Invertible functions are functions whose inverse can be calculated.
The values of the expressions are: [tex]f^{-1}(f(5)) = 5[/tex] and [tex]f(f(5)) = 11[/tex]
The table entry is given as:
x | 5 | 3 | 1 | 18 | 0 | 9
f(x) | 9 | -2 | -5 | -1 | 1 | 11
(a) Calculate f^-1(f(5))
Start by calculating f(5).
From the table, we have:
[tex]f(5) = 9[/tex]
Take inverse function of both sides
[tex]f^{-1}(f(5)) = f^{-1}(9)[/tex]
From the table, the inverse value of 9 is 5.
i.e. [tex]f^{-1}(9) = 5[/tex]
So, we have:
[tex]f^{-1}(f(5)) = 5[/tex]
(b) Calculate f(f(5))
In (a) above, as have:
[tex]f(5) = 9[/tex]
So, the function becomes
[tex]f(f(5)) = f(9)[/tex]
From the table, the value of f(9) is 11.
So, we have:
[tex]f(f(5)) = 11[/tex]
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w/6+5/8=−1 3/8
w=?
I am really in a hurry. If the answer to this question is true, please tell me how to answer it. Thank you.
Answer:
46
Step-by-step explanation:
Calculate in calculator
What is the midpoint of KL¯¯¯¯¯¯
Answer:
I think that it would be -4.5
Step-by-step explanation:
Have a great day!
Answer:
-4.5
Step-by-step explanation:
yeahhhhhhh
6. match each equation with the correct number of solutions *
no solution
infinitely many solutions
one solution
Equations:
4(3x+2) = 4(2x+3)+4x
10(x+4)-3 = 14x+1
Answer:
x^4-3x^3-14x^2+12x+40 =0
Step-by-step explanation:
9. Chocolate Co. mixes two kinds of chocolate bars
in a gift bag that weighs 3 pounds and has a total
cost of $15. The expensive candy bars are $6 a
pound and the other cost $4.50. How many
pounds of each are used to make the gift bag?
Please show work
9514 1404 393
Answer:
1 pound of expensive chocolate2 pounds of other chocolateStep-by-step explanation:
Let e represent the number of pounds of expensive chocolate in the bag. Then (3-e) is the amount of the other chocolate. The total cost of the bag will be ...
6.00e +4.50(3 -e) = 15.00
1.50e = 1.50 . . . . . . collect terms, subtract 13.50
e = 1 . . . . . . . . . . . . .divide by 1.50
1 pound of expensive chocolate is used; 2 pounds of other chocolate is used.
Solve 1/8^-1/3
Write in fraction form plz.
:)
Answer:
[tex] \frac{1} {2^{-1}}[/tex]
Step-by-step explanation:
[tex] \huge \frac{1}{ {8}^{ - \frac{1}{3} } } \\ \\ = \huge \frac{1}{ {( {2}^{3} )}^{ - \frac{1}{3} } } \\ \\ = \huge \frac{1}{ {{2} }^{ - 3 \times \frac{1}{3} } } \\ \\ = \huge \frac{1}{ {{2} }^{ - 1 } } [/tex]
I do not understand how you can do this without more information.
Answer:
Step-by-step explanation:
I think you are correct. The bottom of the drawing has to have a width or someway of finding it. Also the breakup of the height needs some sort of clue where that breakup occurs. I think you likely have to ask your instructor.
Need help ASAP no rocky
Answer:
x = 12
Step-by-step explanation:
The sum of a heptagon interior angles is 900 degrees, so:
10x + 5 + 12x - 9 + 9x + 14 + 133 + 10x + 9 + 10x + 136 = 900
rearrange to make it easier to subtract/add, u don't have to do this it's optional
10x + 12x + 9x + 10x + 10x + 5 - 9 + 9 + 14 + 133 + 136 = 900
add liket terms
22x + 29x + 19 + 269 = 900
51x + 288 = 900
subtract 288 from both sides
51x = 612
divide by 51
x = 12
Rani ate 2/7 of the cake while her brother ate 4/5 part of the remaining. part of the cake left is?
Answer:
Nothing left
Step-by-step explanation:
Nothing left
2/7+4/5=38/35
1 3/35
Answer:
[tex]\frac{1}{7}[/tex]
Step-by-step explanation:
Amount of cake Rani ate = [tex]\frac{2}{7}[/tex]
You need to understand that her brother ate 4/5 of the remaining part, not of the entire cake, so we need to figure out the actual amount out of the entire cake first before calculating how much is left.
