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Given,
The equation of the parabola is y^2+6y+8x+1=0
Required:
The vertex of the parabola.
The equation of the parabola is taken as:
[tex]\begin{gathered} y^2+6y+8x+1=0 \\ y^2+6y+1=-8x \\ y^2+6y+9-9+1=-8x \\ (y+3)^2-9+1=-8x \\ (y+3)^2-8=-8x \\ (y+3)^2=8-8x \\ -8x=(y+3)^2-8 \\ x=\frac{-(y+3)^2}{8}+1 \end{gathered}[/tex]The standard form of the equation is,
[tex]x=a(y-k)^2+h[/tex]Here, h and k are the vertex of the parabola.
On comparing the standard form with given vertex form of the parabola.
[tex](h,k)=(1,-3)[/tex]Hence, the vertex of the parabola is (1, -3).
Related Questions
A triangle has angle measures of 27 degrees , 50 degrees, and x degrees, use the triangle sum theorem to find the value of x.
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ANSWER:
Angle x is 103 degrees
EXPLANATION
The sum of all the angles in a triangle is 180 degrees
Hence, Let angle A = 27 degrees
Angle B = 50 degrees
Angle C = x degrees
Triangle sum theorem state that
50 + 27 + x = 180
77 + x = 180
x = 180 - 77
x = 103 degrees
ANSWER QUESTION 3 PHOTO ATTACHEDFAST REPLY = BETTER RATINGTHANK YOU!
Answers
Given
[tex]f(x)=xe^{7x}[/tex]Calculate the second derivative of f(x), as shown below
[tex]\begin{gathered} \Rightarrow f^{\prime}(x)=e^{7x}+7xe^{7x} \\ and \\ \Rightarrow f^{\prime}^{\prime}(x)=7e^{7x}+7(e^{7x}+7xe^{7x}) \\ \Rightarrow f^{\prime}^{\prime}(x)=14e^{7x}+49xe^{7x} \end{gathered}[/tex]Then, find the interval such that f''(x)>0 in order to find where f(x) is concave up,
[tex]\begin{gathered} 14e^{7x}+49xe^{7x}>0 \\ \Rightarrow2e^{7x}+7x*e^{7x}>0 \\ and \\ e{}^{7x}>0,x\in\Re \end{gathered}[/tex]Then,
[tex]\begin{gathered} 2e^{7x}>-7xe^{7x} \\ \Rightarrow2>-7x \\ \Rightarrow x>-\frac{2}{7} \end{gathered}[/tex]Therefore, f(x) is concave up when x in (-2/7, +infinite).
In the case of concavity down,
[tex]\begin{gathered} f^{\prime}^{\prime}(x)<0 \\ \Rightarrow2e^{7x}+7x*e^{7x}<0 \\ \Rightarrow2+7x<0 \\ \Rightarrow-\frac{2}{7}>x \end{gathered}[/tex]Thus, f(x) is concave down when x in (-infinite, -2/7).
The answer is the fifth and last option (top to bottom).
1. Solve -4x < -3(6x - 2) and sketch the solution set on a number line.
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We need to solve the inequality:
[tex]-4x<-3\mleft(6x-2\mright)[/tex]Let's multiply right side out and take variables to one side and numbers to another. The process is shown below:
[tex]\begin{gathered} -4x<-3\mleft(6x-2\mright) \\ -4x<-18x+6 \\ -4x+18x<6 \\ 14x<6 \\ x<\frac{6}{14} \\ x<\frac{3}{7} \end{gathered}[/tex]The solution set is:
[tex]\begin{gathered} x<\frac{3}{7} \\ or \\ x<0.4286 \end{gathered}[/tex]This means that x is less than 3/7, or
x is less than 0.4286
On the number line it looks:
a teacher performing a demonstration find that a piece of court displaces 23.5 ml of water . the piece of cork had a density of 5.7 grams. what is the density of the cork
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We are asked to determine the density of the cork. To do that we will use the following formula:
[tex]D=\frac{m}{V}[/tex]Where:
[tex]\begin{gathered} D=\text{ density} \\ m=\text{ mass} \\ V=\text{ volume} \end{gathered}[/tex]The volume of the cork is the same as the volume that it displaced of water, therefore, we have:
[tex]V=23.5ml[/tex]Now, we substitute the values and we get:
[tex]D=\frac{5.7g}{23.5ml}[/tex]Solving the operations:
[tex]D=0.24\frac{g}{ml}[/tex]Therefore, the density of the cork is 0.24 g/ml.
