Answers
6. f(x)g(x)+h(x) = 20x3-4x. This answer is arrived at by using the rules of algebra and the values of the given functions.
7. f(x)g(x) = -15x2 - 18x - 15
What are polynomials?Polynomials are algebraic expressions consisting of variables and coefficients that are combined through addition, subtraction, multiplication and division operations. For example, the polynomial 4x² + 3x - 5 can be written as the sum of 4x², 3x and -5.
6. In order to calculate f(x) g(x)+h(x), it is necessary to first multiply f(x) and g(x). Since f(x)=4x and g(x) = 5x2-4, it follows that f(x)g(x)=20x3-4x. Next, it is necessary to add h(x) to this product. Since h(x) = 9x, it follows that f(x)g(x)+h(x) = 20x3-4x+9x = 20x3-4x. Since each coefficient is correctly represented in the answer, it follows that the correct answer is 20x3-4x.
Multiplying f(x) and g(x) gives the product of 20x3-4x, and adding h(x) to this product gives the sum of 20x3-4x. As each coefficient is correctly represented in the answer, the correct answer is 20x3-4x.
7. The product of two polynomials is found by multiplying each term of one polynomial by each term of the other polynomial. This is known as the FOIL method (First, Outer, Inner, Last).
The first term is the product of the first terms of each polynomial, which is 3x x 4x = 12x2.
The second term is the product of the outer terms, which is 3x x -5x = -15x2.
The third term is the product of the inner terms, which is 5 x -5x = -25x.
Finally, the fourth term is the product of the last terms of each polynomial, which is 5 x -3 = -15.
We can now combine the terms to get the product of the two polynomials, which is:
f(x)g(x) = -15x2 - 18x - 15.
Therefore, the correct coefficient for each term is -15x2 for the first term, -18x for the second term, and -15 for the third term.
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Related Questions
Solve the given equation for z and right the correct answer 4z + 9 = 29
Answers
The time Jasmine spends biking is a function of the distance she bikes. Jasmine bikes 18 miles per hour. Assume she bikes at a constant rate
Answers
The function used to represents the time spend by Jasmine in biking for a distance of d miles is given by f(d) = d / 18.
The time Jasmine spends biking is indeed a function of the distance she bikes.
The formula to calculate the time Jasmine takes to bike a certain distance is equal to,
time = distance / speed __(1)
Here the speed is the rate at which Jasmine bikes = 18 miles per hour.
Let us consider 'd' be the distance representing the number of miles Jasmine bikes.
This implies,
The function that represents the time Jasmine spends biking in terms of the distance .
Function f(d) representing the time Jasmine spends biking for a distance of d miles
Substitute all the values in the formula (1) we get,
⇒ f(d) = d / 18
Therefore, the function representing the time spend by Jasmine for distance d is equal to f(d) = d / 18.
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The above question is incomplete , the complete question is:
The time Jasmine spends biking is a function of the distance she bikes. Jasmine bikes 18 miles per hour. Assume she bikes at a constant rate.
Write the function representing the time Jasmine spends biking in terms of the distance?
please help asap look at the screen shot to help
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The mean class size at Mountain View School is 4.4 and at Seaside School is 4.2.
The median class size is 5 for both schools.
The range for Mountain View School is 12 and for Seaside School is 8.
The IQR for Mountain View School is 6 and for Seaside School is 3.
How do we solve this?To find the measures of center, we can calculate the mean and median for both schools.
Mountain View School:
Mean = (2+1+0+5+8+6+9+8+2+0+1+0+6)/15
Mean = 4.4
Median = 5
Seaside School:
Mean = (0+1+2+5+6+8+8+7+6+5+5+4+4+3+1+0)/15
Mean = 4.2
Median = 5
Part B:
To find the measures of variability, we can calculate the range and interquartile range (IQR) for both schools.
Mountain View School:
Range = largest value - smallest value = 12 - 0
Range = 12
IQR = Q3 - Q1 = 8 - 2 = 6
Seaside School:
Range = largest value - smallest value = 8 - 0
Range = 8
IQR = Q3 - Q1 = 7 - 4 = 3
Part C:
If we are interested in a smaller class size, Seaside School would be the better choice. The median class size is the same at both schools, but Seaside School has a smaller mean, which suggests that on average, class sizes are smaller.
