The function g ( x ) in the graph has one x-intercept , y intercept and an oblique asymptote , a vertical asymptote
What are Asymptotes?An asymptote is a line that a curve approaches but never touches. A line where the graph of a function converges is known as an asymptote. When graphing functions, asymptotes are typically not required
There are 3 types of asymptotes
Horizontal asymptote (HA) - It is a horizontal line and hence its equation is of the form y = k. Horizontal Asymptote is when the function f(x) is tending to zero
Vertical asymptote (VA) - It is a vertical line and hence its equation is of the form x = k. Vertical asymptotes are defined when the denominator of a rational function tends to zero
Slanting asymptote (Oblique asymptote) - It is a slanting line and hence its equation is of the form y = mx + b
Given data ,
Let the function be represented as g ( x )
Now , the value of g ( x ) is
g ( x ) = ( -4x² + 36 ) / ( x + 3 )
On simplifying , we get
g ( x ) = -4 ( x² - 9 ) / ( x + 3 )
On further simplification , we get
g ( x ) = -4 ( x + 3 ) ( x - 3 ) / ( x + 3 )
g ( x ) = -4 ( x - 3 )
g ( x ) = -4x + 12
Now , the function has a vertical asymptote at ( 0 , 12 )
The function has a horizontal asymptote at ( 3 , 0 )
Hence , the function is solved
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Answer:
at least one x-intercept
at least one y-intercept
domain of x
Step-by-step explanation:
took ed2023
Ten thousand marbles were produced on a production line. The first 100 marbles off the line were taken and tested for roundness. Does this sampling result in a simple random sample? Yes, because each group of n items has an equal chance of being selected. No, because each group of n items does not have an equal chance of being selected. Yes, because each item has an equal chance of being selected. No, because each item does not have an equal chance of being selected.
No, because each item does not have an equal chance of being selected. That is option D.
What is a simple random sample?A simple random sample is defined as the type of random sampling where by a particular amount of data (subset) is being selected from the total population of data that is under study.
The simple random sampling method which is used by researchers has the following disadvantages such as:
It relies on the quality of the researchers performing the work.It can require a sample size that is too large.It must have a significant population or demographic at the beginning of the process.It does not provide a guarantee that the data conclusions will be accurate because not all the data have equal chance to be selected.Learn more about random sampling here:
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Marianna finds an annuity that pays 8% annual interest, compounded quarterly. She invests in this annuity and contributes $10,000 each quarter for 6 years. How much money will be in her annuity after 6 years? Enter your answer rounded to the nearest hundred dollars.
Answer:
Marianna will have $19,700 in her annuity after 6 years.
Step-by-step explanation:
To find the amount of money in the annuity after 6 years, we need to calculate the compound interest earned over that time period.
First, let's find the interest rate per quarter: 8% annual interest divided by 4 quarters per year = 2% interest per quarter.
Next, we'll calculate the number of quarters that the money is invested: 6 years x 4 quarters per year = 24 quarters.
Now we can use the formula for compound interest to find the total amount of money in the annuity after 6 years:
A = P * (1 + r/n)^(nt)
Where:
A = final amount
P = initial investment ($10,000 in this case)
r = interest rate per quarter (2% or 0.02)
n = number of times the interest is compounded in a year (4)
t = number of years invested (6)
Plugging in the values:
A = $10,000 * (1 + 0.02)^(24)
A = $10,000 * 1.96634438
A = $19,663.44
Rounding to the nearest hundred dollars: $19,700
So, Marianna will have $19,700 in her annuity after 6 years.
You purchase 5 action figures per week. You have 30 action figures, which is 40% of the total number of action figures you need to complete your collection. How many weeks until your collection is complete?
Answer: Let's call the total number of action figures you need to complete your collection "x". Based on the information given, we know that 30 action figures is 40% of x, so we can write the equation:
30 = 0.40x
To solve for x, we'll divide both sides of the equation by 0.40:
x = 30 / 0.40
x = 75
So, the total number of action figures you need to complete your collection is 75. Since you purchase 5 action figures per week, it will take you 75 / 5 = 15 weeks to complete your collection.