Amount of cake brother ate = [tex]\frac{4}{5}[/tex] × ([tex]\frac{7}{7}[/tex] - [tex]\frac{2}{7}[/tex])
= [tex]\frac{4}{5}[/tex] × [tex]\frac{5}{7}[/tex]
= [tex]\frac{4}{7}[/tex]
Amount of cake left = [tex]\frac{7}{7}[/tex] - [tex]\frac{2}{7}[/tex] - [tex]\frac{4}{7}[/tex]
= [tex]\frac{1}{7}[/tex]
help me fill in the boxes please
Answer:m = 5/4 b=2 and y=5/4x +2
Step-by-step explanation:
m = 5/4 b=2 and y=5/4x +2
The graphs below have the same shapes what is the equation of the blue graph
What's the difference in the total value of a $9000 deposit between an account with an annual simple interest rate of 4% and an account with an annual compound interest rate of 4% after 35 years?
Answer:
Step-by-step explanation:
3000
2q-r=p, r=q-s, p=q+2r prove s=2r
Answer:
s=2r
Step-by-step explanation:
Solution:
Given;
2q-r=p
r=q-s
or,q=r+s
p=q+2r
To prove: s=2r
Now,
2q-r=p
or,2(r+s)-r=q+2r
or,2r+2s-r=r+s+2r
or,r+2s=3r+s
or,s=2r
PROVED
If you want any other solutions follow me
THANK YOU
By using the substitution method we can prove s = 2r.
Given,
2p - r = p
r = q - s
p = q + 2r
We need to prove s = 2r.
What is a substitution method?It is a method where we substitute the value of one variable in one equation for the same variable in the other equation.
Example:
x + 4 = y _____(1)
x = y - 4
x + 5 = 2y ______(2)
Putting x = y - 4 in (2)
y - 4 + 5 = 2y
-4 + 5 = 2y - y
1 = y
y = 1
Prove s = 2r.
We have,
2q - r = p ____(1)
r = q - s _____(2)
p = q + 2r ______(3)
From (1) and (2)
Substituting (2) in (1)
2q - (q - s) = p
2q - q + s = p
q + s = p _____(4)
Putting (4) in (3)
q + s = q + 2r
q - q + s = 2r
s = 2r
Hence proved.
Thus we can prove s = 2r.
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The image above is a parallelogram because both pairs of opposite sides are parallel by the converse of the
Alternate (Interior Exterior) Angle Theorem.
Write which word should go in the underlined space after the word Alternate?
Directions for answering:
Choose the correct word in the parenthesis in the sentence above and type it exactly as shown into the answer
space.
Answer:
msnsjakzooapaozoziznzn zjzkzkamamz xnejiqpwkx
Helen and Stephanie par
cipated in the Christmas bird count. Helen
counted four less than twice the number of birds that Stephanie counted. If c
represents the number of birds Stephanie counted, which of the following
expressions gives the number of birds that Helen counted?
i really really really like birds
Write 3 expressions that are equivalent to 9x(78)
Example:9(80-2)
Answer:
3*3(156/2)9(95-17)10-1(80-2)3x-8y=-2 and 14x+8y=36
Answer:
X=2
Y=1
Step-by-step explanation:
........... Solution on the photo above
A barrel of oil was filled at a constant rate of 6.2gal/min. The barrel had 9 gallons before filling began. Enter an equation in standard form.
Answer:
9 + 6.2x = y
Step-by-step explanation:
x - Gallons per minute
y - Total gallons
So, your answer would be:
9 + 6.2x = y
Could also be written as:
y = 9 + 6.2x
Hope this helps :)
Identify the x- and y-intercepts.
Answer:
y = (0,4)
x=(6,0)
(6,4)
Step-by-step explanation:
What is the slope of the line represented by the equation Y=4/5x-3?
WILL GIVE BRAINLIEST!!!
Ignore the "$".
Jenny's grandmother has $24$ cats. Seventeen of the cats do not catch mice. Ten of the cats have black fur. What is the smallest possible number of cats that do not catch mice that have black fur?
Answer:
Note that 24 - 10 = 14 don't have black fur
And suppose that these 14 are part of the 17 that don't catch mice
Then.....3 that catch mice must also have black fur....and this is the smallest number that do not catch mice but have black fur
Solve the equation -3=6x-3y for y
Answer:
y = 2x + 1
Step-by-step explanation:
-3 = 6x - 3y
Add 3y to both sides.
3y - 3 = 6x
Add 3 to both sides.
3y = 6x + 3
Divide both sides by 3.
y = 2x + 1
One factor of x^2 + 5x - 24 is?
Answer:
(x-3)(x+8)
Step-by-step explanation:
Answer:
(x-3)(x+8) take your pick
Camila and her children went into a bakery and she bought $35 worth of cupcakes
and brownies. Each cupcake costs $3.75 and each brownie costs $2.50. She bought a
total of 10 cupcakes and brownies altogether. Write a system of equations that could
be used to determine the number of cupcakes and the number of brownies that
Camila bought. Define the variables that you use to write the system.
Answer:
x + y = 10
3.75x + 2.5y = 35
Step-by-step explanation:
Got it correct
khloe and her children went into a movie theater where they sell bags of popcorn for $7 each and candies for $4 each. khope has $60 and must buy no less than 11 bags of popcorn and candies altogether. if x represents the number of bags of popcorn purchased and y represents the number of candies pruchased, write and solve a system of inequalities and determine one possible solution
both inequalities must start with y
Answer: Khloe could buy 3 bags of popcorn and 9 candies.