Additionally, the range and IQR are both smaller for Seaside School, indicating less variability in class size.
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Doing missing work and I don’t remember how to do these
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The value of x in ΔPQR is 12 and value of x and y are 17.5 and 19.2 respectively, with the scale factor 8 : 5.
What is scale factor?Scale Factοr is used tο scale shapes in different dimensiοns. In geοmetry, we learn abοut different geοmetrical shapes which bοth in twο-dimensiοn and three-dimensiοn. The scale factοr is a measure fοr similar figures, whο lοοk the same but have different scales οr measures. Suppοse, twο circle lοοks similar but they cοuld have varying radii.
The scale factοr states the scale by which a figure is bigger οr smaller than the οriginal figure. It is pοssible tο draw the enlarged shape οr reduced shape οf any οriginal shape with the help οf scale factοr.
4. The scale factor is in the ratio of 2:5
x = QR ≅ VS
x ≅ 30
Now, we have
2/5 = x/30
x = 2/5 × 30
x = 12
Thus, The value of x is 12 when scale factor is 2:5.
5. As ΔABC ≅ ΔAVW
WA = x ≅ CA
x ≅ 28
And in the same way
y ≅ 12
Now, Scale factor is
CB/VW
= 16/10
= 8/5
= 8 : 5
Now,
8/5 = 28/x
x = 28 × 5/8
x = 28 × 5/8
x = 35/2
x = 17.5
And for y
8/5 = y/12
8/5 × 12= y
y = 8/5 × 12
y = 96/5
y = 19.2
Thus, The value of x in ΔPQR is 12 and value of x and y are 17.5 and 19.2 respectively, with the scale factor 8 : 5.
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john conducts emissions inspections on cars. he finds that 6% of cars fail inspection. let the random variable x be the number of cars that john inspects until a car fails an inspection. assume independence. the random variable x is:
Answers
The random variable x in this case is a binomial random variable, representing the number of cars that need to be inspected until a car fails an inspection. A binomial random variable is defined as the number of successes, “s”, in “n” independent trials. In this case, “s” would be 1 (the single failure) and “n” would be the number of cars that John inspects until a car fails inspection.
The probability of success, “p”, in this case is 0.06 since 6% of cars fail inspection. The probability of failure is “q”, which would be 0.94 in this case (1 - 0.06). The mean, “μ”, of the random variable x is equal to n * p, or the total number of trials times the probability of success. In this case, the mean would be equal to n * 0.06, or 6%.
The variance, “σ2”, of the random variable x is equal to n * p * q, or the total number of trials times the probability of success times the probability of failure. In this case, the variance would be equal to n * 0.06 * 0.94, or 5.64%.
The binomial random variable x can be used to calculate the expected number of inspections it will take John until a car fails an inspection, as well as the probability of a car failing an inspection. By knowing the probability of success, the number of trials, and the probability of failure, we can calculate the mean, variance, and expected value of the binomial random variable x.
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Hint
Use the Pythagorean Theorem to solve for the missing sides
Answers
Answer: Shape one: 5, Shape 2: 13
Step-by-step explanation:
shape one
12^2+x^2=13^2
shape two
5^2+12^2=x^2
Answer:
PLEASE MARK ME AS BRAINLLIEST
Step-by-step explanation:
p=12
h=13
b=?
p²+b²=h²
12²+b²=13²
144+b²=169
b²=169-144
= 25
b=root25
b=5m
b=5
p=12
h=?
p²+b²=h²
12²+5²=h²
144+25=h²
h²=169
h=root169
h=13
johnny makes an initial deposit into a bank account that earns compound interest annually. what's the initial deposit? whats the common ratio? whats the interest rate? how much money is there after 8 years? please help me and please be specific!! thank youuu
Answers
1. The initial deposit is $10,000 since John deposited this amount to open the savings account.
2. The common ratio can be calculated using the formula for compound interest: A = P(1 + r/n)^(nt)
3. After 8 years, the amount will be $13,685.70 in the savings account.
How do we get how much money in account after 8 years?The formula which will be used to calculated the compound interest is A = P(1 + r/n)^(nt). For this problem, the interest is compounded annually, so n = 1.