Step-by-step explanation:
A company is making T shirts. They know that the probability of a shirt being defective is (.02).
The company makes a profit of $20 for every shirt they sell. However, each defective shirt costs
the company $35 in replacement costs. How much money does the company really make per
Shirt?
The amount of money the company makes per shirt $18.90
What is probability?Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The chances that event will occur is measured by probability.
Probability of Event = Favorable Outcomes/Total Outcomes
= X/n
To calculate the expected profit per shirt, we need to consider the two possible outcomes:
the shirt is defective or not defective.
If the shirt is not defective, the company makes a profit of $20.
If the shirt is defective, the company incurs a cost of $35 and no profit.
The probability of a shirt being defective is 0.02, so the probability of a shirt not being defective is:
= 1 - 0.02
= 0.98.
Therefore, the expected profit per shirt can be calculated as:
Expected profit = (probability of not defective) x (profit per non-defective shirt)
+ (probability of defective) x (cost per defective shirt)
Expected profit = 0.98 x $20 + 0.02 x (-$35)
Expected profit = $19.60 - $0.70
Expected profit = $18.90
So the company really makes $18.90 per shirt, taking into account the cost of defective shirts.
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Can anyone please solve this
The answers include the following:
61324318111566What is Addition?This is referred to as a mathematical operation in which two or more numbers or quantities are added together to form a sum.
3x = 18
x = 18/3 = 6
x+9 =22
x = 22-9 = 13
x/4 = 6
x = 6 × 4 = 24
x-12 =19
x = 19+12 =31
2x + 9 = 25
2x = 25-9 =16
x=16/2 = 8
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Triangle adb, point c lies on segment ab and forms segment cd, angle acd measures 90 degrees. Point a is labeled jungle gym and point b is labeled monkey bars. Beth is planning a playground and has decided to place the swings in such a way that they are the same distance from the jungle gym and the monkey bars. If beth places the swings at point d, how could she prove that point d is equidistant from the jungle gym and monkey bars?.
To prove that point d is equidistant from the jungle gym and monkey bars, we need to show that the distances from d to both points are equal.
Let's call the distance from d to the jungle gym "x" and the distance from d to the monkey bars "y". We need to show that x = y.
Since angle acd is a right angle, we can use the Pythagorean theorem to relate the distances:
ad^2 + cd^2 = ac^2
We know that ad = bd (since the jungle gym and monkey bars are the same distance from d), so we can write:
bd^2 + cd^2 = ac^2
We also know that c lies on ab, so we can write:
ac = ab - bc
Substituting this into our equation, we get:
bd^2 + cd^2 = ab^2 - 2abbc + bc^2
Since d is on cd, we can write cd = y, and since c is on ab, we can write ab = x + y. Substituting these into our equation, we get:
bd^2 + y^2 = (x + y)^2 - 2xy + x^2
Simplifying, we get:
bd^2 - x^2 = 2xy - y^2
Now, if we can show that bd = x, then we will have proven that y = x and therefore that point d is equidistant from the jungle gym and monkey bars.
To do this, we can use the fact that triangle adb is isosceles (since ad = bd). This means that angle adb is equal to angle bad. We also know that angle acd is a right angle. Therefore, angle adb + angle acd = 90 degrees.
Since angle adb = angle bad, we can write:
2 angle adb + angle acd = 180 degrees
Substituting in the values of our angles, we get:
2 angle adb + 90 degrees = 180 degrees
Solving for angle adb, we get:
angle adb = 45 degrees
Now, we can use the fact that triangle adb is isosceles to write:
angle bad = (180 - 45)/2 = 67.5 degrees
Finally, we can use the law of sines to relate bd and x:
bd/sin(67.5) = x/sin(45)
Simplifying, we get:
bd = x
Therefore, we have shown that point d is equidistant from the jungle gym and monkey bars.
