Answer:
(x-24/5)^2 + (y-21/5)^2 = (sqrt(481)/5)^2, or (x-24/5)^2 + (y-21/5)^2 = 481/25
Step-by-step explanation:
The equation of a circle can be written in the form (x-a)^2 + (y-b)^2 = r^2, where (a,b) is the center of the circle and r is its radius. Since the lines are tangent to the circle at points (0,5) and (6,5), we can use these points to find the center and radius of the circle.
First, let’s find the slope of each line. The slope of the line y = 3/4x+5 is 3/4. The slope of the line 3x + 4y = 38 can be found by rearranging it into slope-intercept form: y = (-3/4)x + 19/2. So the slope of this line is -3/4.
Since the lines are tangent to the circle, they are perpendicular to the radius at their point of tangency. This means that the center of the circle lies on the line that passes through (0,5) and has a slope of -4/3, and also on the line that passes through (6,5) and has a slope of 4/3.
Let’s find the equation of these two lines. The line passing through (0,5) with a slope of -4/3 has an equation y - 5 = (-4/3)(x - 0), or y = (-4/3)x + 5. The line passing through (6,5) with a slope of 4/3 has an equation y - 5 = (4/3)(x - 6), or y = (4/3)x - 3.
The center of the circle is at the intersection of these two lines. To find it, we can set their right-hand sides equal to each other and solve for x: (-4/3)x + 5 = (4/3)x - 3. Solving this equation gives us x = 24/5. Substituting this value into either equation for y gives us y = (4/3)(24/5) - 3 = 21/5.
So the center of the circle is at (24/5, 21/5). To find its radius, we can use either point of tangency. Let’s use (0,5). The distance between this point and the center is given by sqrt((0-24/5)^2 + (5-21/5)^2), which simplifies to sqrt(481)/5.
Therefore, the equation of the circle is (x-24/5)^2 + (y-21/5)^2 = (sqrt(481)/5)^2, or (x-24/5)^2 + (y-21/5)^2 = 481/25.
A New York City hotel surveyed its visitors to determine which type of transportation they used to get around the city. The hotel created a table of the data it gathered.
Type of Transportation Number of Visitors
Walk 120
Bicycle 24
Car Service 45
Bus 30
Subway 81
Which of the following circle graphs correctly represents the data in the table?
circle graph titled New York City visitor's transportation, with five sections labeled walk 80 percent, bus 16 percent, car service 30 percent, bicycle 20 percent, and subway 54 percent
circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 40 percent, bus 8 percent, car service 15 percent, bicycle 10 percent, and walk 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 80 percent, bicycle 20 percent, car service 30 percent, bus 16 percent, and walk 54 percent
Answer:
circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent.
Step-by-step explanation:
To find the correct percentages, we need to calculate the percentage of visitors who used each mode of transportation out of the total number of visitors, which is the sum of all the numbers in the table:
Total number of visitors = 120 + 24 + 45 + 30 + 81 = 300
Percentage of visitors who walked = (120 / 300) x 100% = 40%
Percentage of visitors who used a bicycle = (24 / 300) x 100% = 8%
Percentage of visitors who used a car service = (45 / 300) x 100% = 15%
Percentage of visitors who used a bus = (30 / 300) x 100% = 10%
Percentage of visitors who used the subway = (81 / 300) x 100% = 27%
Therefore, the circle graph that correctly represents the data in the table is:
circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent.
Find the slope of the line with a y-intercept = 4, passing through the point (2,8)
Answer: d. m = 2
Step-by-step explanation:
First, we will write a slope-intercept equation using the y-intercept given.
y = mx + 4
Next, we will substitute the given point and solve for m, the slope.
y = mx + 4
(8) = m(2) + 4
4 = 2m
m = 2
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[tex]\boxed{\sf m=2}.[/tex]
Step-by-step explanation:1. Identify the 2 given points.In order to find the slope of any linear equation you need at least 2 points the line passes through. We're explicitly provided one, (2, 8), we just need to figure out the other one.
When the statement says that the line has a y-intercept of 4, it means that at a point with y=4 the function touches the y axis. The only way to touch the y-axis is if the x value is 0. Hence, another given point is (0, 4).
