the value of f(5) is 10, which is option (b) , the value of f(-2) is -12, which is option (d). To find the value of f(5) using synthetic substitution, we first set up the synthetic division table as follows:
5 | 3 -9 -20
|||___
| | |
We write the coefficients of the polynomial in the top row of the table and the root (in this case, 5) outside the division symbol. We then bring down the first coefficient (3) and multiply it by the root to get 15, which we write below the second coefficient (-9). We add 15 and -9 to get 6, which we then multiply by the root to get 30, which we write below the third coefficient (-20). We add 30 and -20 to get 10, which is the remainder. Therefore, the value of f(5) is 10, which is option (b).
6) To find f(-2) using synthetic substitution, we set up the synthetic division table as follows:
-2 | 1 0 8 24
|_|||
| | | |
We write the coefficients of the polynomial in the top row of the table and the root (in this case, -2) outside the division symbol. We then bring down the first coefficient (1) and multiply it by the root to get -2, which we write below the second coefficient (0). We add -2 and 0 to get -2, which we then multiply by the root to get 4, which we write below the third coefficient (8). We add 4 and 8 to get 12, which we then multiply by the root to get -24, which we write below the fourth coefficient (24). We add 12 and -24 to get -12, which is the remainder. Therefore, the value of f(-2) is -12, which is option (d).
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Plssss help I need now!!!
"A medicine is effective for 80% of patients. The table shows 30 randomly generated numbers from 0 to 999. Use the table to estimate the probability of the event."
6. The medicine is effective on each of three patients.
7. The medicine is effective on fewer than two of the next three patients.
first part.
The probability that the medicine is effective on each of three patients is 0.512 or 51.2%.
second part.
The probability that the medicine is effective on fewer than two of the next three patients is 0.104 or 10.4%.
How to calculate?
Let p be the probability that the medicine is effective for a given patient. p = 0.8.
6. calculating the probability that the medicine is effective for all three patients. , we will multiply their individual probabilities of being effectively treated, because the patients are independent
P(event 6) = p * p * p = 0.8 * 0.8 * 0.8 = 0.512 or 51.2%.
7.
event 7, we will calculate the probability that the medicine is effective on fewer than two of the next three patients.
We apply the binomial distribution with n = 3 (the number of patients) and p = 0.8 (the probability of success).
The probability mass function for the binomial distribution is:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
P(event 7) = P(X=0) + P(X=1)
= (3 choose 0) * 0.8^0 * 0.2^3 + (3 choose 1) * 0.8^1 * 0.2^2
= 0.008 + 0.096
= 0.104 or 10.4%.
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what is the equation for a cosecant function with vertical asymptotes found at such that n is an integer?
The equation for a cosecant function with vertical asymptotes found at x = nπ such that n is an integer is `y = csc(x - nπ)`.
The cosecant function is the reciprocal of the sine function. The cosecant of a particular angle in a right triangle is the ratio of the hypotenuse to the side opposite the angle.
The cosecant function is written as follows: `csc(x) = 1/sin(x)`
Asymptotes are straight lines or curves that a graph approaches but never touches.
As a result, the graph of a curve gets closer and closer to the asymptote as it moves further away from the origin, but it never touches it.
For a function to have vertical asymptotes at `x = nπ`, the denominator of the function should equal zero. In the cosecant function, the denominator is equal to `sin(x - nπ)`.
Therefore, the vertical asymptotes are where `sin(x - nπ) = 0`.
The general form of the cosecant function is `y = A csc(B(x - C)) + D`.
The constants A, B, C, and D are used to alter the form of the graph of the cosecant function.
They can be used to alter the amplitude, period, phase shift, and vertical displacement of the graph, respectively.
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Pls pls pls helpp 10 points
Answer:
y^10
Step-by-step explanation:
Can someone help me with this factoring? I’ll give you points pls help. You found the greatest common factor, 6a. What factor is remaining?
