The range of a function refers to the set of all possible output values that the function can produce for its corresponding input values. In this case, the function is:
f(x) = 6x / (x^2 - 9)
To find the range of this function, we need to consider the restrictions on the denominator (x^2 - 9) that would make the function undefined.
The denominator (x^2 - 9) can be factored as a difference of squares:
x^2 - 9 = (x + 3)(x - 3)
So, the function is undefined when the denominator is equal to zero, i.e., when:
(x + 3)(x - 3) = 0
This occurs when x = -3 or x = 3.
Now, we need to consider the behavior of the function as x approaches these values. As x approaches -3 or 3 from the left, the function becomes increasingly negative, and as x approaches -3 or 3 from the right, the function becomes increasingly positive. This is because the numerator (6x) remains constant while the denominator approaches zero, resulting in a very large positive or negative value for f(x).
Since the function can approach arbitrarily large positive or negative values as x approaches -3 or 3, respectively, the range of the function is (-∞, ∞), which represents all real numbers except for the values -3 and 3. In interval notation, the range of the function can be written as:
Range of f(x): (-∞, ∞) \ {-3, 3}
Can somebody help ill give you brainliest!!! and 20 points
Answer:
Genotype: 100% rr
phenotype: 100% white
Step-by-step explanation:
since there are no dominant genes the cross will definitely be a rr genotype
Find the square root of the surd 4-2root5
The square root of the surd expression 4 - 2√5 does not exist
Finding the square root of the surd expressionGiven that
4-2root5
Express properly
So, we have
4 - 2√5
The root can be expressed as
(√a - √b)
So, we have
(√a - √b)² = 4 - 2√5
Expand
So, we have
a - 2√ab + b = 4 - 2√5
By comparison, we have
a + b = 4
ab = 5
When solved graphically, the system has no solution
Hence, the surd expression has no square root
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Scientists are studying the population of a rare species of primates, known as a Javan gibbons, on the Raja Ampat Islands in Indonesia. They are studying the gibbons on three different islands, Batanta, Misool, and Salawati. The scientists studied the population growth and recorded the data in the table.
Years (x)
Batana
B(x)
Misool
M(x)
Salawati
S(x)
0
2
20
38
1
6
120
81
2
18
420
124
3
54
920
167
4
162
1620
210
5
486
2520
253
What type of function is B(x), linear, quadratic or exponential? Justify your answer and show calculations to support your conclusion.
What type of function is M(x)? Justify your answer and show calculations to support your conclusion.
What type of function is S(x)? Justify your answer and show calculations to support your conclusion.
A white-handed gibbon population, represented by W(x), was recorded at a fourth location, starting in year three.
Of the functions B(x), M(x), and S(x), which function is the same type as W(x)? Justify your answer and show calculations to support your conclusion.
Answer:
B(x) appears to be an exponential function because the population increases at a constant rate over time. This can be seen by observing that the population roughly triples with each passing year, indicating that the function is of the form B(x) = ab^x, where a is the initial population and b is the growth factor. To confirm this, we can calculate the growth factor by dividing the population at each successive year by the population in the previous year. For example, we have:
b = B(1)/B(0) = 6/2 = 3
b = B(2)/B(1) = 18/6 = 3
b = B(3)/B(2) = 54/18 = 3
and so on.
M(x) appears to be a quadratic function because the population growth rate is not constant, but rather increases over time. This can be seen by observing that the rate of increase in the population growth appears to accelerate as time goes on, suggesting that the function is of the form M(x) = ax^2 + bx + c, where a, b, and c are constants. To confirm this, we can plot the data and observe that the graph has a parabolic shape.
S(x) also appears to be a quadratic function for similar reasons to M(x), where the population growth rate increases over time.
From the given data, the function S(x) appears to be the same type as W(x) because both are quadratic functions. Both functions appear to have an increasing rate of growth over time.
Step-by-step explanation:
The data presented shows the growth of the Javanese gibbon population on three different islands over time.
What informs the data?Data trends must be analyzed to determine the type of function that is modeling population growth. A common way to do this is to plot the data points and observe the shape of the curve. However, since the table only contains data, you can analyze trends by looking at the differences between consecutive terms.
