Answers
Answer:
Third Option
[tex]f(x) = 4x,\ g(x)=\frac{1}{4}x[/tex]
Step-by-step explanation:
For a function f(x) it is satisfied that the range of f(x) is equal to the domain of its inverse function. In the same way the domain of f(x) is equal to the range of its inverse.
Therefore, to verify which pair of functions are inverse to each other, perform the composition of both functions and you must obtain
[tex]f(g(x)) = x[/tex] and [tex]g(f(x)) = x[/tex]
For the first option we have:
[tex]f(x) = x,\ g(x)=-x[/tex]
Then
[tex]f(g(x)) = (-x) = -x[/tex] They are not inverse functions
For the second option we have:
[tex]f(x) = 2x,\ g(x)=-\frac{1}{2}x[/tex]
Then
[tex]f(g(x)) = 2(-\frac{1}{2}x) = -x[/tex] They are not inverse functions
For the third option we have:
[tex]f(x) = 4x,\ g(x)=\frac{1}{4}x[/tex]
Then
[tex]f(g(x)) = 4(\frac{1}{4}x) = x[/tex]
[tex]g(f(x)) = \frac{1}{4}(4x) = x[/tex] They are inverse functions
For the fourth option we have:
[tex]f(x) = -8x,\ g(x)=8x[/tex]
Then
[tex]f(g(x)) = -8(8x) = -64x[/tex] They are not inverse functions
Related Questions
<1 and <2 are adjacent angles.
a.) True
b.) False
Answers
Answer:
True, ∠1 and ∠2 are adjacent angles. True
Explanation:
Definition of adjacent angles: Two angles are called adjacent angles if
1. They have a common side
2. Common vertex (corner point)
3. They don't overlap.
Further Explanation:
In the given figure two lines are intersecting each other and form 4 angles, ∠1, ∠2, ∠3 and ∠4.
From the given figure it is clear that, the common vertex of all angles is the point of intersection of both lines. The pairs of adjacent angles are
(i) ∠1 and ∠2
(ii) ∠2 and ∠3
(iii) ∠3 and ∠4
(iv) ∠1 and ∠4
Therefore, ∠1 and ∠2 are adjacent angles and the given statement is true.
Learn More:
Adjacent angles : https://brainly.com/question/11933939 (Answered by MollieToliver)
Adjacent angles : https://brainly.com/question/12256805 (Answered by ApusApus)
Keywords:
Adjacent angles, Intersection of two lines.
When we have an intersection of two lines, four angles are created in that intersection.
With this, we define two adjacent angles as a pair of angles that is separated by one of the lines.
In the image, we can see that:
∠1 and ∠2 are adjacent
∠2 and ∠3 are adjacent
∠3 and ∠4 are adjacent
∠4 and ∠1 are adjacent.
Then the statement:
"∠1 and ∠2 are adjacent"
Is true, by definition of adjacent angles.
If you want to learn more, you can read:
https://brainly.com/question/12838185
A pot of stew is placed on a stove to heat. The temperature of the liquid reaches 170°F, and then the pot is taken off the burner and placed on a kitchen counter. The temperature of the air in the kitchen is 76°F.
If k = 0.34, the temperature of the liquid after 7 hours will be
ºF. (Hint: Use Newton’s cooling model.)
Answers
Final answer:
To calculate the temperature of the liquid after 7 hours, you can use Newton's cooling model. By plugging in the initial temperature, the surrounding temperature, and the cooling constant into the equation T = T0 + (T1 - T0) * e(-kt), you can calculate the temperature after 7 hours. In this case, the temperature after 7 hours is approximately 152.85°F.
Explanation:
In this problem, we can use Newton's cooling model to determine the temperature of the liquid after 7 hours. Newton's cooling model states that the rate of heat loss or gain is directly proportional to the temperature difference between the object and its surroundings. Using the equation T = T0 + (T1 - T0) * e(-kt), where T is the temperature at time t, T0 is the initial temperature, T1 is the surrounding temperature, k is the cooling constant, and e is the base of the natural logarithm, we can calculate the temperature after 7 hours.
