Answer:
19π/6 radians and 31π/6 radians
Step-by-step explanation:
To rotate point A counterclockwise by 7π/6 radians, we can add this angle to the angle of point A, which is 0 radians, to get the angle of point B:
The angle of point B = angle of point A + 7π/6 radians
= 0 radians + 7π/6 radians
= 7π/6 radians
Angle of point B in degrees = (7π/6) * (180/π) degrees
= 210 degrees
To find two other positive angles of rotation that take A to B, we can add any multiple of 2π radians to the angle of point B. This is because adding 2π radians is equivalent to a full rotation around the unit circle, which brings us back to the same point. Therefore, we have:
angle of rotation 1 = angle of point B + 2π radians
= 7π/6 radians + 2π radians
= 19π/6 radians
angle of rotation 1 in degrees = (19π/6) * (180/π) degrees
= 285 degrees
angle of rotation 2 = angle of point B + 4π radians
= 7π/6 radians + 4π radians
= 31π/6 radians
angle of rotation 2 in degrees = (31π/6) * (180/π) degrees
= 465 degrees
So the two other positive angles of rotation that take A to B are (19π/6 radians and 31π/6 radians) or 285 degrees and 465 degrees respectively.
Note:
To convert the angles from radians to degrees, we can use the conversion factor:
1 radian = 180/π degrees
Ben's Barbershop has a rectangular logo for their business that measures 7(1)/(5) feet long with an area that is exactly the maximum area allowed by the building owner. Create an equation that could be used to determine M, the unknown side length of the logo.
An equation that could be used to determine M, the unknown side length of the logo is X = (36/5) x M
Let's assume that the unknown side length of the logo is 'M'. The logo is a rectangle, and the area of a rectangle is given by multiplying its length and width. Since we know the length of the logo is 7(1)/(5) feet, we can write the equation:
A = L x W
where A is the area of the logo, L is the length of the logo, and W is the width of the logo.
Substituting the given values, we get:
A = (7(1)/(5)) x M
or
A = (36/5) x M
Now, we know that the area of the logo is exactly the maximum area allowed by the building owner. Let's assume this maximum area is 'X'. So, we can write another equation:
A = X
Combining both equations, we get:
X = (36/5) x M
This is the required equation that could be used to determine the unknown side length 'M' of the logo if we know the maximum area allowed by the building owner 'X'.
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Which value of y is a solution of this inequality?
3y-4<11
A. y=4
B. y=5
C. y=6
D. y=7
Answer:
B. y=5
Step-by-step explanation:
3y-4<11
3y-4+4<11+4
3y<15
3y/3<15/3
y<5
CAN SOMEONE HELP WITH THIS QUESTION?
a) The velocity function is v(t) = -3 cos(t) - 1.
b) The object's displacement is 3sin(3) - K - 3.
c) The total distance traveled by the object from time 0 to time 3 is 3sin(3) + 3 meters.
a) To find the equation for the velocity of the object, we need to integrate the function for acceleration with respect to time. The velocity function v(t) is the antiderivative of a(t). Since a(t) = 3 sin(t), the antiderivative of a(t) is v(t) = -3 cos(t) + C, where C is the constant of integration.
We can find C using the initial velocity given. Since v(0) = -2m/s, we substitute t=0 and v(0) = -2m/s into the velocity function to get:
v(0) = -3 cos(0) + C = -2
Solving for C, we get C = -1. Now we can write the velocity function as:
v(t) = -3 cos(t) - 1
b) To find the displacement of the object from time 0 to time 3, we need to integrate the velocity function with respect to time over the interval [0,3]. The displacement function s(t) is the antiderivative of v(t):
s(t) = ∫v(t) dt = ∫(-3cos(t) - 1) dt = 3sin(t) - t - K
where K is the constant of integration. Since we want to find the displacement from time 0 to time 3, we evaluate s(3) - s(0):
s(3) - s(0) = (3sin(3) - 3) - (0 - K) = 3sin(3) - K - 3
c) To find the total distance traveled by the object from time 0 to time 3, we need to calculate the area under the absolute value of the velocity curve over the interval [0,3]. Since the velocity is negative for some time intervals, we take the absolute value of the velocity function:
|v(t)| = |-3cos(t) - 1| = 3cos(t) + 1
We can integrate this function from 0 to 3 to get the total distance traveled:
∫|v(t)| dt = ∫(3cos(t) + 1) dt = 3sin(t) + t + C
Evaluating this at t=3 and t=0, we get:
∫|v(t)| dt = (3sin(3) + 3) - (0 + 0) = 3sin(3) + 3
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Help I need the answer
Fast
Answer: 4
Step-by-step explanation: because he needs to divided by 2
Alina wants to make keepsake boxes for her two best friends. She doesn't have a lot of money, so she wants to make each box described so that it holds as much as possible with a limited amount of material.
