Given the function f(x), whose graph is shown, place the black dot at the point the corresponds to f^-1(-1)
Answers
Given: Graph of a function f(x) is provided.
Required: To find the inverse of the function
[tex]f^{-1}(-1)[/tex]Explanation: The inverse of a function is determined by interchanging the domain and the range. The domain is the input values, and the range is the output values where the function is defined.
Hence, to find the inverse of the function at x=-1, we need to look at the graph and find out at which value of x, the value of f(x), is -1. Since if
[tex]\begin{gathered} f(a)=-1 \\ then,f^{-1}(-1)=a \end{gathered}[/tex]Hence we need to look at which point on the x-axis of the given function we have f(x)=-1. This is the point (-3,-1) as
[tex]\begin{gathered} f(-3)=-1 \\ \Rightarrow f^{-1}(-1)=-3 \end{gathered}[/tex]Hence the point corresponding to the inverse is (-1,-3). The point is shown below in the graph-
Final Answer: The point corresponding to the inverse of f at x=-1 is (-1,-3).
Related Questions
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 3.5 years, and standarddeviation of 0.6 years.The 10% of items with the shortest lifespan will last less than how many years?[1])])1)Give your answer to one decimal place.
Answers
1) In this question, we need to make use of a standard normal table to check which is the value (in terms of Z-score) for that 10%.
2) Checking that out, we can see that the Z-score is -1.282. So now, let's plug that into the Z-score formula so that we get the corresponding raw value:
[tex]\begin{gathered} Z=\frac{X-\mu}{\sigma} \\ -1.282=\frac{X-3.5}{0.6} \\ X=2.73\approx2.7 \end{gathered}[/tex]Thus, this is the answer: 2.7 years
Which additional piece of information would you need to prove these two triangles are congruent using the side-side-side or SSS triangle congruence postulate?
Answers
By using congruency of triangles, the result obtained is
The additional information needed to make [tex]\Delta STU \cong \Delta SHU[/tex] by SSS axiom is
TU = SH
Side SH is congruent to side TU
Third option is correct
What is Congruency of triangles?
Two triangles are said to be congruent if the corrosponding sides and corrosponding angles are same.
The different axioms of congruency are SSS axiom, SAS axiom, ASA axiom, AAS axiom, RHS axiom
In [tex]\Delta STU[/tex] and [tex]\Delta SHU[/tex]
ST = HU [Given]
SU is common.
The additional information needed to make [tex]\Delta STU \cong \Delta SHU[/tex] by SSS axiom is
TU = SH
Side SH is congruent to side TU
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what are 4 numbers that are divisible by both 4 and 6
Answers
We need 4 numbers that are divisible by 4 and 6 at the same time, so the first number will be the multiplication of them:
[tex]4\cdot6=24[/tex]Now wecan multiply this new number for 4 or for 6 to get other two numbers:
[tex]\begin{gathered} 24\cdot4=96 \\ 24\cdot6=144 \end{gathered}[/tex]and finally we can multiply 96 for 4 to get the last number:
[tex]96\cdot4=384[/tex]these four numbers works
1. Predict what will happen when a tape diagram has a large number of squares, some squares are removed, and thenthe same amount of squares are added back on.Build a tana diagram mit 10
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When some squares are removed, the number of squares in the tape diagram are reduced but when the same number of squares are added back, then we will find out that the number of squares in the tape diagram remain the same.
In a lottery, the top cash prize was $629 million, going to three lucky winners. Players pick four different numbers from 1 to 56 and one number from 1 to 41.A player wins a minimum award of$525 by correctly matching three numbers drawn from the white balls (1 through 56) and matching the number on the gold ball (1 through 41).What is the probability of winning the minimum award?
Answers
Step 1
Given;
[tex]\begin{gathered} Top\text{ cash prize is \$629} \\ Players\text{ pick four different numbers from 1 to 56 and 1 to 41} \end{gathered}[/tex]Step 2
Probability is given as;
[tex]undefined[/tex]The drink booth at the school fair had these 5 types of drinks: ice tea, root beer, apple cider, lemonade, and orange juice. The 12 students from Mr. Yu's class were asked which drink they ordered. Here are the results: apple cider, orange juice, lemonade, root beer, orange juice, orange juice, lemonade, orange juice, ice tea, root beer, orange juice, orange juice Draw the bar graph for these data. Frequency 24 Explanation root beer Check apple cider lemonade orange juice Type of drink X ? 2022 McGraw H LLC. All Rights Reserved. Terms of
Answers
The first step is to find the frequency of each type of drink. It is shown below
apple cider = 1
Orange juice = 6
Lemonade = 2
root beer = 2
ice tea = 1
The bar graph is shown below
the probability that describe the related frequency of actual observation of an event is an experiment is which of the following
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The relative frequency is an empirical probability. So, the answer is the first option
Is 49 prime or composite?