The annual interest rate is 4%, or 0.04 as a decimal. Plugging these values into the formula, we get:
A = $10,000*(1 + 0.04/1)^(1*8)
A = $10,000*(1.04)^8
A = $10,000*1.36857
A = $13,685.70
Therefore, after 8 years, there will be $13,685.70 in the savings account.
Full question "John deposited $10,000 to open a new savings account that earned 4 percent annual interest, compounded interest. What's the initial deposit? whats the common ratio? whats the interest rate? how much money is there after 8 years?"
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PLEASE HELP, DUE TODAY,
Which of the following tables represents a linear function?
x −4 −1 0 1 2
y −4 2 −4 0 2
x 1 1 1 1 1
y −3 −2 −1 0 1
x −6 −1 0 2 3
y −7 negative sixteen thirds −5 negative thirteen thirds −4
x −2 −1 0 2 4
y −4 negative two thirds −1 two thirds 1
Answers
The table that represents a linear function is table 2.
How to explain the linear functionA linear function is a function whose graph is a straight line, and the equation of such function has the form y = mx + b, where m is the slope of the line and b is the y-intercept. To determine which table represents a linear function, we can calculate the slope between any two points in the table, and see if the slope is the same for all pairs of points.
Table 1:
The slope between (0,-4) and (1,0) is (0 - (-4)) / (1 - 0) = 4/1 = 4.
The slope between (-1,2) and (0,-4) is (-4 - 2) / (0 - (-1)) = -6/1 = -6.
The slope between (1,0) and (2,2) is (2 - 0) / (2 - 1) = 2/1 = 2.
The slopes are not the same for all pairs of points, so this table does not represent a linear function.
Table 3:
The slope between (-1, negative sixteen thirds) and (0,-5) is (-5 - (-16/3)) / (0 - (-1)) = -1/3.
The slope between (0,-5) and (2,-13/3) is (-13/3 - (-5)) / (2 - 0) = -8/3.
The slopes are not the same for all pairs of points, so this table does not represent a linear function.
Table 4:
The slope between (-1,negative two thirds) and (0,-1) is (-1 - (-2/3)) / (0 - (-1)) = -1/3.
The slope between (0,-1) and (2,2/3) is (2/3 - (-1)) / (2 - 0) = 5/6.
The slopes are not the same for all pairs of points, so this table does not represent a linear function.
Therefore, the correct option is table 2.
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How many unique triangles are there in the regular hexagon?
Answers
Answer:
Step-by-step explanation: There are 6 equilateral triangles in a regular hexagon by connecting the opposite vertices of a regular hexagon.
g in a study, the sample is chosen by separating all cars by size, and selecting 10 of each size grouping what is the sampling method?
Answers
The sampling method used in the study where the sample is chosen by separating all cars by size, and selecting 10 of each size grouping is known as stratified random sampling.
Stratified random sampling is a method of sampling that involves dividing the population into smaller sub-groups known as strata. In this method, each stratum is composed of elements that have similar characteristics.
The strata could be based on demographic characteristics such as age, sex, education, and so on. Once the strata have been created, the next step is to select a sample from each of the strata to make up the final sample. The selection is done randomly, and the number of elements selected from each stratum is proportional to the size of the stratum. This ensures that the sample is representative of the entire population in terms of the different characteristics of the population.
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a study indicates that the weights of adults are normally distributed with a mean of 140 lbs and a standard deviation of 25 lbs. what is the probability that a randomly selected adult weights between 120 and 165 lbs?
Answers
The probability that a randomly selected adult weighs between 120 and 165 lbs is approximately 0.8186.
Since the weights of adults are normally distributed with a mean of 140 lbs and a standard deviation of 25 lbs, we can use the standard normal distribution to calculate the probability.