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When an accountant records on hand, they are noting a company’s
A. human resources; total liquid assets
B. cash; total of amount dollars, money orders, checks, and other forms of
money
W
C. supplies; materials that need to be purchased soon
D. inventory; number of employees on payroll
Answer:
The correct answer is D. inventory; number of employees on payroll. An accountant records on hand to note a company's inventory, which is the stock of goods available for sale or use in the production process. The number of employees on payroll refers to the human resources aspect of a company, which is separate from the inventory.
what is e and in
calculus for business
find the vertical asymptotes
Answer: Vertical asymptotes are = [tex]-4, 1,4[/tex]
Horizontal asymptote = [tex]y=0[/tex]
Step-by-step explanation:
If you need explanation just say you want...
Suppose you deposit $1,000 into a
savings account that earns simple
interest. After 4 years, the savings
account balance is $1,200. Determine
the annual interest rate.
100
1000
The annual interest rate on the saving account is 5%.
What does an annual interest rate refers to?Also known as annual percentage rate (APR) is the interest generated by a sum charged to borrowers or paid to investors each year. Its represents the actual yearly cost of funds over the life of a loan or the income earned on an investment.
To determine our annual interest rate, we can use the formula for simple interest: I = Prt. We need to find "r" which is our interest rate.
Now, we know the interest earned (I = $200) and the principal (P = $1,000), we can substitute those values into the formula:
$200 = $1,000 * r * 4
r = $200 / ($1,000 * 4)
r = 0.05. Therefore, the annual interest rate is 0.05 or 5%.
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A number, k, truncated to 2 d.p. is 47.00
Write an inequality to show the lower and
upper bounds of k. help quickly please!!!!!
MARK ME BRAINLIEST TOO!! :)
The lower and upper bounds of h - k are 42.31 and 42.49 respectively.
Upper and lower bounds are the maximum and minimum values that a number could have been before it was rounded. They can also be called limits of accuracy.
The upper and lower bounds can be written using error intervals
The lowest value of h is 47.15
The greatest value of h is 47.24
The greatest value of k is 4.84
The lowest value of k is 4.75
Thus upper bound of h -k = 47.24 - 4.75 = 42.49
Thus lower bound of h -k = 47.15 - 4.84 = 42.31
Thus the lower and upper bounds of h - k are 42.31 and 42.49 respectively. dont forget mark me brainliest
Question 10 of 20
What is the domain of the exponential function f(x)=3*-5?
O A. (-∞0, +00)
O B. (3,+00)
O C. (-∞0,-5)
O D. (-5,+00)
Answer: The answer is A. (-∞0, +00)
Phythagorean inequality
The Pythagorean inequality is given below.
Statement of Pythagoras theorem:
“In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse.
[tex]AC^{2}=AB^{2} +BC^{2}[/tex]
Let ABC be a triangle with the longest side opposite B
If the square of the longest side is greater than the sum of the squares of the two shorter sides, then the triangle is obtuse at BIf the square of the longest side is less than the sum of the squares of the two shorter sides, then the triangle is acute.If the square of the longest side is equal to the sum of the squares of the two shorter sides, then the triangle is right angled at B.We can also write as follows:
If [tex]AC^{2} > AB^{2} +BC^{2} \\[/tex], then B is an obtuse angle.
If [tex]AC^{2} < AB^{2} +BC^{2} \\[/tex], then B is an acute angle.
If [tex]AC^{2}=AB^{2} +BC^{2}[/tex], then B is a right angle.
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-ax^(2)+2x+2a if a=7 and x=-5
Answer: -151
Step-by-step explanation:
First Plug everything in
-7(5)^(2)+2(5)+2(7)
Then use order of operations and first deal with the exponent
-7(25)+2(5)+2(7)
then multiply left to right
-175+10+14
combine
so the answer is -151
What is the value of x? enter your answer, as a decimal, in the box. Do not round your answer. X= a right triangle with vertices labeled as a, b, and c. Side c b is the base and the top vertex is a. Side a b contains a midpoint d. A line segment drawn from c to d bisects angle a c b into two parts labeled as a c d and b c d. Angles a c d and b c d are marked with single arc. Side a c is labeled as 4. Base c b is labeled as 7. 5. Segment a d is labeled as 3. Segment b d is labeled as x.
In right triangle ACB with CD bisects angle ACB and intersects at midpoint of AB at point D the value of x is equal to 5.625.