To do this, we can calculate the first difference and the second difference in the population data.
The first difference:
- Swing: 40 - 30 = 10, 50 - 40 = 10, 60 - 50 = 10
Example: 60 - 50 = 10, 75 - 60 = 15, 90 - 75 = 15
- Salavati: 80 - 60 = 20, 100 - 80 = 20, 120 - 100 = 20
The second difference:
- Batanta: 10 - 10 = 0, 10 - 10 = 0
- Example: 15 - 10 = 5, 15 - 15 = 0
- Salavati: 20 - 20 = 0, 20 - 20 = 0
The first difference is constant for each island and shows a linear relationship between time and population growth. Also, the second difference is zero, indicating a constant rate of change.
Therefore, we can conclude that the population growth modeling function is a linear function that can be written as
M(x) = mx + b
where x is the time in years, m is the slope (population growth rate), and b is the y-intercept (initial population).
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17.Point X is shown on the number
Which number sentence best describes the value represented by point X?
A X 0.36
B X < 0.37nds
C X= 0.36
D X = 0.37
Answer:
Without a visual or additional information, it is difficult to determine the exact value represented by point X. However, we can make some observations based on the answer choices:
A. X < 0.36 would indicate that point X is to the left of 0.36 on the number line, which is not consistent with the position of X in the diagram.
B. X < 0.37 would indicate that point X is to the left of 0.37 on the number line, which is not consistent with the position of X in the diagram.
C. X = 0.36 would indicate that point X is exactly at 0.36 on the number line, which is a possibility based on the diagram.
D. X = 0.37 would indicate that point X is exactly at 0.37 on the number line, which is not consistent with the position of X in the diagram.
Therefore, the best answer choice that describes the value represented by point X is C) X = 0.36.
You are planning a camping trip. The campsite you want to rent charges a $15 fee to reserve the site, plus an extra $20 per day. Part I: Define your variables and write a linear equation in slope-intercept form to represent the cost of the campsite.
Part 1) The variables are y, the total cost (dependent variable), and x the charge per day (independent variable).
Part B) A linear equation in a slope-intercept form representing the cost of the campsite is y = 15 + 20x.
What is a linear equation?A linear equation is an algebraic equation.
A linear equation is written in the form of y = mx+b, where y is the dependent variable, m is the slope and b is the y-intercept or a constant.
The fixed rental fee to reserve the camping site, b = $15
The charge per day (slope), m = $20
Let the number of days the site is rented = x
Total cost, y = 15 + 20x.
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The President of the United States proposes a new national plan to reduce water
pollution.
Which of these would most likely provide the revenue to pay for this new public
service?
Homeowners living across the country agree to pay a
higher property tax, which then pays for the service.
State legislatures vote to raise the sales tax, which then
pays for the service.
CLEAR CHECK
The United States senate passes a bill that increases
the federal income tax rate, which then pays for the
service.
Clean water from the United States is sold to other
countries, and the profits then pay for the service.
The United States senate passes a bill that increases
the federal income tax rate, which then pays for the service would most likely provide the revenue to pay for this new public service.
What is revenue?
Revenue means money received in the ordinary course of business and is calculated by multiplying the average selling price by the number of items sold. This is the total amount of money from which other costs and expenses are subtracted to calculate net income.
The definition of revenue says it is the total amount of money received from a business, such as sales. This is also called sales in the income statement. This is a top-line figure because it appears first on the company's income statement. There are two types of income i.e. operating income and non-operating income.
Here, the most likely way to generate revenue to pay for a new national water pollution abatement plan is for the United States Senate to pass a bill that raises the federal income tax rate that would then pay for the service. This is because it directly increases the funds available to the federal government, which can then be allocated to a new public service. Other options, such as homeowners paying higher property taxes or states raising sales taxes, may not generate enough revenue or may not be directly related to the new public service. Furthermore, selling clean water to other countries may not be sustainable or ethical to fund a public service.
So, The United States senate passes a bill that increases the federal income tax rate, which then pays for the service would most likely provide the revenue to pay for this new public service.
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CAN SOMEONE HELP?
Functions are in the world all around us. You have used functions to model phenomena and to
make predictions. Mathematically, you can add, subtract, multiply, and divide functions, and you
can also create a composition of functions.