We first need to standardize the values using the formula: z = (x - μ) / σ, where x is the weight, μ is the mean, and σ is the standard deviation.
For x = 120 lbs, z = (120 - 140) / 25 = -0.8, and for x = 165 lbs, z = (165 - 140) / 25 = 1.0. We can then use a calculator to find the probability between -0.8 and 1.0, which is approximately 0.8186.
Thus, the chance of picking an adult at random who weighs between 120 and 165 lbs is roughly 0.8186.
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help please i dont get this
Answers
● < P=R " angles opp =sides"
●PQ =QR " Angles opposite = sides"
therefore PQR is an isosceles " 2 opp angles and sides are equal "
If the number of tolls collected varies directly as the number of vehicles and $129 was collected from 20 vehicles, how many vehicles result in the collection of $3225? Show how you arrived at your answer
Answers
Answer:
500 vehicles
Step-by-step explanation:
let t represent number of tolls and v represent number of vehicles.
given that t varies directly with v then the equation relating them is
t = kv ← k is the constant of variation
to find k use the condition t = 129 from v = 20 , then
129 = 20k ( divide both sides by 20 )
6.45 = k
t = 6.45v ← equation of variation
when t = 3225 , then
3225 = 6.45v ( divide both sides by 6.45 )
500 = v
the number of vehicles is 500
4 cleaner can clean all the rooms in a hotel in 7 1/2 hours. How long will it take 6 cleaners working at the same rate to clean all the rooms in the hotel?
Answers
it will take 6 cleaners working at the same rate to clean all the rooms in the hotel in 5 hours.
If 4 cleaners can clean all the rooms in a hotel in 7 1/2 hours, we can start by using the concept of work rate. Work rate is a measure of how much work is completed in a certain amount of time. If we assume that the work rate of each cleaner is constant, we can set up a proportion to find how long it will take 6 cleaners to clean the same amount of rooms:
4 cleaners can clean all the rooms in 7 1/2 hours.
Therefore, 1 cleaner can clean all the rooms in (4 x 7 1/2) hours = 30 hours.
So, if 1 cleaner takes 30 hours to clean all the rooms, then 6 cleaners working at the same rate will take:
(time for 1 cleaner) / (number of cleaners) = (30 hours) / (6 cleaners) = 5 hours
Therefore, it will take 6 cleaners working at the same rate to clean all the rooms in the hotel in 5 hours.
It is important to note that this assumes that the work rate of each cleaner is constant and that there are no factors that may affect the cleaning time, such as interruptions or changes in the number of rooms to be cleaned. Additionally, the optimal number of cleaners may vary depending on the size of the hotel and the specific cleaning needs.
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Help explain how to solve
Answers
The value of the angle U in the triangle is 92.10 degrees.
How to find the angle in a triangle?The angle U in the triangle can be found using cosine rule as follows:
Let's use cosine formula to find the angle U
c² = a² + b² - 2ab cos C
Hence,
Therefore,
a = 58.8
b = 38.4
c = 71.4
Hence,
71.4² = 58.8² + 38.4² - 2(58.8)(38.4) cos U
5097.96 = 3457.44 + 1474.56 - 4515.84 cos U
5097.96 - 4932 = - 4515.84 cos U
165.96 = - 4515.84 cos U
divide both sides by - 4515.84
cos U = 165.96 / - 4515.84
cos U = - 0.03675063775
U = cos⁻¹ - 0.03675063775
U = 92.1032274244
Therefore,
U = 92.10 degrees
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the mean gpa for 127 residents of the local apartment complex is 1.6 . what is the best point estimate for the mean gpa for all residents of the local apartment complex?
Answers
The best point estimate for the mean GPA for all residents of the local apartment complex would be 1.6.
Given, the mean GPA for the 127 residents of the local apartment complex is 1.6.
The mean or sample mean is used as a point estimate for the population mean or population parameter when the value of the mean of the sample is unbiased and accurately represents the mean of the population.
Here, we are given the mean GPA of 127 residents of the local apartment complex, which is 1.6.
Therefore, the best point estimate for the mean GPA for all residents of the local apartment complex would be 1.6.