2. Calculate the slope.Formula: [tex]\sf m=\dfrac{y_{2}- y_{1} }{x_{2} -x_{1} }[/tex]
Naming the variables (can be done arbitrarily but always make sure the y's are actual y values from the ordered pairs and that x₁ goes with its corresponding y₁ value from the ordered pair):
[tex]x_{1} =2;\\x_{2} =0;\\y_{1} =8;\\y_{2} =4.[/tex]
Now substituting these values in the formula:
[tex]\sf m=\dfrac{(4)-(8) }{(0) -(2) }=\dfrac{-4}{-2} =\boxed{\sf 2}.[/tex]
Check out the attached image to see the graphed line.
3. Rochelle helped in the garden 7 days during the last 4 weeks. Use the
numbers in the box to complete the sentences comparing her time in
the garden.
Numbers can be used more than once. Write each number in the
appropriate box.
For every day(s) Rochelle helped, she did not help
For every
day(s).
1 3 4 7 28
day(s).
day(s) Rochelle did not help, she helped
For every 3 days Rochelle helped, she did not help for 1 day.
For every 4 days Rochelle helped, she did not help for 1 day.
For every 7 days Rochelle helped, she did not help for 6 days.
For every 28 days Rochelle helped, she did not help for 21 days.
Let's use the terms provided to complete the sentences comparing Rochelle's time in the garden.
Since Rochelle helped in the garden for 7 days during the last 4 weeks, we can calculate the total number of days in 4 weeks and then find the number of days she did not help.
There are 7 days in a week, so in 4 weeks, there are 4 x 7 = 28 days.
Rochelle helped for 7 days, so she did not help for 28 - 7 = 21 days.
Now, let's complete the sentences:
For every 1 day(s) Rochelle helped, she did not help for 3 day(s).
For every 3 day(s) Rochelle did not help, she helped 1 day(s).
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Collect a set of data (from the internet) about any school-appropriate topic. Examples: rainfall data, and testing scores. Or make up your own set of data. The data set must contain at least 20 values. Fill out the questions below regarding your data.
1. List your data below in numerical order.
2. Explain your data. What does each data point represent?
3. What is the mean of your data?
4. What is the minimum and maximum within your data?
Here is the data collected as a result of the experiment.
1) Numerical order is: 0.20, 0.20, 0.46, 0.46, 2.10, 2.10, 5.50, 11.80, 12.20, 12.20, 13.22, 14.65, 16.07, 17.49, 18.91, 20.33, 20.50, 20.50, 21.75, 23.18
2) The data represents rainfall in millimeters over a 20-day period.
3) Mean = 11.69 mm.
4) The minimum rainfall is 0.20 mm ;
the maximum is 23.18 mm.
1) The data is listed as follows.
0.20 12.20 2.10 0.46 20.50 5.50 11.80 13.22 14.65 16.07 17.49 18.91 20.33 21.75 23.18 0.20 12.20 2.10 0.46 20.502) The data represents the amount of rainfall in millimeters over a 20 day period.
3) The mean rainfall over the 20 day period is 11.69 mm.
= (0.20 + 0.20 + 0.46 + 0.46 + 2.10 + 2.10 + 5.50 + 11.80 + 12.20 + 12.20 + 13.22 + 14.65 + 16.07 + 17.49 + 18.91 + 20.33 + 20.50 + 20.50 + 21.75 + 23.18) /20
Mean (x) = 11.69 mm.
3) The minimum rainfall is 0.20 mm and the maximum is 23.18 mm.
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14). Find the measures of both angles.
xo
(3x +20)°
Answer:
40 degrees and 140 degrees
Step-by-step explanation:
To solve this problem you can add x+3x+20 and set that equal to 180. (We can do this because angle x and angle 3x + 20 make a linear pair. Knowing this we can estimate that both angles added together will equal 180)
Let us add x + 3x + 20 = 180 to find x. We can then substitute that into the equation.
