determine if f, g, and h are true or false. If false, correct the statement with an explanation
Answers
We need to determine if the statements are true or false.
In order to do so, we need to pay attention to the following notations:
[tex]\begin{gathered} (\sin x)^{-1}=\frac{1}{\sin x} \\ \\ \sin^{-1}x=\text{ inverse function of }\sin x \end{gathered}[/tex]The same notations apply to cosine and tangent functions.
The inverse f⁻¹(x) is the function such that:
[tex](f^{-1}\circ f)(x)=f^{-1}(f(x))=x[/tex]Thus, we have:
[tex]\cos^{-1}(\cos(\frac{15\pi}{6}))=\frac{15\pi}{6}[/tex]Therefore, statement g. is true.
In order to show that statements f. and h. are false, let's see what happens for x = 1/2:
[tex]\begin{gathered} \frac{\sin^{-1}(\frac{1}{2})}{\cos^{-1}(\frac{1}{2})}=\frac{\frac{\pi}{6}}{\frac{\pi}{3}}=\frac{3}{6}=0.5\text{ \lparen no units\rparen} \\ \\ \tan^{-1}(\frac{1}{2})\cong0.46\text{ \lparen rad\rparen} \\ \\ \Rightarrow\frac{\sin^{-1}(\frac{1}{2})}{\cos^{-1}(\frac{1}{2})}\ne\tan^{-1}(\frac{1}{2}) \end{gathered}[/tex][tex]\begin{gathered} \sin^{-1}(\frac{1}{2})=\frac{\pi}{6}\cong0.52 \\ \\ \frac{1}{\sin(\frac{1}{2})}\cong2.09 \\ \\ \Rightarrow\sin^{-1}(\frac{1}{2})\ne\frac{1}{\sin(\frac{1}{2})} \end{gathered}[/tex]Answer:
f. False
g. True
h. False
Notice that we can correct the statements f. and h. by using the correct notation:
[tex]\begin{gathered} \text{ f. }\frac{(\sin x)^{-1}}{(\cos x)^{-1}}=(\tan x)^{-1} \\ \\ \text{ h. }(\sin x)^{-1}=\frac{1}{\sin x} \end{gathered}[/tex]Related Questions
he volume of a cylinder with height
h
h and radius
r
r can be found using the formula
V
=
π
r
2
h
V=πr2h
Find the volume of a cylinder with radius 6 feet and height 9 feet, rounded to 1 decimal place.
Answers
Answer:
1018.3
Step-by-step explanation:
The volume of a cylinder=πr2h
=22\7*6*6*9
=1018.3
therefore, the of the cylinder is 1018.3
Solve the following polynomial equation by grouping and factoring. 36y^3−49y=0
Answers
Given:
[tex]36y^3-49y=0[/tex]solve for y:
[tex]\begin{gathered} 36y^3-49y=0 \\ y(36y^2-49)=0 \\ y=0;36y^2-49=0 \end{gathered}[/tex]Value of y is zero and
[tex]\begin{gathered} 36y^2-49=0 \\ 36y^2=49 \\ y^2=\frac{49}{36} \\ y=\pm\sqrt[]{\frac{49}{36}} \\ y=\pm\sqrt[]{1.361111} \\ y=\pm1.166 \\ y=1.166,y=-1.166 \end{gathered}[/tex]What is the correct answer
Answers
∠GJI ≅ ∠LKF is proved below.
What is congruent?If two shapes are similar in size and shape, they are congruent. We can also state that if two shapes are congruent, then their mirror images are identical. If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent, or to be in the relation of congruence.
Given Data
EF║GH
AB║CD
In given figure,
AB║CD,
While line segment GH is the transversal line.
So,
∠GJI ≅ ∠JLK (because it is corresponding angle) ..(1)
Also,
EF ║GH
Line segment DL is the transversal line.
So,
∠JLK ≅ ∠LKF (because it is interior alternate angle)..(2)
From (1) and (2)
∠GJI ≅ ∠LKF
Hence, proved.
