After considering the given data we conclude that the clockwise rotational path of the line segment is a rotation of -59.04 degrees about the point (-6, -1).
We have to evaluate the center and angle of rotation to explain the clockwise rotation of the line segment.
So in the first step, we can evaluate the midpoint of the line segment JK and the midpoint of the line segment J'K'. we can calculate the vector connecting the midpoint of JK to the midpoint of J'K'. This vector is (4-1, 1-(-4) = (3,5)
The center of rotation is the point that is equidistant from the midpoints of JK and J'K'. We can evaluate this point by finding the perpendicular bisector of the line segment connecting the midpoints.
The slope of this line is the negative reciprocal of the slope of the vector we just found, which is -3/5. We can apply the midpoint formula and the point-slope formula to evaluate the equation of the perpendicular bisector:
Midpoint of JK: (1, -4)
Midpoint of J'K': (4, 1)
The slope of the vector: 3/5
(x₁ + x₂)/2, (y₁ + y₂) /2
Point-slope formula: y - y₁ = m(x - x₁)
Perpendicular bisector: y - (-4) = (- 3/5)(x - 1)
Applying simplification , we get: y = (- 3/5)x - 1.2
To evaluate the center of rotation, we need to find the intersection point of the perpendicular bisector and the line passing through the midpoints of JK and J'K'. This line has slope ( 3 - (4)) /(4 - 1) = 7/3 and passes through the point (4, 1). Applying the point-slope formula, we can evaluate its equation:
y - 1 = (7/3)( x - 4)
Apply simplification , we get: y = (7/3)x - 17/3
To evaluate the intersection point, we can solve the system of equations:
y =(- 3/5)x - 1.2 = (7/3)x - 17/3
Evaluating for x and y, we get x = -6 and y = -1.
Therefore, the center of rotation is (-6, -1).
√( 4 - 1)² + ( 1 - ( - 4))²) = 5√(2)
Distance between image points and center of rotation
√( ( 6 - (-6))² + ( 3 - (-1))² = 13
The ratio of these distances gives us the scale factor of the transformation, which is 13/√2).
The angle of rotation is negative as the image moves clockwise direction. We can apply the inverse tangent function to find the angle of the vector connecting the midpoint of JK to the midpoint of J'K':
Angle of vector: arctan(5/3) = 59.04 degrees
Therefore, the clockwise rotational path of the line segment is a rotation of -59.04 degrees about the point (-6, -1).
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themba has 6.75 cups of yogurt and needs to make 5 bowls of fruit dip. each bowl uses 1.5 cups of yogurt
complete the statements about the fruit dip
Answer: Themba needs a total of 7.5 cups of yogurt to make 5 bowls of fruit dip, so 0.75 cup(s) will be needed
Step-by-step explanation:
your welcome.
10% of ivy tech students are dual credit students. If there are 13,129 dual credit students, how many Ivy Tech students are there?
Answer:131290
Step-by-step explanation:13129*100/10=131290
someone pls help me asapppp
Answer:
[tex]a_{n}[/tex] = 3[tex]a_{n-1}[/tex] : a₁ = 7
Step-by-step explanation:
a recursive formula allows a term in the sequence to be found from the preceding term.
the sequence here has a common ratio between consecutive terms
[tex]\frac{21}{7}[/tex] = [tex]\frac{63}{21}[/tex] = 3
thus to find a term in the sequence multiply the previous term by 3, that is
[tex]a_{n}[/tex] = 3[tex]a_{n-1}[/tex] : first term a₁ = 7
Help me… it’s so hard!
The solution of the each given equations:
(1) x = 9
(2) x = -2
(3) x = -2
(4) x = 26
(5) x = 3/5
(6) x = 13/12
(7) x = 15
(8) x = 26
(9) x = 7/3
(10) x = 5/8
We have to solve this given equation in on variable.