Convert the initial temperature, the surrounding temperature, and the time to Kelvin.
Plug the values into the equation and calculate the temperature after 7 hours.
Using the given values of T0 = 170°F, T1 = 76°F, and k = 0.34, we can calculate the temperature after 7 hours.
T0 = 170°F + 459.67 = 629.67 K
T1 = 76°F + 459.67 = 535.67 K
T = 629.67 + (535.67 - 629.67) * e⁻°³⁴*⁷
T ≈ 152.85°F
let f(x)=x^2-2x+2 and g(x)=x-3 find f(x)•g(x)
Answers
Answer:
[tex]\large\boxed{x^3-5x^2+8x-6}[/tex]
Step-by-step explanation:
[tex]f(x)=x^2-2x+2\\\\g(x)=x-3\\\\f(x)\cdot g(x)=(x^2-2x+2)(x-3)\qquad\text{use}\ \bold{FOIL}:\ (a+b)(c+d)=ac+ad+bc+bd\\\\f(x)\cdot g(x)=(x^2)(x)+(x^2)(-3)+(-2x)(x)+(-2x)(-3)+(2)(x)+(2)(-3)\\\\f(x)\cdot g(x)=x^3-3x^2-2x^2+6x+2x-6\qquad\text{combine like terms}\\\\f(x)\cdot g(x)=x^3+(-3x^2-2x^2)+(6x+2x)-6\\\\f(x)\cdot g(x)=x^3-5x^2+8x-6[/tex]
write the slope intercept inequality (0,2) (-1,-2)
Answers
Hey there! :)
(0, 2) & (-1, -2)
Slope-intercept form is : y=mx+b , where m=slope, b=y-intercept
First, we must find the slope using the slope formula, which is :
m = y2-y1/x2-x1
Where y2 = -2 ; y1 = 2 ; x2 = -1 ; x1 = 0
Now, let's plug and chug! :)
m = (-2 - 2) / (-1 - 0)
Simplify.
m = -4/-1 --> Therefore, our slope is : m = 4
Now that we have the slope, we can plug this (and our original coordinates) into point-slope form, which is : y - y1 = m(x - x1) -> use the coordinates (0, 2)
y - 2 = 4(x - 0)
Simplify.
y - 2 = 4x
Add 2 to both sides.
y = 4x + 2
Hope this helped! :)
f(y) = 8y2 – 7y + 6. What is the constant of the function?
Answers
Answer:
+ 6
Step-by-step explanation:
The constant term in the function is the term which is only numeric and has no variable attached to it.
f(y) = 8y² - 7y + 6 → has constant term + 6
Solve the proportion below. X/18= 8.5/17 x=?
Answers
Answer:
x=9
Step-by-step explanation:
we have been given the following proportion;
x/18 = 8.5/17
we are required to solve for x. In order to solve for x, we simply make x the subject on the left hand side . This can be done by multiplying both sides by 18;
(x/18)*18 = (8.5/17)*18
x = 153/17
x = 9
Answer:
9
Step-by-step explanation:
Given: △EIJ, k(O, r)
EI = EJ = r=10 cm
EP ⊥ IJ
Find: JP
Answers
Answer:
[tex]JP=5\sqrt{3}\ cm[/tex]
Step-by-step explanation:
Connecting points O and E and points O and J, we get triangle EOJ. This triangle is equilateral triangle, because OJ=OE=JE=r=10 cm.
Since EP⊥IJ, then segment JP is the height of the triangle EOJ.
The height of the equilateral triangle can be found using formula
[tex]h=\dfrac{a\sqrt{3}}{2},[/tex]
where a is the side length.
So,
[tex]h=\dfrac{10\sqrt{3}}{2}=5\sqrt{3}\ cm.[/tex]
What’s y (Solve and show work): 3(y-2)= -21
Answers
I attached an image doing it out
Answer:
y = -5
Step-by-step explanation:
Equation:
3( y - 2 ) = -21
3y - 6 = -21
3y = -21 + 6
3y = -15
y = [tex]\frac{-15}{3}[/tex]
y = -5
What is the domain of y= 2x - 4/x^2 - 4?