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A bag contains 42 red, 42 green, 20 yellow, and 32 purple candies. You pick one candy at random. Find the probability that it is purple or not red
Answers
Answer:
47/68
Step-by-step explanation:
total candies=136
not red candies=94
94/136=47/68
The cost of attending an amusement park is $15 for children and $35 for adults. On a particular day, the attendance at the amusement park is 25,000 attendees, and the total money earned by the park is $600,000. Use the given matrix equation to solve for the number of children’s tickets sold. Explain the steps that you took to solve this problem.
Answers
The number of children's tickets sold is 13750.
Let the number of children be x and the number of adults be y.
The total number of attendance at the amusement park is 25,000.
So we have an equation
x + y = 25000 ......(i)
The cost for children is $15 and the cost for adults is $35, and the total money earned by the park is $600,000.
So we have another equation,
15x + 35y = 600,000
3x + 7y = 120,000 ......(ii)
Multiplying equation (i) with 3 we get
3x + 3y = 75000
3x + 7y = 120,000
Now subtract both the equation we have,
4y = 45000
y = 11250
Now put the value of y in equation (i) we get
x + 11250 = 25000
x = 13750
Where x is the number of children's tickets sold.
Therefore the number of children's tickets sold is 13750.
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find the absolute value of each number -1/3, 6 & -0.2
Answers
The absolute number of an integer is the distance that separates the number from position zero "0" so, if it is a distance it cannot be a negative value.
Then the absolute value of these numbers is:
HELP FAST. Please explain how to find the answer for the equation step by step.
Answers
The equation for the given summation is:
[tex]\sum_{n=1}^4 u_n = u_1 + u_2 + u_3 + u_4[/tex]
How to find the equation?Here we have a summation of unknown terms of the form:
uₙ
That summation goes between n = 1 and n = 4, this means that we will have a sum of 4 terms, such that:
[tex]\sum_{n=1}^4 u_n[/tex]
Means that we need to sum the terms u₁, u₂, u₃, and u₄, then we can write the equation:
[tex]\sum_{n=1}^4 u_n = u_1 + u_2 + u_3 + u_4[/tex]
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Please help me i’m begging so much
Answers
PLEASE HURRY IM GIVING POINTS!!!!!!!!!
Part A: Given the function
g(x) = |x - 5| describe the graph of the function, including the vertex, domain, and range.
Part B: If the parent function
f(x) = |x| is transformed to
h(x) = Ix| + 3, what transformation occurs from f(x) to h(x)? How are the vertex and range of h(x) affected?
Answers
Part A: The vertex, domain, and range of the function g(x) = |x-5| is
( 5, 0 ), ( - ∞ , ∞ ) and [0, ∞ ).
Part B: The function f(x) = |x| is vertically shifted by 3 units to get the function h(x) = |x| + 3. The y - coordinate of the vertex is shifted by 3 units.
In Part A:
The given function is;
g(x) = | x - 5 |.
Now, The x - coordinate of the vertex will be:
x - 5 = 0
x = 5
Therefore, the y- coordinate of the vertex will be:
y = g(x) = | x - 5 |
y = g(7) = | 5 - 5|
y = 0
So, The vertex of the absolute function is ( 5, 0 ).
Since, All real numbers fall under the expression's domain, with the exception of cases where it is undefined. In this case, the phrase is defined even if there is no real number.
Hence, In Interval Notation the domain is;
⇒ ( - ∞ , ∞ )
And, The set of all legitimate y values is the range.
Hence, In Interval Notation the range is:
⇒ [0, ∞ )
Now, In Part B:
Function h(x) = |x| + 3 is the transformed version of the parent function
f(x) = |x|.
For the parent function f(x) = |x|, the vertex is ( 0, 0).
Since, The range of an absolute function in the form c( | ax + b | ) + k is
f(x) ≥ k.
Therefore, The range of the function f(x) = |x| is f(x) ≥ 0 and in interval notation is [ 0, ∞ ).
For the transformed function h(x) = |x| + 3.
The vertex of the function is ( 0, 3 ).
The range of function is h(x) ≥ 3 and in interval notation is [3, ∞ ).
Hence, the y coordinate of the vertex is transformed by 3 from f (x) to h(x).
So, Part A: The vertex, domain, and range of the function g(x) = |x-7| is
( 5, 0 ), ( - ∞ , ∞ ) and [0, ∞ ).
Part B: The function f(x) = |x| is vertically shifted by 2 units to get the function h(x) = |x| + 3. The y coordinate of the vertex is shifted by 3 units.
