Answers
Since m(n(x)) = n(m(x)) = x, then m(x) and n(x) are inverse functions
What is the inverse of a function?The inverse of a function is a function that can reverse into another function.
If we have function f and g, and f f(x) = y, then g is the inverse of f if and only if g(y) = x
Also, if f is a function f⁻¹ is the inverse of x and ff⁻¹(x) = f⁻¹f(x) = x
How to show that the composite fucntions are inverses?Given the functions m(x) = x³ - 5 and n(x) = ∛(x + 5)
If m(x) and n(x) are inverse, then m(n(x)) = n(m(x)) = x
So, we proceed as follows
m(x) = x³ - 5
m(n(x)) = (∛(x + 5))³ - 5
m(n(x)) = x + 5 - 5
m(n(x)) = x + 0
m(n(x)) = x
Also,
n(x) = ∛(x + 5)
n(m(x)) = ∛(x³ - 5 + 5)
n(m(x)) = ∛(x³ - 0)
n(m(x)) = ∛(x³)
n(m(x)) = x
Since m(n(x)) = n(m(x)) = x, then m(x) and n(x) are inverse functions
Learn more about inverse functions here:
https://brainly.com/question/28034667
#SPJ1
Related Questions
Jeremiah finished 3/4 of his timed math quiz. Of those he attempted, he correctly answered 5/9
Answers
The fractional part of the quiz that he get correct will be 5/12.
How to calculate the value?From the information, Jeremiah finished 3/4 of his timed math quiz. Of those he attempted, he correctly answered 5/9.
The fractional part of the quiz that he get correct will be
= 3/4 × 5/9
= 5/12
Therefore, the fractional part of the quiz that he get correct will be 5/12.
Learn more about fractions on:
brainly.com/question/17220365
#SPJ1
Jeremiah finished 3/4 of his timed math quiz. Of those he attempted, he correctly answered 5/9. What fractional part of the quiz did he get correct?
is making a Rice Krispie cakes.
Timothy
A recipe uses 240g of chocolate and 160g of Rice Krispies to make 24 cakes.
(a) Write down the ratio of chocolate to Rice Krispies in its simplest form.
(b) How much Rice Krispies should Timothy use to make 30 cakes?
Sarah is making shortbread biscuits.
Answers
Answers to both the subparts are as follows:
(A) Ratio of chocolate to Rice Krispies in its simplest form: 3:2(B) Rice Krispies Timothy should use to make 30 cakes: 200gWhat are ratios?A ratio in mathematics indicates how many times one number contains another. For example, if a bowl of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six. Similarly, the lemon to orange ratio is 6:8, and the orange to total fruit ratio is 8:14. Ratios are used to compare two numbers by dividing them. If you want to compare one data point (A) to another (B), your formula would be A/B. This means that you are dividing data A by data B. If A is five and B is ten, your ratio will be 5/10.So, (A) ratio of chocolate to Rice Krispies:
240g : 160g240/160 ⇒ 24/16 ⇒12/8 ⇒ 6/4 ⇒ 3/23 : 2Now, (B) Rice Krispies should Timothy use to make 30 cakes:
Rice Krispies used in 24 cakes: 160g
Then, Rice Krispies used on 1 cake:
160/24 ⇒ 80/12 ⇒ 40/6 ⇒ 20/3 ⇒ 6.67So, Rice Krispies used in 30 cakes:
6.67 × 30 = 200gTherefore, answers to both the subparts are as follows:
(A) Ratio of chocolate to Rice Krispies in its simplest form: 3:2(B) Rice Krispies Timothy should use to make 30 cakes: 200gKnow more about ratios here:
https://brainly.com/question/2328454
#SPJ9
(Cosec a -cot a)^2=1-cos\1+cos
Answers
Answer:
Step-by-step explanation:
[tex]\displaystyle\\(cosec \alpha -cot\alpha )^2=\\\\(\frac{1}{sin\alpha } -\frac{cos\alpha }{sin\alpha })^2 =\\\\(\frac{1-cos\alpha }{sin\alpha } )^2=\\\\\frac{(1-cos\alpha)^2 }{sin^2\alpha }=\\\\ \frac{(1-cos\alpha )^2}{1-cos^2\alpha } =\\\\\frac{(1-cos\alpha )^2}{(1+cos\alpha )(1-cos\alpha )} =\\\\\frac{1-cos\alpha }{1+cos\alpha }[/tex]
help me please please please!!!!