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If a regular polygon had 360 side, what would each exterior angle measure? What would each interior angle measure?
Answers
Therefore, each internal angle would be 178 degrees in a regular polygon with 360 sides.
what is angle ?In mathematics, an angle is a figure made up of two rays that share a shared endpoint and are referred to as the sides of the angle and the vertex of the angle, respectively. Angles are typically measured in degrees, radians, or other angle measurement units. Angles can be categorized based on how wide they are. An acute angle is one that is less than 90 degrees, an obtuse angle is one that is higher than 90 degrees but less than 180 degrees, and a right angle is one that is 90 degrees. A reflex angle is greater than 180 degrees but less than 360 degrees, and a straight angle is precisely 180 degrees.
given
Since a polygon with that many sides would have sides that are extremely tiny in relation to the radius, if a regular polygon has 360 sides, it is a circle. Since every group of points in a regular polygon has an equal exterior angle and the sum of all exterior angles in a circle is 360 degrees, each exterior angle in a regular polygon would be measured as follows:
360 edges / 360 degrees = one degree.
Each interior angle of a regular polygon with n sides can be determined using the following formula:
Inner angle is equal to (n-2) x 180 / n.
When we enter n = 360 into this algorithm, we obtain:
(360-2) x 180 degrees / 360 = 178 degrees is the interior angle.
Therefore, each internal angle would be 178 degrees in a regular polygon with 360 sides.
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Figure ABCD is reflected across the x-axis.
What are the coordinates of A' , B' , C' , and D'
Answers
Answer: A'(-1,-4)B'(-5,-8)C'(-5,-4)D'(-4,-2)
Step-by-step explanation:
We have been given a graph of a quadrilateral and we are asked to find the coordinates of our quadrilateral after reflecting it across the x-axis.We can see that coordinates of quadrilateral ABCD are:A (-1,4),B (-5,8),C (-5,4),D (-4,2).
Since we know that rule for reflecting an image across x-axis is . This means that y-coordinates of our given image will be negative.So after reflecting our given quadrilateral across x-axis, coordinates will be:
A'(-1,-4)B'(-5,-8)C'(-5,-4)D'(-4,-2)
GIVING BRAINLIEST FOR THE CORRECT ANSWER (i need a proof that what you’re saying is right bc ppl are giving me the wrong answers)
Answers
Answer:
x [tex]\geq[/tex]2
Step-by-step explanation:
Since the arrow is pointing to the right, we know that it is greater than two. We also know that it could be equal to 2 because the dot is filled in on the number line. So, the answer is x is greater than or equal to 2.
Jada is training for a swimming race. The more she practices, the less time it takes for her to swim one lap. Name the independent and dependent variables.
Answers
Answer:Independent = Her practice time. Dependent= Her lap time.
Step-by-step explanation: The more she practices the faster she can swim.
true or false (and state why): if a sample from a population is large, a histogram of the values in the sample will be approximately normal, even if the population is not normal.
Answers
By the central limit theorem, with a large random sample, the sample histogram will not closely resemble the normal curve but with a large random sample, the probability density function of the sample mean closely resembles the normal curve.
The central limit theorem for samples says that if we keep drawing larger and larger samples and calculating their means, the sample forms their own normal distribution (the sampling distribution). The normal distribution will have the same mean as the original distribution and a variance that equals the original variance divided by the sample size. The variable n is the number of values that are averaged together,and not the number of times the experiment is done.
Hence,with a large random sample, the sample histogram will not resemble the normal curve but with a large random sample, the probability density function of the sample mean will closely resemble the normal curve.
The complete question is-
true or false: (justify/explain your answer) state whether a or b is the true statement below and then explain why the other statement is false. a. with a large random sample, the sample histogram will closely resemble the normal curve. b. with a large random sample, the probability density function of the sample mean will close resemble the normal curve.
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4
Mrs. Donley's math class has a total of 25 students. On Friday, the class was given an eight question quiz on fractions. The numbe
of incorrect answers given by the students is shown below.
Incorrect Answers Number of Students
What is the relative frequency of students that missed 1 question on the quiz?