For Jen, Alina wants to make a box with a square base whose sides and base are made of wood and whose top is made of metal. The wood she wants to use costs 5 cents per square inch, while the material for the metal top costs 12 cents per square inch. What is the largest possible box (in terms of volume measured in cubic inches) that Alina can make for Jen if she only has $30.00 to spend on materials? (Round your answer to three decimal places.)
Answer:
So Alina can make a box with dimensions 8.445 inches by 8.445 inches by 8.445 inches (with a metal top) that will hold approximately 606.526 cubic inches.
Step-by-step explanation:
Let's assume that the length of one side of the square base of the box is "x". Then the height of the box is also "x" to maximize the volume.
The surface area of the box (excluding the top) is given by:
2(x^2) + 4(x^2) = 6(x^2)
The surface area of the metal top is:
x^2
The total surface area of the box is the sum of the surface area of the box and the surface area of the metal top:
6(x^2) + x^2 = 7(x^2)
The cost of the wood for the box is:
5 cents per square inch * 6(x^2) = 30x^2 cents
The cost of the metal for the top is:
12 cents per square inch * x^2 = 12x^2 cents
The total cost of the box is:
30x^2 + 12x^2 = 42x^2 cents
We want to find the maximum volume of the box that can be made with $30, which is 3000 cents. Therefore, we can set up the equation:
42x^2 = 3000
Solving for x, we get:
x^2 = 71.429
x ≈ 8.445
Therefore, the maximum volume of the box is:
V = x^2 * x = (8.445)^3 ≈ 606.526 cubic inches.
So Alina can make a box with dimensions 8.445 inches by 8.445 inches by 8.445 inches (with a metal top) that will hold approximately 606.526 cubic inches.
what is the answer to what does the transformation F(x)
>I/9f(X) do to the graph of f(x)
The effect of the transformation is a vertical srhink of scale factor 1/9.
What is the effect of the transformation to the graph of f(x)?For a function f(x), can define a vertical dilation of scale factor k as:
g(x) = k*f(x).
if k > 1, we have a stretch.if 0 < k < 1, we have a contraction.In this case the transformation is:
f(x) ---> (1/9)*f(x)
So we have a vertical dilation of scale factor k = 1/9, so we have a vertical contraction.
Then the effect that this will have in the graph is that it will contract/shrink it vertically.
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CAN SOMEONE HELP WITH THIS QUESTION?
Answer:
49
Step-by-step explanation:
[tex]\int\limits^{12}_0 {-0.002t^{2} +0.7t} \, dt \\=(-0.002\frac{{12}^{3} }{3} )+(0.7\frac{{12}^{2} }{2} )\\-(-0.002\frac{{0}^{3} }{3} )-(0.7\frac{{0}^{2} }{2} )\\\\=(-0.002\frac{{12}^{3} }{3} )+(0.7\frac{{12}^{2} }{2} )-0-0\\\\=49.248\\[/tex]
A farmer has 60 metres of perimeter fencing. For every I m² he can keep I chicken. How can he arrange his fence so that the enclosed area gives him the greatest area?
Answer:
The greatest area enclosed by the fence will be a square. If the farmer has 60 metres of perimeter fencing, he can use 15 meters of fencing for each side of the square. This would give him an area of 15² = 225 m². Since he can keep one chicken for every square meter, he can keep 225 chickens. Therefore, the farmer should arrange his fence in the shape of a square to get the greatest area.
The length of the side of a cube is represented
by x-4. Express the surface area of the cube in
terms of x.
The surface area of the cube of side x-4 in terms of x is 6x² - 48x + 96.