Answers
I need to know how how to do these please.
Answers
The scatter plot shows negative correlation because as the plotted values of x increase, the values of y generally decrease.
What is negative correlation?When two variables are said to have negative correlation, it means that they move in the opposite direction from each other. When one variable is increasing, the other variable is decreasing.
The values of x and y in order of x are:
x 3 4 5 6 7 8 9
y 6 7 5 4 3 4 2
As shown above, when x increases, y generally decreases and when x decreases, y generally increases. This is therefore a negative correlation relationship.
Find out more on negative correlation at https://brainly.com/question/16913516
#SPJ1
Subtract.
(2x² + 5) - ( − 3x² + 5)
Answers
Answer:
Step-by-step explanation:
1) distribute the signs to the brackets
2x^2 + 5 + 3x^2 - 5
2) solve
5x^2 + 0
Hopefully, it's correct and helpful
Question 3(Multiple Choice Worth 2 points)
(Solving Equations Using Square and Cube Roots LC)
Solve y³ = -8.
Pre-algebra 8th grade pls help thx!!
Answers
The cubic equation y³ = -8 has the value of y = -2 which is first option.
The cubic equation given to us is y³ = -8
We can shift the power from left hand side to right hand side but the cubic power would turn cube root of -8
We know that square root of any negative number is not a real number but in case of Cube roots , This is possible and the root with negative sign and simple root
Also, when we square root any number we add ± sign but in case of cube root we only add the sign of number whose cube root is taken
y³ = -8
y = ∛-8
y = ∛(-2)(-2)(-2)
y = ∛(-2)³
y = -2
So, The cubic equation y³ = -8 has the value of y = -2 which is first option.
To know more about Cube and cube roots- https://brainly.com/question/12726345
#SPJ1
PLEASE HELP ILL GIVE BRAINELST
Answers
Answer:
1) 8
2) 3
3) 4
4) 5
5) 6
6) 2
7) 1
8) 18
Step-by-step explanation:
whenever you see a letter, just change that letter with whatever the guide says, for example, 6+c would be 6+2, which is 8. Another example is ab, which would be 6 times 3 because a is 6 and b is three
How many natural numbers below 2021 have exactly 15 positive integer factors
Answers
Answer:
ITO PO ANSWER:PA BRAINLEST NALANG PO HEHE
Find the point t=4pi/3
Answers
The point t on the unit circle is ( -1/2, √3 /2 ).
The intersection of the x-axis (the horizontal number line) and the y-axis in the cartesian system divides the coordinate plane into four equal pieces. Because each of these four areas occupies a quarter of the entire coordinate plane, they are collectively referred to as quadrants.
Consider the point t = - 4π/3 on the circle.
Now, the reference angle is π / 3.
- 4π / 3 is in quadrant 2 where the value of cosine is negative and sine is positive.
Therefore, the point t(x,y) will be:
( x, y ) = ( - cos ( π / 3 ), sin ( π / 3 ) )
( x, y ) = ( - 1/ 2 , (√3 )/ 2 )
Learn more about circle here:
https://brainly.com/question/8952990
#SPJ9
PLEASE PLEASE HELP ME!!
Answers
which one do you need answered look it up
Which graph represents the inequality 0.5 is greater than the product of −2.5 and a number?
number line with open circle on point 0.2 and arrow shaded to the left
number line with open circle on point negative 5 and arrow shaded to the left
number line with open circle on point negative 0.2 and arrow shaded to the right
number line with open circle on point negative 5 and arrow shaded to the right
Answers
The correct graph representation of the given inequality is,
⇒ Number line with open circle on point negative 0.2 and arrow shaded to the right.
