The inverse of the given function is [tex]f^{-1}(x) = (x-7)^2[/tex].
What is inverse of function?A function that may reverse into another function is known as an inverse function or anti function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y.
Given that the equation of the function is:
f(x) = √x + 7
Covert the given function into an equation:
y = √x + 7
Interchange the variables in the equation:
x = √y + 7
Isolate the value of y.
Subtract, 7 from both sides of the equation:
x - 7 = √y + 7 - 7
x - 7 = √y
Take square on both sides of the equation:
(x-7)² = (√y)²
(x-7)² = y
Replace, y with [tex]f^{-1}(x)[/tex].
[tex]f^{-1}(x) = (x-7)^2[/tex]
Hence, the inverse of the given function is [tex]f^{-1}(x) = (x-7)^2[/tex].
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Use the theorems from Section 3.2 and the converses of those theorems in this section to write three biconditional statements about parallel lines and transversals.
The slopes of the two lines that form them must be equal (m1 = m2). This implies that the two lines are parallel.
1) Biconditional statement: If two lines are parallel, then the alternate interior angles formed by a transversal are equal.
Formula: m∠1 = m∠3 and m∠2 = m∠4
Calculation: If two lines are parallel with a transversal intersecting them, the slopes of the two lines must be equal (m1 = m2) and the alternate interior angles formed by the transversal must have the same measure (m∠1 = m∠3 and m∠2 = m∠4).
2) Biconditional statement: If two lines are parallel, then the corresponding angles formed by a transversal are equal.
Formula: m∠1 = m∠4 and m∠2 = m∠3
Calculation: If two lines are parallel with a transversal intersecting them, the slopes of the two lines must be equal (m1 = m2) and the corresponding angles formed by the transversal must have the same measure (m∠1 = m∠4 and m∠2 = m∠3).
3) Biconditional statement: If two angles are equal, then the lines that form them are parallel.
Formula: m1 = m2
Calculation: If two angles have the same measure, then the slopes of the two lines that form them must be equal (m1 = m2). This implies that the two lines are parallel.
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Round 11,900 to the nearest thousand.
Answer:
12,000
Step-by-step explanation:
How can we do this?
We can do this by taking the number 11,900,
11,900
looking at the hundredths place,
11,900
and figuring out if it is closer to 10, or 0. 9 is closer to 10, so we round up.
12,000
Therefore, 11,900 rounded to the nearest thousand is 12,000.
please help will mark BRAINLIEST
Answer:
100
Step-by-step explanation:
total angles of any triangle is 180
it tells you one of the base angles is 40, so 2 of them are 80
so the top one is 180-80 =100
Any one help me please the question is in the screenshot.
The answers include the following below:
The sale price is 85% of the regular price.The equation which can be used to find the sale price, s, of an oil change is s = 0.85(30).What is Sale price?This is referred to as the discounted price at which goods or services are being sold.
Since we were told that the discount is 15%, then the sale price will be (100-85)% of $30 which is 85% of $30.
This therefore means that the equation to find the sale price will be 85/100 × 30 = 0.85(30).
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The perimeter of a certain rectangle is 26 m. Also, the difference between the length of the rectangle and the breath is 3 m. Find the length and the breadth of the rectangle.
A rectangle having perimeter 26 m has a length of 8m and breadth of 5m.
What is perimeter?
The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.
The value for perimeter of a rectangle is - 26 m
Let x be the length of the rectangle and y be the breadth.
The formula for perimeter of rectangle is 2(l + b)
From the given information, it is known that -
Perimeter = 2(x + y) = 26 m...(1)
Difference between the length and breadth = x - y = 3 m....(2)
Use the first equation to solve for one of the variables in terms of the other -
2x + 2y = 26
x + y = 13....(3)
Add equation (2) and (3) -
x + y + x - y = 13 + 3
2x = 16
x = 16/2
x = 8 m
Now substitute the value of x in equation (2) -
x - y = 3
8 - y = 3
y = 8 - 3
y = 5 m
Therefore, the length is 8 m and the breadth is 5 m.
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Multiply mentally 70 • 100 • 400 = (Type a whole number)
(-1.2) (-3.5) (-2.7) (-0.4) a positive product?
We have the product of 4 negative numbers, by the rule of signs, we can see that the product is positive.
Is the product positive?Here we need to reember the rule of signs for the product, it is:
(-)*(-) = +
(+)*(+) = +
(+)*(-) = -
(-)*(+) = -
So the product between two negative numbers is positive, now let's look to our product.