(1) Given equation is,
x - 7 = 2
x = 2 + 7 = 9
Hence, the solution is, x = 9
(2) Given equation is,
3x + 4 = -2
3x = -2 -4
3x = -6
x = -6/3 = -2
Hence, the solution is, x = -2
(3) Given equation is,
2x + 7 = x + 5
2x - x = 5 - 7
x = -2
Hence, the solution is, x = -2
(4) Given equation is,
x/2 = 13
x = 2*13 = 26
Hence, the solution is, x = 26
(5) Given equation is,
5(2 + x) = 13
10 + 5x = 13
5x = 13 - 10
5x = 3
x = 3/5
Hence, the solution is, x = 3/5
(6) Given equation is,
6(2x - 1) = 7
12x - 6 = 7
12x = 7 + 6 = 13
x = 13/12
Hence, the solution is, x = 13/12
(7) Given equation is,
2x/5 = 6
2x = 6*5 = 30
x = 30/2 = 15
Hence, the solution is, x = 15
(8) Given equation is,
x/2 = 13
x = 2*13 = 26
Hence, the solution is, x = 26
(9) Given equation is,
(x - 1)3 = 4
3x - 3 = 4
3x = 4 + 3 = 7
x = 7/3
Hence, the solution is, x = 7/3
(10) Given equation is,
(2x - 1)4 = 1
8x - 4 = 1
8x = 1 + 4
8x = 5
x = 5/8
Hence, the solution is, x = 5/8
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Select the correct answer.
What is the value of x in the triangle?
a 30-60-90 triangle with long leg length x and shorter leg length of 7 times the square root of 3
The length of the hypotenuse is 7m.
Let the side opposite to 30° be the shortest leg.
The side opposite to 60° is the longest leg.
So, the side opposite to 90° is hypotenuse.
Length of the shortest side is x.
Length of longest side is [tex]\sqrt{3}x[/tex]
Length of the hypotenuse is 2x.
We know x = 7
So, [tex]\sqrt{3}(x)=\sqrt{3}(7)[/tex]
Thus, the length of the longer leg is [tex]\sqrt{3}(7)[/tex] m
Length of hypotenuse = 2x = 2(7) = 14m
[tex]x^{2} +(\sqrt{3} x)^2 =(2x)^2\\\\(7)^2+(\sqrt{3} (7))^2=(2x)^2\\\\49 + (3(49)) = (2x)^2\\\\49 + 147= (2x)^2\\\\(2x)^2=196[/tex]
Taking square root on both sides:
[tex]2x = \sqrt{196}[/tex]
2x = 14
x = 7
Therefore, the length of the hypotenuse is 7m.
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the area of a circle is 2464 cm². Calculate the diameters to 2 significant figure
Answer:
56 cm
Step-by-step explanation:
have a good day God bless :)
find the mean of brothers and sisters
The mean of brothers and sisters = 3
From the attached data set of brothers and sisters we can write the data values (frequency) as:
1, 5, 4, 2
We need to find the mean of brothers and sisters,
We know that the formula for the mean of data.
mean([tex]\bar{x}[/tex]) = sum of all data values / total number of data values
First we find the sum of all data values.
1 + 5 + 4 + 2 = 12
and the total number of data values = 4
Using above formula of mean,
mean([tex]\bar{x}[/tex]) = sum of all data values / total number of data values
mean([tex]\bar{x}[/tex]) = 12 / 4
mean([tex]\bar{x}[/tex]) = 3
Therefore, the required mean is: 3
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Find the complete question below.
Write a polynomial, P(x), in factored form given the following requirements.
Degree: 4
Leading coefficient 1
Zeros at x=5, x=−2 and x=−3
y-intercept at (0,60)
The polynomial, P(x), in factored form is P(x) = (x - 5)(x + 2)^2(x + 3)
Writing the polynomial, P(x), in factored formFrom the question, we have the following requirements that can be used in our computation:
Degree: 4Leading coefficient 1Zeros at x=5, x=−2 and x=−3y-intercept at (0,60)The polynomial, P(x), in factored form is represented as
P(x) = (x - zeros)
So, we have
P(x) = (x - 5)(x + 2)^2(x + 3)
(x + 2) has an exponent of 2 because it makes the polynomial have a degree of 4
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What is the domain of the function shown on the graph?