Given length of a side of a cube (a) = x-4
The formula for finding the surface area of a cube = 6a²
By, substituting the 'a' value in the above formula we can obtain the surface area of the cube.
6a² = 6 * (x-4)² [a = x-4]
= 6 * (x² - 8x + 16)
= 6x² - 48x + 96
From the above analysis, we can conclude that the surface area of the given cube in terms of 'x' is 6x² - 48x + 96.
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IN CASE YOU ARE LOOKING FOR THE ANSWER
In 2010, the population of Houston, Texas, was 2,099,451 and the population density was 3501 people per square mile.
What was Houston's land area in 2010?
Enter your answer as a decimal in the box. Round your answer to the nearest tenth.
Answer: 599.7 square miles
Step-by-step explanation: Divide 2,099,451 by 3501 and then round to the nearest tenth.
Suppose that the demand of a certain item is x=-0.7p+10.
Evaluate the elasticity at 6.
The item is an inelastic good at a price of 6 because it is negative and have a demand of -0.71.
What is the item's demand if elasticity is at 6?The formula for elasticity of demand is Elasticity of demand = (% change in quantity demanded) / (% change in price)
The initial quantity demanded at a price of 6 and the quantity demanded at a slightly different price must be know.
Let say Initial quantity demanded is:
x = -0.7(6) + 10
x = 5.8
Assume price changes slightly to 6.01, which gives us a new quantity demanded of x:
= -0.7(6.01) + 10
= 5.793
The % change in quantity demanded will be:
= [(new quantity demanded - initial quantity demanded) / initial quantity demanded] x 100%
= [(5.793 - 5.8) / 5.8] x 100%
= -0.12%
As price has changed from 6 to 6.01, we can calculate the percentage change as follows:
% change in price = [(new price - initial price) / initial price] x 100%
= [(6.01 - 6) / 6] x 100%
= 0.17%
Elasticity of demand = (% change in quantity demanded) / (% change in price)
= (-0.12% / 0.17%)
= -0.71
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what is the solution to the equation 0.5x - 1.25 = 3.5?
Answer:
Step-by-step explanation:
Add '-1.25' to each side of the equation.
1.25 + -1.25 + -0.5x = 0.75 + -1.25 + 3.5n
Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -0.5x = 0.75 + -1.25 + 3.5n
-0.5x = 0.75 + -1.25 + 3.5n
Combine like terms: 0.75 + -1.25 = -0.5
-0.5x = -0.5 + 3.5n
Divide each side by '-0.5'.
x = 1 + -7n
Simplifying
x = 1 + -7n
1234-4566/45.44+67*755.34
Answer:
To solve this expression, we need to follow the order of operations (PEMDAS) which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
The expression is:
1234 - 4566 / 45.44 + 67 * 755.34
First, we need to perform the division operation since it comes before addition and multiplication.
4566 / 45.44 = 100.50
Now, we can substitute that into the expression:
1234 - 100.50 + 67 * 755.34
Next, we need to perform the multiplication operation:
67 * 755.34 = 50,548.78
Now, we can substitute that into the expression:
1234 - 100.50 + 50,548.78
Next, we can perform the addition and subtraction operations:
1234 + 50,448.28 = 51,682.28
Therefore, the result of the expression is 51,682.28.
Allison wants to know how many games teenagers at her school have on their phones. Which answer choice gives an example of a random sample Allsion could use to help answer her question?
A Ask all the 30 female teenagers and 30 male teenagers at the grocery store if they have phones.
B Ask the first 100 people at the library on Saturday morning how many games they have on their phones.
C Ask 10 people from each grade level at Allison's school how many games they have on their phones.
D Ask 5 teenagers from 20 different countries how many games they have on their phones.
The answer choice which gives the best-example of the "random-sample" is (c) Ask 10 people from each "grade-level" at Allison's school about how many games they have on their phones.
A "Random-Sample" is a subset of a larger population which is chosen in such a way that each member of the population has an equal chance of being selected.
The Option (c) : gives the best example of a random sample that Allison could use to help answer her question. By asking 10 people from each grade level at her school, Allison can obtain a sample that includes a variety of ages, genders, and backgrounds.