(-1.2)*(-3.5)*(-2.7)*(-0.4)
We can rewrite this as:
(-1.2*-3.5)*(-2.7*-0.4)
The negative sings cancell, then we get:
(-1.2*-3.5)*(-2.7*-0.4)
(4.2)*(1.08)
Now we have the product of two positive numbers, this will be positive.
(4.2)*(1.08) = 4.536
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Please helppp with this question
On solving the system of linear equations 3x + 3y = 45 and x + 2y = 24, the cost for each shirt is obtained as $6, and cost for each pair of pants is obtained as $9.
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
Let the cost of shirts be x and the cost of pair of pants be y.
The number of shirts bought by person A = 3
The number of pair of pants bought by person B = 3
The total cost for person A = $45
The equation for person A is -
3x + 3y = 45....(1)
The number of shirts bought by person B = 1
The number of pair of pants bought by person B = 2
The total cost for person B = $24
The equation for person B is -
x + 2y = 24....(2)
Multiply equation (2) by 3 -
3(x + 2y) = 24 × 3
3x + 6y = 72....(3)
Subtraction equation (1) from equation (3) -
3x + 6y - (3x + 3y) = 72 - 45
3x + 6y - 3x - 3y = 27
3y = 27
y = 9
Substitute the value of y in equation (2) -
x + 2(9) = 24
x + 18 = 24
x = 24 - 18
x = 6
Therefore, the cost of shirts and pants is x = 6 and y = 9 respectively.
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you and friends go to the state fair . it costs $6 to get into the fair and $2 each time you go on a ride consider the relationship between number of rides (x) and total cost (y)
It costs $6 to enter the fair, and each ride costs $2, thus the equation is x = 6+ 2y.
what is equation ?Its core idea is understood to be the number's minimal equivalent fraction. How to determine the simplest form. A fractional figure can be checked to discover if it is a prime number. A phrase having two equal sides and now an equal sign in the middle is referred to as a mathematical equation. Every variable's degrees are listed in ranking in the general form of any equation. Its general form of a two-variable linear equation is an x + b y + c = 0. (or something similar). Perhaps conditional equations of identities are categories for equations.
given
Suppose the total cost is x and there are y rides.
Each ride costs two dollars. Thus, the price of the rides will be:
= Number of rides * Price per ride
=> y * 2
=> 2 y
Thus, the final price will be:
Total price = Admission price + ride prices
Total cost: $6 plus $2. (Number of rides)
x = 6 + 2y
It costs $6 to enter the fair, and each ride costs $2, thus the equation is x = 6+ 2y.
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Evaluate the given function as required.
Calculate R(0) and R(30) if R(t) is as shown below. (Round your answer to two decimal places.)
R(t)=328-296e⁻o.oo4t
The numeric values of the function R(t) = 328 - 296e^(-0.004t) at t = 0 and t = 30 are given as follows:
R(0) = 32. R(30) = 65.47.How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The function for this problem is defined as follows:
R(t) = 328 - 296e^(-0.004t)
At t = 0, the numeric value is found replacing the lone instance of t by zero, hence:
R(0) = 328 - 296e^(-0.004(0))
R(0) = 32.
At t = 30, the numeric value is found replacing the lone instance of t by 30, hence:
R(30) = 328 - 296e^(-0.004(30))
R(30) = 65.47.
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Graph the inequality below on the number line.
y>-10
The graph of the inequality y > -10 is given by the image presented at the end of the answer.
What are the inequality symbols?The four inequality symbols, along with their meaning, are presented as follows:
> x: greater than x.< x: less than x.≥ x: at least x.≤ at most x.The inequality for this problem is given as follows:
y > -10.
Which means that the solution is the numbers that are greater = to the right of -10, with an open interval.
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In order to set premiums at profitable levels, insurance companies must estimate how much they will to pay in claims on cars of each make and model, based on the value of the car and how much damage it sustains in accidents. Let C be a random variable that represents the cost of a randomly selected car of one model to the insurance company. The probability distribution of C is given below C $0 $1000 $4000 $10,000 P(C) 0.60 0.05 0.13 0.22 The probability that the insurance company will have to pay a claim of at least $4000 for a randomly selected car is: a.0.05 b.0.13. c.0.22. d.0.35. e.0.406. The expected value of C is a.$0 b.$554 c.$2770 d.$3750 e.$40577. Which of the following is the best interpretation of expected value? (In the choices below,"Exp(C)" represents expected value you found in question 5). a.If the company insures 10 cars of this model, they know they will incur 10×Exp(C) in costs. b.The maximum cost to the company for insuring this car model is Exp(C) per car. c.The company must insure at least Exp(C) of these cars to make a profit. d.If the company insures a large number of these cars, they canexpect the cost per car to average approximately Exp(C). e.If the company insures a large number of these cars, they can expect the variability in cost per car to average approximately Exp(C).