Answer:
A
Step-by-step explanation:
the domain is the values of x covered by the graph
on the left the graph → - ∞
on the right the graph tends to + ∞
there are no excluded values of x on the domain , so
domain is - ∞ < x < ∞
An employee is considering two job offers.
First offer: $57,000 yearly salary with an 8% matching 401k
Second offer: $63,000 yearly salary with a 4% matching 401k
The employee plans to stay at either job for at least 4 years, assumes there are no salary increases, and will make 401k contributions at the same rate the company matches. After 4 years, the total value of the first offer, including gross income and total 401k contributions, is $264,480.
Which job has the better overall pay structure, and by how much?
(MULTIPLE CHOICE ONLY)
The second job offer is better by $6,780.
The first job offer is better by $6,780.
The second job offer is better by $7,680.
The first job offer is better by $7,680.
The second job offer is better by $21,840.
We have :
An employee is considering two job offers.
First offer: $57,000 yearly salary with an 8% matching 401k
Second offer: $63,000 yearly salary with a 4% matching 401k
Let's calculate the total value of the second offer after 4 years:
Yearly salary is : $63,000
Total gross income after 4 years: $63,000 x 4 = $252,000
The company matches 5% of the employee's salary.
So, the employee contributes 5% of $63,000 = $3,150 per year
After 4 years,
Company matches: $3,150 x 4 = $12,600
Employee contributions: $3,150 x 4 = $12,600
Total 401k contributions: $12,600 + $12,600 = $25,200
The total value of the second offer after 4 years is:
Total value: $252,000 + $25,200 = $277,200
Now, let's compare this to the total value of the first offer, which is : $255,360.
Therefore, the second job offer is better by:
$277,200 - $255,360 = $21,840
Hence, The second job offer is better by $21,840.
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Tommy's Diner offers its clients a choice of regular and diet soda. Last night, the diner served 18 regular sodas and 82 diet sodas. What percentage of the sodas served were regular?
The percentage of the sodas that was served which were regular would be = 18%
How to calculate the percentage of sodas served?The quantity of regular sodas served = 18
The quantity of diet soda served = 82
The total number of soda served = 18+82 = 100
Therefore the percentage of soda that were regular would be;
= 18/100 × 100/1
= 18%
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evaluate.
20
Σ4 (8)n-1
n = 1
S = [?]
Answer:
32.5861
Step-by-step explanation:
The area of a desert in Africa is times the area of a desert in Asia. If the area of a desert in Asia is square miles, express the area of a desert in Africa as an algebraic expression in .
The algebraic expression for the area of a desert in Africa in terms of the area of a desert in Asia is y = 12x.
If the area of a desert in Asia is x square miles, then the area of a desert in Africa is 12 times that, or 12x square miles. We can express this algebraically by using a variable to represent the area of the desert in Africa, such as y:
y = 12x
Here, y represents the area of the desert in Africa, and we know that it is 12 times the area of the desert in Asia, represented by x. We can substitute any value for x to find the corresponding value of y. For example, if the area of the desert in Asia is 1000 square miles, then the area of the desert in Africa is:
y = 12x = 12(1000) = 12,000 square miles
Correct Question:
The area of a desert in Africa is 12 times the area of a desert in Asia. If the area of a desert in Asia is x square miles , express the area of a desert in Africa as an algebraic expression x.
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Need help don’t get it
Answer:
[tex] \frac{210}{360} = \frac{7}{12} [/tex]
This figure represents 7/12 of the circle.
Two step for T+4=-7 ?
Answer:
Step-by-step explanation:
T+4 = -7
T = -7 -4
T = -11
A certain virus infects one in every 300 people. A Test used to detect the virus in a person is positive 85% of the time if that prerson has the virus and 5% of the time if the person does not have the virus. This 5% result is called a false positive. Let "A" be the event the person is infected and "B" the event the person tests positive. Find the probability that a person has the virus given that they have tested positive find the P(A/B)= Round to nearest tenth of a % Don't include % sign.
