Answer:
[tex]t = 18.9[/tex]
Information given :
We know that:
- Element X is a radioactive isotope such that every 20 years, its mass decreases by half
- the initial mass of a sample of Element X is 770 grams
And we must find how long it would be until the mass of the sample reached 400 grams
Step-by-step explanation:
To find it, we need to use the following formula:-
[tex]A(t) = A(0)(0.5)^{\frac{t}{20} }[/tex]
- A(0) is the initial amount
From given information, A(0) = 770 grams
Now, replacing the value in t :
[tex]A(t) = (770)(0.5)^{\frac{t}{20} }[/tex]
Then, we must solve for t :-
[tex]400 = 770(0.5)^{\frac{t}{20} } \\\frac{400}{700}= (0.5)^{\frac{t}{20} } \\\\ 0.51948 = (0.5)^{\frac{t}{20} } \\\\log(0.51948) = log((0.5)^{\frac{t}{20} }) \\\\\\log(0.519,48) = \frac{t}{20} log (0.5)\\t=\frac{20*log(0.519,48)}{log(0.5)} \\t=\frac{20(-0.284431}{-0.301029} \\giving\\t=18.9[/tex]
Hope this helps you out and if does so just mark me as brainliest as this answer took a lot of time to plot down so that it acts as a fuel to your learning,
Stay positive,
a fellow comrade,
Cheers !
Use a law of exponents to write (-3mn^5)^4 as a product of powers
The exponent is 81[tex]m^{} 4[/tex] [tex]n^{20}[/tex]
Here we have to determine the sign for exponential or radical expression
(-3m[tex]n^{5}[/tex])^4
Simplify using the exponent rule with the same exponent [tex](ab)^{n}[/tex] = [tex]a^{n}[/tex] . [tex]b^{n}[/tex]
Similarly
(-3m[tex]n^{5}[/tex])^4
= [tex](-3)^{4}[/tex] . [tex]m^{4}[/tex]. [tex](n^{5} )^{4}[/tex]
Now using the exponent power rule [tex](a^{n} )^{m}[/tex] = [tex]a^{nm}[/tex]. We get
= 81 . [tex]m^{4}[/tex].[tex]n^{20}[/tex]
Therefore the exponent as a product of power is 81[tex]m^{4} n^{20}[/tex].
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how do we do this one there three parts to it
Given the following question:
Part A:
Your answer is option B, you can find this by checking the values. We are given 107, 128, 163, 212, 275 if you check the values on the graph, you can see that they are exact. So, your answer is option B.
Given a || b , and c is not parallel to a or b, which statements must be true? a 1/2 3 / 4 Select each correct answer b . 5/6 7/8 mZ2 = m_7 9/10 C m27 = m_10 11 / 12 mZ8 = m29 m24 = m28
m∠2 = m∠7
and
m∠4 = m∠8
Both are correct answers and should be ticked
Here, we want to select which of the statements must be correct based on the diagram given
a) m∠2 = m∠7
This is correct
m∠2 = m∠3 as they are vertically opposite angles
However, m∠3 = m∠7 as they are vertically opposite angles
b) m∠7 = m∠10
We cannot compare the relationship between b and c as the pair are not parallel lines
c) m∠8 = m∠9
This is not correct also as the pair of lines are not parallel
d) m∠4 = m∠8
These two are corresponding angles, so they are congruent and thus equal in value
Is a tutor availible
So if i have a bag of rice of 3.5 pounds, that means that it weighs:
[tex]3.5\text{ pounds = 56 ounces}[/tex]since
[tex]3.5\text{ x 16 = 56}[/tex]that means that you will have enough rice for the recipe
If x = 2 and y=-3, then xy^2 =
Step-by-step explanation:
Answer:
-18
Step-by-step explanation:
-xy^2 =
Let x=2 and y = -3
-(2) (-3)^2
-2 (9)
-18
Answer:
18.
Step-by-step explanation:
(2)(-3)^2
Parentheses first. There's nothing to do so, the exponent is next. -3^2 is 9. 9 * 2 = 18.
Hope this helps! :)
Assuming the population has an approximate normal distribution,
if a sample size n = 12 has a sample mean
= 36 with a sample standard deviations = 9, find the margin of error at a 98% confidence level. Round
the answer to two decimal places.
E = 38.33 the margin of error at a 98% confidence level by standard deviation mean.
What does standard deviation mean ?