The probability of a claim of at least $4000 is 0.35, option(d), the expected value of C is $2770 option (c), and the best interpretation is If the company insures a large number of these cars, they can expect the cost per car to average approximately Exp(C), option(d).
Given probability distribution
C $0 $1000 $4000 $10000
P(C) 0.60 0.05 0.13 0.22
The probability that the insurance company will have to pay a claim of at least $4000 for a randomly selected car is
= (1-0.60-0.05) = 0.35
so the expected value of C
= 0x0.60 + 1000x0.05 + 4000x0.13 + 10000x0.22
= 50+520+2200 = $2770
Now, the best interpretation of expected value:
If the company insures a large number of these cars, they can expect the cost per car to average approximately Exp(C).
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A biologist is studying the plant diversity in 15 million acres of the Sierra Nevada Mountains. He will count the number of species in 150 acres. Match the strategies to their corresponding sampling techniques.
The biologist goes to his 150 favorite hiking places and looks at an acres along each trail.
The biologist orders the 15 million acres by latitude and then surveys every 100000th acre on the list.
The biologist classifies the Sierras into 10 different ecological types and then makes sure that the proportion of each ecological type from the sample is the same as the proportion of that of the population.
The biologist goes to 15 diverse locations that have 10 acres each and surveys all 10 acres for each of these 15 locations.
The biologist enters the 15 million acres into a data base and had a computer randomly select 150 of these acres.
Cluster Sampling
Systematic Sampling
Convenience Sampling
Stratified Sampling
Simple Random Sampling
Answer:
The biologist goes to his 150 favorite hiking places and looks at an acre along each trail: Random Sampling.
The biologist orders the 15 million acres by latitude and then surveys every 100000th acre on the list: Stratified Sampling.
The biologist classifies the Sierras into 10 different ecological types and then makes sure that the proportion of each ecological type from the sample is the same as the proportion of that of the population: Stratified Sampling.
The biologist goes to 15 diverse locations that have 10 acres each and surveys all 10 acres for each of these 15 locations: Cluster Sampling.
The biologist enters the 15 million acres into a data base and had a computer randomly select 150 of these acres: Random Sampling.
give me brainiestbig lake bob spends his time carving fishing lures and duck decoys. if big lake bob spends all of his time carving fishing lures he can carve 125 lures in a week. if he spends all of his time carving duck decoys he can carve 20 decoys in a week. for every 4 duck decoys big lake bob carves he must give up 25 fishing lures. Fill in the values in the table below to complete Big Lake Bob's production possibilities schedule. Fising Lures Duck Decoys 100 0 0 30
50 fishing lures are carved in a week.
A) Big Lake Bob
Production Possibilities Schedule:
Fishing Lures Duck Decoys
100 0
90 5
80 10
70 15
60 20
50 25
40 30
30 35
20 40
10 45
0 50
50 fishing lures are carved in a week.
25 duck decoys are crafted in a week.
This implies that Big Lake Bob forgoes 10 fishing lures for every 5 duck decoys he carves.
Large Lake Schedule of Bob's productivity potentials
B) Bob's potential for production The schedule is a table of numbers that shows the various combinations of two items that can be created using the restricted resources (labor hours, capital, materials, etc.) and technology in Bob's economy.
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using a table or diagram write an equation that represents the linear function shown in the table or mapping diagram
An equation that represents the linear function shown in the table or mapping diagram is y = -x/4 - 3.
How to write an equation that represents the linear function?In order to write an equation that represents the linear function, we would use the point-slope form. Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.Next, we would determine the linear function representing the line which passes through the data points (-4, 6) and (8, 3) by using the point-slope form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 6 = (3 - 6)/(8 - (-4))(x - (-4))
y - 6 = (3 - 6)/(8 + 4)(x + 4)
y - 6 = -3/12(x + 4)
y - 6 = -x/4 - 9
y = -x/4 - 9 + 6
y = -x/4 - 3
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Ian travels 225 km in 2.5 hours. At what speed does he travel?
Answer:
90 km/h
Step-by-step explanation:
speed = distance/time
speed = 225 km / 2.5 h
speed = 90 km/h
Answer:
90km/hr
Step-by-step explanation:
To find the speed, take the distance and divide it by the time.
225 km/ 2.5 hours
90km/hr
Which figures have rotational symmetry?