The probability that a person has the virus given that they have tested positive find the P(A/B)=0.0045
We can use Bayes' theorem to find the probability that a person has the virus given that they have tested positive:
P(A | B) = P(B | A) * P(A) / P(B)
where P(B | A) is the probability of testing positive given that the person has the virus, P(A) is the prior probability of a person having the virus (1/300), and P(B) is the total probability of testing positive.
To find P(B), we can use the law of total probability, which states that:
P(B) = P(B | A) * P(A) + P(B | not A) * P(not A)
where P(B | not A) is the probability of testing positive given that the person does not have the virus. This is the false positive rate, which is 5% or 0.05 in this case. P(not A) is the complement of P(A), which is 299/300.
Substituting the values, we get:
P(B) = 0.85 * 1/300 + 0.05 * 299/300
= 0.059
Now we can plug in the values into Bayes' theorem:
P(A | B) = 0.85 * 1/300 / 0.059
= 0.0045 or 0.45%
Therefore, the probability that a person has the virus given that they have tested positive is 0.45% or 0.0045 (rounded to the nearest tenth of a percent).
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The sum of the interior angles of the 10-sided polygon on the left is ____
Answer:
The sum of the interior angles of a 10-sided polygon is 1,440 degrees.
To find the sum of the interior angles of any polygon, you can use the formula:
sum of interior angles = (n - 2) x 180 degrees
where n is the number of sides of the polygon.
So, for a 10-sided polygon, we have:
sum of interior angles = (10 - 2) x 180 degrees
sum of interior angles = 8 x 180 degrees
sum of interior angles = 1,440 degrees
Therefore, the sum of the interior angles of the 10-sided polygon on the left is 1,440 degrees.
Answer:
1440 degrees
Step-by-step explanation:
Credit to the the first person who answered. :)
Which of the following points are on the line given by the equation y = x? Check all that apply. A. (3, 6) B. (4, 2) C. (3, 15) D. (-2, 1) E. (2, 1) F. (-2, -1)
Answer:
The points that are on the line given by the equation y = x are:
A. (3, 3)
B. (2, 2)
D. (-1, -1)
E. (1, 1)
To check if a point is on the line, you can substitute its coordinates into the equation and see if the equation is true. For example, for point (3, 6), we have:
y = x
6 = 3
This is not true, so the point (3, 6) is not on the line. Repeat this process for each point to determine which points are on the line.
Jill Janzen's gross weekly pay is $298. Her earnings to date for the year total $14,900. What amount is deducted from her pay each week for Social Security, which is taxed at 6.2%?
Jill's annual earnings can be calculated by multiplying her weekly pay by the number of weeks in a year: $298/week x 52 weeks/year = $15,496/year. Her earnings to date are $14,900, so she has earned an additional $596 in the current week.
Social Security is taxed at 6.2%, so the amount deducted from her pay each week is 6.2% of her gross weekly pay. That's 0.062 x $298 = $18.48.
Is the figure line symmetric?
If yes, how many lines of symmetry does the figure have?
Snow flake
A.
No
B.
Yes; 3 lines of symmetry
C.
Yes; 6 lines of symmetry
D.
Yes; 12 lines of symmetry
The figure is indeed symmetric and the number of lines of symmetry the snowflake has is C. Yes; 6 lines of symmetry.
How many lines of symmetry does a snowflake have ?Generally a snowflake is hexagonal and has 6-way radial symmetry. Thus, one can rotate it 60 degrees (the sixth of full rotation) and it still appears the same.
So, overall, this means that a snowflake holds 6 lines of symmetry which divide it into two identical halves reflecting each other. Consequently, it can be rotated in 60-degree increments and still holds identicality. Akin to this final property, the snowflake artifact possesses six uniquely divided
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Maggie bought 50 lbs of clay for her art projects. She used 15.6 lbs to make a sculpture, and 0.84 lbs for each mug. How many mugs did Maggie make if she had 19.28 lbs of clay left over? Solve on paper. Then check your work on Zearn.
