All solutions to the cubic equation, 4•x³ + 16•x² + 28•x = 0, are presented as follows;
0, -2 + i•√(3), -2 - i•√(3), which is the option;
0, negative 2 + i StartRoot 3 EndRoot, negative 2 minus i StartRoot 3 EndRootWhat are the solutions to a cubic function?The solutions of a cubic function are given by the values at which the graph intersects the horizontal axis.
First Part
The graph showing the shaded region of the inequality is left out
Second part;
The given equation can be presented as follows;
4•x³ + 16•x² + 28•x = 0
Required;
To find all the solutions of the equation
Solution;
The solutions of the equation are given by the locations on the graph where the equation intersects the x–axis, which are therefore, the points where the function is equal to 0
The equation 4•x³ + 16•x² + 28•x = 0 can therefore be used to find the solution as follows;
4•x³ + 16•x² + 28•x = 0
x•(4•x² + 16•x + 28) = 0
x•(4)•(x² + 4•x + 7) = 0
x•(x² + 4•x + 7) = 0 ÷ (4) = 0
x•(x² + 4•x + 7) = 0
Which by the multiplicative identity of 0, gives;
x = 0 or x² + 4•x + 7 = 0Therefore;
x = 0 is a solution to the equation
The other solutions are found from the quadratic equation, x² + 4•x + 7 = 0, using the quadratic formula that gives the solution to the general quadratic equation, a•x² + b•x + c = 0, as follows;
[tex] \displaystyle{x = \frac{ - b \pm \sqrt{ {b}^{2} - 4 \times a \times c } }{2 \times a }}[/tex]
Comparing the general form of the quadratic equation to the quadratic equation from the question;
a•x² + b•x + c = 0
x² + 4•x + 7 = 0
Gives;
a = 1
b = 4
c = 7
Plugging in the above values of a, b, and c, we get;
[tex] \displaystyle{x = \frac{ - 4 \pm \sqrt{ {4}^{2} - 4 \times 1 \times 7 } }{2 \times 1} = \frac{ - 4 \pm 2 \cdot\sqrt{ - 3} }{2} }[/tex]
Which gives;
x = -2 ± √(-3) = -2 ± i•√(3)
The other solutions are therefore;
x = -2 + i•√(3) and x = -2 - i•√(3)The solutions of the equation, 4•x³ + 16•x² + 28•x = 0, are therefore;
x = 0, x = -2+i•√(3), and x = -2 - i•√(3)
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Unoccupied seats on flights cause airlines to loose revenue. Suppose a large airline wants to estimate its average number of unoccupied seats per flight over the past year. To accomplish this, the records of 225 flights are randomly selected, and the number of unoccupied seats is noted for each of the sampled flights. The sample mean and standard deviations are
x-bar =11.6 seats s=4.1 seats
Use Central Limit Theorem to help the company estimate its average number of unoccupied seats per flight over the past year.
The mean number of unoccupied seats per flight during the past year will lie between 11.15 and 12.05.
What is mean in mathematics?
There are many mean types in maths, particularly in statistics. Each mean serves to condense a specific set of data, frequently so that the general magnitude and sign of the data set can be better understood.
The arithmetic mean, also referred to as "arithmetic average," is a calculation that divides the total number of values in a data collection by their sum to get the central tendency of that set of numbers.
a) Calculations:
Degrees of freedom = n - 1 = 225 - 1 = 224
For 224 degrees of freedom and 90% confidence interval,
Critical t value = 1.652
Hence,
90% confidence interval will be:
[tex]11.6 \pm 1.652*4.1/\sqrt{225}[/tex]
[tex]11.6 \pm 0.45[/tex]
(11.15, 12.05)
b) Interpretation:
We are 90% confident that the population mean number of unoccupied seats will lie between 11.15 and 12.05
c) Caution with interpretation:
In this scenario, individual confidence interval should be calculated rather than mean number of unoccupied seats since we can't generalize this interpretation for individual flights.
d) To narrow a confidence interval, we can either increase the sample size or can decrease the confidence level.