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
The written expression is given as,
0.5 is greater than the product of −2.5 and a number.
Let a number is x.
Then, The given expression is written as;
0.5 > -2.5x
Now, We can solve as;
0.5 > -2.5x
Multiply by -1 we get;
- 0.5 < 2.5x
-0.2 < x
Hence, The graph of inequality is;
⇒ Number line with Open circle on point negative 0.2 and arrow shaded to the right.
So, The correct graph representation of the given inequality is,
⇒ Number line with open circle on point negative 0.2 and arrow shaded to the right.
Learn more about the inequality visit:
https://brainly.com/question/26158293
#SPJ1
Answer:
A
Step-by-step explanation:
dose the base have to be flat when finding base x height?
for finding the parallegram for height dose the height have to touch and make a 90 degree angle?
Answers
B) the hight is actually not the sides, the hight is found by measuring the point we’re the top line ends down (to the side there is space inside the shape for that
Pls help me with my math
Answers
|18 + x/2| > 10
|1/2x + 18| > 10
Solve Absolute Value.
|1/2x + 18| > 10
We know either
1/2x + 18 > 10
or
1/2x + 18 < −10
(Possibility 1)
1/2x + 18 > 10
1/2x + 18 − 18 > 10 − 18
(Subtract 18 from both sides)
1/2x > − 8
2* (1/2x) > (2)* (−8)
(Multiply both sides by 2)
x > -16
(Possibility 2)
1/2x + 18 < −10
1/2x + 18 − 18 < -10 − 18
(Subtract 18 from both sides)
1/2x < −28
2* (1/2x) < (2)* (−28)
(Multiply both sides by 2)
x < -56
(Answer)
x > -16 or x < −56
What is the arena of the circle for model 3
Answers
The area of the circle is approximately 78.5 square meters
What are areas?The area of a shape is the amount of space on the shape
How to determine the area of the circle?The given parameters are:
Radius = 5
The area of a circle is calculated using
A = pi r^2
In this case
pi = 3.14
So, we have:
A = 3.14 * 5^2
Evaluate the product
A = 78.5
Hence, the area of the circle is approximately 78.5 square meters
Read more about area at:
brainly.com/question/25292087
#SPJ1
Possible question
What is the area of a circle for model 3 where the radius is 5 meters.
Use pi approx3.14 . The area of the circle is approximately square meters
Enter only the number.
your sports drink is 5/6 full after practice its now 3/8 full write the difference of the amounts after practice and before pracices
Answers
Answer: The difference of the amounts after practice and before practices = 11/24
Step-by-step explanation:
Given data,
Initial quantity of drink = 5/6
After practice quantity = 3/8
difference of the amounts after practice and before practices
difference of amount = Initial quantity of drink - After practice quantity
= (5/6) - (3/8)
= (20-9)/24
difference of amount = 11/24
Therefore,
The difference of the amounts after practice and before practices = 11/24
Learn more about event correlation here: brainly.com/question/11779090
#SPJ9
The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $3005 to rent trucks plus an additional fee of $100.50 for each ton of sugar. The second company does not charge to rent trucks but charges $250.75 for each ton of sugar.
Answers
The amount of sugar that the two companies charge the same is 20 tons
The cost when the two companies charge the same is $5,015
What is breakeven amount of sugar for the two companies?
The amount of sugar that the two companies charge the same is derived at the point when the total cost of both companies are the same, bearing in mind that the total cost in this case is made of fixed cost to rent truck and variable cost, which is additional fee for each ton of sugar moved.