Can Mario organize his marbles into equal piles ?
Answers
an object is thrown upward from the top of a 160 foots building with an initial velocity of 48 feet per second .solve the equation -16^2 + 48t + 160=0 find the time(t) in seconds at which the object hits the ground.
Answers
The given equation represents the distance travelled by the object at time t.
The given equation is expressed as
-16t^2 + 48t + 160
At the point where it hits the ground, the distance woule be 0. Thus, we would so;ve the equation,
-16t^2 + 48t + 160=0
We would divide through by - 16. We have
t^2 - 3t - 10 = 0
We would find two terms such that their sum or difference is - 3t and their product is - 10t^2. They are 2t and - 5t. We have
t^2 + 2t - 5t - 10 = 0
By factorising, we have
t(t + 2) - 5(t + 2) = 0
(t + 2)(t - 5) = 0
t + 2 = 0 or t - 5 = 0
t = - 2 or t = 5
Since the time cannot be negative, the correct answer is
time = 5 seconds
What was the total length of all the scarves put together?
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ANSWER :
37.8 feet
EXPLANATION :
From the problem, each scarf is 50.4 inches long.
Since there's a total of 9 scarfs.
The total length will be :
[tex]9(50.4)=453.6\text{ }in[/tex]There are 12 inches in 1 foot.
Divide the result by 12 to get the number of feet.
[tex]\frac{453.6}{12}=37.8\text{ }feet[/tex]Evaluate the expression when a=-5 and c=27c-a
Answers
Given:
7c - a
a=-5 and c = 2
Substitute the values into the expression
7(2) - (-5)
=14 + 5
= 19
Which equation has (1,1),(2,4),(3,7) and (4,10) as solutions?A)y=2x - 1.B)y= 2x+3.C)y=3x-2.D)y=3x+1.
Answers
Answer:
y=3x-2
Explanation:
The equation that has the given solutions is the equation that satisfies all the given (x, y) pairs.
From the given options:
[tex]\begin{gathered} \text{When x=1} \\ y=3x-2 \\ y=3(1)-2=1 \\ \implies(1,1) \end{gathered}[/tex]Likewise:
[tex]\begin{gathered} \text{When x=}2 \\ y=3x-2 \\ y=3(2)-2=4 \\ \implies(2,4) \end{gathered}[/tex]Also when x=3:
[tex]\begin{gathered} y=3\mleft(3\mright)-2=7 \\ \implies(3,7) \end{gathered}[/tex]Finally, when x=4
[tex]\begin{gathered} y=3\mleft(4\mright)-2=10 \\ \implies(4,10) \end{gathered}[/tex]Thus, since y=3x-2 satisfies all four points, it is the right equation.
the minimum point on the graph of the equation y = f(x) is (-1,-3). what is the minimum point on the graph of the equation y=f(x)+5?
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the minimum point on the graph of the equation y = f(x) is (-1,-3). what is the minimum point on the graph of the equation y=f(x)+5?
we have that
the rule of this transformation is equal to
(x,y) ------> (x, y+5)
so
(-1,3) -----> (-1,3+5)
(-1,8) is the minimum pointI think I got the two that I did but I’m not sure and really need help
Answers
b) You have the following expression:
[tex]x^3=\frac{27}{64}[/tex]Take into account that 27/64 can be written as follow:
[tex]\frac{27}{64}=\frac{3}{4}\cdot\frac{3}{4}\cdot\frac{3}{4}[/tex]Then, x = 3/4
c) For the following expression:
[tex]x^3=\frac{1}{8}[/tex]you can write it as follow:
[tex]\frac{1}{8}=\frac{1}{2}\cdot\frac{1}{2}\cdot\frac{1}{2}[/tex]Then, x = 1/2
3SpointsWhich is the image of vertex C after the triangle is rotated 180 degrees about the origin?
Answers
T' (3,0) A' (5,-1) and C' (2,-4)
1) Considering that the Pre-image coordinates are :T(-3,0), A (-5,1) C(-2,4)
and there was a rotation 180º about the origin, then
2) In the Rotation, the rules for 180º rotation Counterclockwise and clockwise is
Pre-image Image
(x,y) ---- (-x, -y)
3)
Thus,
T' (3,0) A' (5,-1) and C' (2,-4)
1. Gustava Valadez opened a new checking account by depositing her paycheck for$347.95. The check register shows her transactions since opening her account.What should her new balance be?
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When he deposite the paycheck for $347.95. An amount of $347.95 will be creted to in his account.