Select all of the constraints that apply to this situation $1.25x when x <12$12.00 + $0.75(x-12) when X_>12$1.25x when x _>120.75x when x >12$12.00 + $0.75x when x >12
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We want to write expressions that describe the cost of the cookies. Let say we sell x cookies. If x is less than 12, then the cost per cookie is 1.25. So the cost of x cookies would be the product of this numbers, so it would be
[tex]1.25x,x<12[/tex]Note that when x=12 the cost should be 12. Also note that for each extra cookie, starting at 12, each cookie costs 0.75. If we buy x cookies , to calculate the extra cookies, with respect to 12, we simply substract 12 from x and we multiply it by 0.75. This would be
[tex]0.75\cdot(x\text{ -12)}[/tex]as this is an additional cost to the 12, we add 12 to this expression. THen we get
[tex]12+0.75\cdot(x\text{ -12)}[/tex]Note that for this expression, when x=12, we get that the expression becomes
[tex]12+0.75\cdot(12\text{ -12)=12}[/tex]THis means that the expression applies from 12 and on, so we have the followin inequality12
[tex]12+0.75\cdot(x\text{ -12), x}\ge12[/tex]A bag of numbered lottery balls contains the numbers 1 through 50. What is the probability that a randomly selected ball will be a number that is not a multiple of 8? Give your answer as a simplified fraction.
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A bag of numbered lottery balls contains he numbers 1 through 50.
One ball is selected at random.
From 50 balls, one ball can be selected in 50 different ways.
So, the total number of points in sample space is 50.
Let us consider the event that the number is a multiple of 8 be A.
There are six numbers between 1 o 50 which are multiple of 8.
Therefore, one ball can be selected from 6 balls in 6 different ways.
So, the number of points in sample space in favour of the event A is 6.
Therefore, by the classical definition of probability,
[tex]\begin{gathered} P(A)=\frac{6}{50} \\ =\frac{3}{25} \end{gathered}[/tex]Then, the probability that the selected number is not a multiple of 8 is
[tex]\begin{gathered} P(A^C)=1-P(A) \\ =1-\frac{3}{25} \\ =\frac{22}{25} \end{gathered}[/tex]So, the required probability is 22/25.
Maggie graphed a scatter plot of the numberof hours she drove, t, and the number of milesshe traveled, d. She then found a trend line ofher data to be d = 45.5t + 8. What is thepredicted distance Maggie will travel # shedrives for 4 hours?A 182 milesB 372 milesC 364 milesD 190 milesWhat’s the answer ?
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WE have the following:
[tex]d=45.5t+8[/tex]When t = 4
[tex]undefined[/tex]Two cards are drawn from a deck of 52 cards. The first card is replaced before drawing the second card. Find the probability that the first card is red and the second card is a 7
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The probability that the first card is red and the second card is a 7 is 1/26.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
Probability that the first card is a red and the second is a 7 = (number of red cards / total number of cards) x (number of 7 / total number of card)
Probability that the first card is a red and the second is a 7 = (26 / 52) x (4/52) = 1/26
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solution of the system of equations.2. (3, 0) 2x+y=-63x + 2y = 94. (-2,3) y =2x+75x+y=-76. (0,-7) 2x -2y = 14X-Y=-7
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We can solve these systems of equations as follows:
First CaseWe have:
[tex]\begin{cases}2x+y=-6 \\ 3x+2y=9\end{cases}[/tex]And we can solve this system by substitution as follows:
[tex]\begin{gathered} 2x+y=-6 \\ 2x-2x+y=-6-2x \\ y=-6-2x \end{gathered}[/tex]Now, we can substitute the corresponding value of y into the second equation as follows:
[tex]\begin{gathered} y=-6-2x \\ 3x+2y=9 \\ 3x+2(-6-2x)=9 \\ 3x+(2)(-6)+(2)(-2x)=9 \\ 3x-12-4x=9 \\ 3x-4x-12=9 \\ -x-12=9 \\ -x-12+12=9+12 \\ -x=21\Rightarrow x=-21 \end{gathered}[/tex]Now, we can substitute the value x = -21 into either of the original equations to find the value of y. We will use the first equation:
[tex]\begin{gathered} 2x+y=-6 \\ 2(-21)+y=-6 \\ -42+y=-6 \\ -42+42+y=-6+42 \\ y=36 \end{gathered}[/tex]Therefore, the solution to this first system is (-21, 36).