6ax^2 + 6ax + 6a( )
Answer:
The answer to your problem is, 6a
How to find the GCF:
List the prime factors of each number.Circle every common prime factor — that is, every prime factor that’s a factor of every number in the set.Multiply all the circled numbers.The result is the GCF.6a(x²+x+1)
Use that problem
The answer to your problem is, 6a
1. Determine the scale factor. The point of center is the origin.
M(-12,18) M(-2,3)
Scale factor = 36
(new/old)
2. Determine the scale factor. The point of center is the origin.
M(-2,3) M'(-12,18)
scale factor = 4/9
(new/old)
3. A dilation with a scale factor less than 1 is an enlargement
A. True
B. False
please help me!!
(1) The scale factor for this dilation is 1/6.
(2) The scale factor for this dilation is 6.
(3) False. A dilation with a scale factor less than 1 is a reduction, not an enlargement.
What is the scale factor?1. To find the scale factor for the dilation with center at the origin that maps point M(-12,18) to M(-2,3) we can use the formula:
new coordinate / old coordinate = scale factor
For the x-coordinate:
-2 / -12 = 1/6
For the y-coordinate:
3 / 18 = 1/6
Since both coordinates have the same scale factor, we can conclude that the scale factor for this dilation is 1/6.
2. To find the scale factor for the dilation with center at the origin that maps point M(-2,3) to M'(-12,18) we can again use the formula:
new coordinate / old coordinate = scale factor
For the x-coordinate:
-12 / -2 = 6
For the y-coordinate:
18 / 3 = 6
Since both coordinates have the same scale factor, we can conclude that the scale factor for this dilation is 6.
3. False. A dilation with a scale factor less than 1 is a reduction, not an enlargement. An enlargement is a dilation with a scale factor greater than 1.
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The geese population at Whitney National Park was 450 in 1999. If it increased by 24% within a one year period, what was the geese population at Whitney National Park in 2000?
Answer:
558
Step-by-step explanation:
To find the geese population at Whitney National Park in 2000, we need to add 24% of the population in 1999 to the population in 1999.
First, we need to calculate 24% of 450:
24% of 450 = 0.24 x 450 = 108
So the increase in the geese population from 1999 to 2000 is 108.
To find the population in 2000, we need to add this increase to the population in 1999:
Population in 2000 = Population in 1999 + Increase
Population in 2000 = 450 + 108
Population in 2000 = 558
Therefore, the geese population at Whitney National Park in 2000 was 558.
Amari gathered a random sample of oranges in her town. She calculated data on different variables. For one of the variables that she collected, she constructed a bar graph.
Which of the following variables did she use?
Type of orange
Diameter of the oranges
Number of navel oranges
Price per pound of oranges
Based οn the given οptiοns, it is mοst likely that Amari used the variable "Type οf οrange" tο cοnstruct the bar graphs.
What is a bar graph?A bar graph is a chart that displays categοrical data using rectangular bars with heights οr lengths prοpοrtiοnal tο the values they represent. The bars can be οriented hοrizοntally οr vertically, and each bar represents a categοry οr grοup οf categοries.
In a bar graph, the x-axis typically represents the categοries being cοmpared, while the y-axis represents the frequency, cοunt, οr percentage οf the οbservatiοns that belοng tο each categοry. The height οr length οf each bar is determined by the value οr frequency οf the categοry it represents.
The variable that Amari used tο cοnstruct a bar graph is nοt specified. Hοwever, since a bar graph is a type οf chart that displays categοrical data with rectangular bars, it is likely that she used a variable that represents a categοrical variable, such as the type οf οrange (e.g. Valencia, Navel, Blοοd, etc.).
Therefοre, based οn the given οptiοns, it is mοst likely that Amari used the variable "Type οf οrange" tο cοnstruct the bar graph.
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Points D,B, and E are collinear. Find the value of x so that points A,B, and C are collinear
Answer:
11? I only think this because it says that EBD are collinear and it equals 99 so for (9x) to equal 99, it would have to be nine times 11.