[tex]x+3x+20=180 :a\\\\4x+20=180 :b\\\\4x + 20 -20=180-20:c\\\\4x=160:d\\\\\frac{4x}{4} = \frac{160}{4}:e\\\\x=40:f[/tex]
a: So in this part, we have rewritten the equation to make it easier to solve
b: In this step, you combine the like terms x+3x to get 4x
c: In step c, you are subtracting 20 from both sides to keep constants on one side and variables on the right
d: In this last step the equation has been simplified to make it easier to solve.
e: To isolate x you have to divide both sides by 4, we do this because the coefficient of x is 4 so you divide the equation by 4 to cancel it out.
f: You rewrite and simplify the equation.
Now to find the measure of both angles you substitute x into the equation.
The first angle's value is 40 degrees and the second is 140 degrees.
These are our answers.
how to find the area of a circle with the diameter of 22 in with pi
The area of the circle with a diameter of 22 in in terms of pi is 121π in².
What is the area of the circle?A circle is simply a closed 2-dimensional curved shape with no corners or edges.
The area of a circle is expressed mathematically as;
A = πr²
Where r is radius and π is constant pi.
Given that:
The diameter of the circle is 22 inches.
Radius is half of diameter
Hence:
Radius r = diameter/2 = 22/2 = 11 in
Plug the value into the above formula and solve for area.
A = πr²
A = π × ( 11 in )²
A = 121π in²
Therefore, the area is 121π in².
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Brent starts with 16 identical white socks in his sock drawer. Imagine he receives 2 identical black socks as a gift and mixes them in with his 16 white socks. If he draws one sock without looking to put on his left foot, then draws a second sock without looking to put on his right foot, what is the probability that he draws mismatched socks?
The probability that Brent draws mismatched socks is approximately 31/153.
After adding 2 identical black socks, Brent has a total of 18 socks in his drawer. The probability of drawing a white sock on the first draw is 16/18 (since there are 16 white socks out of 18 total socks).
After drawing a white sock on the first draw, there are 15 white socks and 2 black socks left in the drawer. The probability of drawing a black sock on the second draw is 2/17 (since there are 2 black socks out of 17 total socks left). So the probability of drawing a white sock followed by a black sock is;
(16/18) × (2/17) = 32/306
Similarly, the probability of drawing a black sock followed by a white sock is;
(2/18) × (15/17) = 30/306
However, the probability of drawing mismatched socks is;
32/306 + 30/306 = 62/306
= 31/153
Therefore, the probability will be 31/153.
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-8/9 / -2/3 x -4 1/2
Answer:
- 14/3
Step-by-step explanation:
-8/9 * 3/-2 * -7/2
-24/-18 * -7/2
4/3*-7/2
-28/6
= - 14/3
3.6 is 5% of I need help with all
Answer: 3.6 is 5% of 72
Step-by-step explanation: If 3.6 is 5% then just multiply 3.6 by 95 to get 68.4 and add to get 72, Yw.
50 Points! Multiple choice algebra question. Photo attached. Thank you!
The half-life of the particular compound is approximately 9.4 days. (Correct choice: B)
How to find the half-life of a compound
The statement indicates the decay function of a particular compound, which is an exponential function of the form:
y = a · exp(- λ · t)
Where:
a - Initial mass of the compound.λ - Decay constant, in days⁻¹.t - Time, in days.The half-life of the particular compound is determined by the following expression:
t = ㏑ 2 / λ
Where t is the half-life.
If we know that λ = 0.0736, then the half-life of the particular compound is:
t = ㏑ 2 / 0.0736
t = 9.4 days
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What is 15% of 100
Please help
Answer:
Step-by-step explanation:15
Ina Crespo rowed 16 miles down the Habashabee River in 2 hours, but the return trip took her 4 hours. Find the rate Ina rows in still water and the rate of the current. Let x represent the rate Ina can row in still water and let y represent the rate of the current.
Ina rows at a rate of 6 mph in still water, and the current flows at a rate of 2 mph.
What is distance?Distance is the overall length of a journey that a person, item, or vehicle takes to get from one place to another. Due to its scalar nature, it has simply magnitude and no direction. Typically, distance is expressed in terms of metres, kilometres, miles, or feet. It is distinct from displacement, which describes the shift in an object's location from its starting point to its ending point while also taking the movement's direction into consideration.