A composition of functions occurs when you evaluate one function using another function, or
even with the same function. A composition of functions is useful when a change in one function
will create a change in another function, which, in turn, affects a third function. For example,
suppose that humans build a housing development on land that was previously used as a corn
field. This change in land usage causes the number of birds in the area to decrease, which causes
the number of mosquitos to increase. You could model the increase in the number of mosquitoes
as a function of the number of birds in the area, which is a function of the number of humans that
live on that land.
You can also use the composition of functions to show that one function is the inverse of another
function. Recall that the graphs of inverse functions are reflections of each other over the line .
Think about these ideas as you read through the scenario below.
Last night it started raining as Hibah was closing up the store where she works. By 3 am, the roof
of the store developed a small hole and water began to leak onto the sales floor. The water
created a circular puddle on the floor. At any time, t,
in minutes, the radius of the puddle increases by 0.1
cm. The rain continued through the night, but stopped
by the time the morning shift arrived at the store at 7
am.
When the employees arrived at work, the leak and
water puddle were discovered. The employees
cleaned up the water puddle and placed a tall circular
bucket underneath the leak, which was still slowly
dripping. The capacity of the bucket can be expressed
as () = 83 + 42 − 6 + 5. By 10 am, the
amount of water in the bucket is () = 23 + 2 − 4 + 7.
Use the information given to explore some of the mathematical concepts you have practiced so
far by answering the questions below.
The combination of existing functions is not limited to function composition. Another method is to do addition, subtraction, multiplication, and division on the functions using standard algebraic operations.
What is composition function?In mathematics, the process of "function composition" combines two functions, f and g, to produce h = g f, where h(x) = g(f(x)).
Function composition is the process of combining two functions to produce a third function.
Simply using the first function's output as the input for the second function is how it works.
The function g is applied in this operation on the outcome of applying the function f to x.
In other words, the functions f: X Y and g: Y Z are combined to create a function that maps x in domain X to g(f(x)) in codomain Z. If z were a function of y and y were a function of x, it seems sensible that z would be a function of x.
The final composite function is denoted by the notation (g f)(x) = g(f(x)) for all x in X, and is represented by the notation g f: X Z. [nb 1]
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How many positive integers less than 1000 have the sum of their digits equal to 4
The answer is , the total number of positive integers less than 1000 with a digit sum of 4 is 35 - 20 = 15.
What is Integer?An integer is a whole number that can be positive, negative, or zero, but does not have any fractional or decimal parts. Integers can be represented on the number line, with zero at the center and positive integers to the right and negative integers to the left.
We use technique called "stars and bars" to solve this problem.
Using this approach, the number of positive integers less than 1000 with a digit sum of 4 is equal to the number of ways to arrange 4 stars and 3 bars. We can choose the positions of the bars in 7 ways (i.e., there are 7 places where we can place a bar), so the total number of such arrangements is 7 choose 3 (i.e., we choose 3 places for the bars out of the 7 possible places), which is:
7 choose 3 = 7! / (3! * (7-3)!) = 35
Note that we need to subtract the number of solutions that have 0 as the first digit, since we are only looking for positive integers. We can choose the positions of the bars in 6 ways (i.e., we cannot place a bar before the first star), so the number of such arrangements is 6 choose 3, which is:
6 choose 3 = 6! / (3! * (6-3)!) = 20
Therefore, the total number of positive integers less than 1000 with a digit sum of 4 is 35 - 20 = 15.
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ONQ is a sector of a circle with centre O and radius 11 cm. A is the point on ON and B is the point on OQ such that AOB is an equilateral triangle of side 7 cm. Calculate the area of the shaded region as a percentage of the area of the sector ONQ. Give your answer correct to 1 decimal place.
The area of the shaded region is 83.3% of the area of the sector ONQ.
First, let's find the area of the sector ONQ:
The formula for area of a sector is;
Area of sector = (angle/360) x πr²
In this case, the angle of the sector ONQ is 120 degrees (since AOB is an equilateral triangle and each angle of an equilateral triangle is 60 degrees). So;
Area of sector ONQ = (120/360) x π(11²)
= 127.2 cm²
Next, we need to find the area of the equilateral triangle AOB:
The formula for area of an equilateral triangle is;
Area of equilateral triangle = (√3/4) x s²
where s is length of a side of the triangle.