Answers
Answer:
{x while x ≠2, -2}
Step-by-step explanation:
First let's define domain,
Domain is the set of all values on which the function is defined i.e. the function doesn't approach to infinity.
Given function is:
[tex]y = \frac{2x-4}{x^{2} -4}[/tex]
We will look for all the values of x on which the function will become undefined:
We can see that x= 2 and x=-2 will make the denominator zero as there is x^2 involved. The denominator zero will make the function undefined.
So, the domain of the function is set of all real numbers except 2 nd -2 {x while x ≠2, -2} ..
Answer:
[tex](-\infty,-2)\cup (-2,2)\cup (2,+\infty)[/tex]
Step-by-step explanation:
The given rational expression is:
[tex]y=\frac{2x-4}{x^2-4}[/tex]
We factor this expression to obtain:
[tex]y=\frac{2(x-2)}{(x-2)(x+2)}[/tex]
We can see that, this rational function has a hole at x=2 and a vertical asymptote at x=-2
Therefore the domain is
[tex]x\ne 2\: and\:x\ne -2[/tex]
Or
[tex](-\infty,-2)\cup (-2,2)\cup (2,+\infty)[/tex]
Mr. bean just won the lottery and is going to pay it forward! He's going to give students he see's in the hall $4 and teachers he see's in the hall $7. even though he won $100,000,000,000 he's only willing to give out $100
a) create an equation to model this situation
b) solve your equation in terms of the variable you designated for the number of students that mr. bean gave money to
Answers
Answer:
a) 4x +7y =100 b) 4x = 100-7y
Step-by-step explanation:
students = 4x
teachers = 7y
4x +7y = 100
4x =100 -7y
Final answer:
The equation is solved to determine the number of students Mr. Bean gave money to as 2.
Explanation:
a) Equation:
Let x be the number of students and y be the number of teachers Mr. Bean gave money to.
Equation: 4x + 7y = 100
b) Solving the equation:
Given that Mr. Bean only gave out $100, we substitute this into the equation:
4x + 7y = 100
4x + 7(14-x) = 100
4x + 98 - 7x = 100
98 - 3x = 100
-3x = 2
x = -2/-3 = 2/3
Therefore, Mr. Bean gave money to 2 students.
Learn more about Equation solving here:
What is the common between 2,8, 14, 20, 26
Answers
Answer:
So i believe the answer is 2.
Step-by-step explanation:
The common denominator? Right? If so
2: 1 and 2
8: 1,8,2, and 4
14: 1,14,2, and 7
20:,1,20,2,10,4, and 5
26:1,26,13, and 2
Hope my answer has helped you!
Which binomial is equivalent to (xy + z)(xy − z)?
Answers
Final answer:
The binomial equivalent to (xy + z)(xy - z) is found by applying the difference of squares formula, resulting in x²y² - z².
Explanation:
The question asks which binomial is equivalent to the expression (xy + z)(xy - z). This can be simplified using the difference of squares formula, which is a² - b² = (a + b)(a - b). In this case, a is xy and b is z.
Applying the formula, we have:
First, square a: (xy)² = x²y²
Then, square b: z²
Subtract the square of b from the square of a to get the answer: x²y² - z²
Therefore, the binomial equivalent to (xy + z)(xy - z) is x²y² - z².
If f(x) = 4x + 5, which of these is the inverse of f(x)?
Answers
Answer:
A
Step-by-step explanation:
y=4x+5
x=4y+5
4y+5=x
4y+5-5=x-5
4y=x-5
4y/4= x/4 - 5/4
y= x-5/4
To find the inverse of the function f(x) = 4x + 5, switch x and y in the equation, then solve for y to get the inverse function, which is f-1(x) = (x - 5) / 4.