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Complete question
Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to estimate its average number of unoccupied seats per flight over the past year. To accomplish this, the records of 225 flights are randomly selected, and the number of unoccupied seats is noted for each of the sampled flights (from text, p. 306, example 6.3; use NOSHOW excel file). Given the mean number of unoccupied seats for the 225 random flights is 11.6 and the standard deviation is 4.1, estimate μ, the mean number of unoccupied seats per flight during the past year, using a 90% confidence interval.
a. Calculations
b.Interpretation
c.Caution with interpretation
d.How to narrow a confidence interval
9) A swimsuit is on sale for $45.50. If the sale price is discounted 5% from the
original price, what was the original price? Round to the nearest cent.
Answer:
47.900
Step-by-step explanation
45.50 plus 2.275 is 47.825 rounded is 47.9
question in screenshot
The vertical and horizontal asymptotes for the graphed function are given as follows:
a) The vertical asymptotes are given at x = -1 and x = 2.
b) The horizontal asymptote is given at y = -1.
What are the asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator, and in the graph, they are represented by vertical dashed lines.The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity, and in the graph, they are represented by horizontal dashed lines.In the context of this problem, we have that the asymptotes can be extracted from the graph as follows:
In item a, there are two vertical dashed lines, at x = -1 and x = 2, hence those are the vertical asymptotes of the graphed function.In item b, there is one horizontal dashed line, at y = -1, hence this is the horizontal asymptote of the graphed function.More can be learned about asymptotes at https://brainly.com/question/4138300
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Simplify the root below and leave your answer in the form \frac{a}{b} \sqrt[]{ \frac{405}{324} } Our value for a is AnswerOur value for a is Answer
We are asked to simplify the following expression
[tex]\sqrt[]{\frac{405}{324}}[/tex]Recall the quotient rule of radicands given by
[tex]\sqrt[]{\frac{a}{b}}=\frac{\sqrt[]{a}}{\sqrt[]{b}}[/tex]Applying the above rule to the given expression
[tex]\sqrt[]{\frac{405}{324}}=\frac{\sqrt[]{405}}{\sqrt[]{324}}[/tex]Notice that the square root of 324 is equal to 18
[tex]\frac{\sqrt[]{405}}{\sqrt[]{324}}=\frac{\sqrt[]{405}}{18}[/tex]Also, notice that we can break 405 into factors as
[tex]\sqrt[]{405}=\sqrt[]{81\times5}=\sqrt[]{81}\cdot\sqrt[]{5}=9\cdot\sqrt[]{5}[/tex]So, the expression becomes
[tex]\frac{\sqrt[]{405}}{18}=\frac{9\cdot\sqrt[]{5}}{18}=\frac{\sqrt[]{5}}{2}[/tex]Therefore, the simplified expression is
[tex]\frac{\sqrt[]{5}}{2}[/tex]a = √5
b = 2
What is the value of p?
when a number is power to a number a, and it is also power to another number b we can apply the property
[tex](x^a)^b=x^{a\cdot b}[/tex]apply this to the expression above
[tex]\begin{gathered} x^{22}\cdot(x^{7\cdot3)} \\ x^{22}\cdot x^{21} \end{gathered}[/tex]continue by applying the property of a product between the same number as a base but with a different exponent
[tex]x^a\cdot x^b=x^{a+b}[/tex]apply this to the expression above
[tex]\begin{gathered} x^{22}\cdot x^{21^{}} \\ x^{43} \end{gathered}[/tex]the value of p is equal to 43.
PLEASE CAN SOMEONE HELP ME !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!a) Fully factorise 5y² + 13y + 6
b) Use your answer to part a) to solve
5y² + 13y+6=0
Answer:
(y +2)(5y +3)y = -2, -3/5Step-by-step explanation:
You want the factors of 5y² +13y +6, and the solutions to 5y² +13y +6 = 0.
a) FactorsThe quadratic ax²+bx+c with a leading coefficient a≠1 can be factored by considering the factors of the product 'ac' that have a sum of 'b'.
5·6 = 30 = (1)(30) = (2)(15) = (3)(10) = (5)(6)
The sums of these factor pairs are, respectively, 31, 17, 13, 11. The factor pair with a sum of 13 is (3)(10).