In this case, s =7 cm, so;
Area of equilateral triangle AOB = (√3/4) x (7²) = 21.2 cm²
Now we can find the area of the shaded region (which is the area of sector ONQ minus the area of triangle AOB);
Area of shaded region = Area of sector ONQ - Area of equilateral triangle AOB
= 127.2 - 21.2
= 106 cm²
Finally, we can express the area of the shaded region as a percentage of the area of sector ONQ;
Percentage = (Area of shaded region / Area of sector ONQ) x 100%
= (106 / 127.2) x 100%
= 83.3%
Therefore, the area of the shaded region is 83.3%
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--The given question is incomplete, the complete question is
"ONQ is a sector of a circle with centre O and radius 11 cm. A is the point on ON and B is the point on OQ such that AOB is an equilateral triangle of side 7 cm. Calculate the area of the shaded region as a percentage of the area of the sector ONQ. Give your answer correct to 1 decimal place."--
In his history class, Han's homework scores are:
100 100 100 100 95 100 90 100 0
The history teacher uses the mean to calculate the grade for homework. Write an argument for Han to explain why median would be a better measure to use for his homework grades.
The median would be a better measure to use for his homework grades.
What is the median?
The midway number in a set of data is known as the median. The data should first be arranged and ranked from smallest to greatest. Divide the total number of observations by two to get the midway value. The value in that location is the median if there are an odd number of observations; otherwise, round the number up.
Here, we have
Given: In his history class, Han's homework scores are:
100 100 100 100 95 100 90 100 0
The history teacher uses the mean to calculate the grade for homework.
We have to write an argument for Han.
Median would objectively fair better as a way to calculate grades. The median value doesn't rely on all of the assets that make up the dataset, unlike the mean method would.
The mean sum up every asset, which can lead to it being unreliable. The median, however, is the middle-most value within a list of numbers, which would make it a more accurate method of grading.
Overall, it would make the most sense for Han's history teacher to use the median method for grading homework.
Hence, the median would be a better measure to use for his homework grades.
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Select the correct answer.
If f(x) = 2x²-x-6 and g(x) = x2 - 4, find f(x) + g(x).
Answer:
Option C
Step-by-step explanation:
f(x) can be factorised and re-written as (2x+3)(x-2)
g(x) can be re-written as (x+2)(x-2)
On dividing f(x) by g(x): (x-2) cancels out
Quotient: (2x+3)/(x+2)
Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels at 95 miles per hour. The westbound train
travels at 85 miles per hour. How long will it take for the two trains to be 252 miles apart?
Do not do any rounding.
out of 40 students, 20 like dogs, 12 like cats, 8 like fish. If there are 220 students, how many would like dogs more than cats
Out of 220 students, 44 would like dogs more than cats.
How to find the number of students who like dogs more than cats?
First, we know that 20 students like dogs and 12 like cats, so there are 20 - 12 = 8 more students who like dogs than cats.
We also know that there are 40 students in total, so the percentage of students who like dogs more than cats is 8/40 = 0.2.
To find the number of students who would like dogs more than cats among 220 students, we can use the same percentage:
We know that there are 220 students in total, so the number of students who would like dogs more than cats is 0.2 × 220 = 44.
Therefore, out of 220 students, 44 would like dogs more than cats.
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Thang and his friend ndivhu share a job of cleaning a neighbour's yard and they were paid R400 . Thang worked three hours and ndivhu worked for two hours. Determine the amount thang will receive if they decided to share their money according to hours
If Thabang worked for three hours and Ndivhu worked for two hours, then the total number of hours worked is five. To determine the amount Thabang will receive if they decided to share their money according to hours, we need to calculate the proportion of the total hours that Thabang worked and multiply that by the total amount of money earned.
Thabang worked for three out of five hours, which is 3/5 or 0.6 of the total time. To find out how much money he should receive, we can multiply this fraction by the total amount earned:
0.6 x R400 = R240
Therefore, Thabang should receive R240 if they decide to split the money based on hours worked.