This can help to ensure that the sample is representative of the population she is interested in studying.
Option (a) : is not a random sample because it only includes teenagers who happen to be at the grocery store at the time Allison is conducting her survey. This may not represent entire population of teenagers at her school.
Option (b) : is not a random sample either because it only includes people who happen to be at the library on Saturday morning. This may not be representative of the entire population of teenagers at her school.
Option (d) : is not a random sample because it only includes teenagers from 20 different countries. This may not be representative of the population of teenagers at Allison's school or in her local area.
Therefore, the correct option is (c).
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A circle has a radius of 9 cm and a sector of the circle has an arc length of 9.7 cm. The angle at the centre of the sector is xº. Calculate the value of x to the nearest degree. 9 cm X 3 9.7 cm
Answer:
62 degrees
Step-by-step explanation:
Hope this helps! If it’s wrong I’m really sorry. I used the formula θ = s/r then converted it from radians to degrees.
Pls give brainliest!
What are the solutions to these -6(n-1) < 3 or 2(+1) > 0?
Answer:
When n is greater than 1/2 or always true
n > 1/2
Step-by-step explanation:
Rewrite.
0+0+6(n−1)=2(n+1)
Simplify by adding zeros.
6(n−1)=2(n+1)
Apply the distributive property.
6n+6⋅−1=2(n+1)
Multiply 6 by −1.6n−6=2(n+1)
Simplify 2(n+1).
6n−6=2n+2
Move all terms containing n to the left side of the equation.
4n−6=2
Move all terms not containing n to the right side of the equation.
4n=8
Divide each term in 4n=8 by 4 and simplify.
n=2
The curve above is the graph of a sinusoidal function. It goes through the points
and
. Find a sinusoidal function that matches the given graph. If needed, you can enter
=3.1416... as 'pi' in your answer, otherwise use at least 3 decimal digits.
The sinusoidal function that matches the specified graph, expressed using π ≈ 3.1416 is; y ≈ 4·sin(0.628·(x + 3))
What is a sinusoidal function?A sinusoidal function is a periodic function that is based on either the sine or the cosine function.
The general form of a sinusoidal function is; y = A·cos(B·(x - C)) + D
The peak and the trough of the graph of the function indicates that the amplitude, A = (4 - (-4))/2 = 4
The vertical shift, D = (4 + (-4))/2 = 0
The period, P = 2·π/B
A cycle is completed in -0.5 - (-10.5) = 10 units of the x-value interval
P = 10 = 2·π/B
Therefore; B = π/5
When x = -8, y = 0, therefore;
0 = 4·sin((π/5)·((-8) - C)) + 0
4·sin((π/5)·((-8) - C)) = 0
sin((π/5)·((-8) - C)) = 0
(π/5)·((-8) - C) = 0
((-8) - C) = 0
C = -8
When x = 2, y = 0, therefore;
0 = 4·sin((π/5)·(2 - C)) + 0
4·sin((π/5)·(2 - C)) = 0
sin((π/5)·(2 - C)) = 0
(π/5)·(2 - C) = 0
(2 - C) = 0
C = 2
Similarly; When x = -3, y = 0, therefore; C = -3
y = 4·sin((π/5)·(x + 3))
The value C = -3, corresponds to the horizontal shift of the graph of the sine function, which is shifted 3 units to the left
The sinusoidal function, where π ≈ 3.1416 is therefore;
y ≈ 4·sin((0.628)·(x + 3))
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HELP PLS Triangle D has been dilated to create triangle D′. Use the image to answer the question.
Determine the scale factor used.
Scale factor of one third
Scale factor of 3
Scale factor of 4
Scale factor of one fourth
The scale factor will be one-third which is 1/3. Then the correct option is A.
Given that:
Dimension of a small triangle, 6, 8, and 10
Dimension of a giant triangle, 18, 24, and 30
Dilation is the process of increasing the size of an item without affecting its form. The object's size can be raised or lowered depending on the scale factor. There is no effect of dilation on the angle.
The scale factor is calculated as,
SF = 6 / 18
SF = 1 / 3
The scale factor will be one-third which is 1/3. Then the correct option is A.
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Answer:
1/3
Step-by-step explanation:
I took the test!
Please help!