Therfore, the new balance is $347.95
15x+3x^2+55x^2+3x+155+3x+15x^2which is written in standard form.
Answers
ANSWER
[tex]5x^{2}+3x+15[/tex]EXPLANATION
A standard quadratic equation must be of the form;
[tex]ax^2+bx+c=0[/tex]Hence, the standard equation is;
[tex]5x^2+3x+15[/tex]In a circle of radius 10 cm, there are two parallel chords (in different sides of a circle) of lengths 16 cm and 12 cm. Calculate the distance between the chords.
Answers
The distance between the chords is 14 cm
Given that AB=16 cm and CD=12 cm
So, AL=8 cm and CM=6 cm (⊥ from the centre to the chord bisect the chord)
In right triangles OLA and OMC,
By Pythagoras theorem,
OA² = OL²+AL²
and OC² = OM²+CM²
⇒ 10² = OL²+8²
and 10² = OM²+6²
⇒ OL²=100-64
and OM² = 100 - 36
⇒ OL² = 36 and OM² = 64
⇒ OL = 6 cm
and OM = 8 cm
In the second case distance between AB and CD is:
LM=OM+OL
= 8+6
= 14 cm
Hence distance between the chords is 14 cm,
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. Find an ordered pair that represents a solution to the equation x + 2y = 20
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we have
x + 2y = 20
The linear equation represent the equation of a line
If a ordered pair is a solution of the equation, that means that the ordered pair lies on the line
so
Find a ordered pair that represents a solution
Assume the value of x
so
For x=1
substitute in the equation
(1)+2y=20
solve for y
2y=20-1
2y=19
y=19/2
y=9.5
therefore
The ordered pair (1,9.5) represents a solutionIn a game, 2 players each flip a coin. If both land on heads, player A gets 2points and player B loses 1 points. If both land on tails, player B gets 2 points andplayer A loses 1 point. Find the expected value of the game for each player.
Answers
The expected value for player A is:
[tex]\begin{gathered} (\frac{1}{2}\times\frac{1}{2}\times2)-(1\times\frac{1}{2}\times\frac{1}{2}) \\ =(\frac{1}{4}\times2)-(1\times\frac{1}{4}) \\ =(\frac{1}{2})-(\frac{1}{4}) \\ =\frac{1}{4} \end{gathered}[/tex]The expected value of player B is:
[tex]\begin{gathered} (\frac{1}{2}\times\frac{1}{2}\times2)-(1\times\frac{1}{2}\times\frac{1}{2}) \\ =(\frac{1}{4}\times2)-(1\times\frac{1}{4}) \\ =(\frac{1}{2})-(\frac{1}{4}) \\ =\frac{1}{4} \end{gathered}[/tex]The sale Price of a swing set is $90. What is the original price?Sale:75% Round your answer to the whole dollar
Answers
To solve this problem we can use the expression that defines percents. What price has a 75% of $90?
[tex]\text{Total}\cdot\frac{\text{percent}}{100}=\text{equivalent number to the percent}[/tex]With the information given, we know that the equivalent number to the percent is $90 and the percent is 75%.
Then, substitute and solve for the total variable:
[tex]\begin{gathered} \text{Total}\cdot\frac{75}{100}=90 \\ \text{Total}=\frac{90\cdot100}{75} \\ \text{Total}=120 \end{gathered}[/tex]The original price of the swing set is $120.
6 cm Find the missing dimension of each figure. Round your answer to the nearest tenth. 5. V=252 ft 4. V=100 in 6 ft 12 in 14 ft rin. eft Find the volume of each composite figure. Round your answer to the nearest tenth. 6. 6 in. 7. A cylindrical-shaped hole is cut from 11 in. the center of a cube. 2.5 cm 15 in.solve #5 please
Answers
The volume of cuboid is V = 252 ft^3.
The width of cuboid is w = 14 ft.
The height of cuboid is h = 6 ft.
The formula for the volume of cuboid is,
[tex]V=l\cdot w\cdot h[/tex]Substitute the values in the formula to determine the length of cuboid.
[tex]\begin{gathered} 252=l\cdot14\cdot6 \\ l=\frac{252}{84} \\ =3 \end{gathered}[/tex]So length (missing dimension) of the cuboid is 3 ft.
Which one of the following equations could describe the above graph?OA. Y=1.5^(x+2)-3OB. Y=2^x+6Oc. = y=(1/2)^x+6D. Y= 3^(x-1)
Answers
Given:
The points lie on the graph are (1,1) and (2,3).
Required:
We need to find the equation of the given graph.
Explanation:
Consider the individual equation.
A.
[tex]y=1.5^{(x+2)}-3[/tex]Substitute x =1 and y =1 in the equation.