First company:
TC=3005+100.50x
Second company:
TC=250.75x
3005+100.50x=250.75x
3005=250.75x-100.50x
3005=150.25x
x=3005/150.25
x=20 tons of sugar
Total cost of 20 tons=250.75*20=$5,015
Find out more about breakeven cost on:
#SPJ1
Full question:
The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $3005 to rent trucks plus an additional fee of $100.50 for each ton of sugar. The second company does not charge to rent trucks but charges $250.75 for each ton of sugar
For what amount of sugar do the two companies charge the same?
What is the cost when the two companies charge the same?
Zendaya has $540 to spend at a bicycle store for some new gear
and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $269.88.
She buys 4 bicycle reflectors for $10.57 each and a pair of a
bike gloves for $17.76.
She plans to spend some or all of the money she has left to
buy new biking outfits for $65.65 each.
Write and solve an inequality which can be used to determine
x, the number of outfits Zendaya can purchase while staying
within her budget.
Answers
The inequality that can be used to determine x, the number of outfits Zendaya can purchase is 329.92 + 65.65x <= 540
How to write and solve an inequality which can be used to determine x, the number of outfits Zendaya can purchase while staying within her budget?The given parameters are:
Budget = $540
New bicycle = $269.88.
4 bicycle reflectors = $10.57 each
Pair of a bike gloves = $17.76.
New biking outfits = $65.65 each.
Let the number of new biking outfits be x
So, we have
New bicycle + 4 * price of bicycle reflectors + Pair of a bike gloves + New biking outfits <= Budget
This gives
269.88 + 4 * 10.57+ 17.76 + 65.65x <= 540
This gives
329.92 + 65.65x <= 540
Solve the inequality
65.65x <= 210.08
Divide by 65.65
x <= 3.2
Hence, the inequality that can be used to determine x, the number of outfits Zendaya can purchase is 329.92 + 65.65x <= 540
Read more about inequality at
https://brainly.com/question/24372553
#SPJ1
On April 1, Mr. Olson’s meter read 7,329 kw-hr. On may 1, the meter read 8,284 kw-hr. At $.08 per kw-hr, what was his electric bill for the month of April?
Answers
His electric bill for the month of April is $76.4
How to determine his electric bill for the month of April?The given parameters are
April 1 = 7,329 kw-hr.
May 1 = 8,284 kw-hr
Rate = $.08 per kw-hr
His electric bill for the month of April is calculated as
Bill = (May 1 - April 1) * Rate
So, we have
Bill = (8,284 - 7,329) * .08
Evaluate
Bill = 76.4
Hence, his electric bill for the month of April is $76.4
Read more about electric bill at
https://brainly.com/question/14277272
#SPJ1
Which angle number represents an angle adjacent to
SOMEONE PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!
Answers
The angle number represents an angle adjacent to ∠DGA is angle 2.
∠DGB.
Which angle is the adjacent angle?When two angles share a shared vertex and side, they are said to be neighboring. The terminus of the rays that create the sides of an angle is referred to as the vertex of an angle. Adjacent angles can be complimentary or supplementary if they have a shared vertex and side.
Briefing:Adjacent angles seem to be two angles that share a shared vertex and then a common side but do not overlap. Angles 1 and 2 in the figure are adjacent. They have the same vertex as well as a common side. In the diagram, angles 1 and 3 are not contiguous.
How can you recognize neighboring angles?When two angles have a common side as well as a common vertex (corner point) but do not overlap, they are said to be adjacent.
What's the distinction here between adjacent angle and?Adjacent angles comprise two angles with the same arm and vertex. When two lines meet at the vertex as well as form a pair of opposite angles, vertical angles are formed. They share an arm and a vertex. They share a vertex of the arm but no arm.