The term "standard deviation" (or "") refers to a measurement of the data's divergence from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.The average degree of variability in your dataset is represented by the standard deviation. It reveals the average error of each statistic from the mean.Given that,
bar x = 36
s = 9
n = 12
Degrees of freedom = df = n - 1 =12 - 1 = 11
At 98% confidence level the t is ,
∝ = 1 - 98% = 1 - 0.98 ⇒ 0.02
∝/2 = 0.02/2 = 0.01
t∝/2 df = t0.01 ,11 = 1.231
Margin of error = E = t∝/2, df * ( s/n/sqrtn)
E = 1.231 * ( 9 /0.01/sqrt12)
E = 38.33
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Emily works at a factory that makes computer parts. The machine that produces internal hard drives results in a certain number of defects during the day. The table below represents the probability density function for the random variable X, the number of defects per day. Find the standard deviation of X. Round the final answer to two decimal places.
The standard deviation of the discrete distribution of the number of defects in a day is of 0.75 defects.
What are the mean and the standard deviation of a discrete distribution?The mean of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.The standard deviation of a discrete distribution is given by the square root of the sum of the difference squared between each outcome and the mean, multiplied by it's respective probability.From the distribution at the end of the answer, the mean is:
E(X) = 0.1667 x 4 + 0.3333 x 5 + 0.5 x 6 = 5.3333.
Hence the standard deviation is of:
S(X) = sqrt(0.1667 x (4-5.3333)² + 0.3333 x (5 - 5.3333)² + 0.5 x (6 - 5.3333)²) = 0.75 defects.
What is the missing information?The distribution is missing, and is given as follows:
P(X = 4) = 0.1667.P(X = 5) = 0.3333.P(X = 6) = 0.5.More can be learned about the standard deviation of a discrete distribution at https://brainly.com/question/19054123
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You went to an action figure shop to buy a figure of your favorite anime character. The purchase price was $20, and the selling price was $30. You gave the shop owner $100, but the owner didn't have any change. So he went to the neighboring shop, got change for $100, and gave you $70. Unfortunately, the neighboring shop owner found out that the 100-dollar bill given to him was fake, so he went to the action figure shop and got back his change of $100. Now the question is, how much did the owner of the action figure store lose in total?
The owner loses the figure and the $70 that gives back, so the total amount he loses is $90.
How much did the owner of the action figure store lose in total?
We know that the owner initially has a figure whose price is $20, and he sells it for $30.
Then, he sells it for a $100 bill, so he gives $70 back.
The problem is that the $100 bill was fake, so at this point the total amount that he loses is:
The value of the action figure (which is $20) plus the $70 that he gives back.
Adding these two we get:
$20 + $70 = $90
The owner loses $90 in total.
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What is the distance between points A(2,9) and B(-2,6)? Round to the nearest whole number.
The distance between the two points is 5.
The formula to find the distance between two points (x1, y1) and (x2, y2)
distance = [tex]\sqrt{(x2-x1)^{2} + (\\ y2-y1)^{2} }[/tex]
Substituting points A(2,9) and B(-2,6), we get
distance = [tex]\sqrt{(-2-2)^{2} + ( 6-9)^{2} }[/tex]
=[tex]\sqrt{(-4)^{2} + (-3)^{2} }[/tex]
= [tex]\sqrt{16 + 9}[/tex]
=[tex]\sqrt{25}[/tex]
= 5
Therefore the distance between the two points is 5.
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A wheel on Amanda's bicycle is 0.3 m in diameter. Amanda races the bicycle for 35 m. How many times does the wheel turn as the bicycle travels this distance?
Use the value 3,14 for π. Round your answer to the nearest tenth. Do not round any intermediate steps.
Answer:
37.2 rotations
Step-by-step explanation:
35 / (3.14 x .3) = 37.15499
Rounded = 37.2 rotations
Riders for the Kiddie Koaster at the State Fair must be no more than 48 inches tall. Which inequality best expresses the height of the riders?