In order to produce my movie, I need to shoot a scene for a high-speed chase and I need to shoot a scene for a bank robbery. The film production crew will be putting the movie together. I have the stunt crew for the chase scene from 10 am to 11 am and I have the stunt crew for the robbery from 6pm to 7 pm. Will the order I shoot the scenes in matter? What mathematical property did you use to answer this question?
The order in which you shoot the scenes will not matter in terms of the final outcome of the movie.
The mathematical property that one can use to answer this question is scheduling.
How to illustrate the information?From the information, in order to produce the movie, one needs to shoot a scene for a high-speed chase and need to shoot a scene for a bank robbery.
Here, the film production crew will be putting the movie together. However, it may impact the logistics of the production process and the scheduling of the crews. It is not a mathematical property that I used to answer this question. It is simply a matter of logistics and scheduling.
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f(x) = 3x and g(x)=x-2, find f(g(4))
If f(x) = 3x and g(x)=x-2, then the value of f(g(4)) is 6.
What is a function?
A function is a mathematical object that assigns exactly one output to each input of a specified type. In other words, a function is a rule that takes in certain inputs (or "arguments") and produces a unique output. The inputs to a function are called the domain, while the set of possible outputs is called the range.
The given functions are f(x) = 3x and g(x)=x-2.
To find f(g(4)), we first need to evaluate g(4). The function g is defined as g(x) = x - 2, so g(4) = 4 - 2 = 2.
Next, we need to evaluate f(2), where f is defined as f(x) = 3x. So, f(2) = 3 * 2 = 6.
Therefore, f(g(4)) = f(2) = 6.
Hence, if f(x) = 3x and g(x)=x-2, then the value of f(g(4)) is 6.
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mation.
2) (x-3)(x-8)= 0
Answer:
x-3 =0 or x-8 =0
x= +3 or x = +8
item 18 time remaining 4 hours 13 minutes 48 seconds 04:13:48 ebook item 18 time remaining 4 hours 13 minutes 48 seconds04:13:48 if bob can produce more donuts in one day, if
If Bob is able to produce more donuts than Sue in one day, that means that Bob has an absolute advantage in the production pf donuts.
Absolute advantage is when a particular person is able to produce more amount of product than the other with the same amount of input of resources, for example, time. Comparative advantage on the other hand is based on the opportunity cost.
Comparative advantage is basically the ability to produce a good or a service for an opportunity cost which is lower than that of a competitor. Since, Bob is able to produce more donuts than Sue, Bob has an absolute advantage over Sue.
--The given question is incomplete, the complete question is
If Bob can produce more donuts in one day than Sue can produce in one day, then:
a. Bob has a comparative advantage in the production of donuts.
b. Sue has a comparative advantage in the production of donuts.
c. Bob has an absolute advantage in the production of donuts.
d. Sue has an absolute advantage in the production of donuts."--
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(v) (5-6i)+(3+4i) - (5-7)
Answer:
Step-by-step explanation
The sum of two numbers is 62. 3 times the smaller number exceeds twice the larger number by one. What are the numbers.
The smaller number is 25 and larger number is 37
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here; The sum of two numbers is 62 and 3 times the smaller number exceeds twice the larger number by one.
let the smaller number be x and the larger number be y then we have
x+y=62
3x-2y=1
Thus solving this system of linear equations by method of elimination we get
5y=185
y=37
∴ x=25
Hence, The smaller number is 25 and larger number is 37
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Find the value of x PLEASE HELP FOR BRAINLIEST
Answer:
31.81
Step-by-step explanation:
the dotted line ² = (22²-16²)
x = sq root of [dotted line² +(44-16)² ]
= sq root of [22²-16²+28²]
31.81
Solve the inequality and the graph the solution
An inequality with two variables has a graph, which is a collection of points that shows all possible solution is x≤ 5 3/10.
How to find the calculation?The boundary line between the coordinate plane's two halves, one of which represents the inequality's solutions, is created by a linear inequality.
x + 1 1/2 ≤ 6 8/10 :
Solution : x ≤ 5 3/10
Decimal : x ≤ 5.3
Interval notation : (-∝ , 53/10)
Steps:
x + 1 1/2 ≤ 6 8/10 :
Convert mixed Number to improper Fraction : 1 1/2 = 3/2
1 1/2
Convert mixed numbers to improper fraction ; a (b/c ) = a. c +b /c
1 1/2 = 1.2 + 1 /2
=3/2.
x + 1 1/2 ≤ 6 8/10 :
Convert mixed Number to improper Fraction : 6 8/10 = 68/10
6 8/10
Convert mixed numbers to improper fraction ; a (b/c ) = a. c +b /c
6 8/10 = 6.10 + 8 /10
=68/10
x+ 3/2 ≤ 68/10
Cancel the Common factor :2
x + 3/2 ≤ 34/5
Move 3/2 to the right side
x ≤ 53/10
Convert improper Fraction to mixed Numbers: 53/10 = 5 3/10
53/10 = 5 Reminder 3
Convert to mixed Number : Quotient (Remainder / Divisor)
53/10 = 5 3/10
x≤ 5 3/10
x≤ 5 3/10.