Using the numbers -9 to 9 create a set of 3 points that would have a positive linear association if they were graphed in a scatterpolt
One possible set of points: (-9, 1), (-3, 5), (3, 9) which would have a positive linear association if they were graphed in a scatterplot.
What is scatterplot?A scatterplot is a graph that displays the relationship between two quantitative variables. It is a useful tool for exploring patterns and relationships in data, and can help identify trends, outliers, and potential correlations.
In the given question,
To create a set of 3 points with a positive linear association, we want to choose three points where the y-coordinate increases as the x-coordinate increases. Here's one possible set of points:
(-9, 1), (-3, 5), (3, 9)
If we graph these points on a scatterplot, we can see that there is a clear positive trend. As x increases, y also increases, suggesting a positive linear association between the two variables.
Note that there are many other sets of points we could choose that would also have a positive linear association. The key is to choose points where the y-coordinate tends to increase as the x-coordinate increases.
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What single percentage change is equivalent to a 17% decrease followed by a 12% increase?
2.96% decrease
7.04% increase
7.04% decrease
92.96% increase
2.96% increase
92.96% decrease
let's call our number hmmm Z, now, let's reduce it by 17%, so 100% - 17% = 83%, so the new size for Z is 83% off the original, hmm how much is that?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{83\% of Z}}{\left( \cfrac{83}{100} \right)Z}\implies 0.83Z[/tex]
now, let's increase it by 12%, so the new size will be 100% + 12% = 112%, so 112% of 0.83Z, let's check how much is that
[tex]\stackrel{\textit{112\% of 0.83Z}}{\left( \cfrac{112}{100} \right)0.83Z}\implies 0.9296Z[/tex]
now, let's convert that to a percent format by simply multiplying it by 100, so that'd be 100 * 0.9296Z = 92.96% of Z. Well, hell 92.96% is less than 100%, so is really 100% - 92.96% = 7.04% less.
So, instead of all that rigamarole, we could have just reduced Z by 7.04% in one fell swoop and obtain the same thing.
The velocity (in meters per second) with which a roller coaster moves can be given by the function f(t) = (t - 3)3 t. find the acceleration function a(t).
The acceleration function is a(t) = 6(t - 3).
Acceleration is the rate at which an object changes its velocity. The acceleration function is a mathematical function that gives the acceleration of an object at any given time
To find the acceleration function, we need to take the second derivative of the given velocity function f(t).
f(t) = (t - 3)^3 + t
First, let's find the first derivative of f(t)
f'(t) = 3 × (t - 3)^2 + 1
Now, let's find the second derivative of f(t) ( the acceleration function )
a(t) = f''( t )
= d/dt [3 × (t - 3)^2 + 1]
Do the derivation
= 6(t - 3)
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The given question is incomplete, the complete question is:
The velocity (in meters per second) with which a roller coaster moves can be given by the function f(t) = (t - 3)^3 + t. find the acceleration function a(t).
Perform the indicated operation, and write the answer in lowest terms.
−16/5 ⋅ (−15/56)
Answer:
6/7
Step-by-step explanation:
First, cancel out 16 and 56 by a common factor of 8. The resulting expression is -2/5*-15/7. Then, simply 5 and 15 by a common factor of 5. Then, you will get: -2*(-3/7). The negatives cancel out, so the answer is 6/7.
Which car park should I use?
There is a Park and Ride service where it costs 40p per hour to park, but you also have to pay 60p for the bus fare into town.
Alternatively, I could park for free at the railway station and get the train to Mathstown - a return ticket costs £3.50.
What advice would you give me if I was trying to decide whether to use one of the car parks, the Park and Ride, or the train?
Answer:
To determine which option is the most cost-effective, you can use some simple math. Let's assume you need to park for 8 hours:
Park and Ride:
Parking cost: 8 hours x £0.40 = £3.20
Bus fare: £0.60 x 2 (round trip) = £1.20
Total cost: £4.40
Free parking at the railway station:
Train fare: £3.50 x 2 (round trip) = £7.00
Total cost: £7.00
Based on the calculations above, the Park and Ride option is cheaper for an 8-hour parking period. However, you should also consider factors such as convenience and travel time when making your decision. If the railway station is closer to your destination or has more frequent train services, it may be the better option despite the higher cost.