Answer:Note that at least means greater than or equal to (≥) . It was stated that you must be at least 48 inches tall to ride the roller coaster. Hence, the inequality is h≥48 h ≥ 48
Step-by-step explanation: poopity poop UWU UWU UWU oodfijdisfioahgioahiodfhipodioajhierfia MUSIC MUSIC MUSIC MUSIC MUSIC MUSIC HACKER HACKER HAKER HACKER HACKER OMG UWU UWU UWU YOUR 13 LOL YOUR FATHERLESS GT DELETED TRASH KID
Together, Luke and James have never eaten more than 16 pieces of pizza at one time.Which equation describes y, the total number of pieces that Luke has eaten at one time givenx, the number of pieces that James has eaten?a. y <_16-x b. y>_16-x c. y=16-x d. not here
y ≤ 16 - x (option A)
Explanation:let the total number of pieces Luke ate at a time = y
Let the total number of pieces James ate at a time = x
They have never eaten more than 16 pices of pizza
This is written as:
maximum 16 : ≤ 16
number of pieces Luke ate at a time + total number of pieces James ate at a time ≤ 16
y + x ≤ 16
rewritting to make y subject of formula:
y ≤ 16 - x (option A)
Matt and Wei are selling boxes of fruit for a Habitat for Humanity fundraiser. Customers can buy small boxes of fruit and large boxes of fruit. Matt sold 18 small boxes of fruit and 25 large boxes of fruit for a total of $529.50. Wei sold 18 small boxes of fruit and 10 large boxes of fruit for a total of $282.00. Find the cost of one small box of fruit and the cost of one large box of fruit.
Answer:
The small box price is 6.5 and The large box price is 16.5
Step-by-step explanation:
I did the question with a simultaneous equation
let's say the price of the small box = x and the price of the large box = y
Then, I just subtract downward;
18x+25y=529.50
- 18x+10y=282.00
_____________
0+15y=247.50
15y=247.50
— ————
15 15
I just canceled 15 by 15:
Then, y=247.50÷15=16.5
so I just find the value of Y which is 16.5, then I insert it into the second equation:
18x+10y=282
18x+10(16.5)=282
18x+165=282
18x=282-165
18x=117
— —
18 18
Cancel 18 by 18
finally x=6.5
Insert x and y into both equations, it works
Shureka Washburn has scores of 86, 84, 83, and 49 on her algebra tests.
a. Use an inequality to find the scores she must make on the final exam to pass the course with an average of 76 or higher, given that the final exam counts as two tests.
b. Explain the meaning of the answer to part (a).
The most appropriate choice for average will be given by-
Shureka Washburn must get 78 or higher in her final exam to make her average 76 or higher.
What is average?
In a data set, there are many numbers. Average is the single number which acts as a representative of all the numbers in the data set.
Average is calculated by sum of all observations divided by total number of observations.
Here,
Let the score of Shureka Washburn in her last test be x
Score of Shurek Washburn on first test = 86
Score of Shurek Washburn on second test = 84
Score of Shurek Washburn on third test = 83
Score of Shurek Washburn on fourth test = 49
Total sum of all her scores = 86 + 84 + 83 + 49 + x
= 302 + x
Average = [tex]\frac{302 + x }{5}[/tex]
By the problem,
[tex]\frac{302 + x}{5} \geq 76[/tex]
[tex]302 + x \geq 76[/tex] [tex]\times 5[/tex]
[tex]302 + x \geq 380[/tex]
[tex]x \geq 380 - 302[/tex]
[tex]x \geq 78[/tex]
Shureka Washburn must get 78 or higher in her final exam to make her average 76 or higher.
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[(2,0)((-1, 3){(1,0)[(-1, -3)(0, 2)[(-3,-1)]Line 1Line 2Point of Intersection(0, 2). (-5, -3)(0,5). (-5, -5)(-2, 1), (-3,-1)(0, 2), (2,0)(4,-2), (1,1)(4,2), (0, -2)(2,-2), (0, 2)(2, 1), (3, 2)ResetNext
Line (0, 2), (-5, -3) ---> y = x + 2
Line (0, 5), (-5, -5) ---> y = 2x + 5
Point of intersection ---> we need to equate both equations:
[tex]x+2=2x+5\Rightarrow-5+2=2x-x\Rightarrow-3=x[/tex]If x = -3 ---> y = -3 + 2 ---> y = -1
The point of intersection in this case is (-3, -1) (the last one, from left to right).
Second caseLine (-2, 1), (-3, -1) ---> y = 2x + 5
Line (0, 2), (2, 0) ---> y = -x + 2
Equating both equations to find the intersection point:
[tex]2x+5=-x+2\Rightarrow2x+x=2-5\Rightarrow3x=-3\Rightarrow x=-1[/tex]If x = -1, then y = -(-1) + 2 ---> y = 1 + 2 ---> y = 3
The point of intersection is (-1, 3) (the second one, from left to right).