The number of mugs that Maggie made with the left over clay that she had would be = 23 mugs
How to calculate the quantity of mug made by Maggie?The total quantity of clay that Maggie bought = 50lbs
The quantity she used for sculpture = 15.6lbs
The quantity of clay she used for mug = 0.84 lbs
The quantity of clay left = 19.28 lbs
If 0.84 = 1 mug
19.28 = X
make X the subject of formula:
X = 19.28/0.84
= 23 mugs
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PLEASE HELP!!
What is the area of the circle? Approximate using pi equals 22 over 7. a circle with radius labeled 42 yards 22,176 square yards 5,544 square yards 264 square yards 132 square yards
The calculated value of the area of the circle is 5544 square yards
What is the area of the given circle?From the question, we have the following parameters that can be used in our computation:
Radius, r = 42
Using the above as a guide, we have the following:
Area = π * r^2
Substitute the known values in the above equation, so, we have the following representation
Area = 22/7 * 42^2
Evaluate the products and exponents
Area = 5544
Approximate
Area = 5544
Hence, the value of the area is 5544 square yards
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slope of A=(9,8) B=(-2,0)
Answer: 8/11
Step-by-step explanation:
Slope is given by rise/run or (y_2-y_1)/(x_2-x_1).
(x_1,y_1)=(9,8) and (x_2,y_2)=(-2,0)
So (y_2-y_1)/(x_2-x_1)= (0-8)/(-2-9)=-8/-11=8/11
Calculate the volume of this cylinder in terms of Pi and to the nearest hundredth
The volume of the given cylinder in terms of pi as required to be determined in the task content is; 5000 pi.
What is the volume of the given cylinder?It follows from the task content that the volume of the cylinder which is as represented is to be determined.
Since the volume of a cylinder is;
V = 2πr²h
where r = 10 and h = 25.
V = 2π × 10² × 25.
V = 5000π.
Ultimately, the volume of the given cylinder as required to be determined is; V = 5000 pi.
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Given that cos(x) =
A.
B.
2/3 113
D.
C. 1
13
2/3
3'
Mark this and return
find sin (90-x).
Please select the best answer from the choices provided
Save and Exit
Next
Su
Answer:
C
Step-by-step explanation:
cos x and sin(90 - x) are cofunctions and are equal , then
cos x = [tex]\frac{1}{3}[/tex] , then sin(90 - x) = [tex]\frac{1}{3}[/tex]
I NEED HELP
Please!!!!!!!!!!!!!!!
The exponential function for the given data is y = 1.806(1.107)ˣ ,
Interpretation about parameters are,
a represents initial population and b increase in growth by 10.7%.
Population size during 35th year is 63.
The exponential function that best represents the population growth of the species of crocodiles.
Values for parameters a and b in equation y = abˣ that best fit given data.
Using the data in the table, set up a system of equations as follows,
2 = ab¹
5 = ab¹⁰
12 = ab²⁰
22 = ab³⁰
25 = ab⁴⁰
To solve for a and b, we can divide the equations to eliminate a.
5/2 = (ab¹⁰)/(ab¹)
⇒5/2 = b⁹
12/5 = (ab²⁰)/(ab¹⁰)
⇒ 12/5= b¹⁰
22/12 = (ab³⁰)/(ab²⁰)
⇒ 22/12= b³/²
25/22 = (ab⁴⁰)/(ab³⁰)
⇒25/22 = b⁴/³
Taking the ninth root of the first equation,
The tenth root of the second
b = 1.107
a = 1.806
Exponential function that best represents the population growth of species of crocodiles is y = 1.806(1.107)ˣ
Interpreting the parameters of the model in the context of the problem.
a represents the initial population when x = 0 which is not given in the table.
And b represents the growth factor or rate of increase.
The growth factor is approximately 1.107, meaning that the population is increasing by about 10.7% each year.