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if lines m and n are parallel, and ∠ 8 measures 110°, which is the measure of ∠7
Answer:
∡7 = 70°
Step-by-step explanation:
∡7 and ∡8 are supplementary angles
∡7 + ∡8 = 180°
If:
∡8 = 110°
Then:
∡7 = 180 - 110
∡7 = 70°
a reporter for an international newspaper is given an assignment that is randomly chosen from the following destinations worldwide: 8 continental united states assignments, 29 south american assignments, 15 european union assignments, and 22 asian assignments. find the probability that he gets an assignment in the united states or asia . express your answer as a fraction
The probability that the reporter gets an assignment in the United States or Asia is 15/37.
To find the probability that the reporter gets an assignment in the United States or Asia, we first need to determine the total number of assignments in the pool.
Total number of assignments = 8 + 29 + 15 + 22 = 74
Next, we need to determine the number of assignments that are in the United States or Asia.
Number of assignments in the United States or Asia = 8 + 22 = 30
Finally, we can calculate the probability of the reporter getting an assignment in the United States or Asia by dividing the number of assignments in the United States or Asia by the total number of assignments:
Probability of getting an assignment in the United States or Asia = (Number of assignments in the United States or Asia) / (Total number of assignments)
Probability of getting an assignment in the United States or Asia = 30/74
Therefore, the probability of the reporter getting an assignment in the United States or Asia is 30/74, which can be simplified by dividing both the numerator and denominator by their greatest common factor (GCF), which in this case is 2:
Probability of getting an assignment in the United States or Asia = 15/37
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If the measure of angle 11 is 90 degrees, and the measure of angle 9 is 60 degrees, what is the measure of angle 10?
The measure of angle 10 is 30 degrees.
What is an angle?
we can see that angle 10 and angle 11 form a straight line, and angle 9 and angle 10 form a triangle with angle 11.
Since angle 11 is a right angle with a measure of 90 degrees, the sum of angles 9 and 10 in the triangle must be 90 degrees.
We know that the measure of angle 9 is 60 degrees, so we can solve for the measure of angle 10 as follows:
angle 9 + angle 10 = 90 degrees
60 degrees + angle 10 = 90 degrees
angle 10 = 90 degrees - 60 degrees
angle 10 = 30 degrees
Therefore, the measure of angle 10 is 30 degrees.
What is triangle ?
A triangle is a closed geometric shape that consists of three line segments that connect three non-collinear points. The points where the line segments intersect are called the vertices of the triangle, and the line segments themselves are the sides of the triangle.
Triangles are two-dimensional objects that lie flat in a plane, and they have a variety of properties and characteristics that make them important in mathematics and other fields. The angles and sides of a triangle can be measured and related to one another through various geometric formulas and theorems, and triangles are used in a wide range of applications, from basic geometry and trigonometry to engineering, physics, and computer graphics.
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Complete question is: If the measure of angle 11 is 90 degrees, and the measure of angle 9 is 60 degrees, the measure of angle 10 is 30 degrees.
PLS HELP WITH THIS QUESTION
Answer:
even
Step-by-step explanation:
It lands on 10, and 8, take that, divide by 2, and mutiply by 8.
Find the inverse function, f-4 (x) : f(x) = 4(3x + 2).
Answer:
To find the inverse function of f(x) = 4(3x + 2), we need to solve for x in terms of f(x) and then interchange the roles of x and f(x) in the expression to obtain the inverse function.
Let y = f(x) = 4(3x + 2)
Dividing both sides by 4, we get:
y/4 = 3x + 2
Subtracting 2 from both sides, we get:
y/4 - 2 = 3x
Dividing both sides by 3, we get:
(y/4 - 2) / 3 = x
Hence, the inverse function is:
f^-1(x) = (x/4 - 2) / 3
Or we can also write it as:
f^-1(x) = (1/3)x/4 - 2/3
Therefore, the inverse function of f(x) = 4(3x + 2) is f^-1(x) = (1/3)x/4 - 2/3.