Third caseLine (4, -2), (1, 1) ---> y = -x +2
Line (4, 2), (0, -2) ---> y = x - 2
Then, we have ---> intersection point:
[tex]-x+2=x-2\Rightarrow2+2=x+x\Rightarrow4=2x\Rightarrow x=2[/tex]Using the second equation to find y ---> y = 2 -2 ---> y = 0
The point of intersection is (2, 0) (the first point, from left to right).
Fourth caseLine (2, -2) (0, 2) ---> y = -2x + 2
Line (2, 1), (3, 2) ---> y = x - 1
Then, we have:
[tex]-2x+2=x-1\Rightarrow1+2=x+2x\Rightarrow3=3x\Rightarrow x=1[/tex]Using the second equation to find y ---> y = 1 - 1 ---> y = 0
The point of intesection is (1, 0) ( the third point, from left to right).
7.
Write and solve the system of equations needed to model this situation: You have thirty coins
a total value of $3.40, which are made up of nickels, dimes, and quarters. There are twice as many
nickels than quarters. How many of each type of coin do you have?
The system of equations for the given conditions in question includes equation: 3.40 = 0.05x + 0.1y + 0.25z, and 2x = z. and we have 2 nickels, 23 dimes, and 4 quarters.
What is system of equations?
A system of equations is a collection of some equations with one or more numbers of variables. Systems of equations have solutions that are either the variable mappings that satisfy each component equation or the intersections of all of these equations.
Let the quantities of nickels, dimes, and quarters are x, y, and z respectively.
We know that, 1 nickel = $0.05, 1 dime = $0.1, and 1 quarter = $0.25
So, the values of nickels, dimes, and quarters would be value of one times total quantity.
Nickels = 0.05x, dimes = 0.1y, and quarters = 0.25z
As given in the question, the total value is 3.40
So, we get equation:
3.40 = 0.05x + 0.1y + 0.25z
Also it is given that there are twice as many nickels than quarters.
2x = z
Combining above two equations
3.40 = 0.05x + 0.1y + 0.25(2x)
3.40 = 0.05x + 0.1y + 0.5x
3.40 = 0.55x + 0.1y
Lets put 2 in place of x, we get y
(3.40 - 1.1)0.1 = y
y = 23.
Now, putting values of x, y in equation to get value of z
3.40 = 0.05(2) + 0.1(23) + 0.25z
3.40 = 0.1 + 2.3 + 0.25z
(3.40 - 2.4)/0.25 = z
z = 4
Therefore, we have 2 nickels, 23 dimes, and 4 quarters.
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HURRY Find all solutions to the equation x3 + 100x + 8x2 = –800.
–10, –8, 10
–10, 8, 10
8, –10i, 10i
–8, –10i, 10i
Answer:
-8, -10i, 10i
Step-by-step explanation:
x^3 + 8x^2 + 11x = -800
I just plugged it into my calculator
Find the midpoint of the line segment joining the points (-2,-3) and (-4,10)
THE MIDPOINT FORMULAR IS GIVEN BY
[tex]( \frac{x1 + x2}{2} . \frac{y1 + y2}{2} ) \\ \\ = (\frac{ - 2 + ( - 4)}{2} . \frac{ - 3 + 10}{2} ) \\ = ( \frac{ - 6}{2} . \frac{7}{2} ) \\ = ( - 3. \frac{7}{2} )[/tex]
ATTACHED IS THE SOLUTION
4. (01.02 LC) Brandi earned $78 in interest after one and one half years on an account that paid 7.5% simple interest annually. Use the formula I = Prt to find Brandi's principal balance. Round to the nearest hundredth. (1 point) $69.33 $87.75 $693.33 $768.00
The principal amount is $693.33.
What is Simple Interest?Simple interest is a quick and simple approach to figure out how much money has accrued interest. Interest is always applied to the original principal amount and is calculated at the same rate for each period of time. Any bank where we deposit money will pay us interest on that amount.
The formula is
Simple Interest = P x R x T/100
Given:
Interest = 78
Rate= 7.5%
Time= 1 and half year = 1.5 year
Now, Simple Interest= P x R x T / 100
78 = P x 7.5 x 1.5 / 100
7800= P x 11.25
P = 7800/11.25
P = 693.33
Hence, the principal amount is $693.33.
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Recall that the sum of the measures of the angles of a triangle is 180°. In the triangle below, angle Chas the same measure as angle B, and angle measures 42° less than angle B.
Find the measure of each angle.
