describing the relationship between the input (x) and the output (f(x)) is called the function f(x). Any equation that represents the connection between an input x and an output f is referred to as the function f(x) (x).
A function can be expressed as a graph or table in addition to the standard form of an equation. Functions can be stated using symbols and phrases in addition to equations. A function could be expressed, for instance, as "the square of x" or "f of x equals x squared."
Whatever form a function takes, it's critical to keep in mind that the input (x) always yields the same result (f(x)).
In the given question,
The maximum height of the rocket is achieved at the point when the velocity of the rocket is 112 feet. This can be determined by taking the derivative of the function S(t).
S'(t) = 112
Therefore, when S'(t) = 112, t = 3.5.
This means that the rocket reaches its maximum height at t = 3.5 seconds.
Therefore, the time at which the rocket reaches its maximum height is 3.5 seconds.
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PROBABILITY IN FRACTIONS PLSSSSSSS
relationship btw three set( in a market survey 100traders sell fruit, 40sell Apple, 46 sell Orange, 50 mango, 15sell Apple and Mango, 10 sell the three
fruit draw a venn diagram
Number of student that sell mango and orange
Answer:
7 traders sell oranges and mangoes alone.
Step-by-step explanation:
(21 + 4 + 5 + 10 + x + 35 – x + 32 – x = 100)
(107 – x = 100)
(x = 107 – 100 = 7)
Therefore, 7 traders sell oranges and mangoes alone.
(b) (312_{four} + 52_{x} = 96_{ten})
(312_{4} = 3 times 4^{2} + 1 times 4^{1} + 2 times 4^{0})
= (48 + 4 + 2 = 54_{10})
(52_{x} = 5 times x^{1} + 2 times x^{0})
= ((5x + 2)_{10})
(therefore 54 + (5x + 2) = 96)
(56 + 5x = 96 implies 5x = 96 – 56 = 40)
(x = 8)
(therefore 312_{4} + 52_{8} = 96_{10})
Question 7. A boat rental shop rents paddleboats for a fee plus an additional cost per hour. * O
The cost of renting for different numbers of hours is shown in table. Use the table and the
variables to write an equation. Let y = cost and x = hours.
The equation of the given information is y(x) = 5x+10
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between.
Given that cost of renting for different numbers of hours.
The initial cost, regardless of time, is; $10. then the cost will increase at a rate of $5 per hour that the boat is rented.
Therefore, the cost (y) of renting a paddle boat for 'x' hours is:
y(x) = 5x+10
here linear relationship between x and y, where 5 is the slope of the equation, 10 is the y-intercept, the number of hours is the independent variable, and the cost is the dependent variable.
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In the diagram below, RA is parallel to ET, and RT is 21 units long. Find the length of ST.
Answer:
ST = 12 units
Step-by-step explanation:
Δ STE and Δ SRA are similar ( AA postulate ) , then the ratios of corresponding sides are in proportion, that is
[tex]\frac{ST}{SR}[/tex] = [tex]\frac{TE}{RA}[/tex] ( substitute values )
[tex]\frac{ST}{21-ST}[/tex] = [tex]\frac{8}{6}[/tex] ( cross- multiply )
6 ST = 8(21 - ST)
6 ST = 168 - 8 ST ( add 8 ST to both sides )
14 ST = 168 ( divide both sides by 14 )
ST = 12 units
three vertices of ABCD are A(2,4) b(5,2) c(3,-1) find the coordinates of vertex D
The coordinates of vertex D of the parallelogram is; (0, 1)
How to find the coordinates of a Parallelogram?We are given the coordinates of the parallelogram as;
A(2,4), B(5,2) and C(3,-1)
Now, we know that the diagonals of a parallelogram bisect each other. So, the midpoint of AC is same as the mid point of BD.