Explanation:To find the inverse of the function f(x) = 4x + 5, you would follow these steps:
Replace f(x) with y: y = 4x + 5.Switch the roles of x and y: x = 4y + 5.Solve the equation for y to find the inverse function:Subtract 5 from both sides: x - 5 = 4y.Divide by 4: y = (x - 5) / 4.The inverse function is: f-1(x) = (x - 5) / 4.This inverse function will satisfy the condition that f(f-1(x)) = x and f-1(f(x)) = x, which is the defining property of an inverse function.
Which of the following is a solution of y > |x| - 6?
(-5, 1)
(-1, -5)
(5, -1)
Answers
ANSWER
(-5,1) is the correct answer
EXPLANATION
The given inequality is:
[tex]y \: > \: |x|- 6[/tex]
If any point satisfies this inequality, then it is a solution.
We need to substitute each point into the given inequality.
We substitute (-5,1) to get:
[tex]1\: > \: | - 5|- 6 \implies1\: > \: - 1[/tex]
This statement is true. Hence (-5,1) is a solution.
For (-1,-5), we have
[tex] - 5\: > \: | - 1|- 6 \implies - 5\: > \: - 5[/tex]
This is false.
For (5,-1), we have
[tex] - 1\: > \: | 5|- 6 \implies - 1\: > \: - 1[/tex]
This is also false.
Answer:
(-5,1) is the correct answer
What is the relationship between the volume and surface area of the sphere shown?
a. V < SA
b. V = SA
c. V > SA
Will give brainliest!
Answers
Answer:
B
Step-by-step explanation:
V=4/3 x 3.14 x 3^3
V= 113.04
SA= 4 x 3.14 x 3^2
SA= 113.04
Answer:
The answer is V=SA
Step-by-step explanation:
V=4/3 x 3.14 x 3^3
V= 113.04
SA= 4 x 3.14 x 3^2
SA= 113.04
So the relationship should be V=SA, because the equaled amount on both ends was the same.
Given the function f(x) = 2x + 6/x^2 + 5x + 6 , evaluate the function with the domain values {-3, -2, 0, 2, 3}. What is the valid domain of this function? Show all work.
Answers
Answer:
domain; x<0 or x>0
Step-by-step explanation:
We have been given the following function;
f(x) = 2x + 6/x^2 + 5x + 6
We need to evaluate the values of f(x) for the following domain values;
{-3, -2, 0, 2, 3}
f(-3) = 2(-3) + 6/(-3)^2 + 5(-3) + 6
= -43/3
f(-2) = 2(-2) + 6/(-2)^2 + 5(-2) + 6
= -6.5
f(0) = 2(0) + 6/(0)^2 + 5(0) + 6
= undefined
f(2) = 2(2) + 6/(2)^2 + 5(2) + 6
= 21.5
f(3) = 2(3) + 6/(3)^2 + 5(3) + 6
= 83/3
The function is real and defined for every value of x in its domain except where x = 0 . This is a point of discontinuity.
Find the attachment below;
Nick and June win some money and share it in the ratio 5:3. Nick gets £26 more than June. How much did June get?
Answers
The difference between the ratio 5:3 is 2 ( 5-3 = 2)
Nick gets 2 extra shares which is equal to £26
1 share = 26 / 2 = 13
June gets 3 shares: 3 x 13 = £39
June gets 3 shares: 3 x 13 is equal to the $39.
Nick and June win some money and share it in the ratio of 5:3.
Nick gets $26 more than June.
What is the difference?The word difference is the result of subtracting one number from another.
The difference between the ratio of 5:3 is 2 ( 5-3 = 2)
Nick gets 2 extra shares which is equal to $26.
1 share = 26 / 2 = 13
June gets 3 shares: 3 x 13 is equal to the $39.
To learn more about the amount visit:
https://brainly.com/question/1153322
#SPJ2
9. David had $350. After shopping, he was left with $235. If c represents the amount he spent, write an equation to represent
this situation. Then use the equation to find the amount of money David spent.
Answers
Answer: meow 1. −6z + 13 = −11z − 7
2. 6 + 17z = 13z + 18
3. 4
5 k – 5 = –7 +
2
5 k
4. − 4
5 w +
1
4 =
1
5 +
1
3 w
5. 15(−42x + 40) = 15(−8x + 244)
6. 4 – 3
5 (3a + 4) = 7
7. 1
2 (15 + 7d) = − d
Step-by-step explanation:
Answer:
The amount of money David spent is $115.