Whoever answers right gets brainliest!!!!
Answer:
[tex]y - 4 = - 3(x - 2)[/tex]
There are 90 kids in the band. 20% of the kids own their own instruments, and the rest rent them.
a) 18 Kids own their own instruments.
b) 72 kids rent instruments.
c) 80% percentage of the kids rent their instruments.
We have,
There are 90 kids in the band.
20% of the kids own their own instruments.
a. How many kids own their own instruments?
So, 20% of 90
= 20/100 x 90
= 1/5 x 90
= 18 kids
b. How many kids rent instruments?
= 90 - 18
= 72 Kids
c. . What percentage of the kids rent their instruments?
So, x% of 90 = 72
90x = 7200
x= 80%
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Select the correct answer.
What are the zeros of g(x) = x³ + 6x² - 9x-54?
A. 1, 2,27
B.3, -3, -6
C.-6, 3, 6
D. 2, -1, 18
Answer:
The answer is C
Step-by-step explanation:
The zeros of g(x) = x³ + 6x² - 9x-54 are -6, 3, 6. Therefore, the correct answer is C.
What is the main idea of beauty algebra? 
Answer:
Beauty algebra is not a recognized term or concept within the field of mathematics. Therefore, there is no main idea associated with it in mathematical context. It is possible that the term is used in a different context or field, but without additional information, it is not possible to provide a more accurate answer.
Lawrence is increasing the rectangular patio in his backyard. His patio is currently 12
feet by 10 feet. He wants to increase the patio by adding a decorative tile the same width (x) all the way around creating a total area of 180 square feet. Select all the quadratic equations that represent Lawrence’s new patio area.
The quadratic equation representing the new patio area after adding a decorative tile of width x all the way around is: 0 = 4x^2 + 44x - 60
Options A and E are correct.
What is a Quadratic Function?In mathematics, a polynomial of degree two in one or more variables is referred to as a quadratic polynomial. The polynomial function that a quadratic polynomial defines is known as a quadratic function.
Since the area of the new patio is given as 180 square feet, we can create a quadratic equation to represent the new patio area:
Area = length × width
180 = (12 + 2x) × (10 + 2x)
After we expand, the answer is given as 0 = 4x^2 + 44x - 60
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Untitled Question
9. Use Figure 10.2. John Noel and his wife have insured their home for 80 percent of its
replacement value of $250,000. The home is of brick construction and is rated in fire
protection class 5. What is their annual insurance premium? (Section 10-7)
a. $515
c. $717
b. $616
d. $414
O A
P New Tab NCCG endeu
B
D
The annual insurance premium for John Noel and his wife is $616, which corresponds to option (b).
The annual insurance premium can be calculated using the following formula:
Annual premium = (Amount of insurance coverage / $100) x Rate per $100 of insurance
The amount of insurance coverage is 80% of the replacement value of the home, which is $250,000, so it is:
Amount of insurance coverage = 0.8 x $250,000 = $200,000
The rate per $100 of insurance depends on the fire protection class of the home. According to industry standards, fire protection class 5 has a rate of $0.308 per $100 of insurance.
Therefore, the rate per $1 of insurance is:
Rate per $1 of insurance = $0.308 / 100 = $0.00308
The rate per $100 of insurance is:
Rate per $100 of insurance = $0.00308 x 100 = $0.308
Using the formula above, we can calculate the annual insurance premium:
Annual premium = ($200,000 / $100) x $0.308 = $616
Therefore, the annual insurance premium for John Noel and his wife is $616, which corresponds to option (b).
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8) A hexagonal pyramid 10 mi tall with a regular
base measuring 6 mi on each side and an
apothem of length 5.2 mi.
A) 936 mi³
C) 315 mi³
B) 312 mi³
D) 52 mi³
The volume of the pyramid is 936 mi³
What is volume of a pyramid?A pyramid has a polygonal base and flat triangular faces, which join at a common point called the apex.
The volume of a pyramid is expressed as;
V = 1/3bh
where b is the base area and h is the height of the pyramid.