The formula for the midpoint between two coordinates is;
(x1 + x2)/2, (y1 + y2)/2
Thus;
Midpoint of AC = (2 + 3)/2, (4 - 1)/2 = 5/2, 3/2
Midpoint of BD = (5 + x)/2, (2 + y)/2
Thus;
(5 + x)/2 = 5/2
x = 0
(2 + y)/2 = 3/2
2 + y = 3
y = 1
Coordinate of D = (0, 1)
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Please help me by finding the degree measure of angle x
Triangle ABC is the term used to refer to a triangle with the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered [tex]A^2 = B ^2 + c^2[/tex] => AC = [tex]\sqrt{115}[/tex]
What is the Pythagorean theorem?Given that it has three sides and three vertices, a triangle qualifies as a polygon. It belongs to the fundamental geometric shapes.
Triangles are polygons because they have three sides and three corners. The points where the three sides of the triangle converge are referred to as the triangle's corners. 180 degrees is obtained by multiplying three triangle angles.
Here, in this triangle by Pythagorean theorem
[tex]A^2 = B ^2 + c^2[/tex]
AC = [tex]\sqrt{14^2- 9^2}[/tex]
AC = [tex]\sqrt{196- 81}[/tex]
Ac = [tex]\sqrt{115}[/tex]
Therefore, We can state that this triangle conforms to the Pythagorean theorem after answering the offered question.
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How many terms are in this expression?
4n + 6m
Answer:
2
Step-by-step explanation: this is because the plus sign splits the terms so simply 2 terms
What is the total number of different 10-letter arrangements that can be formed using the letters in the word SPEECHLESS?
The number of ways the letters can be permutated in the word SPEECHLESS is 100800.
What is meant by permutation?
An arrangement of items in a specific order is referred to as a permutation. A set can be permuted by arranging its components in a linear or sequential order, or by rearrangement of its components if the set is already ordered. When the order of the arrangements counts, it is a mathematical technique that establishes the total number of alternative arrangements in a collection. Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems.
The number of letters in SPEECHLESS = 10
The letter E repeats 3 times
The letter S repeats 3 times
The letters P,C,H,L repeats one time.
When there are repeating letters in a word, the total number of distinct ways the letters in the words can be permutated is:
[tex]N= \frac{n!}{r_1!r_2!.....r_m!}[/tex]
where N = number of arrangements
n = number of letters
r = total number of times one letter is repeated in the word
For SPEECHLESS,
Therefore the number of ways the letters can be permutated is:
[tex]N= \frac{10!}{3!3!}[/tex] = 100800
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Assignment
E
7m
K
6m 20 m
A
28 m
F
5 m J
24 m
G
Intro
LL
L
Mai enlarges a triangular sign by a multiple of 4
creating similar triangles. The bottom of the original
sign is side EG. Which side of the enlarged sign
corresponds to side EG?
If she wanted to turn the sign so that side JK was on the
bottom, what side of the original sign would this
correspond to?
Done
See below for the description of the enlarged shapes when dilated
How to determine the side of the enlarged sign corresponds to side EG?From the question, we have the following parameters that can be used in our computation:
Scale factor = 4
This means that if Mai enlarges the triangular sign by a multiple of 4,
Then the corresponding side in the enlarged sign to side EG is 4 times the length of side EG.
i.e Corresponding side = 4 * Original side
If Mai wanted to turn the sign so that side JK was on the bottom,
Then the corresponding side of the original sign would be the side that was previously opposite to JK.
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I don’t how to solve it
Answer:
Step-by-step explanation:
Since they are congruent, you know that 8=x-3. 11-3=8. and 14=x+6=8. x is 8
What is the solution to the following system of equations
4x+2y=6
X-y=3
Answer:
The solution of the equation 4x + 2y = 6 and x − y = 3 will be D. (2, –1)
Step-by-step explanation:
4x + 2y = 6 ....… (1)
x − y = 3 …..... (2)
Example, for equation 2 is:
x - y = 3
x = 3 + y
Put in equation 1:
4(y + 3) + 2y = 6
4y + 12 + 2y = 6
6y = -6
y = -6/6
y = -1
We have the value of y, then the value of x will be:
x = 3 + y
= 3 + (-1)
= 3 - 1
= 2
So, the solution of the equation 4x + 2y = 6 and x − y = 3 will be (2, –1)
Select the correct answer from each drop-down menu.
Observe the given functions.
Complete the sentences to compare the two functions.