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Bert and Ernie both start at point A. They each walk in a straight line at an angle of 100 degrees to each other. After 1 hour, Bert walked 5 miles and Ernie walked 6.5 miles. How far apart are they?
The distance between Bert and Ernie is 8.8 miles.
What is law of cosine?
According to a trigonometry rule, the square of a side in a plane triangle is equal to the total of the squares of the other sides minus twice that amount, along with the cosine of the angle that separates them.
Here using law of cosine we can find the distance between Bert and Ernie. Then,
[tex]a^2=b^2+c^2-2ab cos(A)[/tex]
Here a = BC , b = 5 mi , c = 6.5 mi and A = 100° then,
=> [tex]BC^2 = 5^2+6.5^2-2\times5\times6.5\times cos (100\textdegree)[/tex]
=> [tex]BC ^2= 25+42.25-65\times(0.1736)[/tex]
=> [tex]BC^2= 78.534[/tex]
=> BC = 8.8 miles.
Hence the distance between Bert and Ernie is 8.8 miles.
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Find the area of a segment of a circle if the central angle of the segment is 50° and the radius is 15
In conclusion the area of the segment is approximately 32.76 square units.
How to find?
To find the area of a segment of a circle, we can use the formula:
Area of segment = (θ/360)πr²2 - (1/2)rsin(θ)
where:
θ is the central angle of the segment in degrees
r is the radius of the circle
π is a constant approximately equal to 3.14
sin is the sine function
In this case, the central angle is 50° and the radius is 15. Substituting these values into the formula, we get:
Area of segment = (50/360)π(15)²2 - (1/2)(15)sin(50)
= (5/36)π(225) - (1/2)(15)(0.766)
= 32.76 square units (rounded to two decimal places)
Therefore, the area of the segment is approximately 32.76 square units.
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evaluate C(4,2)
-6
-12
-24
Answer:
(4,2) represents the number of ways to choose 2 items from a set of 4 distinct items. The formula for C(n,r) is n! / (r! * (n-r)!), where n is the total number of items and r is the number of items being chosen. Plugging in the values for C(4,2), we get: C(4,2) = 4! / (2! * (4-2)!) = 24 / (2 * 2) = 6 Therefore, there are 6 ways to choose 2 items from a set of 4 distinct items.
0 / 350
The value of the given combination C(4, 2) by applying the combination formula in factorial form is equals to option 6.
To evaluate C(4, 2), we use the combination formula, also known as "n choose r" or "C(n, r)",
which calculates the number of ways to choose r items from a set of n distinct items without considering their order. The formula for C(n, r) is:
C(n, r) = n! / (r! × (n - r)!)
Where "!" denotes the factorial of a number, which is the product of all positive integers up to that number.
For example,
4! = 4 × 3 ×2 × 1
= 24.
Now, let's plug the values into the formula for C(4, 2):
C(4, 2) = 4! / (2! × (4 - 2)!)
= 4! / (2! × 2!)
= (4 × 3 × 2 × 1) / ((2 × 1) × (2 × 1))
= (24) / (4)
= 6
Therefore , the value of the combination C(4, 2) equals to option 6.
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Find the value of < Z O X
< Z O X = °
The unknown angles on the straight line is as follows:
∠ZOX = 64 degrees
How to find the angles on a straight line?The sum of angles in a line segment is 180 degrees. Therefore, let's find the angle ∠ZOX as follows:
∠YOX = ∠YOZ + ∠ZOX
Therefore,
∠ZOX = ∠YOX - ∠YOZ
∠YOX = 180°
Therefore,
5x + 6 + 3x - 2 = 180
8x + 4 = 180
8x = 180 - 4
8x = 176
x = 176 / 8
x = 22
Hence,
∠ZOX = 3x - 2
∠ZOX = 3(22) - 2
∠ZOX = 66 - 2
∠ZOX = 64 degrees
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In a class of 40 students each student take at least One of Physics and Chemistry. If the number of student that take Physics is three times the number that take both Subsect and the number that take chemistry is twice the number that take Physic, find the number of Student that take Physics only
the number of students who take only Physics is 15.