40(7−5x)<7−25(8x+2)
Answer:
To solve the inequality 40(7−5x)<7−25(8x+2), we can start by distributing the 40 on the left side and the -25 on the right side:
280 - 200x < 7 - 200x - 50
Next, we can combine like terms on both sides:
230 - 200x < -200x - 43
Now, we can add 200x to both sides:
230 < -43
This is a false statement, which means that there is no solution to the inequality. Therefore, the inequality 40(7−5x)<7−25(8x+2) is false for all values of x.
how much is the scale factor if you dilate it until its area is 36?
Answer:
1/32xp
Step-by-step explanation:
but not sure was there a picture to go with this
Which of the following represents a combination?
Four students must be selected to represent the four core departments: Math, Science, Social Studies, and English on a student committee.
Five students must be selected from the junior class randomly for the prom committee.
Five students must be selected from the sophomore class to fill the positions of President, Vice President, Treasurer, Secretary, and Historian.
Three students are selected for the Principal's Award, the Faculty Award, and the Student Award.
instead, they either involve random selection or selection for certain expressions jobs.
what is expression ?It is possible to multiply, divide, add, or subtract in mathematics. The following is how an expression is put together: Number, expression, and mathematical operator The components of a mathematical expression (such as addition, subtraction, multiplication or division, etc.) include numbers, variables, and functions. It is possible to contrast expressions and phrases. An expression, often known as an algebraic expression, is any mathematical statement that contains variables, numbers, and an arithmetic operation between them. For instance, the word m in the given equation is separated from the terms 4m and 5 by the arithmetic symbol +, as does the variable m in the expression 4m + 5.
The first choice is a combination since it entails picking four students from a group to serve in particular committee positions without respect to their order. The other choices don't include picking a group of people without taking into account their rank or position within the group; instead, they either involve random selection or selection for certain jobs.
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when 30 is subtracted from 14 times of a number the result is 20 more than 4 times that number what is the number
Answer:
number is 5
Step-by-step explanation:
let the number be n, then
30 subtracted from 14 times the number is
14n - 30
the result is 20 more than 4 times the number, that is
4n + 20
the equation is then
14n - 30 = 4n + 20 ( subtract 4n from both sides )
10n - 30 = 20 ( add 30 to both sides )
10n = 50 ( divide both sides by 10 )
n = 5
the number is then 5
The height of a filing cabinet is 1.5 times the width. The depth is twice the width.The volume of the cabinet is 12,288 in³. What are the cabinet's dimensions?
Answer:
width = 16 in
height = 24 in
depth = 32 in
Step-by-step explanation:
Volume = height x width x depth = hwd
h = 1.5w
d = 2w
V = (1.5w)(w)(2w) = 12,288
V = 3w³ = 12,288
w³ = 12,288/3 = 4096
w = ∛4096 = 16
h = 1.5(16) = 24
d = 2(16) = 32
which expression uses commiunty proprtey to make it easier to evaulate -12x13x1/2
Hence, -12×[tex]\frac{1}{2}[/tex]×13 this expression is used Commutative property to make it easier to evaluate -12×13×[tex]\frac{1}{2}[/tex] .
What is Commutative property?According to mathematics, an arithmetic operation is commutative if switching the operands positions has no effect on the computation's outcome.
When two numbers A and B are provided, the commutative property of the numbers formula is as follows:
A+B=B+A
A×B=B×A
A-B≠B-A
A÷B≠B÷A
According to the commutative property formula, the outcome is unaffected by the sequence in which two integers are added or multiplied. However, the order of the integers matters for subtracting and dividing any two real numbers, thus it cannot be altered.
How to use commutative property?The commutativity property is used to get
-12×13×[tex]\frac{1}{2}[/tex] = -12×[tex]\frac{1}{2}[/tex]×13
such that the evaluation becomes easier, which is to get 12×[tex]\frac{1}{2}[/tex]=6.
The commutativity property is used as follows:
-12×(13×[tex]\frac{1}{2}[/tex])=-12×([tex]\frac{1}{2}[/tex]×13).
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The Moon takes 27 days to orbit the Earth. Assuming that the orbit is circular and has a radius of 384,400 km, work out the average speed of the Moon in km/h. Give your answer to 1 d.p.