We can check this result if we substitute both values into the original equations:
[tex]\begin{gathered} \begin{cases}2x+y=-6 \\ 3x+2y=9\end{cases} \\ x=-21,y=36 \\ \begin{cases}2(-21)+36=-6 \\ 3(-21)+2(36)=9\end{cases} \\ \begin{cases}-42+36=-6 \\ -63+72=9\end{cases} \\ \begin{cases}-6=-6\Rightarrow This\text{ is true.} \\ 9=9\Rightarrow This\text{ is true.}\end{cases} \end{gathered}[/tex]Therefore, the solution to the first system of equations is (-21, 36).
Second Case
[tex]\begin{cases}y=2x+7 \\ 5x+y=-7\end{cases}[/tex]We can rewrite the system as follows:
[tex]\begin{cases}-2x+y=7 \\ 5x+y=-7\end{cases}[/tex]And we can solve this system by the elimination method: We have to multiply one of the equations by -1 and then add them algebraically as follows:
[tex]\begin{gathered} \begin{cases}-2x+y=7 \\ -1(5x+y=-7)\end{cases} \\ \begin{cases}-2x+y=7 \\ (-1)(5x)+(-1)(y)=(-1)(-7)\end{cases} \\ \begin{cases}-2x+y=7 \\ -5x-y=7\end{cases} \end{gathered}[/tex]If we add both equations, then we have:
[tex]\begin{gathered} \frac{\begin{cases}-2x+y=7 \\ -5x-y=7\end{cases}}{-7x=14} \\ -\frac{7x}{-7}=\frac{14}{-7} \\ x=-2 \end{gathered}[/tex]And now we can substitute this value in either equation to find y:
[tex]\begin{gathered} y=2x+7 \\ y=2(-2)+7 \\ y=-4+7 \\ y=3 \end{gathered}[/tex]And we got y = 3.
Therefore, the solution to this system is equal to (-2, 3), and we can also check the solutions using the original equations:
[tex]\begin{gathered} \begin{cases}y=2x+7 \\ 5x+y=-7\end{cases} \\ \begin{cases}3=2(-2)+7 \\ 5(-2)+3=-7\end{cases} \\ \begin{cases}3=-4+7 \\ -10+3=-7\end{cases} \\ \begin{cases}3=3\Rightarrow This\text{ is true.} \\ -7=-7\Rightarrow This\text{ is true.}\end{cases} \end{gathered}[/tex]In summary, we have that:
The solution to the first system ---> (-21, 36).
The solution to the second system ---> (-2, 3).
If a bow requires 3/4 yards of lace how many bows can u make with 12 yards of lace
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3/4 yards of a lace for each bow
for 12 yards of lace:?