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21/24 simplified plsssssssssssssssssssssssss
Answers
(Divide both 21 and 24 by the greatest common factor, 3)
Answer:
7/8
Step-by-step explanation:
(g) distance from the x-axis is equal to the distance to the y-axis.
Answers
Part a
Remember that the ordinate is the y-coordinate and the abscisa is the x-coordinate
so
(x, 2x+1)
y=2x+1
Part b
[tex](\frac{1}{2}y^2,y)[/tex]x=(1/2)y^2
Part c
x^2+y^2=25
Part e
y=2
Part f
x=7
Part g
x=y
Part h
[tex]\sqrt[\square]{x^2+y^2}=5[/tex]Part i
[tex]\sqrt[\square]{(x-2)^2+(y-3)^2}=5[/tex]Calculate the root mean square velocity, in m/s, of Ne at 273.0 K. Assume ideal gas behavior.
I meant to put this in chemistry
Answers
The root mean square velocity of Neon, in m/s as required in the task content is; 18.45 m/s.
What is the root mean square velocity of Neon as required?It follows from the task content that the root mean square velocity of Neon is to be determined.
Since the molar mass of Neon is; 20 while the gas constant, R = 8.314 and T = 273K.
It follows from the root mean square velocity formula that we have;
R.M.S = √(3RT/M)
R.M.S = √{(3×8.314×273)/20}
R.M.S = √340.46
R.M.S = 18.45 m/s.
Hence, the root mean square velocity of Neon, Ne under the given condition is; 18.45 m/s.
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What is the slope of the line on the graph?
Enter your answer in the box.
PLEAZ HELP
Answers
Answer:
-2, 6 or -2/6 is what im seeing i could be wrong though
Step-by-step explanation:
sub to imaginefn
12345678912345678912456789
Answers
Answer:
3 is missing in there numbers,the last pair
Here are the approximate populations of three cities in the United States, expressedin scientific notation: San Jose: 1.1 x 10^6; Washington: 7 x 10^5 ; Atlanta: 4.8 x 10^5.a. Lin says that about 6.2 x 10^5 more people live in San Jose than in Atlanta. Doyou agree with her? Explain your reasoning.Your answer
Answers
Lin says that about 6.2 x 10^5 more people live in San Jose than in Atlanta. To find if she is right you substract the population of Atlanta from the population in San Jose:
Substraction of numbers in scientific notation:
1. Turn the numbers to get the same power of base 10.
You move to the left the decimal to increase the power of base 10 and move to the right to g
[tex]undefined[/tex]Write a unit rate for the situation
$45.00 for 9 pounds
$24 for 3 pound
$390 for 6 pounds
$42 for 21 pounds
$180 for 10 pounds
$864 for 8
Answers
The unit rate for each situation is $5.00 for 1 pound, $8 for 1 pound, $65 for 1 pound, $2 for 1 pound, $18 for 1 pound, $108 for 1 pound
What is unit rate and how to compute it?
Unit rate is the rate for 1 unit and to compute the unit rate we divide the total price by the total number of elements
We are given certain price we have to find there unit rate
a) $45 for 9 pound
Divide both sides by 9 to find the unit rate
we get $5 for 1 pound
a) $24 for 3 pound
Divide both sides by 3 to find the unit rate
we get $8 for 1 pound
a) $390 for 6 pound
Divide both sides by 6 to find the unit rate
we get $65 for 1 pound
a) $42 for 21 pound
Divide both sides by 21 to find the unit rate
we get $2 for 1 pound
a) $180 for 10 pound
Divide both sides by 10 to find the unit rate
we get $18 for 1 pound
a) $864 for 8 pound
Divide both sides by 8 to find the unit rate
we get $108 for 1 pound
Hence the unit rates are for each situation is $5.00 for 1 pound, $8 for 1 pound, $65 for 1 pound, $2 for 1 pound, $18 for 1 pound, $108 for 1 pound
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Find the altitude of rhombus whose area is 208 cm² and perimeter is 64 cm.
Answers
Given the area of a rhombus is 208 cm square and the perimeter of rhombus is 64 cm.
Recall that all the sides of the rhombus are equal.