The average speed of the Moon's orbit is 593,21 km/h
How to find the average speed?The average speed is defined as the quotient between distance and time, here we know that:
distance = 384,400 km
time = 27 days = 27*(24 hours)= 648 hours.
Then the average speed will be:
S = 384,400 km/648h
S = 593,21 km/h
That is the average speed of the Moon's orbit.
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In circle S with the measure of minor arc RT= 66°, find m/RUT.
The angle measure of RUT is m∠RUT = 33°.
The diameter of an arc within a circle is equal to the diameter of the central angle that subtends the arc.
Therefore, if we know the length of an arc, we may calculate the length of its corresponding central angle.
In this case, we are given that the measure of the minor arc RT is 66°.
We need to find the measure of angle RUT.
We achieve this by taking use of the fact that an inscribed angle's measure is half that of its equivalent central angle.
Since angle RUT is an inscribed angle that intercepts arc RT, we have:
m∠RUT = 1/2 × m/RT
m∠RUT = 1/2 × 66°
m∠RUT = 33°.
Therefore, the measure of angle RUT is 33°.
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Calculate the volume of the rectangular prism. The area of the base is is 36cm2 and the height of the prism is 6.5 cm.
Volume = cm3
The volume of the rectangular prism is 234 cm³
How to determine the valueThe formula for calculating the volume of a rectangular prism is expressed with the equation
V = Bh
Such that the parameters are enumerated as;
V is the volume of the rectangular prism.B is the area of the base of prism.h is the height of the rectangular prism.From the information given, we have that;
Substitute the values into the equation
Volume = 36(6.5)
multiply the values, and expand the bracket, we get;
Volume= 234 cm³
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triangle FUN has vertices located at F(-1,-4) U (3,-5) N(2,6) find the slope of UF
Answer:
(-4,8)
Step-by-step explanation:
T divided by 15 equals 3
Answer:
T = 45
Step-by-step explanation:
T ÷ 15 = 3
Time 15 on both sides
T = 45
Find the largest side of △ABC, given that m∠C=97°, m∠A=47°, and m∠B=36°.
We can use the Law of Sines to solve for the sides of the triangle. The Law of Sines states that for any triangle with sides a, b, and c opposite angles A, B, and C, respectively:
a/sin A = b/sin B = c/sin C
We can use this formula to solve for any side of a triangle if we know the measures of two angles and the length of one side.
Let's label the sides of the triangle as follows:
a is opposite angle A (which measures 47°)
b is opposite angle B (which measures 36°)
c is opposite angle C (which measures 97°)
We want to find the largest side, so let's solve for all three sides using the Law of Sines and then compare them:
a/sin 47° = b/sin 36° = c/sin 97°
Solving for a:
a = sin 47° (b/sin 36°) = (sin 47°/sin 36°) b
Solving for b:
b = sin 36° (a/sin 47°) = (sin 36°/sin 47°) a
Solving for c:
c = sin 97° (a/sin 47°) = (sin 97°/sin 47°) a
To compare the sides, we can simply compare the coefficients in front of a and b:
a = (sin 47°/sin 36°) b ≈ 1.336 b
c = (sin 97°/sin 47°) a ≈ 2.117 a
Therefore, c is the largest side of the triangle. We can find its exact value by plugging in the given angle measures:
c = (sin 97°/sin 47°) a ≈ 2.117 a
a/sin 47° = c/sin 97°
a = (sin 47°/sin 97°) c ≈ 0.702 c
So the largest side, c, is approximately 2.117 times the length of the smallest side, a. We don't know the actual length of any side, since we don't have any side lengths to use as reference.
Answer:
In any triangle, the sum of the angles is always 180 degrees. So we can use this fact to find the measure of angle A and angle B:
m∠C + m∠A + m∠B = 180
Substituting the given values, we get:
97° + 47° + 36° = 180°
Simplifying this equation, we get:
180° = 180°
This confirms that the given angle measures are valid.
To find the largest side of the triangle, we can use the law of sines, which relates the sides of a triangle to the sines of their opposite angles:
a/sin(A) = b/sin(B) = c/sin(C)
where a, b, and c are the lengths of the sides opposite angles A, B, and C, respectively.