To know more about Adjacent angles visit:
https://brainly.com/question/12838185
#SPJ9
NEED SOLUTION
Give the quotient of the following:
Need solution
1.168 ÷ 8
2.246÷12
3.4328÷4
4.729÷9
5.8415÷5
Answers
Answer
1.168 ÷ 8= 0.146
2.246÷12= 0.1871
3.4328÷4=0.8582
4.729÷9=0.5254
5.8415÷5=1.168
Step-by-step explanation:
Choose the equation that represents the graph below (1point) graph of a line passing threw points negative 2 comma 0 and 0 comma negative 4 y =-2x- 4y=2x+4y=-2x+4y=2x-4
Answers
The equation of line is,
⇒ y = -2x - 4
What is equation of line?
The equation of line with slope m is given by;
⇒ y = mx + b
Now, The points are;
(-2, 0) and (0, -4)
Hence, slope = (-4 - 0) / (0 - (-2) = -4 / 2 = -2
Since, Equation of line with slope (m) is;
y = mx + b
Here, Slope (m) = -2
To find the value of b we use either of the points;
Take point (0,-4)
x = 0 and y = -4
We get after substitute;
-4 = -2(0) + b
-4 = b
Hence, The equation of line is,
⇒ y = -2x - 4
Learn more about the equation of line visit:
https://brainly.com/question/27680685
#SPJ1
Frances left a 22% tip on a meal. Including the tip, its cost was 21.96 what was the cost of the meal before the tip
Answers
Hence we would conclude that If Frances left the tip of 22 percent on a meal, the cost of the meal before the tip would be 18 dollars.
How to solve for the cost of the tipLet us define x to be the cost of the meal
such that we would have
x + 22%x = 21.96
= x + 0.22x = 21.96
1.22x = 21.96
We would have to divide through the equation that we have by 1.22
x = 21.96 / 1.22
x = 18
X is the cost for the meal that that Frances ate before she gave the tip that she did to the waiter.
Hence we would conclude that If Frances left the tip of 22 percent on a meal, the cost of the meal before the tip would be 18 dollars.
Read more on cost here:
https://brainly.com/question/2021001
#SPJ1
A number is divided by 3, and then 4 is added to the quotient. the result is 8 find the number
Answers
12 divided by 3 = 4 + 4 =8
Help solve the perimeter of this shape.
Answers
The perimeter CDE of the triangle is solved to be 9.66 (to the nearest hundredth)
How to find the perimeter of CDE
Given data
C ( 4, -1 )
D ( 4, -5)
E ( 2, -3 )
perimeter of CDE = CD + CE + DE
length = √(x2 - x1)^2 + (y2 - y1)^2
using C ( 4, -1 ) and D ( 2, -3 )
CD = √(4 - 4)^2 + (-1+5)^2
CD = √(4)^2
CD = 4
using C ( 4, -1 ) and E ( 2, -3 )
CE = √(4 - 2)^2 + (-1+3)^2
CE = √(2)^2 + (2)^2
CE = √8
using D ( 4, -5) and E ( 2, -3 )
CD = √(4 - 2)^2 + (-5 + 3)^2
CD = √(2)^2 + (-2)^2
CD = √8
the perimeter = 4 + √8 + √8
the perimeter = 4 + √8 + √8
the perimeter = 9.6568
the perimeter = 9.66 (to the nearest hundredth)
Read more on perimeter here: https://brainly.com/question/19819849
#SPJ1
John runs a cake bakery in his home town he wants to bake a chocolate cake needs 3 1/4 of melted chocolate milk and 2 1/2 of melted dark chocolate milk much will he need together?
Answers
Answer:
J.o.i.n p.l.z zfd-isvq-wrr
factor 3a^2b^2+15ab^3 please show work
Answers
Answer:
3ab²(a + 5b)
Step-by-step explanation:
3a²b² + 15ab³ ← factor out 3ab² from each term )
= 3ab²(a + 5b)
Katya is making rectangular table that is
3/4.The table has an area of
1 1/5 m2.How long is the table?
Answers
Answer:
which step by step
rectangular table
Simplify a raised to the negative two power over quantity 3 times b raised to the fourth power end quantity all cubed.