Over the interval ____, the average rate of change of g is greater than the average rate of change of f. As the value of x increases, the average rates of change of f and g _________, respectively. When the value of x is equal to 7, the value of _________
It can be further generalized that a quantity increasing exponentially will ___ exceed a quantity increasing linearly.
The correct answer for each of the math expressions is given below:
1. (4,5)2. remain constant and increase3. g(x) exceeds the value of f(x)4. eventuallyWhat is a Graph?The graph of a function f in mathematics is the collection of ordered pairs where displaystyle f(x)=y.
These pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.
Hence, given that in the graph,
f(x) = 4x + 3
g(x) = [tex]\frac{5}{3} ^x[/tex]
Over the interval (4,5), the average rate of change of g is greater than the average rate of change of f.
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you could measure arrival delay by recording the amount of time between actual arrival time and scheduled arrival time (with positive numbers representing delays and negative numbers representing early arrivals). is this variable categorical or quantitative? if the variable is quantitative, classify it as discrete or continuous.
It is a continuous variable, as it can take on any value within a certain range (i.e., any value between a positive delay and a negative early arrival).
The variable described is quantitative, as it represents a numerical measurement of time, which is a continuous variable that can take on any value within a certain range. The range includes both positive values, representing delays, and negative values, representing early arrivals. This variable is a useful metric for tracking the performance of transportation systems or airlines, as it provides an objective measure of the amount of time a flight is delayed or arrives early. By analyzing the distribution of arrival delay times, policymakers and transportation providers can identify patterns, trends, and potential areas for improvement in their service delivery.
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A coin is flipped 14 times and lands on heads 8 times. The theoretical probability that the next coin flip will be heads is 50%.
The statement, coin is flipped 14 times and lands on heads 8 times. The theoretical probability that the next coin flip will be heads is 50% is True.
What is probability?The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place. A definite occurrence has a chance of 1 while an impossible event has a probability of 0.
When a coin is flipped the probability of getting a heads and a tail is 50%.
Hence, without the consideration of the flips and the result the theoretical probability that the next coin flip will be heads is 50%.
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the hockey surface at a community centre is 61 m by 30.5m.FIeld hockey is played outdoors on a surface 91.5 by 54.9m.Which surface has the larger area and by how much?
The area of field hockey is larger by 3162.85 [tex]m^2[/tex].
What is Area ?The amount of unit squares that cover an enclosed figure's surface is its area. Square units like [tex]cm^2[/tex] and [tex]m^2[/tex] are used to measure area. A shape's area is a two-dimensional measurement. The space inside the perimeter or boundaries of a closed shape is known as the "area."
The hockey surface given here is in rectangular shape, so,
Area = length x breadth
Area of the hockey surface at a community centre is,
= 61 m x 30.5 m
=1860.5 [tex]m^2[/tex]
Area of field hockey played at outdoors,
= 91.5 m x 54.9 m
= 5023.35 [tex]m^2[/tex]
Clearly, we can see that area of field hockey is larger.
Difference between both the areas = 5023.35 -1860.5 = 3162.85 [tex]m^2[/tex].
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a lamppost, cab, bent at point a after a storm. the tip of the lamppost touched the ground at point c, as shown below: triangle abc has measure of angle c equal to 55 degrees, measure of angle abc equal to 90 degrees, and length of bc equal to 20 feet. what is the height, in feet, of the portion ab of the lamppost?
The height of the portion AB of the lamppost is approximately 27.8 feet, as calculated using the tangent function with angle 55 degrees and length BC 20 feet.
Based on the given information, we can use trigonometry to find the height of the portion AB of the lamppost.
Let's call the height of AB "x". We can use the tangent function to solve for x:
tan(55) = x/20
Multiplying both sides by 20:
x = 20 tan(55)
Using a calculator, we get:
x ≈ 27.8 feet
Therefore,
The height of the portion AB of the lamppost is approximately 27.8 feet.
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Answer: 20 tan 55
Step-by-step explanation:
took test and got it right
assume that earth is a sphere with radius 3960 miles a town is at latidtude 32 n find the distance in miles from the town to the north pole
The distance from the town to the North Pole is approximately 2290 miles.