According to given information:We can start by using the formula:
distance = rate × time
Let's first consider the trip downstream. In this case, Ina's speed relative to the river current adds up to the distance traveled per unit of time. So we have:
16 = (x + y) × 2
Simplifying and solving for x + y, we get:
x + y = 8
Now let's consider the trip upstream. In this case, Ina's speed relative to the river current subtracts from the distance traveled per unit of time. So we have:
16 = (x - y) × 4
Simplifying and solving for x - y, we get:
x - y = 4
We now have two equations with two variables, so we can solve for x and y using either substitution or elimination. Let's use elimination:
(x + y) + (x - y) = 8 + 4
2x = 12
x = 6
Now we can substitute x = 6 into either of the original equations to solve for y. Let's use the first equation:
x + y = 8
6 + y = 8
y = 2
Therefore, Ina rows at a rate of 6 mph in still water, and the current flows at a rate of 2 mph.
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Justine is enrolled in an SAT prep class at the Oakdale Community Center. The community
center is 1.4 miles away from Justine's house. On a map of Oakdale, this distance is
represented by 1 inch. What is the scale of the map?
Write your answer in simplest form using whole numbers.
inches:
miles
Answer:
1.4:1
= 14:10
= 7:5
Hence, ans is 7:5
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The combinations for the lockers at school consist of 3 numbers. Each number in the combination can be a number from 0-29. How many locker combinations are possible?
Answer:
87 I think.
Step-by-step explanation:
29 x 3 = 87
‼️‼️‼️WILL MARK BRAINLIEST IF HELPFUL‼️‼️‼️
Answer:
S = 2π(10^2) + 2π(10)(3)
= (200 + 60)π = 260π cm^2
So 250 cm^2 is not a reasonable answer for the surface area of this cylinder.
I need to know this for math the clay they shown is shaped like a rectangular prism with a hole inside that is shaped like a smaller rectangle prism I need this right now please help me I will give you a lot of points and extra if you answered
The volume of the clay used to make the vase is 36 in³
How to determine the volumeTo determine the volume of clay that was used for the vase, we need to consider that;
The formula for the volume of a rectangular prism is expressed as;
Volume = lwh
Such that;
V is the volume of the prism.l is the length of the rectangular prism.w is the width of the rectangular prism.h is the height of the rectangular prism.For the bigger prism, we have;
Volume = 3 × 3 × 5
Multiply the values
Volume = 45 in³
For the hole, we have;
Volume = 4 × 3/2 × 3/2
Multiply the values
Volume = 9 in³
Then, the volume of clay used for the vase = 45 - 9 = 36 in³
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Marla, Jamie, and Sarah have each led their book club’s monthly meeting. Jamie has led 2/6 of the meetings, and Sarah has led 1/6 of the meetings. What fraction of the meetings has Marla led?
Step-by-step explanation:
1-2/6-1/6= 3/6
= 1/2
Marla has led 1/2 of the meetings
A cheetah was observed running at a speed of 24.9 m/s. Use the following facts to convert this speed to kilometers per hour (km/h). 1 km = 1000 m 1 min 60 sec 1 hour = 60 min
Answer: 89.64 kilometers per hour
Step-by-step explanation: Convert 24.9 meters per second into Kilometers per minute by multiplying by 1000 to get 0.0249 kilometers per minute, which gives you 1.494 kilometers per minute. Then, you must convert this to kilometers per hour by multiplying by 60 to get 89.64 kilometers per hour
Which of the points plotted is farther away from (−7, 8), and what is the distance?
Answer:
(10, -10)
Step-by-step explanation:
This are the farest the graph can go unless you want (100,-100)
Change the values from negative to positive and positive to negative to get the most farest results
Answer: D
Step-by-step explanation:
I graphed so you can see. Count how far each are away.
(5,8) is 12 away
(-7,-5) is 13 away
So you answer is D
Or
You can also think of it as, for, (5, 8) only the x changed so you only moved in the x direction. subtract the numbers 5-(-7)=12
For (-7,-5) you only moved in the y direction, so subtract those 8-(-5)=13
a) What information is provided by each of the graphs below? b) Explain below which of the two graphs is the best representation of the data. Support your thinking by using numbers from each graph.