Simply divide the 12 yards of lace by the lace required by each bow (3/4)
12 / (3/4) = 16 bows
Multiply the following polynomials. Once simplified, name the resulting polynomial. (x + 2) (4x^2 - 3x - 2)name:
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The resulting polynomial consists of four terms , it is called a quadrinomial.
find the area of the circle with a diameter of 8.6 ft
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Given:
Diameter of the circle, d = 8.6 ft
To find the area of a circle, use the formula below:
[tex]undefined[/tex]Diameter of the circle, d
Type the correct answer in each box. Use numerals instead of words.The exterior of a solid cone is painted. The height of the cone is 11.4 centimeters, and the diameter of its opening is 5 centimeters.What is the surface area of the solid cone requiring paint to the nearest square centimeter?The surface area of the solid cone requiring paint rounded to the nearest whole number is square centimeters.
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The surface area of a cone with diameter d and height h is given by:
[tex]A=\pi(\frac{d}{2})^2+\pi\cdot\frac{d}{2}\cdot\sqrt[]{h^2+(\frac{d}{2})^2}[/tex]For d = 5 cm and h = 11.4 cm, we have:
[tex]\begin{gathered} A=\pi(\frac{5}{2})^2+\pi\frac{5}{2}\sqrt[]{11.4^2+(\frac{5}{2})^2} \\ A=\frac{25}{2}\pi+\pi\frac{25}{2}\sqrt[]{129.96+\frac{25}{2}} \\ A=12.5\pi+12.5\cdot\pi\cdot\sqrt[]{142.46} \\ A\approx12.5\pi+12.5\cdot11.94\cdot\pi \\ A\approx508cm^2 \end{gathered}[/tex]Multiply. Write the result in standard form.(2 + 1)(3^4 + 7 + 2)
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To multiply polynomials, we use the distributive law
[tex]\begin{gathered} (2x+1)(3x^4+7x+2)=(2x+1)(3x^4)+(2x+1)(7x)+(2x+1)(2) \\ =2x(3x^4)+1(3x^4)+2x(7x)+1(7x)+2x(2)+1(2)_{} \\ =6x^5+3x^4+14x^2+7x+4x+2 \end{gathered}[/tex]The last part follows by the laws of exponentials, finally we combine like terms
[tex]\begin{gathered} 6x^5+3x^4+14x^2+7x+4x+2=6x^5+3x^4+14x^2+(7+4)x+2 \\ =6x^5+3x^4+14x^2+11x+2 \end{gathered}[/tex]Please Help! An eight foot ladder leans against a building. if the ladder makes an angle of 60 degrees with the ground, haw far from the building is the base of the ladder. Round you answer to the nearest tenth.
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The base of the ladder is 4 ft away from the buliding
Here, we want to calculate the distance from the building to the base of the ladder
To properly answer this, an image of the question is needed
We have this as follows;
From the diagram, what we want to calculate is the distance d
To calculate this, we need the appropriate trigonometric identity
Firstly, we need to identify the parts of the triangle present
As we can see, we have the hypotenuse which is the side that faces the right angle and also is the longest side
The side we want to get is the adjacent
Mathematically, the trigonometric ratio that connects the adjacent to the hypotenuse is the cosine
Thus, we have it that;
[tex]\begin{gathered} \cos \text{ 60 = }\frac{d}{8} \\ \\ d\text{ = 8 cos 60} \\ d\text{ = }4.0\text{ ft} \end{gathered}[/tex]Mariah needs to randomly select one of three groups of students to make their presentation first. Which simulation tools could she use in thissituation?O a bag containing 12 chips in three different colors, with four of each coloro a six-sided number cubea full standard deck of cardsa spinner divided evenly into four sections, with each section a different colorO two coins
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the correct answer is a bag containing 12 chips in three different colors, with four of each color (option A)
Explanation:
number of groups of student = 3
We need to select one out of the three.
The option that can be used to simulate this choice is having 12 chips in three different colours. Each colour will have 4 each.
The 3 different colours represent the 3 different groups. While each 4 number of a colour represent the number of students in each group.
Hence, the correct answer is a bag containing 12 chips in three different colors, with four of each color (option A)
Translate this sentence into an equation 43 is the difference of Chrissy’s age and 14 Use the variable c to represent Chrissy’s age
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When translating into mathematical equations, "is" uses the equal sign and "difference" means that the operation to be used is subtraction.