Define equationAn equation is a mathematical statement that shows that two expressions are equal. It is typically written using an equal sign (=) between the two expressions. The expressions on either side of the equal sign are called the left-hand side (LHS) and the right-hand side (RHS) of the equation.
Let's denote the number of students who take only Physics by x.
The total number of students who take Physics or Chemistry=40The number of Physics students is three times the number who take both: number of Physics students = 3The number of Chemistry students is twice the number who take Physics: number of Chemistry students = 2We can use these equations to solve for x, the number of students who take only Physics:
40 = 3(number who take both) + 2(number of Physics students) - number who take both40 = 2(number who take both) + 2(number of Physics students)20 = number who take both + number of Physics studentsSubstituting the expression for the number of Physics students in terms of the number who take both, we get:
20 = number who take both + 3(number who take both)
20 = 4(number who take both)
number who take both = 5
this value in the expression for the number of Physics students, we get:
number of Physics students = 3(number who take both) = 15
Finally, we can use the first equation to solve for the number of students who take only Physics:
40 = 15 + 2(number of students who take only Physics) - 5
40 = 10 + 2(number of students who take only Physics)
number of students who take only Physics = 15
Therefore, the number of students who take only Physics is 15.
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Find two examples of the use of data or probability in the news. You can use online news sources, magazines, or newspapers. Describe in detail how probability concepts are applied. Cite your sources.
Please follow these guidelines for your discussion posts:
Write at least 150–300 words.
Make sure your posts are grammatically and mechanically correct.
Address all parts of the prompt.
Provide at least one example to support your response. (Example choices include an anecdote, statistic, and/or textual evidence.)
Two examples that show the use of data and probability are an article about covid and an article about the use of predictive analysis.
What are two examples of the use of data or probability?Example 1: According to a recent article in The New York Times, data from the Centers for Disease Control and Prevention (CDC) shows that individuals who are fully vaccinated against COVID-19 are much less likely to be hospitalized or die from the virus. The article cites a study that found the Pfizer-BioNTech vaccine was 91 percent effective in preventing hospitalization and 95 percent effective in preventing death. This data reinforces the importance of vaccination in preventing severe illness and death from COVID-19.
Example 2: A recent article in The Wall Street Journal discusses the use of predictive analytics in the insurance industry. The article explains that insurance companies are increasingly using data and probability models to predict and mitigate risks associated with climate change, natural disasters, and other potential events that could result in insurance claims.
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Backing into a driveway or an alley on the right sidea.is illegal in most states.b. often causes collisions.C.is the safest turnaboutmaneuver.d. should be done only in heavy traffic,Injuries and deaths frommotorcycle collisions are primarily froma.driving too fast.b.the exposed position ofthe rider.c,other vehicles hitting them.d. hitting deer, 21.
Backing into a driveway or an alley on the right side, none of the options are correct
A) Backing into a driveway or alley on the right side is not necessarily illegal in most states. However, some states may have specific laws or regulations related to this maneuver, so it is important to check local laws.
B) Backing into a driveway or alley on the right side can be risky and may increase the likelihood of collisions, particularly if the driver is not paying close attention or if the view is obstructed. However, it does not always cause collisions and may be necessary in certain situations.
C) The safest turnabout maneuver depends on the specific situation and the layout of the road. In some cases, backing into a driveway or alley may be the safest option, while in other situations, a three-point turn or U-turn may be safer.
D) Whether to perform a backing maneuver in heavy traffic depends on the situation. In general, it is advisable to avoid backing up in heavy traffic if possible, as it can increase the risk of collisions. However, if there is no other option, the driver should proceed with caution and take all necessary precautions to ensure safety.