There are a couple of methods that can be used to apply this knowledge to the factorization of the quadratic. Perhaps the most straightforward is to write the quadratic as 4 terms, using the found values to rewrite the linear term as their sum:
5y² +13y +6 = 5y² +3y +10y +6 . . . . . . . . . 13 ⇒ 3 +10
Now, pairs of terms can be factored:
= y(5y +3) +2(5y +3)
= (y +2)(5y +3) . . . . . . . fully factored expression
b) SolutionThe solutions that makes the product of factors be zero will be the values of x that make the factors be zero. A product is only zero if one of the factors is.
y +2 = 0 ⇒ y = -2
5y +3 = 0 ⇒ y = -3/5
The solutions to the quadratic equation are y = {-2, -3/5}.
__
Additional comment
Another way to find the factors is this. For factors p, q that have a product of 'ac' and a sum of 'b', the factorization can be ...
(ay +p)(ay +q)/a
For the values in this problem, this would be ...
(5y +3)(5y +10)/5
The latter of these factors can be divided by 5, so this can be simplified to ...
(5y +3)(y +2) . . . . as above
Lesly graphed two lines in order to find thesolution to a given system of equations.What is the solution?1.) (3, -8)2.) (-3, -8)3.) (8, 3)4.) (-8, -3)
The solution of the system of equation is the point where the 2 lines cross each other.
By looking at the graph, we can see that they cross each other at (-3,-8)
Correct option: 2
Which construction is illustrated above?
O an angle congruent to a given angle
O the angle bisector of a given angle
O a perpendicular to a given line from a point on the line
O a line segment congruent to a given line segment
Answer:
The construction is a parallel line to a given line from a point not on the line.
Step-by-step explanation:
For a given figure,
To construct a parallel line
Step 1 : Draw transversal line through any point not on line which is given.
Step 2: Using construction copy an angle, construct same angle formed by transversal line and given line.
Step 3: This is the last step in which when the copy of an angle completed draw a line parallel to the line
Step-by-step explanation:
Name the property which justifies the following conclusion:
Given: m = n
Conclusion: 3m = 3n
A Reflexive Property of Equality
B Multiplication Property of Equality
C Symmetric Property of Equality
D Transitive Property of Equality
Answer:
A) Reflexive Property of Equality
Step-by-step explanation:
If you look at your reflection in a mirror, you see yourself! Likewise, by the Reflexive Property, any number is its own mirror image. Any number (such as a real number) is equal to itself!
What this means is that any number is the answer as no number is given. It could be 3m = 3n, 10m = 10n, or 85m - 85n as long as the number of "m" is the same to the number of "n."
-3x + 7y = 24
3x + 2y = 3
Answer: x = -1 y=3
Step-by-step explanation:
yeah just do AP algebra.2 then you'll know the answers
Give the slope of a line that is parallel to −3x−3y=1.
Step-by-step explanation:
y = mX + c
3y = -3x - 1
divide by 3
y = -x -1/3
slope = -1 of this line and parallel lines
Answer:
-1 is the slope beause lines with the same slope are parallel.
Can someone explain this ???
The intersection point of the circle and the line is at-(2.68, 7.36).
What is defined as the equation of circle?A circle is a confined curve drawn from a fixed point known as the centre, with all points on the curve sharing the same distance as from centre point. (x-h)² + (y-k)² = r² is the equation for a circle with (h, k) centre and r radius.For the given question;
The equation of the line is; y = 2x + 2 ......eq 1
The centre of the circle (h,k) = (0,2)
The radius of the circle = 6 units.
This is the equation's standard form.
(x - h)² + (y - k)² = r²
Put the values in the formula;
(x - 0)² + (y - 2)² = r²
(x)² + (y - 2)² = r²
Put the value of y from eq 1.
(x)² + (2x + 2 - 2)² = 6²
(x)² + (2x)² = 36
Simplifying;
x = ±6/√5
But the intersection must be in first quadrant.
x = 6/√5 = 2.68
Put the value of x in eq 1.
y = 2x + 2
y = 2×2.68 + 2
y = 7.36
Thus, the coordinates of the intersection of the line and the circle are (2.68, 7.36).
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1) Analia thought of two different ways to define this quantity. Identify these two definitions among the
following options.