So, "43 is the difference of Chrissy's age and 14" is written as:
43 = C - 14
I inserted a picture of the question answer choices E. 15 F.x
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Recall that two terms are called like terms if they have the same variables with the same exponents, in simpler words, two terms are like terms if when adding them the result is a simplification of the sum.
Answer: 8 and 12, 1, and 15 are like terms.
Samuel is 10 years old. He moaned the neighbors lawn on Saturday and I and $40. It took him 2 hours come on the lawn in 2 hours to clean his room. How much money did Samuel earn an hour? A) $4.00B) $6.67C) $10.00D) 20.00
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If he earned $40 in total and it took 4 hours to finish everything, he earns in an hour:
[tex]\frac{40}{4}=10[/tex]Answer: Samuel earns $10.00. Letter C.
Answer:
He got paid 10$ an hour. It does not say he gets paid for cleaning his room. Step-by-step explanation:10 x 4 = 40$
Step-by-step explanation:
Victor took a survey of high school students to see how many had part-time jobs last summer. The results of the survey are shown in the table. Compare theprobability that a student in the sophomore class had a part-time job to the probability that a student in the junior class had a part-time job.
Answers
Answer:
A sophomore is less likely than a Junior to have a job.
Explanation:
Given the table in the attached image.
The total number of sophomores is
[tex]35[/tex]The number of sophomores with a job is;
[tex]12[/tex]The probability that a sophomore had a job is;
[tex]P_S=\frac{12}{35}[/tex]The total number of Juniors is
[tex]37[/tex]The number of Juniors with a job is;
[tex]27[/tex]The probability that a Junior had a job is;
[tex]P_J=\frac{27}{37}[/tex]From the derived Probability, we can observe that the probability that a Junior had a job is greater than the probability that a Sophomore had a job.
[tex]P_J>P_S[/tex]Therefore, A sophomore is less likely than a Junior to have a job.
8. If the slope of the equation y = -3/5x + 4 is changed to 3/5 and the y-intercept is changed to -4, which statement best describes this situation? You can use a calculator to graph or create your own graph.*A The new line is perpendicular to the original line. B The new line is parallel to the original line. C The new line and the original line have the same y-intercept. D The new line and the original line have the same x-intercept.
Answers
Answer:
Explanation:
Given that the line
[tex]y=-\frac{3}{5}x+4[/tex]is changed to
[tex]y=\frac{3}{5}x-4[/tex]Which two ratios are equivalent to 11/12?A. 4/5 and 12/13B. 22/24 and 33/36C. 22/33 and 33/34D. 23/24 and 35/36
Answers
Two ratios are equivalent if the division between them is equal to one. We need to look at the options to check for which these are true.
For A:
[tex]\frac{\frac{11}{12}}{\frac{4}{5}}=\frac{11}{12}\cdot\frac{5}{4}=\frac{55}{48}[/tex]Since the answer is different than one, this is not the correct option.
For B:
[tex]\frac{\frac{11}{12}}{\frac{22}{24}}=\frac{11}{12}\cdot\frac{24}{22}=\frac{264}{264}=1[/tex][tex]\frac{\frac{11}{12}}{\frac{33}{36}}=\frac{11}{12}\cdot\frac{36}{33}=\frac{396}{396}=1[/tex]Since the result of the division is one for both ratios, the correct option is "B".
Helpppppppp I can’t answer because I am bad at math
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The magnitude of a number is the absoulute value of the number. Recall, the absolute value of a number is always positive. The absolute value of a is written as IaI
Hence,
magnitude of - 7.5 is 7.5
The correct option is D
Solve the system of two linear inequalities graphically,2y <&- 1618v 2 - 7x+56Step 1 of 3: Graph the solution set of the festlinear InequallyAnswerThe line will be drawn once all required data is provided and will update whenever a value is updated. The regions will be added once the line is drawEnable ZoonpanChoose the type of boundary linesSolid (-) Dashed)Enter two points on the boundarytine:10Select the region you wish to be shaded:
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Given
[tex]\begin{gathered} 2y<8x-16 \\ 8y\ge7x+56 \end{gathered}[/tex]The graph
Two boundary points
(0,7) (2,0)
5) Given the following matrices, find the products of LN and MN
Answers
Answer:
The products MN and LN are not possible.