Area of the hexagon = 1/2 × p × a
perimeter = 6 × 6 = 36 mi
area = 1/2 × p × a
= 1/2 × 36 × 5.2
= 187.2/2
= 93.6 mi²
Volume = 93.6 × 10
= 936 mi³
therefore the volume of the pyramid is 936 mi³
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The table below shows different possibilities for the number of games a team would
need to win to maintain a certain percentage of wins.
A 18 20
B 30 20
POSSIBLE BASEBALL
GAMES WON
C 18 30
D 50 30
Number of
Games Won
6
24
36
42
Which ratio of the number of games won to the number of games played could also be
included in this table?
Number of
Games Played
10
40
60
70
The ratio that could also be included in this table is (c) 18 : 30
Calculating the ratio that could also be included in this table?From the question, we have the following parameters that can be used in our computation:
Games won Games played
6 10
24 40
36 60
42 70
From the above, we have the ratio of the number of games won to the number of games played to be
Ratio = 6 : 10
Simplify
Ratio = 3 : 5
From the options, we have
(c) 18 : 30
Simplify
Ratio = 3 : 5
Hence, the ratio that could also be included in this table is (c) 18 : 30
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Write a recursive sequence that represents the sequence defined by the following explicit formula:
A recursive sequence are -20, -80, -320 and -1280.
To write a recursive sequence that represents the sequence defined by the given explicit formula, we need to find a rule that relates each term of the sequence to the previous term.
The explicit formula for the sequence is
[tex]a_{n}[/tex] = -5 [tex](4)^{n-1}[/tex]
To find the recursive formula, we need to express each term in terms of the previous term. Let's say the first term of the sequence is [tex]a_{1[/tex].
[tex]a_{1[/tex] = -5 * 1 = -5
[tex]a_{2}[/tex] = -5 * 4 = -20
[tex]a_{3}[/tex] = -5 * 16 = -80
...
[tex]a_{n}[/tex] = -5 [tex](4)^{n-1}[/tex]
We can see that each term in the sequence is 4 times the previous term, so we can express the nth term in terms of the (n-1)th term as follows
[tex]a_{1[/tex] = -5
[tex]a_{n}[/tex] = 4[tex]a_{n-1}[/tex] , for n > 1
This gives us the recursive formula for the sequence. To generate the sequence, we start with the initial term [tex]a_{1[/tex] =-5 and use the recursive formula to find the subsequent terms.
For example, if we want to find a5, we can use the recursive formula
[tex]a_{2}[/tex] = 4[tex]a_{1[/tex] = 4(-5) = -20
[tex]a_{3}[/tex] = 4[tex]a_{2}[/tex] = 4(-20) = -80
[tex]a_{4}[/tex] = 4[tex]a_{3}[/tex] = 4(-80) = -320
[tex]a_{5}[/tex] = 4[tex]a_{4}[/tex] = 4(-320) = -1280
Therefore, [tex]a_{5}[/tex] = -1280.
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What is the sum of the geometric series
10
∑6(2)^n ?
N-1
A.15,658
B.6,138
C12,276
D756
The sum of the geometric series is -12,276.
So, the correct answer is C. -12,276.
To find the sum of the geometric series, we can use the formula:
[tex]S = a \times (1 - r^n) / (1 - r),[/tex]
where S is the sum of the series,
a is the first term,
r is the common ratio, and
n is the number of terms.
In this case, the first term (a) is 6(2) = 12, the common ratio (r) is 2, and the number of terms (n) is 10.
Plugging these values into the formula, we get:
[tex]S = 12 \times (1 - 2^{10} ) / (1 - 2).[/tex]
Calculating further:
[tex]S = 12 \times (1 - 1024) / (-1) = 12 \times 1023 = 12276.[/tex]
Therefore, the sum of the geometric series is -12,276.
So, the correct answer is C. -12,276.
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Given ƒ(x) = −2x² + x − 8, find ƒ (9)
Answer: -161
Step-by-step explanation: you solve by plugging 9 in for x so you get f(9) = -2(9)^2 +9-8 you solve using PEMDAS and you get -161
using the line of best fit
The monthly cell phone bill when shared data equals zero is given as follows:
$26.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.The intercept of the line in this problem is given as follows:
b = 26.
Hence $26 is the monthly cell phone bill when shared data equals zero.
More can be learned about linear functions at https://brainly.com/question/24808124
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