Determine the conditions for when a function has an inverse. Use the horizontal line test to recognize when a function is one-to-one. Find the inverse of a given function.
What is a horizontal line test?It is simple to establish whether the inverse of a function is also a function using the horizontal line test.
Because it fails the vertical line test, a function's inverse might not actually be a function.
Graph of the line
f\left( x \right) = - x + 2
f(x)=−x+2.
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the 5th term of an A.P is 9 and the 8th term is 27.Find the 31st term
Answer:
189
Step-by-step explanation:
The difference between consecutive terms of an arithmetic sequence, known as the common difference is given by
d = a(k) - a(k-1) where k = 1,2,3 ....n
We have the 5th term as a(5) = 9
The 6th term is 9 + d
The 7th term is 9 + 2d
The 8th term is 9 + 3d
Each successive term adds a d to the previous term
We have 8th term = 27
So 9 + 3d = 27
3d = 27 - 9 (subtract 9 from both sides)
3d = 18
Divide above by 3 on both sides to get
d = 18/3 = 6
So the common difference is 6
Let's figure out how to calculate the 31st term
We can see that the 5th term can be expressed as
9 + 0d = 9 + 0.6 = 9
The sixth term is
9 + 1d = 9 + 1(6) = 9 + 6 = 15
The seventh term is 9 + 2d = 9 + 12 = 21 and so on
Therefore the general equation for the nth term, given the 5th term
is
a(n) = a(5) + (n - 5)(6) 9 + 6(n - 5)
So the 31st term is
a(31) = 9 + 6(31-1) 9 + 6 x 30 = 9 + 180 = 189
Answer: 31st term is 189
Jake ran 121.3 miles a week. if jake ran an equal number of miles each day, then what distance did he run in a day? (write the answer up to two decimal places)
Distance ran by Jake in a day is 17.33 miles.
It is given in the question that Jake ran 121.3 miles in a week. Also, Jake ran an equal number of miles each day.
We have to find the distance ran by him in a day.
Let the distance ran by him in a day be x miles.
We know that there are 7 days in a week.
Hence, according to the data given in the question, we can write,
Number of days in a week * distance ran in a day = total distance
Hence,
7*x = 121.3 miles
Solving the linear equation, we get,
x = 121.3/7 miles
x = 17.3285 ≈ 17.33 miles
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Jolene works at Food Lion and she makes $13.25. She works 4 hours a day Monday through Friday and 8 hours a day on the weekend. How much would she make during a 7-day week?
She would make $477 during a 7-day week
How much would she make during a 7-day week?The given parameters are
Hourly rate = $13.25Weekdays = 4 hours dailyWeekends = 8 hours dailyThere are 5 days in a weekday and 2 in a weekend
So, the total earning is
Total = Rate * [Weekday hours * 5 + Weekend hours * 2]
This gives
Total = $13.25 * [4 * 5 + 8 * 2]
Evaluate
Total = $477
Hence, she would make $477 during a 7-day week
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45h + 1895 = 5000
What is the value of H
Answer:
69
Step-by-step explanation:
45*69+1895=5000
Answer:
h = 69
Step-by-step explanation:
45h + 1895 = 5000 ( subtract 1895 from both sides )
45h = 3105 ( divide both sides by 45 )
h = 69
In Exercise 25, as the value of x increases, what happens to the value of 3*?
Step-by-step explanation:
it grows exponentially.
a negative exponent like
n^-a
means only
1/(n^a)
-3 1/3³ = 1/27
-2 1/3² = 1/9
-1 1/3¹ = 1/3
0 3⁰ = 1
1 3¹ = 3
2 3² = 9
3 3³ = 27
so, 3^x comes from very small but positive values, and grows very fast (much faster than x itself and with ever increasing speed hence "exponentially") to very large and still positive numbers.
The length of a rectangle is four meters less than twice its width. If the perimeter of the rectangle is 88 meters, what is the width?
A. 24m
B. 16m
C. 32m
D. 8m
The width of the rectangle is determined as: B. 16 m.
How to Determine the Measurement of a Rectangle?The perimeter of a rectangle = 2(l + w)
l = length of the rectanglew = width of the rectangleGiven the parameters:
Perimeter of rectangle = 88 meters
Width of the rectangle = w meters
Length = 2w - 4 meters
Plug in the values into the perimeter formula of a rectangle
2(2w - 4 + w) = 88
2(3w - 4) = 88
6w - 8 = 88
6w = 88 + 8
6w = 96
6w/6 = 96/6
w = 16
Thus, the width of the rectangle is determined as: B. 16 m.