Therefore, the none of the options are correct
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The given question is incomplete, the complete question is:
Backing into a driveway or an alley on the right side a.is illegal in most states b. often causes collisions .c is the safest turn about maneuver d. should be done only in heavy traffic
Given mn, find the value of x.
+
(8x+6)°
(9x-30)°
B
PLS HURRY!!
value of variable x on the parallel line is 12.
Define co exterior angleIn geometry, a co exterior angle is an angle that is formed outside of a geometric figure by extending one of its sides. More specifically, a co exterior angle is formed when a transversal intersects two parallel lines, and it is an angle that is located outside of the parallel lines and on the same side of the transversal as one of the angles formed by the intersection.
Given
m ║n
8x+6 and 9x-30 are co exterior angle
8x+6+9x-30=180°
17x-24=180°
x=12
hence, value of variable x on the parallel line is 12.
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does anyone know the answer
In rewriting the expression in equivalent form, C. Tony made an error in Step 3. He should have multiplied each exponent by 4 instead of adding 4.
How to take exponents to powers ?When writing in equivalent form such that one converts the expression ( a ² b ³ / c) ⁴, one can use the law of exponents.
In this instance, the law of exponents states that if you are taking an exponent with a certain base, to another exponent, you multiply the exponents to get the new exponent.
In step 3, Tony should have multiplied each exponent by 4 instead of adding 4.
Find out more on exponents at https://brainly.com/question/31242983
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What is the range of the function f(x) = |x| – 3?
{f(x) ∈ ℝ | f(x) ≥ –3}
{f(x) ∈ ℝ | f(x) < –3}
{f(x) ∈ ℝ | f(x) ≤ –3}
{f(x) ∈ ℝ | f(x) > –3}
Answer:
{f(x) ∈ ℝ | f(x) ≥ –3}
Step-by-step explanation:
f(x)=|x|-3
|x| have range x≥0 .
f(x)≥0-3
f(x)≥-3
First answer {f(x) ∈ ℝ | f(x) ≥ –3}
Find the surface area of the pyramid.
A triangular pyramid. The base triangle has a base of 20 yards and a height of 17.3 yards. The height of a triangular face is labeled 12 yards.
The surface area is
square yards.
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Find the surface area of the pyramid.
A triangular pyramid. The base triangle has a base of 20 yards and a height of 17.3 yards. The height of a triangular face is labeled 12 yards.
The surface area is
square yards.
Skip to navigation
Find the SA of a triangular pyramid, the base triangle is 20, the height of 17.3 yard, and 12
Step-By-Step:
The height triangle has a height of 17.3 yards and a width of 12 yards. 3. Finally, connect the two triangles to create the pyramid's surface area. The surface area of the pyramid is 116.7 yards².
Answer:
116.7 yards².
Answer:
The first step is to find the area of the base triangle:
Area = (1/2) x base x height
Area = (1/2) x 20 yards x 17.3 yards
Area = 173 square yards
To find the surface area of the pyramid, we need to find the areas of the four triangular faces and add them to the base area.
Area of a triangular face = (1/2) x base x height
Area of each face = (1/2) x 20 yards x 12 yards
Area of each face = 120 square yards
Now we can add up all the areas:
Surface area = base area + area of four faces
Surface area = 173 square yards + 4 x 120 square yards
Surface area = 653 square yards
Therefore, the surface area of the pyramid is 653 square yards.
Find the general term of 6,12,24,48,...
Answer:
an = 6 * 2^(n-1)
Step-by-step explanation:
To find the general term of the sequence 6, 12, 24, 48, ... , we need to observe that each term is obtained by multiplying the previous term by 2. Therefore, the sequence is a geometric sequence with first term a = 6 and common ratio r = 2.
The formula for the nth term of a geometric sequence is:
an = a * r^(n-1)
Substituting a = 6 and r = 2, we get:
an = 6 * 2^(n-1)
Therefore, the general term of the sequence 6, 12, 24, 48, ... is given by the formula an = 6 * 2^(n-1).