A: 1 over quantity 9 times a raised to the sixth power times b raised to the twelfth power end quantity
B: 1 over quantity 27 times a raised to the sixth power times b raised to the twelfth power end quantity
C: 27b12a6
D: quantity 27 times b raised to the twelfth power end quantity over a raised to the sixth power
Answers
The solution to simplifying the given expression using laws of exponents is; B: 1 over quantity 27 times a raised to the sixth power times b raised to the twelfth power end quantity
How to use laws of exponents?
Some of the Laws of Exponents are;
When multiplying similar bases, retain the base as same and add the exponents. When raising a base with a power raised to another one, retain the base the same and multiply the exponents. When dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent.We want to simplify a raised to the negative two power over quantity 3 times b raised to the fourth power end quantity all cubed. This is expressed as;
(a⁻²/3b⁴)³
Using the second law of exponent quoted above, we have;
(a⁻²*³)/(3³b⁴*³) = a⁻⁶/27b¹² = 1/a⁶27b¹²
Read more about Laws of Exponents at; https://brainly.com/question/11761858
#SPJ1
y = -2x - 4
y= 3x + 1
What is the solution to the system of equations?
Answers
Answer:
x = -1
y = -2
Step-by-step explanation:
We are given the following equations:
[tex]y = -2x - 4[/tex]
[tex]y = 3x + 1[/tex]
As we can see, the expressions [tex]{-2x - 4}[/tex] and [tex]3x + 1[/tex] are both equal to [tex]y[/tex]. Therefore, we can equate them:
[tex]-2x - 4 = 3x + 1[/tex]
Now we can solve for [tex]x[/tex] by making [tex]x[/tex] the subject of the equation:
⇒ [tex]-2x - 4 -3x = 3x + 1 - 3x[/tex] [Subtracting [tex]3x[/tex] from both sides]
⇒ [tex]-5x - 4 = 1[/tex]
⇒ [tex]-5x - 4 + 4 = 1 + 4[/tex] [Adding 4 to both sides of equation]
⇒ [tex]-5x = 5[/tex]
⇒ [tex]\frac{-5}{-5}x = \frac{5}{-5}[/tex] [Dividing both sides by -5]
⇒ [tex]x = \bf -1[/tex]
Now that we know the value of [tex]x[/tex], we can calculate the value of [tex]y[/tex] by replacing the [tex]x[/tex] with -1 in any of the equations for [tex]y[/tex] given above:
[tex]y = 3x + 1[/tex]
⇒ [tex]y = 3(-1) + 1[/tex]
⇒ [tex]y = -3 + 1[/tex]
⇒ [tex]y = \bf -2[/tex]
Therefore, the solution to the system of equations is : x = -1, y = -2.
Answer:
x = -1
y = -2
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}y = -2x - 4\\y= 3x + 1\end{cases}[/tex]
Use the method of substitution to solve for x:
[tex]\begin{aligned}& \textsf{Substitute}: & 3x+1 & = -2x-4\\& \textsf{Add $2x$ to both sides}: & 3x+1+2x & = -2x-4+2x\\& \textsf{Combine like terms}: & 5x+1 & = -4\\& \textsf{Subtract $1$ from both sides}: & 5x+1 -1& = -4-1\\& \textsf{Simplify}: & 5x & = -5\\& \textsf{Divide both sides by $5$}: & \dfrac{5x}{5} & = \dfrac{-5}{5}\\& \textsf{Simplify}: & x & = -1\end{aligned}[/tex]
Substitute the found value of x into one of the equations and solve for y:
[tex]\begin{aligned}& \textsf{Equation}: & y& = 3x+1\\& \textsf{Substitute in $x=-1$}: & y & = 3(-1)+1\\& \textsf{Multiply the numbers}: \quad & y & = -3+1\\& \textsf{Simplify}: & y & = -2\\\end{aligned}[/tex]
Therefore, the solution to the given systems of equations is (-1, -2).
Learn more about systems of equations here:
https://brainly.com/question/27868619