Answers
Answer: To find the relative frequency of students that missed 1 question on the quiz, we need to first determine the total number of students who missed 1 question. From the table, we see that 9 students missed 1 question.
The relative frequency of students that missed 1 question can be calculated as:
Relative frequency = (Number of students who missed 1 question) / (Total number of students)
Relative frequency = 9 / 25
Relative frequency = 0.36
Therefore, the relative frequency of students that missed 1 question on the quiz is 0.36 or 36%.
Step-by-step explanation:
What is the end behavior of function h? h(x)=-4x^2+11
Answers
We can conclude that the end behavior of the function [tex]$h(x)$[/tex] is that it approaches negative infinity as [tex]$x$[/tex] approaches either positive or negative infinity.
What is meant by end behavior?
End behavior refers to the behavior of a function as the input (usually denoted by x) becomes extremely large (approaches positive or negative infinity). It describes the trend of the function as the input approaches infinity or negative infinity, and is determined by the highest-degree term of the function.
To determine the end behavior of the function [tex]$h(x)=-4x^2+11$[/tex], we can use limits. Specifically, we can evaluate the limit of [tex]$h(x)$[/tex] as [tex]$x$[/tex] approaches positive infinity and as [tex]$x$[/tex] approaches negative infinity.
As [tex]$x$[/tex] approaches positive infinity, we have:
[tex]\lim_{x \to \infty} h(x)= \lim_{x \to \infty} (-4x^2+11) = - \infty[/tex]
This tells us that as [tex]$x$[/tex] gets larger and larger, the value of [tex]$h(x)$[/tex] becomes more and more negative, eventually approaching negative infinity.
Similarly, as [tex]$x$[/tex] approaches negative infinity, we have:
[tex]\lim_{x \to -\infty} h(x)= \lim_{x \to -\infty} (-4x^2+11) = - \infty[/tex]
This tells us that as [tex]$x$[/tex] gets more and more negative, the value of [tex]$h(x)$[/tex] becomes more and more negative, also approaching negative infinity.
Therefore, we can conclude that the end behavior of the function [tex]$h(x)$[/tex] is that it approaches negative infinity as [tex]$x$[/tex] approaches either positive or negative infinity.
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the radius of a circle is changing at .5 cm/sec. find the rate of change of the area when the radius is 4 cm.
Answers
The rate of change of the area of a circle when the radius is 4 cm is 4π cm2/sec.
This can be calculated using the formula for the area of a circle (A = πr2) and the chain rule for derivatives. The chain rule states that when the radius (r) changes, the area of a circle (A) is equal to 2πr times the rate of change of the radius (dr/dt).
Therefore, the rate of change of the area of a circle when the radius is 4 cm is equal to 2π(4 cm) × (0.5 cm/sec) = 4π cm2/sec.
Note that if the rate of change of the radius were different, the rate of change of the area would also be different. This formula can be used to calculate the rate of change of the area of a circle at any given radius, as long as the rate of change of the radius is known.
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by how much must the sample size n be increased if the width of the ci (7.5) is to be halved? if the sample size is increased by a factor of 25, what effect will this have on the width of the interval? justify your assertions.
Answers
The width of the interval will be reduced to 1.5 if the sample size is increased by a factor of 25.
To find how much the sample size n must be increased if the width of the confidence interval is to be halved, use the following formula:
W = (zα/2 x σ/√n)W/2 = (zα/2 x σ/√n')
Where W is the initial width of the confidence interval,
zα/2 is the critical value of the standard normal distribution that corresponds to the level of significance α and the appropriate two-tailed area,
σ is the population standard deviation,
n is the initial sample size, and
n' is the new sample size needed to halve the width of the interval.
Rearranging the second equation to solve for n', we get:
n' = n(4)
So the sample size needs to be increased by a factor of 4, or 300% if the width of the confidence interval is to be halved.
If the sample size is increased by a factor of 25, the effect it will have on the width of the interval can be found using the following formula:
W' = (zα/2*σ/√25n) = (zα/2*σ/5√n)
The width of the interval will be divided by 5, or reduced to one-fifth of its initial value.