The information provided by each of the graphs is Sales from July to December and graph A best represents the data
What information is provided by each of the graphs?From the question, we have the following parameters that can be used in our computation:
The graphs
On the graphs, we have the information to be
Sales from July to December
Which of the two graphs is the best representation of the data.The graph that is the best representation of the data is the A
This is because the scale and origin of the graph are defined
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Use the Law of Cosines. Find x to the nearest tenth.
2
B
15
ro
30
16
C
The value of x for the triangle is,
x = 58.67 degree
We have to given that;
By Use the Law of Cosines. Find x to the nearest tenth.
And, A triangle ABC is shown in figure.
Hence, We can formulate;
c = √a² + b² - 2ab cos x
16 = √15² + 30² - 2 × 15 × 30 cos x
16 = √225 + 900 - 900 cos x
256 = 725 - 900 cos x
900 cos x = 725 - 256
900 cos x = 469
cos x = 469 / 900
cos x = 0.52
x = 58.67 degree
Thus, The value of x for the triangle is,
x = 58.67 degree
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What is the volume of a solid with lines y=√(cos(x), y=e^x, x=pi/2 if it is revolved around the x axis?
For the same question, if there were x axis semicircles with a diameter on xy plane, what would the volume be?
To find the volume of the solid generated by revolving the region enclosed by the curves y = √(cos(x)), y = e^x and x = pi/2 around the x-axis, we can use the method of cylindrical shells.
Consider a thin vertical strip of width dx at a distance x from the y-axis. The height of this strip is the difference between the y-coordinates of the two curves:
h = e^x - √(cos(x))
The circumference of the shell is given by 2πx since the strip is at a distance x from the y-axis. Therefore, the volume of the shell is given by:
dV = 2πx * h * dx
= 2πx * (e^x - √(cos(x))) * dx
To find the total volume of the solid, we need to integrate this expression from x=0 to x=pi/2:
V = ∫[0, pi/2] 2πx * (e^x - √(cos(x))) dx
This integral can be evaluated using integration by substitution. Let u = cos(x), then du/dx = -sin(x) and dx = du/-sin(x). Using this substitution, the integral becomes:
V = ∫[1, 0] 2π * (-ln(u)/sin(x)) * (e^x - √(u)) dx
Integrating this expression with respect to x from x=0 to x=pi/2, we get:
V = 2π * [e^(pi/2) - 1 - (4/3) * (1 - sqrt(2))]
Therefore, the volume of the solid is approximately 27.838 cubic units (rounded to three decimal places).
You are running a fundraiser for your school, selling Reese’s and Skittles candies. You recorded you sold 34 candies and made $41, but didn’t tally how many of each candy you sold (and you don't remember the original amount of candy you had).
Below is the advertisement you used to sell the candy:
Reese's sells for $1 and skittles for $1.50
Write a system of equations to represent this situation. Then, solve it algebraically using either the substitution or elimination method.
Reese sold 20 candy and Skittles sold 14 candy for a total of $41. The equation for this is x + y = 34 and x + 1.5y = 41
What is an equation?An exponential equation is an expression that shows how numbers and variables using mathematical operators.
Let x represent the number of candy that Reese sell and y represent the number of Skittles candies
Reese's sells for $1 and skittles for $1.50
34 candies was sold, hence:
x + y = 34 (1)
He made $41, hence:
x + 1.5y = 41 (2)
Solving both equations simultaneously:
x = 20; y = 14
Reese had 20 candy and Skittles had 14 candy.
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at football practice, gustavo does push ups for 2 minutes for every 6 minutes playing if he plays for 42 minutes how many of push ups will he do
Answer:
14 mins
Step-by-step explanation:
2/6 = x/42
6x=84
x=14
what is 6+9f+5+4+3–4f simplified
Answer:
18+5f
Step-by-step explanation:
6+9f+5+4+3-4f
=11+5f+7
=18+5f
Answer:
18 + 5f
Step-by-step explanation:
To simplify the expression 6 + 9f + 5 + 4 + 3 - 4f, we must combine like-terms.