Step-by-step explanation:
\underline{\text{Variable Definitions:}}
Variable Definitions:
x=
x=
\,\,\text{the number of bags of popcorn}
the number of bags of popcorn
y=
y=
\,\,\text{the number of candies}
the number of candies
\text{\textquotedblleft no less than 11 items"}\rightarrow \text{11 or more items}
“no less than 11 items"→11 or more items
Use a \ge≥ symbol
Therefore the total number of bags of popcorn and candies, x+yx+y, must be greater than or equal to 11:11:
x+y\ge 11
x+y≥11
\text{\textquotedblleft \$60 to spend"}\rightarrow \text{can spend \$60 or less}
“$60 to spend"→can spend $60 or less
Use a \le≤ symbol
One bag of popcorn costs $7, so xx bags of popcorn cost 7x.7x. One candy costs $4, so yy candies cost 4y.4y. The total 7x+4y7x+4y must be less than or equal to \$60:$60:
7x+4y\le 60
7x+4y≤60
\text{Solve each inequality for }y\text{:}
Solve each inequality for y:
\begin{aligned}x+y\ge 11\hspace{30px}& 7x+4y\le 60 \\[0.8em] y\ge 11-x \hspace{30px}& 4y\le 60-7x \\[0.8em] \hspace{30px}& y\le \frac{60-7x}{4} \\[0.8em] & y\le 15-\frac{7}{4}x\end{aligned}
x+y≥11
y≥11−x
7x+4y≤60
4y≤60−7x
y≤
4
60−7x
y≤15−
4
7
x
Graph y\ge 11-xy≥11−x by shading up and graph y\le 15-\frac{7}{4}xy≤15−
4
7
x by shading down:
0
the number of bags of popcorn
the number of candies
x
y
0
the number of bags of popcorn
the number of candies
(3, 9)
Since the point (3, 9(3,9) is inside the double shaded region, one possible solution to the system of inequalities would be:
Khloe could buy 3 bags of popcorn and 9 candies.
The system of inequalities are x + y ≥ 11 and 7x + 4y ≤ 60 and the solution is given by the point P ( 3 , 9 ) where x represents the number of bags of popcorn purchased and y represents the number of candies purchased
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Let x represents the number of bags of popcorn purchased and y represents the number of candies purchased
Now , the total number of bags should be no less than 11
And , the inequality is
x + y ≥ 11 be equation (1)
And , cost of each popcorn bag = $ 7
So , the cost of x bags = 7x
And , cost of each candy bag = $ 4
So , the cost of y bags = 4y
The total amount with Khloe = $ 60
And , the inequality is
7x + 4y ≤ 60 be equation (2)
On graphing the inequalities , we can see that the point P ( 3 , 9 ) lies inside the solution
So , 7 ( 3 ) + 4 ( 9 ) ≤ 60
21 + 36 ≤ 60
57 ≤ 60
And , 3 + 9 ≥ 11
12 ≥ 11
Hence , the system of inequalities are solved and the graph is plotted
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The last 40 boat rentals at a boat rental company were 22 sunfish, 10 kayaks, and 8 rowboats.
4/3 in a mixed numbers
Answer:
the answer is
[tex]1 \frac{1}{3} [/tex]
can someone help ill give brainliest
Answer:
a=55%
b=190%
c=54 pounds
Step-by-step explanation:
ok
a.
33/60=0.55
55%
b.
114/60=1.9
or 190%
c
60/100=0.6
0.6=1 percent
54
Answer:
a=55%
b=190%
c=54 pounds
Step-by-step explanation:
HELPPPP!!!! Use the diagram to complete the statement.
60% 0f 20 is ____
the answer os 60% of 20 is 12
Please someone solve this
Answer:
a)
(4a - 3b + 4) + (a + 3b - 1) =
4a - 3b + 4 + a + 3b - 1 =
5a + 3
b)
(2x^2 - 3x - 3) + (-x^2 - 6x + 8) =
2x^2 - 3x - 3 - x^2 - 6x + 8 =
x^2 - 9x + 5
c)
(3m^2 + 5m - 6) + (-m^2 - 4n + 5) =
3m^2 + 5m - 6 - m^2 - 4n + 5 =
m^2 + 5m - 4n -1
d)
(4x^3 - 3xy^2) + (x^3 - 5xy^2 - 5y^2) =
4x^3 - 3xy^2 + x^3 - 5xy^2 - 5y^2 =
7x^3 - 8xy^2 - 5y^2
e)
(5m + 2lm) + (l^2 - 3m^2 - 2lm) =
5m + 2lm + l^2 - 3m^2 - 2lm =
5m + l^2 - 3m^2
Given h(x) = -x + 5, find h(-5).
Answer:
10
Step-by-step explanation:
h(x) = -(-5) + 5
h(x) = 5 + 5
h(x) = 10