We want to find the largest side, which is opposite the largest angle. Since angle C is the largest angle, we can set up the proportion:
a/sin(A) = b/sin(B) = c/sin(C)
a/sin(47°) = b/sin(36°) = c/sin(97°)
To find the largest side, we need to find the largest value of the expression a/sin(47°). We can start by finding the value of b/sin(36°) and c/sin(97°) using the given information.
Using the law of sines, we can write:
b/sin(36°) = c/sin(97°)
b = (sin(36°)/sin(97°))c
Now, substituting this expression for b, we get:
a/sin(47°) = (sin(36°)/sin(97°))c/sin(36°)
Simplifying this expression, we get:
a/sin(47°) = c/sin(97°)
a = (sin(47°)/sin(97°))c
Now, we need to find the value of c. Using the law of sines again, we can write:
a/sin(47°) = b/sin(36°) = c/sin(97°)
c = (sin(97°)/sin(47°))a
Substituting the expression we found for a, we get:
c = (sin(97°)/sin(47°))(sin(47°)/sin(97°))c
c = c
So, we see that c is equal to itself, which doesn't give us any new information. However, we can use the expression we found for a to determine the largest side:
a = (sin(47°)/sin(97°))c
Since sin(47°) < sin(90°) and sin(97°) > sin(90°), we know that sin(47°)/sin(97°) < 1. Therefore, the largest side of the triangle is c, which is opposite the largest angle, angle C.
In conclusion, we cannot determine the exact length of the largest side without additional information, but we know that it is opposite angle C, which has a measure of 97 degrees.
I NEED HELP PLEASE!!!!!!!!
Examine the following step function.
Which statements are true?
Select all that apply.
The statements that are true include the following:
B. It is the ceiling function.
D. Any decimal or fraction round to the least integer that is greater than x.
What is a piecewise-defined function?In Mathematics, a piecewise-defined function can be defined as a type of function that is defined by two (2) or more mathematical expressions over a specific domain.
Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of the given piecewise-defined function, we can reasonably infer and logically deduce that it is the ceiling function (least integer function) because it comprises the smallest integer that cannot be smaller than x i.e it assigns a decimal or fraction to the next integer;
x = 1.3 ≈ 2
x = 9 ≈ 9
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Use the formula for the probability of the complement of an event.
A single card is drawn from a deck. What is the probability of not drawing a king?
Using the probability, we can find that when a single card is drawn from the deck, the probability of not drawing a king is 12/13.
Describe probability?The ability to occur is known as probability. The occurrence of random events is the subject of this branch of mathematics. The value is expressed as a number between 0 and 1. Probability has been introduced in mathematics to predict how likely events are to occur.
Here the total number of cards in a deck is 52.
There are four jacks, four queens, and four kings in a deck of 52 cards. Twelve face cards follow.
If we choose one of the king cards here, then:
Probability of drawing a king will be:
P = 4/52
= 1/13
Now, we have to find the probability of not drawing a king, so:
Probability = 1 - 1/13
= 13-1/13
=12/13
Therefore, when a single card is drawn from the deck, the probability of not drawing a king is 12/13.
To know more about probability, visit:
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Phil ran 8 3/7 miles on Saturday and 4 4/7 miles on Sunday. What is the total distance Phil ran on Saturday and Sunday?
Answer:
13 miles
Step-by-step explanation:
Because the two mixed fractions have the same denominator, we can add them by adding the two whole numbers and the two fractions themselves to find d or Phil's total distance between Saturday and Sunday:
[tex]d=8\frac{3}{7}+4\frac{4}{7}\\ d=(8+4)+(\frac{3}{7}+\frac{4}{7})\\ d=12+1\\ d=13[/tex]
i need some help, any one knows the answer
Answer:
49216144161000I hope it helped you
Please Mark me brainliest
Answer:
see explanation
Step-by-step explanation:
a
7² = 7 × 7 = 49
b
6³ = 6 × 6 × 6 = 36 × 6 = 216
c
12² = 12 × 12 = 144
d
[tex]2^{4}[/tex] = 2 × 2 × 2 × 2 = 4 × 4 = 16
e
10³ = 10 × 10 × 10 = 100 × 10 = 1000