Step-by-step explanation:
Consider the provided information.
David had $350. After shopping, he was left with $235.
Let the money spent by David is c.
As some money are spent from the total amount, So use a "-" sign and put the equation equals to 235, as this is the amount he left with.
The equation can be represented as:
350 - c = 235
Now simplify the above equation in order to find the money spent by David.
Isolate the variable by adding c and subtracting 235 from both sides.
350 - c + c -235 = 235 + c -235
115 = c
Hence, the amount of money David spent is $115.
How to do it? Its URGENT!!!I need it right now!!!?!? I will give 10 points! Pls!!!
Answers
Answer: $360
Step-by-step explanation:
Let Mp the manufacturing price.
First step:
Manufacturer sells at a profit of 25% = Mp + Mp·0.25 = Mp·1.25
Second step:
Agency sells at a profit of 10% = 1.25Mp + 1.25Mp·0.10 = Mp·1.375
Third step:
Shopkeeper sells at a profit of 20% = 1.375Mp + 1.375Mp·0.20 = Mp·1.65
Then the final price = 1.65·Mp
1.65Mp = $594
Mp = $594/1.65 = $360 ►Manufacturer price
Answer: $360
Verification
Manufacturer sells at a profit of 25% = 25/100 = 0.25:
$360 + $360·0.25 = $360(1 + 0.25) = $360 + $90 = $450
Agency sells at a profit of 10% = 10/100 = 0.10:
$450 + $450·0.10 = $450(1 + 0.10) = $450 + $45 = $495
Shopkeeper sells at a profit of 20% = 20/100 = 0.20
$495 + $495·0.20 = $495(1 + 0.20) = $495 + $99 = $594 Checked!
[tex]\textit{\textbf{Spymore}}[/tex]
Select all that apply.
Given the points (3, 2) and (6,4), which of the following are true about the line passing through these points?
The line has a slope of 3/2
The line represents a direct variation function.
The line has a slope of 2/3
The point (-6.9) is also on the line.
Answers
Answer: The line represents a direct variation function.
Step-by-step explanation: Rest of them are not true. for 1 and 3, plug in the x and y value to the equation y=mx + b.
(x,y)
the average speed of a train, r, is found by dividing its distance traveled, d, by its time spent traveling, t. Write a formula for the average speed of a train. Then solve the formula for d.
Answers
Answer: distance = rate x time
Step-by-step explanation: divided by distance then multiply by rate
You select a card from a standard shuffled deck of 52 cards. Without replacing, you select another card. Find the probability that you select a black card, then a red card.
Answers
In a standard shuffled deck of 52 cards, half of the cards are black and half of the cards are red: (26 black cards, 26 red cards).
Since we are interested in pulling a black card first, the probability is 26/52.
Without replacing the card we have chosen, we are left with 51 total cards in the entire deck (25 black cards, 26 red cards).
Now that we want to pull a red card, we know that the probability will be 26/51.
Since we are interested in both events occurring simultaneously, we must multiply the probability of the first by the probability of the second, aka: (26/52) * (26/51)
The answer we are given is 0.2549
The probability of picking a black card and then a red card from a standard deck without replacement is 13/51.
To calculate the probability of selecting a black card and then a red card from a standard deck without replacement, we need to consider the sequence of the two events. Initially, the deck contains 26 black cards (spades and clubs) and 26 red cards (diamonds and hearts). The probability P(A) of picking a black card first is 26/52 or 1/2.
After one black card has been removed, there are now 51 cards left in the deck with 26 red cards remaining. The probability P(B) of then picking a red card is 26/51. To find the overall probability of both events happening in sequence, we multiply the probabilities:
[tex]P(A and B) = P(A) \times P(B) = (\frac{1}{2}) \times (\frac{26}{51})[/tex]
This simplifies to P(A and B) = [tex](\frac{26}{102})[/tex] which can be further simplified to [tex](\frac{13}{51}).[/tex]
independent of dependent plzzz help
Answers
Answer:first one is dependent
second one is independent
Step-by-step explanation:
I do exercises on it
BC is tangent to circle A at point B. What is m2ACB if mZCAB = 22° ?