Choose 2 answers:
Graduation rate divided by number of teachers
Graduation rate divided by teachers per student
SAT average divided by number of teachers
SAT average divided by teachers per student
Analia proposed the following two measures to determine which school had a better academic record:
B. Graduation rate and student budget
D. Average SAT score / Per-student budget
How to determine the various amounts Which school has the best academic performance, according to Analia?To specify a number that represents academic accomplishment;
We compare the budget per pupil for each school to a corresponding metric or parameter that measures the academic performance of the students in each school.
The following variables could be used to gauge academic achievement:
the success rate of every school.
The SAT score of each institution.
Consequently, the amount to assess academic success in relation to each student's budget may be represented as;
Graduation rate and student budget
Average SAT score / Per-student budget
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Three times a number decreased by five ikbetween 41 and 58. Enter your answer in interval notation.Interval notation of valid valuesO No interval of valid values
Answer:
(-12, 21)
Explanation:
3 times a number decreased by 5 means 3x -5.
This number is between -41 and 58; therefore,
[tex]-41<3x-5<58[/tex]Now we solve for the unknown number x.
Adding 5 to the three sides gives
[tex]\begin{gathered} -41+5<3x-5<58+5 \\ -36<3x<63 \end{gathered}[/tex]finally, dividing the inequality by 3 gives
[tex]-12which in interval notation we write as [tex](-12,21)[/tex]the parenthesis indicates that the -12 and 21 are not included in the solution interval =.
In Mr. Stowe's math class, Katherine earned an 88 in the 1st quarter and a 94 in the end quarter. What is the percentage of increase? Round to the nearest hundredth.
How many times greater is 4.65 x 108 than 7.5 x 106? Express your answer using
either standard notation or scientific notation.
Hello,
Can someone help me with this paper
Written work please if u dont mind
The value of x is (t - ab)/ad while taking the subject x.
What does it mean when some variable is made the subject?Making x the subject of an equation or formula entails rearranging the equation or formula so that the x variable is equal to the other variables. The variable being calculated is the formula's subject. On one side of the equals sign, it is identifiable as the letter on its own. When changing a formula's subject, we rearrange the formula's components to create a new subject. In other words, alter the operation to do the opposite if you move a term from one side of the equals sign to the other. (An operation's inverse is known as the operation's opposite.)So, t = a(b + dx):
Now, solve taking the subject 'x' as follows:
t = a(b + dx)t = ab + adxt - ab = adx(t - ab)/ad = xx = (t - ab)/adTherefore, the value of x is (t - ab)/ad while taking the subject x.
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Solve. (Enter your answer using interval notation.)
|3x + 15| > 21
Answer:
(-∞, -12), (2, ∞)
or
(-∞, -12) U (2, ∞)
Step-by-step explanation:
|3x + 15| > 21, |3x + 15| < -21
3x + 15 > 21, 3x + 15 < - 21
-15 -15 -15 -15
------------------ -------------------
3x > 6 3x < - 36
÷3 ÷3 ÷3 ÷3
------------ ------------------
x > 2 x < -12
(-∞, -12), (2, ∞)
or
(-∞, -12) U (2, ∞)
I hope this helps!
Approximate -16 + square root of 40
The result of the approximation of -16 + square root of 40 is -3.35.
What is defined as the approximation?An approximation refers to anything which is similar to but not identical to something else.
Rounding can be used to approximate a number. Before performing the operations, an estimate can be approximated by rounding this same values within it.
Look just at digit with in tens column to get an approximation to the nearest ten.Look at the digit with in hundreds column to get an estimate to the nearest hundred.Look at the digit with in thousands column for the nearest thousand.For the given number;
-16 + square root of 40 can be written as.
= -16 + √40
Find the factors of 40 by prime factorization;
40 = 2×2×2×5
Put the value in expression.
= -16 + √2×2×2×5
Take out square root of 2.
= -16 + 2√2×5
= -16 + 2√10
Fine the approximate value of √10 as this is near to √9.
Thus, √10 = 3.12
Put the value in expression.
= -16 + 2×3.12
= -16 + 12.649
= -3.35
Thus, the approximation of -16 + square root of 40 is -3.35.
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5(3x + 10)³ can be expanded and fully simplified
to give an expression of the form
ax³ + bx² + cx + d.
Work out the values of a, b, c and d
After simplified the equation we get
a=54
b= 540
c=1800
d=2000
What is simplified expression?