Answer:
180=x+42
collect like terms
x=180-42
x=138
Are these right? Geometry by the way, someone please help
With regards to the rigid transformations, Yes, it is true to state that ∠ABD is congruent to ∠EFM. This can be justified by translating ∠ABD by superimposing it on ∠EFM.
It is also true to state that ∠ ABD is congruent to ∠GFHG. To justify this, rotate ∠ABD by 180°
What is a rigid transformation?A rigid transformation in mathematics is a geometric transformation of a Euclidean space that retains the Euclidean distance between each pair of points. Rotations, translations, reflections, and any combination of these are examples of rigid transformations.
Hence, the above statements are true. Note that rigid transformations do not modify the distance angles, size or shape.
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A car travels a distance of 100km for 1h38min45sec.a)Round off the time to the nearest 1/4 hour b)Use the rounded time to find the average speed for the journey
Answer: 57.14 km/hr
Step-by-step explanation: if an hour is divided into quarters it will be in increments of 15 minutes, since one hour is 60 minutes. 60 minutes divided by 5 is 15 minutes.
So 1 hour and 38 minutes is rounded off to 1 hour and 45 minutes.
this is 1 hour + 3/4 hour = 1 3/4 hour. This is same as 1.75 hour
3/4 is .75
speed divided by the time will give the average speed.
100km/1.75hours = 57.14 km/per hour
Answer:
(a) 1 hour 45 min
(b) 57.1 km/h (nearest tenth)
Step-by-step explanation:
Given information:
Distance = 100 kmTime = 1 h 38 min 45 sec[tex]\large\boxed{\sf Speed=\dfrac{Distance}{Time}}[/tex]
Part (a)[tex]\begin{aligned}\sf \dfrac{1}{4}\;hour &= \sf 1 \; hour \div 4 \\& = \sf 60 \;mins \div 4\\& = \sf 15 \; mins\end{aligned}[/tex]
Therefore, the nearest ¹/₄ hours either side of the given time is:
1 hour 30 min1 hour 45 min1 h 38 min 45 sec is 8 min 45 sec more than 1 hour 30 min.
1 h 38 min 45 sec is 6 min 15 sec less than 1 hour 45 min.
Therefore, the nearest ¹/₄ hour to the given time is:
1 hour 45 min.Part (b)1 hour 45 min = 1.75 min (in decimal form)
Substitute the given distance and the rounded time (in decimal form) into the formula and solve for speed:
[tex]\begin{aligned} \implies \sf Speed & =\sf \dfrac{Distance}{Time}\\\\& = \sf \dfrac{100}{1.75}\\\\& = \sf 57.1\;km/h\;(nearest\;tenth)\end{aligned}[/tex]
The lengths of the side of a triangle are 6, 8, 10. Can the triangle be a right triangle?
Yes, the triangle is a right-angle triangle.
Right angle triangle is a triangle in which one of the angles as 90 degree.
For the triangle to be right angle triangle
perpendicular² + base² = hypotenuse²
The three sides of a triangle are 6, 8 and 10
So,
6² + 8² = 10²
36 + 64 = 100
100 = 100
Therefore the triangle is a right-angle triangle.
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A phone company offers two monthly charge plans. In Plan A, the customer pays a monthly fee of $35 and then an additional 6 cents per minute of use.
For what amounts of monthly phone use will Plan A cost less than Plan B?
Use m for the number of minutes of phone use, and solve your inequality for m
Answer: Less than 470 minutes
Step-by-step explanation:
This equation represents this problem.
0.04x + 44.4 = 0.06x + 35
Solve,
0.02x = 9.4
1 / .02 = 50
x = 470
At 470 minutes they're equal and we are looking for when Plan A is cheaper then Plan B, so x < 470
Use m instead of x in this problem, sorry didn't read the last line.
You roll two fair dice, a green one and a red one. (a) What is the probability of getting a sum of 6? (b) What is the probability of getting a sum of 4? (c) What is the probability of getting a sum of 6 or 4? Are these outcomes mutually exclusive?
Based on the number of dice rolled, the probability of getting the sum of 6, and 4 and 6 or 4 can be found to be:
Probability of getting sum of 6 = 5 / 36Probability of getting sum of 4 = 1 / 12Probability of getting sum of 6 or 4 = 2 / 9How to find the probability?Probability of getting sum of 6:
(1 and 5) (2 and 4) (3 and 3) (4 and 2) ( 5 and 1)
= 5 / (6 x 6)
= 5 / 36
The number of sums of 4 are:
= (1 and 3), (2 and 2), (3 and 1)
= 3 / (6 x 6)
= 1 / 12
The probability of getting sums of 6 and 4 are:
= (5 + 3) / (6 x 6)
= 8 / 36
= 2 / 9
These events are mutually exclusive because they cannot roll a sum of 6 or 4.