To predict the population size during their 35th year, we simply plug x = 35 into the equation.
y = 1.806(1.107)³⁵
= 63.4
= 63(whole number)
Predict that population size of species of crocodiles during their 35th year will be approximately 63 individuals.
Therefore, the exponential function is y = 1.806(1.107)ˣ ,
Interpretation of parameters are a is the initial population and b represents the growth increased by 10.7%.
During 35th year population is 63.
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Please im begging someone please help me this is so hard. If you help me ill give you 60 points. PLEASE ILL GIVE BRAINLIEST
Answer: B, C, D
Step-by-step explanation:
Looking at the parabola, this is a width vs area graph.
A) Incorrect. the greatest possible area is not 10. Area goes higher
B) True. The highest possible area, highest point for area is 100
C) True. The area is 0 when width is 0
D)True. The area is also 0 when the width is 20
a ball leaves a bat in a horizontal direction from a height of 0.39 m above the ground. the speed of the ball is 35ms-1. the ball takes 0.28 seconds to reach the ground again. what is the horizontal distance the ball has travelled?
The horizontal distance the ball travelled is 2.73 m.
What is a projectile?A projectile is any object that is moving in space under the influence of gravity and its momentum. The horizontal distance covered by a projectile from its point of projection is called range. It can be determined by;
R = U[tex]\sqrt{\frac{2H}{g} }[/tex]
where u is the initial speed of the object, H is the height of projection and g is the gravitational constant.
So that in the information given, we can determine the range as;
R = U[tex]\sqrt{\frac{2H}{g} }[/tex]
= 35[tex]\sqrt{\frac{2*0.39}{10} }[/tex]
= 35*0.078
= 2.73
R = 2.73 m
The horizontal distance the ball has travelled is 2.73 m.
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Karissa wants to use the data to determine which brand is most absorbent. Based on the data collected at the beginning of the contest, enter the approximate number of paper towels needed to clean each square foot of the spill. Enter the number of Brand A paper towels needed per square foot in the first box. Enter the number of Brand B paper towels needed per square foot in the second box. Enter the number of Brand C paper towels needed per square foot in the third box.
Therefore, we need 17 towels of brand C to clean a single sq ft
How to solveBrand A:
we add up all the sq ft cleaned by brand a
0.75+1.50+2.25=4.5
and we add up all paper towels used in total
6+13+20=39
now
to clean 4.5 square ft, we need 39 towels. how many we need to clean a single square foot?
4.5 sq ft ___________39 towels
1 sq ft_____________A
and A= 1 sq ft * 39 towels / 4.5 sq ft
and that gives us 8.6 towels, so we need 9 towels to clan a square foot with the brand A
now we repeat this with bran b and c
brand B:
0.75+1.75+2=4.5 sq ft
9+22+25= 56 towels
4.5 sq ft________56 towels
1 sq ft__________B
B= 1 sq ft * 56 towels / 4.5 sq ft = 12.4
so we need 13 towels of brand B
at last
brand C:
1+1.75+2.5=5.25 sq ft
17+29+41= 87 towels
5.25 sq ft________87 towels
1 sq ft__________C
C= 1 sq ft * 87 towels / 5.25 sq ft = 16.57 towels
Therefore, we need 17 towels of brand C to clean a single sq ft
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A scientist has 68 lbs of a material. In 40 years , there is 63.3 lbs left. How much will be there be left in 200 years?
Evaluating the exponential decay we can see that 200 years, there will be 47.43 pounds left of the material.
How much will be there be left in 200 years?A general exponential decay is:
f(x) = A*(b)^x
Where A is the initial value, b is the rate of decay, x is the variable.
We know that we start with 68 pounds, and after 40 years there are 63.3 pounds left, so we have an exponential decay:
63.3 = 68*(b)^40
Where b defines how it decays, we can solve that equation for b to get:
(63.3/68)^(1/40) = b
0.9982 = b
Then the decay is:
f(x) = 68*(0.9982)^x
The amount left after 200 years will be:
f(200) = 68*(0.9982)^200 = 47.43
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