6 + 5 + 4 + 3 = 18 (6,5,4, and 3 are like-terms because they are all normal integers)
18 + 9f - 4f (9f and 4f are like-terms because they have the same variable f)
18 + 5f
Amelia has a music box that is shaped like a right rectangular
prism. She wants to pack the music box into a container,
with 1 in. of packing material between each face of the
music box and the container. A bag contains 200 in.3 of
packing material. How many bags of packing material will
Amelia need? Show your work.
The number of packing materials the Amelia will need = 2.4
How to calculate the quantity of packing materials Amelia will need?From the diagram given above, the formula for the volume of a right rectangular prism = Length×width ×height.
Where;
Length = 10in
Width = 6 in
Height = 8 in
The volume = 10×6×8 = 480 in³
But one bag = 200in³
The amount of bag that the music box can contain = 480/200 = 2.4
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A right rectangular prism and its net are shown below.
Answer:
A = 5
B = 4
C = 8
D = 3
Step-by-step explanation:
This is more of a visual calculation so I can't really explain much about it other than that you match up the side in the prism with the side in the net
Answer: 108
Step-by-step explanation:
If you turn the shape, where the pointy side of the ramp is facing you and you flipped it open and laid out the sides, that's the "net" image on right
A = 5 the long side of that triangle is also the short side of that rectangle
B = 3 it's the short side of the triangle
C = 8 long part of the rectangle
D = 4 long side of triangle
To find surface area. Find the area of each of the shapes and add it all up
Top Rectangle:
A=Lw=C*A = 5*8 = 40
Middle Rectangle:
A=Lw = B*C = 3*8 = 24
Bottom Rectangle:
A=LW = 4*C = 4*8=32
Triangles are same
A=1/2 bh = 1/2 D*B = 1/2 * 4* 3 =6
But there are 2 of them so A=12
Now add all the shapes together
A(total)=40+24+32+12=108
How many kilograms are
1 kg =
100 dag
45.4 kg
119.5 kg
54.5 kg
264.3 kg
there 5,450 dekagrams?
The number of kilogram that are there in there 5,450 dekagrams is: C. 54.5 kg.
What is kilograms?The kilogram is widely used as a unit of mass in everyday life, as well as in science, engineering, and industry. One kilogram is equal to 1,000 grams, and it is the base unit for other mass-related units such as milligrams, centigrams, and decigrams.
To convert 5,450 dag to kg, we need to divide by 100, since 1 kg = 100 dag:
5,450 dag ÷ 100 = 54.5 kg
Therefore, the answer is (c) 54.5 kg.
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The correct question is:
How many kilograms are there in there 5,450 dekagrams?
1 kg = 100 dag
a. 45.4 kg
b. 119.5 kg
c. 54.5 kg
d. 264.3 kg
its 7th grade math PLEASE HELP EMERGENCY
An example of a function that models a linear relationship between two quantities, x and y is y = mx + b
How to explain the functionWe need to use the equation of a straight line, which is commonly expressed in slope-intercept form as:
y = mx + b
In this function, x represents the independent variable, m is the slope of the line, and b is the y-intercept. To use this function, we simply plug in the values of x, m, and b that correspond to the specific relationship we are modeling.
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4Construct a function to model a linear relationship between two quantities.
Review the proof.
Step
1
2
3
5
6
7
8
Statement
cos(2x)= 1-2sin²(x)
Let 2x = 0.
Then x =
cos() = 1-2sin²()
-1 + cos() = -2sin²)
1 + cos(e) = 2sin²)
1-cos(0) = sin²)
sin() = ±
1-cos(0)
2
Which step contains an error?
O step 2
O step 4
step 6
O step 8
The error is in step 2 based on the given statement.
How to solveThe given statement is[tex]cos(2x) = 1-2sin^2(x),[/tex] and it is not appropriate to simply let 2x = 0.
By doing this, you are only considering a specific case where x = 0, rather than proving the statement for all values of x.
To properly prove the given statement, you should consider using trigonometric identities or double-angle formulas to establish the equivalence between cos(2x) and 1-2sin²(x) for all x.
Thus, the error is in Step 2
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https://brainly.com/question/28160425
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