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Austin bought 1 pound of melon and 0.83 pounds of cherries. How much fruit did he buy in all?
Answers
Answer:
1.83 pounds of fruit in all
Step-by-step explanation:
1 pound of melon + 0.83 pounds of cherries = 1.83 pounds in all
Answer: He bought 1.83 pounds of fruit
Step-by-step explanation:
Hope this helps :3
You are offered a job that pays $34,000 during the first year, with an annual increase of 6% per year beginning in the second year. That is, beginning in year 2, your salary will be 1.06 times what it was in the previous year. What can you expect to earn in your fourth year on the job? Round your answer to the nearest dollar.
Answers
Year 2 salary: 1.06 x $34,000 = $36,040
Year 3 salary: 1.06 x $36,040 = $38,316.40
Year 4 salary: 1.06 x $38,316.40 = $40,850.38
Rounding to the nearest dollar, you can expect to earn $40,850 in your fourth year on the job.
Help please it’s urgent
Answers
The system of equation with the same solution with 2x + 2y = 16 3x - y = 4 is 2x + 2y = 16, 6x - 2y = 8. Therefore, the answer is 2.
How to solve system of equation?System of equation can be solved using different method such as elimination method, substitution method and graphical method. Therefore, let's solve the system of equation as follows;
2x + 2y = 16
3x - y = 4
multiply equation(ii) by 2
2x + 2y = 16
6x - 2y = 8
add the equations
8x = 24
x = 24 / 8
x = 3
y = 3x - 4
y = 3(3) - 4
y = 9 - 4
y = 5
Therefore,
2x + 2y = 16
6x - 2y = 8
add the equation
8x = 24
x = 24 / 8
x = 3
Therefore,
2(3) + 2y = 16
6 + 2y = 16
2y = 16 - 6
2y = 10
y = 5
Therefore, the equation with the same solution is 2x + 2y = 16
6x - 2y = 8.
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Exact value of sec 5pi/6
Answers
By trigonometric formula, the trigonometric function sec (5π / 6) has the exact value - 2√3 / 3.
How to determine the exact value of a trigonometric function
In this problem we find the case of a trigonometric function, whose exact value can be found by means of trigonometric formula and tables of values:
sec θ = 1 / cos θ
sec (5π / 6) = 1 / cos (5π / 6)
sec (5π / 6) = - 1 / cos (π / 6)
sec (5π / 6) = 1 / (- √3 / 2)
sec (5π / 6) = - 2 / √3
sec (5π / 6) = - 2√3 / 3
The exact value of the trigonometric function sec (5π / 6) is equal to - 2√3 / 3.
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Write an equation for the function g whose graph is the graph f(t) = -100(1.05)^t translated to the right 5 units and up 50 units.
Answers
g(t) = -100 * [tex](1.05)^t[/tex] +[tex](1.05)^(-5)[/tex] 50 is equation for the function g whose graph is the graph f(t) = -100[tex](1.05)^t[/tex] translated to the right 5 units and up 50 units.
Starting with the function f(t) = -100[tex](1.05)^t[/tex], to translate it 5 units to the right and 50 units up, we can replace t with (t - 5) to shift it to the right, and add 50 to the whole function to shift it up. This gives us:
g(t) = f(t - 5) + 50
g(t) = -100[tex](1.05)^(t - 5)[/tex]+ 50
Simplifying this equation, we can use the properties of exponents to rewrite [tex](1.05)^(t - 5)[/tex] as [tex](1.05)^t[/tex] * [tex](1.05)^(-5)[/tex]:
g(t) = -100[tex](1.05)^t[/tex] *[tex](1.05)^(-5)[/tex]+ 50
g(t) = -100[tex](1.05)^(-5)[/tex] * [tex](1.05)^t[/tex] + 50
So the equation for the function g whose graph is the graph f(t) = -100[tex](1.05)^t[/tex] translated 5 units to the right and 50 units up is:
g(t) = -100[tex](1.05)^(-5)[/tex]* [tex](1.05)^t[/tex]+ 50
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