Explanation:
Matrix multiplication is only possible when the column number of the first matrix equals the row number of the second matrix.
Now, matrix L is a 2 x 2 matrix and N is a 5 x 2 matrix. Now L has 2 columns and N has 5 rows. Meaning, that columns of L are not equal to the rows of N. Therefore, matrix multiplication is not possible.
Matrix M is 2 x 4 and matrix N is 2 x 2. Since columns of matrix M equal the rows of matrix N, matrix multiplication is possible.
Therefore,
[tex][/tex]Express - 345 asin simplest form, where m and n are integers.Enter the correct answer in the box.-345 =
Answers
As -345 is an integer, the simplest fraction form is:
[tex]\frac{-345}{1}[/tex]or -345/1 (m=-345, n=1).
I need help on 4 please it says find the value of x round each answer to the nearest tenth
Answers
The pythagorean theorem is :
[tex]c^2=a^2+b^2[/tex]where c is the hypotenuse
a and b are the legs of the triangle.
From the problem, a = x, b = 19.1 and c = 30.5
Using the formula :
[tex]\begin{gathered} 30.5^2=x^2+19.1^2 \\ 930.25=x^2+364.81 \\ x^2=930.25-364.81 \\ x^2=565.44 \\ x=\sqrt[]{565.44} \\ x=23.779 \end{gathered}[/tex]The answer rounded to the nearest tenth is x = 23.8
Find the standard deviation for the following wroup of data Hems, Round your answer to the nearest tenth for one decimal place), 7,9,11,14,15,16
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The standard deviation of the groups of data is 3.3 .
The standard deviation is calculated using the formula [tex]{\displaystyle \sigma={\sqrt {{\frac {1}{N}}\sum _{i=1}^{N}\left(x_{i}-{\mu }\right)^{2}}}}[/tex]
Where σ is the standard deviation.
x denotes the data of the population.
N is the size of the population.
μ is the mean of the population.
The given population is 7,9,11,14,15,16
Here N= 6
Mean (μ) = (7+9+11+14+15+16)÷6 = 72/6=12
Now we will put the values in the above equation to calculate the sd.
[tex]{\displaystyle \sigma={\sqrt {{\frac {1}{6}}\sum _{i=1}^{6}\left(x_{i}-{12 }\right)^{2}}}}[/tex]
Simplifying we get:
σ = √(64/6)
σ = 3.2659..
σ = 3.3
The standard deviation is a statistic that indicates the degree of volatility or dispersion in a set of numerical values.
A low standard deviation shows that possibly the values tend toward being close to the mean, sometimes referred to as the expected value of the set, whereas a large standard deviation suggests that the values are distributed over a wider range.
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The graph of g consists of two straight lines and a semi circle. Evaluate each
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Given:
a)
[tex]\int ^1_0g(x)dx[/tex]Consider the shape included in the region from 0 to 1 of g(x).
The area is,
[tex]\int ^1_0g(x)dx=\frac{1}{2}\times1\times4=2[/tex]b) From x = to x = 6 includes the semi-circle. Its area is calculated as,
[tex]\int ^6_2g(x)dx=-\frac{1}{2}(\pi\times r^2)=-\frac{1}{2}(\pi\times2^2)=-2\pi=-6.28[/tex]Which of the following transformations shows a rotation 270 degrees counterclockwise? *
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Explanation:
A rotation 270 degrees counterclockwise happens when the y and x axis value are interchanged and the interchanged y value becomes negative.
When we look at the options given, we look for the image whose rotation is in the positive x axis and negative y axis.
Also the movement will be thrice while moving anticlockwise.
From the options, the one which fits into the description above is B.
There is a movement of counterclockwise