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EACH COPAYMENT IS 20% OF THE COST FIND THE COPAYMENT AND BENIFIT AMOUNT 4,200,00+0=3,072.00
The copayment amount, given that it is 20 % of the amount is $ 840
The benefit amount is $ 3, 360
How to find the copayment amount ?A copayment for health insurance is a defined dollar amount that is determined by the insurance plan and used to divide the cost of covered treatments between the plan and the consumer.
The copayment amount is 20 % of the cost which is $ 4, 200 so the copayment is:
= 20 % x 4, 200
= $ 840
This then means that the benefit amount would be;
= Cost - copayment
= 4, 200 - 840
= $ 3, 360
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Is x = 6 a solution to the equation 5(x – 3) = x + 13? Follow the steps to find out.
1. Rewrite the equation 5(x – 3) = x + 13 with 6 substituted for x. Write a question mark over the equal sign to show that you're testing to see if the equation is true.
2. Simplify both sides. Show your work.
3. Is x = 6 a solution to the equation? Why or why not?
4. Find a value of x that is a solution to 5(x – 3) = x + 13. Describe how you found the solution. (3 points)
Answer:
see below
Step-by-step explanation:
Step 1
5(x – 3) = x + 13
Step 2
See if x is a solution
5 (6-3) ?= 6+13
5 (3) ?= 19
15 ?= 19
Step 3
This is not true so it is not a solution
Step 4
5(x – 3) = x + 13
Distribute
5x-15 = x+3
Subtract x from each side
5x-x -15 = x+13-x
4x-15 = 13
Add 15 to each side
4x-13+13 = 15+13
4x =28
Divide each side by 4
4x/4 = 28/4
x = 7
7 is a solution
Answer:
First you substitute 6 for x!
5(6 - 3) = 6 + 13
6 - 3 = 3
The equation is now:
5 * 3 = 6 + 13
5 * 3 = 15
6 + 13 = 19
The result is:
15 = 19 which is not a true statement.
x is not equal to 6.
Now lets try 7.
5(7 - 3) = 7 + 13
7 - 3 = 4
7 + 13 = 20
5 * 4 = 20
Thus: x = 7
Step-by-step explanation:
Hope it helps! =D
The average pencil has 5,425 pencil shavings. How many pencils are found in 76,450 pencil shavings?
Answer:
14
Step-by-step explanation:
We can divide 76,450 shavings by the average shavings per pencil, 5,425 to get an answer of 14.09... This can be rounded to 14.
Exercise 2:
Identify the missing terms:
4a (-2a³+4__+3)+ 2a(__a³- 2a+_)= -2a*+12a²+26a
JE
The complete expression of the algebra is;
4a(-2a³ + 4a + 3) + 2a(3a³ - 2a + 7) = -2a⁴ + 12a² + 26a
How to expand algebraic expressions?We are given the expression as;
4a(-2a³ + 4__ + 3) + 2a(__a³ - 2a + _) = -2a* + 12a² + 26a
Expanding the left hand side gives;
-8a⁴ + __(16a) + 12a + __(2a⁴) - 4a² + __(2a)
Grouping like terms gives;
-8a⁴ + __(2a⁴) + 12a + __(2a) + __(16a) - 4a²
Factorizing out exponents gives;
a⁴(-8 + __(2)) + a(12 + __(2)) + a²((16/a) - 4)
Comparing this with the right hand side gives;
a⁴(-8 + __(2)) = -2a* -----(1)
((16/a) - 4)a² = 12a² -----(2)
(12 + __(2))a = 26a ----(3)
From eq 1, we can see that;
* = 4
From eq 2;
((16/a) - 4) = 12
16/a = 12 + 4
a = 16/16
a = 1
From eq 3;
(12 + __(2)) = 26
___ * 2 = 26 - 12
___ = 14/2
___ = 7
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Find the Area of the figure below, composed of a rectangle with a semicircle removed from it. Round to the nearest tenths place.
Answer:
39.9
Step-by-step explanation:
Rectangle: area = length × width
Semicircle: area = 0.5πr²
total area = 9 × 6 - 0.5 × 3.14159 × 3²
total area = 39.9