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What value of n makes a true statement? 4^nx4² = 16,384
Liza earned some money by taking care of her neighbors pet. she bought a drink for $1.95 and a concert ticket for $30. she bought a ring for $7.20 and then two-thirds of the remaining money on a wireless speaker. if liza has 38.50 left, write and solve an equation to find the amount of money m liza earned by taking care of her neighbors pet.
The equation is 1.95+30+7.20+2/3(m-1.95-30-7.20)+38.50=m
The amount of money Liza earned is $154.65
What is Unitary method?It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.
let the money she earn be m.
the remaining money = m-1.95-30-7.20
So, her total earning is,
1.95+30+7.20+2/3(m-1.95-30-7.20)+38.50=m
39.15+38.50+2/3(m-39.15)=m
77.65+2m/3-26.10=m
77.65-26.10=m-2m/3
51.55=(3m-2m)/3
51.55*3=m
m=$154.65
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What is the classification for this polynomial?
-4a³b5 + 3a²
A. monomial
B. binomial
C. trinomial
It's been a while but I think binomial. There are two nonzero terms, -4a3b5, and 3a2, making it a binomial.
How do you add and subtract radicals? If you could please give me the instructions step by step and with examples, that would be helpful too.
It is for a homework assignment in school, but I wasn't there the day they did it.
p.s I need an explanation right away.
You can add and subtract radicals by ensuring that they have same radical parts.
What's radical?It should be noted that a radical expression is an expression that contains the radical symbol which is ✓.
The necessary steps to add or subtract radicals include:
Identify the radical parts.
Add them together.
If there's unlike radical parts, one will manipulate the parts involved before solving.
Example: Add ✓63 + 5✓7
It should be noted that ✓63 = ✓9 × ✓7 = 3✓7
Therefore, ✓63 + 5✓7 will be:
= 3✓7 + 5✓7
= 8✓7.
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find the value of x ?
The value of x from the given diagram is 64 degrees
Lines and anglesA line is defined as the shortest distance between two points. From the given diagram, we have that the line AB bisects FAB, hence;
<FAB = <CAB = 58 degrees
Also since the sum of angles on a straight line is 180 degrees, hence;
58 + 58 + x = 180
116 + x = 180
x = 180 - 116
x = 64 degrees
Hence the value of x from the given diagram is 64 degrees
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In a recent year, 17.3% of all registered doctors were female. If there were 41,400 female registered doctors that year, what was the total number of registered doctors?
Round your answer to the nearest whole number.
Answer: 239,306 total registered doctors
Step-by-step explanation:
1. Form the ratio of amount of female doctors(41,400) to total amount of doctors(x) and compare it to percent of female doctors in the field(17.3) to total percent of doctors(100).
[tex]\frac{41400}{x}=\frac{17.3}{100}[/tex]
2. Cross Multiply the amount of female doctors(41,400) to the total percent of doctors(100) so that it stays equal to the percent of female doctors(17.3) to the amount of doctors(x).
[tex]41400*100 = 17.3x[/tex]
3. Simplify
Start by multiplying the amount of female doctors(41,400) by the total percent(100) to get 4.240.000 to keep both sides equal[tex]414*10^{4} = 17.3x[/tex]Then apply the division property of equality by dividing both sides of the equality by the percent of female doctors to the amount of doctors(17.3).[tex]\frac{414*10^{4} }{17.3} = \frac{17.3x}{17.3}[/tex]
After dividing both sides by 17.3 you will find out that there are about 239,306 registered doctors.Atsu and Sabu shared an amount of money in the ratio 3:7 respectively. if Sabu received 20 cedis more than Atsu, how much was shared
Answer:
Step-by-step explanation:
Atsu : Sabu
3 : 7
x : x + 20
x is equal to the number of cedis
cross multiply the ratio above
3(x+20) = 7x
3x + (20×3) = 7x
3x + 60 = 7x
3x - 3x + 60 = 7x - 3x (put - 3x on both sides of the equation)
60 = 4x
60/4 = 4x/4 (divide both sides by 4)
15 = x
Which of the following numbers can be expressed as decimals that terminate? (1 point) 5 over 2 , 4 over 5 , 2 over 7 , 4 over 3 5 over 2 and 2 over 7 4 over 5 and 4 over 3 5 over 2 and 4 over 5 2 over 7 and 4 over 3
Answer:
all of them are terminating decimals
Step-by-step explanation:
5/2=2.5
4/5=1.25
2/7=3.5
4/5=1.25
4/3=0.75
5/2=2.5
4/5=1.25
2/7=3.5
4/3=0.75
they are terminating decimals because they have a finite end
1.) Raisins and nuts were mixed in a
bowl. If 34 of the mixture was
made up of nuts, what was the
ratio of raisins to nuts?