Answers
Answer:
68°
Step-by-step explanation:
We know that sum of 3 angles in a triangle is 180°.
In ΔBAC, there are angles B, A, and C. Thus we can say:
B + A + C = 180
Since, BC is tangent to circle, the point of tangency, B is a 90 degree angle. So angle B is 90.
Also, given angle CAB is 22, which, in other word, is angle A is 22.
Thus, we can write:
B + A + C = 180
90 + 22 + C = 180
112 + C = 180
C = 180 - 112 = 68
Measure of angle ACB = 68°
The measure of angle ACB is 68°.
We know that sum of 3 angles in a triangle is 180°.
In ΔBAC, there are angles B, A, and C. Thus we can say:
B + A + C = 180
Since, BC is tangent to circle, the point of tangency, B is a 90 degree angle. So angle B is 90.
Also, given angle CAB is 22, which, in other word, is angle A is 22.
Thus, we can write:
B + A + C = 180
90 + 22 + C = 180
112 + C = 180
C = 180 - 112 = 68
5x(2)
Explain to me please
Thanks
Answers
Answer:
10x
Step-by-step explanation:
5x(2)
When this is simplified, the answer is 10x
5x(2)
5x multiplied by 2 is 10x
The answer is 10x
This is because 5x is being multiplied by 2. We know this because parentheses are one of the several symbols of multiplication.
Even though 5 has an x attached to it you can just ignore it for now, multiply 2 to the 5 then just reattach the x at the end of your answer
Hope this helped!
~Just a girl in love with Shawn Mendes
Ruth bought cutter s and screwdrivers to upgrade the computers in her company. A cutter costs 15.2$ and a screw driver costs $2. She bought a total of 29 tools and spent 150.40$. how many of each tool did ruth buy?
Answers
solve it with a system
x=screwdriver
y=cutter
x+y=29
2x+15.2y=150.40
PLEASE ANSWER RIGHT AWAY
Answers
Second from top down
What is 10% of $4.30 ?
Answers
Answer: 0.43
Step-by-step explanation: if you ever need help like this for percentages again i just use this website its reallyyyy helpful :) https://percentagecalculator.net/
$4.30 times 0.1
4.30 x .1
•Answer:0.43
what is this simplified?
Answers
Answer:
2 time 5 squared is simplified form of 60 they both get the end result of 7.4
Step-by-step explanation:
Answer:
The correct answer is second option
2√15
Step-by-step explanation:
From the attached question we can see that,
√60
To find the value of √60
We know that, 60 = 4 * 15
and √4 = 2
Therefore √60 can be written as,
√60 = √(4 * 15)
= 2√15
The correct answer is 2√15
Therefore the correct option is second option.
√60 = 2√15
Determine whether the function f(x) = -2x - 5x is even, odd, or neither.
Answers
Answer: odd
Step-by-step explanation:
A function is even if for any input value x and -x there is the same output value y. In other words, a function is even if:
[tex]f (-x) = f (x)[/tex]
A function is odd if it is true that:
[tex]f (-x) = -f (x)[/tex]
Then we must test if [tex]f(-x) = f(x)[/tex] for the function: [tex]f(x)=-2x - 5x[/tex]
[tex]f(-x)=-2(-x) - 5(-x)[/tex]
[tex]f(-x)=2x + 5x[/tex]
So [tex]f(-x) \neq f(x)[/tex]
The function is not even
Now we must test if [tex]f (-x) = -f (x)[/tex] for the function.
[tex]f(-x)=-2(-x) - 5(-x)[/tex]
[tex]f(-x)=2x + 5x[/tex]
[tex]f(-x)=-(-2x -5x)[/tex] and [tex]f(x)=-2x - 5x[/tex]
So [tex]f(-x) = -f(x)[/tex]
Finally the function is odd