[tex]1=1.5^{(1+2)}-3[/tex][tex]1=0.375[/tex]This is not true,
This is not a required equation.
B.
[tex]y=2^x+6[/tex]Substitute x =1 and y =1 in the equation.
[tex]1=2^1+6[/tex][tex]1=8[/tex]This is not true,
This is not a required equation.
C.
[tex]y=(\frac{1}{2})^x+6[/tex]Substitute x =1 and y =1 in the equation.
[tex]1=(\frac{1}{2})^1+6[/tex][tex]1=6.5[/tex]This is not true,
This is not a required equation.
D.
[tex]y=3^{(x-1)}[/tex]Substitute x =1 and y =1 in the equation.
[tex]1=3^{(1-1)}[/tex][tex]1=1[/tex]This is true.
Substitute x =2 and y =3 in the equation.
[tex]3=3^{(2-1)}[/tex][tex]3=3[/tex]This is true.
This is a required equation.
Final answer:
[tex]y=3^{(x-1)}[/tex]Both customers spent same amount of money. customer one bought 8 chicken wings and left a tip of four dollars. second customer bought 10 chicken wings and left a tip of $2.50. how much is each chicken wing?
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the representation of the chicken wings
Let the chicken wing be represented by x
[tex]\begin{gathered} For\text{ Customer 1, he spent;} \\ 8x+4 \\ From\text{ second customer, he spent} \\ 10x+2.50 \end{gathered}[/tex]STEP 2: Equate the two amounts
Since they both spent same amount of money, this means that;
[tex]8x+4=10x+2.50[/tex]STEP 3: Solve for x
[tex]\begin{gathered} Collecting\text{ like terms:} \\ 8x-10x=2.50-4 \\ -2x=-1.5 \\ Divide\text{ both sides by -2} \\ \frac{-2x}{-2}=\frac{-1.5}{-2} \\ x=0.75 \end{gathered}[/tex]Hence, each chicken wing costs $0.75
The ratio of short to pants is 1:2 if there are eight shorts how many pants are there? 16,4,6,or 8
Answers
There are 16 pants
Explanation:Ratio of short to pants = 1:2
There are 8 shorts
Let x be the number of pants, then
8/x = 1/2
x = 8 * 2
= 16
There are 16 pants
What was the median price of new home in 1981
Answers
1) In this question, let's spot in the graph the median price given by the blue curve on the graph.
2) Examining it we can see that the y-axis point that corresponds to the Median Price in 1981 is:
[tex]\$70,000[/tex]
There are 30 boys in a sporting club, 20 of them play hockey and 15 play volleyball. Each play at least one 9f the two games. Illustrate this using:
A. The Venn diagram.
B. Only volleyball
C. Both games
Answers
The students who play both hockey and volleyball 5 and the Venn diagram is shown below.
What are Venn diagrams?A Venn diagram uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items. Often, they serve to graphically organize things, highlighting how the items are similar and different.A Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things. Circles that overlap have a commonality while circles that do not overlap do not share those traits. Venn diagrams help to visually represent the similarities and differences between two concepts.So, the Venn digram will be:
The total number of boys are 30.Boys playing hockey are 20.The boys playing volleyball are 15.A Number of students who play both:
(20+15) - 3035 - 305So, the Venn diagram will be:
(Refer to the Venn diagram attached below)Therefore, the students who play both hockey and volleyball 5 and the Venn diagram is shown below.
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Solve by substitution method. a) x + y = 8 and x - y = 4
Answers
Answer:
x = 6
y = 2
Step-by-step explanation:
x + y = 8 ---> (1)
x - y = 4 ---> (2)
First, let us find the value of x.
For that, add both equations.
(1) + (2)
x + y + ( x - y ) = 8 + 4
Solve the brackets.
x + y + x - y = 8 + 4
2x = 12
Divide both sides by 2.
x = 6
Now let us find the value of y.
For that, let us use equation 1 and replace x with 6.
x + y = 8
6 + y = 8
Subtract 6 from both sides.
y = 8 - 6
y = 2
Any answer?? I'm struggling to find the answer to this equation
Answers
The last option is the correct answer ( no solution)
3x-8=2x+18Solve for x
Answers
x=26
Explanation
[tex]3x-8=2x+18[/tex]Step 1
subtract 2x in both sides
[tex]\begin{gathered} 3x-8=2x+18 \\ 3x-8-2x=2x+18-2x \\ x-8=18 \end{gathered}[/tex]Step 2
add 8 in both sides
[tex]\begin{gathered} x-8=18 \\ x-8+8=18+8 \\ x=26 \end{gathered}[/tex]I hope this helps you