Hence,
[tex]\begin{gathered} \text{perimeter}=4\times sides \\ 64=4\times\text{side} \\ 16cm=\text{side} \end{gathered}[/tex]Area of rhombus is :
[tex]\begin{gathered} area=base\times height \\ 208=16\times h \\ h=\frac{208}{16} \\ h=13\operatorname{cm} \end{gathered}[/tex]Hence the altitude of the Rhombus is 13 cm.
Altred is saving up money for a down payment on a house. He currently has $4739, but knows he can get a loan at a lower interest rate if he can put down $5336. If heinvests the $4739 in an account that earns 5.1 % annually, compounded monthly, how long will it take Alfred to accumulate the $5336? Round your answer to two decimal places, if necessary.
Answers
Given the word problem, we can deduce the following information:
Principal amount = $4739
Future amount = $5336
Interest = 5.1 % =0.051
To determine the time to accumulate the $5336, we use the compound interest formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]A=Future amount=$5336
P=Present amount=$4739
r=interest rate = 0.051
n=number of compounding periods =12
t=time in years
We also note that the number of compounding periods must be 12 since the investment is compounded monthly.
We plug in what we know:
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ 5336=4739(1+\frac{0.051}{12})^{12t} \\ Simplify\text{ and rearrange} \\ 5336=4739(\frac{12.051}{12})^{12t} \\ 12t=\frac{\ln\frac{5336}{4739}}{\ln\frac{12.051}{12}} \\ t=\frac{\operatorname{\ln}\frac{5,336}{4,739}}{12\operatorname{\ln}\frac{12.051}{12}} \\ Calculate \\ t=2.33 \end{gathered}[/tex]Therefore, the answer is 2.33 years.
Questiona + 4 = 10. If a must be equal to one of the values below, what is the value of a?Select the correct answer below:4679
Answers
1) In this question, we can solve it in two different ways. Either algebraically, or by mental Math.
2) Algebraically we have:
[tex]\begin{gathered} a+4=10 \\ a+4-4=10-4 \\ a=6 \end{gathered}[/tex]By mental math, we just need to ask ourselves how much can I add to 4 and get 10,? The answer will be six.
3) Thus, the answer is 6
the table shows the population of California during the 20th century. which type of function best models this data?
Answers
Given data:
The given table is shown.
Draw the points on the graph paper as shown below.
If 2x - 2 < 8 + x, then x <
A) 2
B) 4
C) 9
D) 10
Answers
Answer:
D) 10
Step-by-step explanation:
2x - 2 < 8 + x
add 2 to both sides:
2x - 2 + 2 < 8 + x + 2
2x < 10 + x
subtract x from both sides:
2x - x < 10 + x - x
x < 10
WILL GIVE BRAININESS HELP PLEASE Which function is increasing at the highest rate?
Answers
The first equation is increasing at highest rate.
Which function has highest increasing rate?
We can know which function has the highest rate of increase by looking at its slope. The function with the highest slope will have the highest rate.
In equation first m = 2 and is highest among every slope.
12x - 6y = -24
-6y = -12x -24
y = 2x +4
m = 2 (increasing)
In second equation m = 1
m = (-4 + 5)/(2-1) = 1
for a straight line function , the slope is given by
m = ( y₂ -y₁)/(x₂-x₁)
m = ( -3 -3)/(2- (-1)) = -6 /3 = -2
Therefore the function is decreasing
8,0) (0,-4)
m = (-4 -0) /(0-8) = 4/8 = 1/2
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Eva and her friend are making friendship bracelets. Eva has 11 meters of yarn, and she gives
2 meters of the yarn to her friend. Each bracelet uses 1 1/2 meters of yarn. How many bracelets can Eva make with the yarn she has left?
Let n equal the number of bracelets Eva can make.
Write an equation that represents the situation.
Answers
6 bracelets Eva can make with the yarn she has left with .
The equation is [tex]\frac{3n}{2}=9[/tex]
What is basic algebra ?Algebra is a branch of mathematics that helps translate real-world situations or problems into mathematical truths. Mathematical operations like addition, subtraction, multiplication, and division are needed in addition to variables like x, y, and z to construct a meaningful mathematical expression. All branches of mathematics, such as calculus, trigonometry, and coordinate geometry, employ algebra. A fundamental algebraic expression is 2x + 4 = 8, which results from operations like addition, subtraction, multiplication, and division on variables and constants. Algebraic expressions are obtained as the mathematical statement.