Solving a math problem is the same thing as simplifying an expression. You basically try to write an expression as simply as you can when you simplify it. At the conclusion, there shouldn't be any more multiplying, dividing, adding, or removing to do. Take this formula, for instance: 4 + 6 + 5. To simplify an expression, create an equivalent expression without any terms that are similar. The expression will then be rewritten using the fewest terms possible. When confronted with the phrase 4x+5(3x12),
Sol-
2(3x+10)^3
=2(Bx)^3+3.(3x)^2.10+3.3x.10^2+10^3
=2(27x^3+270x^2+900x+1000)
=54x^3+540x^2+1800x+2000
So,
a=54
b=540
c=1800
d=2000
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A bookshelf has 7 shelves, each measuring 4 feet 3 inches in length.
The average width of a book is ; inch. How many books will the
shelves hold?
Answer:
I think its 64 please let me know if its wrong
if the sum of the interior Angele measures of a convex ploygon is 2.60 how many sides does the polygon have?
Answer:
The polygon has 14 sides.
Explanation:
Given that the sum of the interior angles of the polygon is 2,160.
[tex]T=2,160[/tex]Recall that the sum of interior angles of a polygon can be calculated using the formula;
[tex]\begin{gathered} T=180(n-2) \\ \text{where;} \\ n=\text{ number of sides} \\ T=\text{ sum of the interior angles of the polygon.} \end{gathered}[/tex]Substituting the value of T, to solve for n;
[tex]\begin{gathered} 2,160=180(n-2) \\ \frac{2160}{180}=n-2 \\ 12=n-2 \\ n=12+2 \\ n=14 \end{gathered}[/tex]Therefore, the polygon has 14 sides.
pls be very specific with steps find x and y
Firstly, we want to start by drawing the triangles
We have this as follow;
For triangle HOT, we have;
We want to get the values of x and y firstly
Since both triangles are congruent, the order of the sides match
Hence, we have angle O and H equal
Thus, we have that;
[tex]\begin{gathered} 5x-1\text{ = 3x+ 17} \\ 5x-3x\text{ = 17+1} \\ 2x\text{ = 18} \\ x\text{ = }\frac{18}{2} \\ x\text{ = 9} \end{gathered}[/tex]Now, to find Y, we need the measure of angle N
Angle N is same as W which we already have as 5y+ 26
Substitute N for Y
Since all the angles of a triangle sum up to 180, we have it that;
[tex]\begin{gathered} 5x-1\text{ + 4x + 9 + }(5y\text{ + 26) = 180} \\ 9x+8+5y+26\text{ = 180} \\ 9(9)\text{ + 5y + 34 = 180} \\ 5y\text{ = 180-34-81} \\ 5y\text{ = 65} \\ y\text{ = }\frac{65}{5} \\ y\text{ = 13} \end{gathered}[/tex]Now, we want the measure of each of the angles;
1. W = N = 5y+ 26 = 5(13) + 26 = 91
2. H = O = 5x-1 = 5(9) - 1 = 44
3. Y = T = 4x + 9 = 4(9) + 9 = 45
Find the measure of the angle at the center of atom B inside the triangle
The measure of the angle having the question mark, found using the law of sines is ? ≈ 140°
What is the law of sines?The law of sines states that the sine of an interior angle of a triangle is proportional to the the length of the side opposite to the angle.
The given parameters are;
The radius of circle A = 6.4
The radius of circle B = 4.0
The radius of circle C = 3.0
The measure of angle at C = 24°
The length of the segment AB = 6.4 + 4 = 10.4
According to the law of sines, we have;
[tex]\dfrac{sin(A)}{a} = \dfrac{sin(B)}{b} = \dfrac{sin(C)}{c}[/tex]
Where;
a = The length of the side opposite angle ∠A
b = The length of the side opposite angle ∠B
c = the length of the side opposite angle ∠C
From the diagram, the side opposite angle ∠C, is AB, which by comparison indicates that when side c = AB = 10.4
c = 10.4
Similarly, the side opposite angle ∠A = a = BC = 4 + 3 = 7
a = 7
The known information are therefore; ∠C = 24°, a = 7, c = 10.4
[tex]\dfrac{sin(A)}{a} = \dfrac{sin(C)}{c}[/tex]
[tex]\dfrac{sin(A)}{7} = \dfrac{sin(24^{\circ})}{10.4}[/tex]
[tex]sin(A) = \dfrac{sin(24^{\circ})}{10.4}\times 7[/tex]
[tex]\angle A = arcsine \left( \dfrac{sin(24^{\circ})}{10.4}\times 7\right)[/tex]
∠A + ∠B + ∠C = 180° (angle sum property of a triangle)
∠B = 180° - (∠A + ∠C)
Which gives;
[tex]\angle B = 180^{\circ} -\left(24^{\circ} + arcsine \left( \dfrac{sin(24^{\circ})}{10.4}\times 7\right)\right) \approx 140^{\circ}[/tex]
The measure of the angle is ∠B ≈ 140°
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what is the equation to 500
The correct equation to be written for 500 will be 5*100 = 500. This same can also be written as 50*10 = 500 in the equational form to represent 500.