To find the distance in miles from the town to the North Pole, we need to calculate the length of the meridian arc from the town to the North Pole. The meridian arc is a portion of a great circle passing through the town and the North Pole.
The length of the meridian arc can be calculated using the formula:
Length = (π/180) x radius of the Earth x angle in degrees
where π is approximately 3.14159, and the radius of the Earth is 3960 miles.
Since the town is located at latitude 32°N, the angle between the town and the North Pole is 90° - 32° = 58°.
Plugging in these values into the formula, we get:
Length = (π/180) x 3960 miles x 58°
Length = (3.14159/180) x 3960 miles x 58
Length ≈ 2290 miles
Therefore, the distance from the town to the North Pole is approximately 2290 miles.
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Uhmmm I don’t know this pla
Answer:
y = 2x - 3
Step-by-step explanation:
Pick two random points for slope
slope = m = rise/run = [tex]\frac{(-3-(-5))}{0-(-1)} = \frac{2}{1} = 2[/tex]
y intercept form:
y = 2x - 3
HELP DUE IN 20 MINS!!!!!
Boris's company makes solid balls out of scrap metal for various industrial uses. His current task is to make a batch of lead balls with radius 3 in. If he has a 3 total of 28,260 in³ of lead, how many balls can he make? Use 3.14 for , and do not round your answer.
The number of balls that he can make is given as follows:
249 balls.
How to obtain the volume of a sphere?The volume of a sphere of radius r is given by the equation presented as follows:
V = 4πr³/3.
Considering the radius of 3 inches, the volume of each ball is given as follows:
V = 4π x 3³/3
V = 113.1 in³.
He has a total of 28,260 in³ of material, hence the number of balls that he can make is given as follows:
28260/113.1 = 249 balls.
(rounding down, as there will not be enough material for the 250th ball).
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In a triangle ABC, AB = 5cm , BC = 7cm and CA = 8cm. Id D and E are reep mid points of AB and BC, find the length of DE.
The measured length of DE will be 4 cm.
What is the similarity?Two objects are said to be comparable if they have the same shape. Therefore, two figures are said to be comparable in mathematics if they share the same shapes, lines, or angles.
Given that AB is 5 cm, BC is 7 cm, and CA is 8 cm in the triangle ABC. The reep midpoints of AB and BC are Ids D and E.
The two triangles ABC and ADE will be similar to each other. The measure of the length DE will be calculated as:-
AC = DE = 7 / 3.5
DE = AC / 2
DE = 8 / 2
DE = 4 cm
Hence, the value of the side DE will be 4 cm.
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A total of 709 tickets were sold for the school play. They were either adult tickets or student tickets. There were 59 more student
tickets sold than adult tickets. How many adult tickets were sold?
Solving the Question
First, assign variables to the given information:
Let the number of student tickets sold be x.Let the number of adult tickets sold be y.We're given:
[tex]x+y=709[/tex][tex]x=59+y[/tex]Plug the second equation into the first and solve using substitution:
[tex]x+y=709\\59+y+y=709\\59+2y=709\\2y=650\\y=325[/tex]
Therefore, 325 adult tickets were sold.
Answer325 adult tickets were sold.
In a class of 55 student 21 study Physic, 24 study geography, 23 study econs, 6study both phy and geo, 4 study both geo and econs, 5 both econs and phy, if X study all the three subject and 20 study non of the three subject
find the value of X
find the Number of student that study phy only
No of student that study one of the 2 subject
X = 2 (two) students study all three subjects (physics, geography, and economics). This can be found by adding the number of students who study only two subjects (6 + 4 + 5 = 15) and subtracting that from the total number of students who study at least one subject (55 - 20 = 35), since each of these 15 students who study two subjects is counted twice in the totals for each subject.
How do we get the responses to other questions?The number of students who study physics only is 10. This can be found by subtracting the number of students who study physics and at least one other subject (21 - 6 - 5 - 2 = 8) from the total number of students who study physics (21).
The number of students who study exactly one of the two subjects is 25. This can be found by adding the number of students who study each subject only (10 + 11 + 9) and subtracting that from the total number of students (55 - 20 = 35).
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