Eva has 11 meters of yarn and she gives 2 meters of the yarn to her friend
Now she left with 11 -2 = 9
As Each bracelet uses [tex]\frac{3}{2}[/tex] meters of yarn
n braclet = [tex]\frac{3n}{2}[/tex]
9= [tex]\frac{3n}{2}[/tex]
n = [tex]\frac{18}{3}[/tex]
=6
6 bracelets Eva can make with the yarn she has left with .
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After 6 weeks, a plant is 11 inches tall. After 8 weeks, it is 13 inches tall. After 10 weeks, it is 15 inches tall.
Write an equation to describe the relationship between the height of the plant, y, and the number of weeks it has been growing, x
Answers
The equation to describe the relationship between the height of the plant and the number of weeks is
y = x + 5
Given,
The height of the plant = x
The number of weeks = y
The height of plant at 6th week = 11 inches
The height of plant at 8th week = 13 inches
The height of plant at 10th week = 15 inches
We have to find the equation to describe the relationship between the height of the plant and the number of weeks.
Lets see,
x = 6 and y = 11, y – x = 11 – 6 = 5
x = 8 and y = 13, y – x = 13 – 8 = 5
x = 10 and y = 15, y – x = 15 – 10 = 5
That is,
y – x = 5.
y = x + 5
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Jeffrey has been visiting family in Arizona and is about
511 miles away from home.
If Jeffrey drives an average speed of 60 mph, how
many hours will it take for him to get home? (Round
your answer as seems appropriate.)
Define your variable:
Label for Solution
Change My Variable
Equation (use x)
Answers
We can conclude that Jeffry will reach his home in the time of 9 hours.
What is time?Time can be described in mathematics as an ongoing and continuous series of events that take place one after another, from the past through the present and into the future. The duration of events or the gaps between them can be measured, compared, or even ordered using time.So, the time taken by Jeffrey to get home:
The distance is 511 miles.The speed is 60 mph.The time formula: T = d/sWhere d is distance and s is speed.Now calculate time as follows:
T = d/sT = 511/60T = 8.51Rounding off: 9 hours
Therefore, we can conclude that Jeffry will reach his home in the time of 9 hours.
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The total value of the invoice is Q.10,000.00, the customs agent will be paid 3 per thousand. What amount will we pay you?
Answers
3 per thousand?
10000 ------------------------- 1000
x ------------------------ 3
x = (3 x 10000)/1000
x = 30000/1000
x = 30
The answer is 30
The test statistic for an ANOVA hypothesis test is an F-statistic. Is the P-value the area to the right or left the F-statistic?
Answers
The test statistic for the anova is an F test and it is said to be positively skewed which would be to the right of the F test statistic.
What is the ANOVA?This is the term that is used to refer to the short form of the term that says analysis of variance.
The ANOVA is used to show the variation that would be in existence of a group of observations.
The F test is known to be positively skewed at all times. So we would have it that the P value would have to be to the right and not to the left in the ANOVA hypothesis.
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Simplify these below with explainations please. Thank you
Answers
Answer:
3x^5y^8
Step-by-step explanation:
so the cube root of 27 is 3
to find the cube root of x^15 divide the exponent by 3 which gets you x^5
do the same thing for y^24 and that gets you y^8
mhm and i think thats right
What is 3/7 + 4/18 estimated 0 1/2!or 1
Answers
1 .
Notice that 3/7 is close to 1/2 and 5/9 is also close to 1/2.
Therefore, an estimate for 3/7 + 5/9 is 1/2 + 1/2 = 1.
To estimate fractions using mental math, start by simplifying the fraction to the lowest possible denominator. Then, look at the fraction and round it to the nearest fraction that you feel comfortable working with which could be ¼, ⅓, ½, ¾, or even 1.
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consider a quadrilateral and its diagonals.wich conjecture below would best describe a quadrilateral whose diagonals divide into four isosceles triangles
Answers
Isosceles triangle have 2 equal lengths
Square or Rectangle have 4 equal teiangles
Isosceles trapezoid also divides
Then answer is
Isosceles trapezoid. Option A)