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Solving a value mixture problem using a system of linear....
Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost $20 and same-day tickets cost $35. For one performance,
there were 60 tickets sold in all, and the total amount paid for them was $1500. How many tickets of each type were sold?
Number of advance tickets sold:
Number of same-day tickets sold:
The linear equation 20x + 35(60-x) = 1500 can be solved to find the number of tickets.
What is an equation?
An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. The word equation and its related terms in various languages may have somewhat different definitions; for example, in French, an equation is described as including one or more elements, but in English, an equation is any well-formed formula that includes two expressions linked by an equals sign.
Let the number of advance tickets sold = x
And then, the number of same-day tickets sold = 60 - x
Then, the equation formed is
20x + 35(60-x) = 1500
=> 20x + 2100 - 35x = 1500
=> -15x = 1500 - 2100
=> x = -600/ -15 = 40
Hence, the number of advance tickets sold = 40
And the number of same-day tickets sold = 60 - 40 = 20
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Answer this Graph based Question I will make you brailiest and provide you 50 points. And also explain the (vii) Question..
Answer:
(i) -2, (ii) Attached, (iii) x = - 1, (iv) y=6 maximum, y= - 2 minimum, (v) x = 0.723, (vi) y = - 3, (vii) y = - 1
Step-by-step explanation:
GivenFunction y = (x + 1)² - 3(i) Find the value of y when x = - 2
y = (- 2 + 1)² - 3 = (-1)² - 3 = 1 - 3 = - 2(ii) See the graph attached
(iii) The axis of symmetry is the vertical line passing through the vertex, which is x + 1 = 0 or x = - 1.
This is also reflected on the attached graph.
(iv) From the graph it is visible that in the given interval the function is decreasing, so the value at x = - 4 is the maximum and the value at x = - 2 is minimum:
y(-4) = (-4 + 1)² - 3 = 9 - 3 = 6 maximumy(-2) = (-2 + 1)² - 3 = 1 - 3 = - 2 minimumThese two points too are given on the same graph.
(v) There ate two x-intercepts, the one on the right is the larger one.
It is (0.732, 0), marked on the graph.
(vi) This function is the standard form of the given:
(x + 1)² - 3 = x² + 2x + 1 - 3 = x² + 2x - 2With the positive leading coefficient of 1, it has a minimum value but no maximum. The minimum of this function is at its vertex, which is (- 1, 3) as per graph.
(vii) The function y = x² + 2x is the translation of the given function up by two units.
So its minimum value is 2 units greater:
(-1, - 3+2) = (-1, -1)(X^3- 5x+ 3) ÷ (x- 2)
2(x+4)-3(2x-5)=-3
What is the answer
Answer: x= 13/2 or 6 1/2
Step-by-step explanation:
2(x+4)-3(2x-5)=-3
Simplify the equation,
2x+8-6x+15 = -3
-4x+23= -3
-4x = -26
Cancel the minus sign, now we get
2x = 13
i.e., x= 13/2
(A.) Given the one-to-one function f(x)= 7x - 2, find it's inverse function.
Which is f ^ -1(x)= 1/7x - 2/7
(B.) The graphs of f and f^ -1 are symmetric with respect to the line defined by
y = _______
The inverse function of one-to-one function f(x)= 7x - 2 is [tex]f^{-1}=\frac{x}{7}+\frac{2}{7}[/tex].
The graphs of f and [tex]f^{-1}[/tex] are symmetric with respect to the line defined by y = x.
Given that:-
f(x)= 7x - 2
Let f(x) = y
Hence,
[tex]f^{-1}(y)=x[/tex]
Hence, we can write,
y = 7x - 2
y + 2 = 7x
x = y/7 + 2/7
[tex]f^{-1}(y) = y/7 + 2/7[/tex]
Replacing y by x, we get,
[tex]f^{-1}(x) = x/7 + 2/7[/tex]
Hence, the inverse function of f(x) is [tex]f^{-1}(x) = x/7 + 2/7[/tex].
The graph of inverse is always the mirror image of the function's graph in the line y = x. It is because they're basically 100% similar but in reverse just like you in a mirror.
To learn more about inverse function, here:-
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