Answer:
8−5=3
Step-by-step explanation:
find the product of 12 0.6 and 6 1/4
What is the lowest common multiple of 9 and 7 ?
Answer:
Step-by-step explanation:
The answer is 63
hope this helps :)
Which driver's race times were the most variable if Driver A has a mean of 4.01 seconds and a standard deviation of 0.05 seconds and Driver B has a mean of 3.96 seconds and a standard deviation of 0.12 seconds and Driver C has a mean of 3.99 seconds and a standard deviation of 0.19 seconds?
The driver B has the fastest typical race time.
It is required to find which driver's race times were the most variable.
What is a statement?A statement is a declarative sentence that is either true or false but not both. A statement is sometimes called a proposition. The key is that there must be no ambiguity. To be a statement, a sentence must be true or false, and it cannot be both.
Given:
From the options presented, driver B has the fastest typical race time because he recorded the smallest time taken to complete an individual race.
Also from the standard deviation given 3.96 seconds for driver B, it shows that the individual time spread from the standard deviation is minimal and that the driver maintained a fairly consistent time of race throughout the racing period.
Therefore, the driver B has the fastest typical race time.
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Miguel tracks four stocks during the day. The changes for the stocks are shown in the table. A 2-column table with 4 rows. Column 1 is labeled Stock with entries A, B, C, D. Column 2 is labeled Change with entries negative three-fourths, 0.7, negative 1, 0.2. Which list shows the values of the changes in order, from least to greatest?
Stock A, Stock B, Stock C, Stock D
Stock B, Stock D, Stock A, Stock C
Stock C, Stock A, Stock D, Stock B
Stock D, Stock C, Stock B, Stock A
The list shows the values of the changes in order, from least to greatest as Stock C, Stock A, Stock D, and Stock B which is the correct option (C).
What is descending order?Descending order is defined as when numbers (or other items) are arranged from the largest numbers to the least numbers, it is said to be in descending order.
What is ascending order?Ascending order is defined as when numbers (or other items) are arranged from the least numbers to the largest numbers, it is said to be in ascending order.
We have been given four stocks during the day. The changes for the stocks are shown in the table.
-3/4, 0.7, -1, 0.2
Here the least numbers to the largest numbers, it is said to be in ascending order.
⇒ -1 < -3/4 < 0.2 < 0.7
Arrange the stock in increasing order.
Stock C, Stock A, Stock D, Stock B
Therefore, the list shows the values of the changes in order, from least to greatest as Stock C, Stock A, Stock D, and Stock B.
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Your question is incomplete, probably the missing part is:
A 10-lb bag of flour costs $3.69. A 5-lb bag costs $1.55. How much can you save if you buy the big bag instead of 2 small bags?
You will $0.29, if you will purchase 2 small bags of flour instead of 1 big bag.
What exactly is the unitary method?The unitary method is an approach that calculates the value of a specific unit utilizing the values of multiple units, in addition to determining the value of multiple units based on the value of a single unit.To figure out the value of one item, we must first divide it, and then multiply it by the number of things we want to find the value of.For the given question;
The total cost of one big bag that is 10-lb bag of flour = $3.69.
Now, the cost of one small bag that is 5-lb = $1.55.
Thus, the cost for two small bag that is 5-lb = $3.10.
The difference in the cost = big bag cost - 2 small bag costs.
The difference in the cost = $3.69 - $3.10
The difference in the cost = $0.29.
Thus, you will save $0.29 for the purchase of 2 small bags of floor instead of one big bag.
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CH#6 LINES & ANGLES
I. In fig. the values of x and y are equal to:
(a) 130⁰
(b) 150⁰
c) 160⁰
(d) 135⁰
A teacher claims that the relationship between
number of hours studied for a test and test score can be
described by g(x) = 45 + 9x, where x represents the
number of hours studied. Graph this function
The graph representing the given function g(x) = 45 + 9x is as drawn in the attachment.
How to draw a Linear Equation Graph?