What is an Equation?A mathematical equation can be stated as a formula that uses the equals sign in order to represent the equality of two expressions. In other words, it's a statement that shows that the values of two mathematical expressions are equal.
The equality between the equations here is shown by the equals (=) sign
As an example, 3x + 5 = 14 can be stated as an equation, in which 3x + 5 and 14 are two expressions that are connected by an ‘equal’ sign, thus providing an equation form.
Types of EquationsIf you set on typing the actual types of equations, then you will just find many to categorize from.
But mainly the types of equations can be classified as:
1) Algebraic Equations (includes linear, quadratic, cubic, polynomial equations)
2) Radical Equations
3) Exponential Equations
4) Rational Equations
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Since a sample is a subset of the population, the sample mean Incorrect Response is always smaller than the mean of the population. is always larger than the mean of the population. must be equal to the mean of the population. Correct Answer varies around the mean of the population.
Since a sample is a subset of the population the sample mean varies around the mean of the population.
What is a sample mean about?An average of a group of data is called a sample mean. A data set's central tendency, standard deviation, and variance can all be determined using the sample mean. A population average can be determined using the sample mean, among other things.
The statistic known as the sample mean is created by arithmetically averaging the values of a variable in a sample. The sample mean is an estimator of the expected value if the sample is taken from probability distributions with a common expected value.
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Can you guys help me solve this
q + r = p is the equation formed by using the details in the question
What is a linear equation ?In an algebraic equation of the form y=mx+b, where m denotes the slope and b the y-intercept, a linear equation is a first-order (linear) term and a constant. Sometimes the phrase "linear equation with two variables" is used to describe the previous equation, which contains the variables y and x.
Ax+By=C is the standard form for two-variable linear equations. Standard form is used, for instance, in the linear equation 2x+3y=5. This method makes it simple to find an equation's two intercepts (x and y).
Calculationp the stove is hot
q the soup is cold
r the food is done
equation to be created was
the food is done and the soup is cold , then the stove is hot.
and means +
therefore equation formed by plugging in the values will be ,
q + r = p
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What is the slope in pages per hour? Number of Hours 2 4 6 8 Pages Completed 3 6 9 12
Suppose that there is a negative correlation between the variables k and l. If l is 150 when k is 7, which of these is most likely to be the value of l when k is 14.A. 300B. 150C. 75D. 225
Answer:Explanation:
C. 75
n cthe oomparison of variables, a negative correlation means that as the value of one of the variables increases, the value of the other variable decreases.
Given the variables k and l.
• L=150 when k = 7
,• L=? when k=14
The variable k has increased.
Thus, to satisfy the condition for a negative correlation, the variable, l must decrease.
Thus, the only likely possible value of l is 75.
Option C is correct.
Graph the image of the given triangle, reflected across the y-axis. Select the Polygon tool. Then, click the points of the triangle vertices to create the triangle by connecting the sides.
The image of the transformation are (2, -9), (-9, -7), (-7, -4)
How to perform the transformation?The coordinates of the triangle are given as
(-2, -9), (9, -7), (7, -4)
The transformation is given as
Reflection across the y-axis
This is represented as
(x, y) ⇒ (-x, y)
This means that the transformation is (-x, y)
When this rule is applied on the coordinates, we have
(2, -9), (-9, -7), (-7, -4)
Next, we plot the image of the transformation on a coordinate plane
See attachment for the image of the transformation
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