We are given the equation of line as;
g(x) = 45 + 9x
Where;
x represents the number of hours studied.
g(x) represents the test score
Thus, to plot this graph, we need to input some x values and find their corresponding g(x) values
At x = -10;
g(x) = 45 + 9(-10)
g(x) = -45
At x = -1;
g(x) = 45 + 9(-1)
g(x) = 35
At x = 0;
g(x) = 45 + 9(0)
g(x) = 45
At x = 1;
g(x) = 45 + 9(1)
g(x) = 54
At x = 2;
g(x) = 45 + 9(2)
g(x) = 63
At x = 3;
g(x) = 45 + 9(3)
g(x) = 72
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Each side of a square is lengthened by 2 inches. The area of
this new, larger square is 36 square inches. Find the length of
a side of the original square.
Please help using systems of equations!!
Answer:
4 inches.
Step-by-step explanation:
Since the shape is a square, each side length will be the same. This mean that you must find the square root of 36 to find the length of each side of the new square.
√36=6
Each side of the new square is 6. It says it was lengthened by 2 inches. Subtract 2 from 6.
6-2=4
Each side of the original square is 4 inches.
Hope this helps!
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A square room has a floor area of 144 square feet. the hieght of the room is 6 feet what is the area of one wall
The area of one wall of the room is 72 square feet.
What is the area of a square?The area of a square is given by -
A{S} = a²
where -
{a} is side of square.
Given is a square room has a floor area of 144 square feet. The height of the room is 6 feet.
It is given that -
floor area = 144
a² = 144
a = √(144)
a = √(12 x 12)
a = 12
The area of the wall will be equivalent to -
A{W} = h x a
A{W} = 6 x 12
A{W} = 72 square feet.
Therefore, the area of one wall of the room is 72 square feet.
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Find the equation of the line shown.
The equation of the line shown in the diagram is y = 0.5x+0.5.
What is a line?A line is a mark connecting two points.
To calculate the equation of the line, we use the formula below
Formula:
y = mx+c.............. Equation 1Where:
m = Slope of the graphc = Intercept on the vertical axis.From the diagram,
Given:
m = 1/2 = 0.5c = 0.5Substitute these values into equation 1
y = 0.5x+0.5Hence, the equation of the line shown in the diagram is y = 0.5x+0.5.
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Hans spent $38 on fruit at the grocery store. He spent a total of $40 at the store. What percentage of the total did he spend on fruit?
What is 0.2302 to the thousands place
A seller leaves a buyer approximately one half of a tank of heating oil at the closing. if the tank measures 4' x 2' x 3', how many cubic feet did the buyer receive?
The answer is 12 cubic feet
To rent a bike (r), kyre pays the flat rate of 5 pesos plus an hourly rental fee (f) of 2 pesos and 50 centavos
The cost of renting the bike will rise at a rate of (B) $2.5 per hour as the number of rent hours increases.
What is a linear function?A linear function represents a straight line on the coordinate plane.The slope of a linear function is always the same and constant.A linear function, in other words, is one that varies linearly with respect to a changing variable.To find what is the rate of change in the cost to rent the bike with respect to the number of rent hours:
The rate of change is also known as the function's slope.Because it is a linear function, the slope will be constant.Slope = difference in ys coordinate/difference in xs coordinateSlope = (30-5)/(10-0) = 2.5Therefore, the cost of renting the bike will rise at a rate of (B) $2.5 per hour as the number of rent hours increases.
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The correct question is given below:
To rent a bike, Max pays a flat rate of $5 plus an hourly rental fee. The graph shows the amount, C, in dollars, that Max pays based on the number of hours, t, that Max rents the bike. What is the rate of change in the cost to rent the bike with respect to the number of rental hours?
(A) $5 per hour
(B) $2.50 per hour
(C) $2 per hour
(D) $7.50 per hour
In mapping diagram D, what is the range?
The range of the relation that is represented in the mapping shown in the diagram attached below is: {3, 5, 11, 21}.
What is the range of a Relation?If we are given a mapping that represents a relation, the input values (x-values) make up the domain of the relation while the output values (y-values) make up the range of the relation.
In the mapping shown in the diagram attached below, we have the following:
The domain of the relation is: {-1, 0, 1, 2, 3}
The range of the relation is: {3, 5, 11, 21}
Thus, we can conclude that, the range of the relation that is represented in the mapping shown in the diagram attached below is: {3, 5, 11, 21}.
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