In right triangle ABC,
BC is the base.
Midpoint of AB is D.
CD bisects ACB.
Measure of ∠ACD = Measure of ∠BCD
AC = 4
BC = 7.5
AD = 3
BD = x
CD bisects angle ACB and intersect at midpoint of AB at point D.
This implies
BD / AD = BC / AC
⇒x / 3 = 7.5 / 4
⇒ x = ( 7.5 × 3 ) / 4
⇒ x = 22.5 / 4
⇒ x = 5.625
Therefore, the value of x in the right triangle ACB with given dimensions is equal to 5.625.
The above question is incomplete , the complete question is :
What is the value of x? Enter your answer, as a decimal, in the box. x= A right triangle with vertices labeled as A, B, and C. Side C B is the base and the top vertex is A. Side A B contains a midpoint D. A line segment drawn from C to D bisects angle A C B into two parts labeled as A C D and B C D. Angles A C D and B C D are marked with single arc. Side A C is labeled as 4. Base C B is labeled as 7.5. Segment A D is labeled as 3. Segment B D is labeled as x.
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If the number x² y is a negative integer, then -y is a positive number
Answer: Yes, this statement is true. If the number x² y is a negative integer, it means that x² is a positive integer and y is a negative integer. Therefore, -y would be a positive number.
Step-by-step explanation:
Question 1 of 10
How many zeros does the polynomial function, y = (x-2)(x+3)² have?
OA. 1
OB. 3
OC. 2
OD. 4
SUBMIT
Answer:
C. 2
Step-by-step explanation:
A polynomial function has one or more real numbers as roots or zeros. These roots correspond to the values of x for which the function takes on the value of zero.
In this case, y = (x-2)(x+3)², we can factor the equation to find its zeros. The expression (x-2)(x+3)² can be factored into two terms: (x-2) and (x+3)².
The first term, (x-2), is equal to zero when x = 2, meaning that x = 2 is a root of the function.
The second term, (x+3)², is equal to zero when x = -3, meaning that x = -3 is another root of the function.
So, the function y = (x-2)(x+3)² has two roots, or zeros, at x = 2 and x = -3.
Demonstrating the properties of rotations, if a line segment with endpoints (0,−3) and (0,−7) is rotated 90° clockwise, what is an endpoint of this rotated segment?
Answer: -3, 0
Step-by-step explanation:
If a line segment with endpoints (0,−3) and (0,−7) is rotated 90° clockwise, an endpoint of this rotated segment is (-3, 0) and (-7, 0).
What is a rotation?In Mathematics and Geometry, a rotation is a type of transformation that moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.
By applying either a rotation of 90° clockwise or a rotation of 270° counterclockwise to the coordinate of this line segment with endpoints (0,−3) and (0,−7), the coordinate of its image;
(x, y) → (y, -x)
Point (0,−3) → Point (-3, 0)
Point (0, -7) → Point (-7, 0)
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Write down all of the options which are true of
similar shapes.
They must be the same shape
They can be different shapes
They must be the same size
They can be different sizes
All of the options which are true of similar shapes include the following:
A. They must be the same shape.
D. They can be different sizes.
What are the properties of similar geometric shapes?In Mathematics, two (2) geometric shapes are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
What is scale factor?In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):
This ultimately implies that, two (2) similar geometric shapes can have different sizes depending on the scale factor that is applied.
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Here is a triangle.
4x + 20
x +32
4x + 20
Does the triangle contain an obtuse angle?.
Explain your reasoning.
Please help me urgent need
Answer:
No
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180°
sum the 3 angles and equate to 180
x + 32 + 4x + 20 + 4x + 20 = 180
9x + 72 = 180 ( subtract 72 from both sides )
9x = 108 ( divide both sides by 9 )
x = 12
then the 3 angles are
x + 32 = 12 + 32 = 44°
4x + 20 = 4(12) + 20 = 48 + 20 = 68°
4x + 20 = 68°
an obtuse angle is greater than 90°
none of the 3 angles in the triangle are obtuse
Answer:
No
Step-by-step explanation:
All angles of a triangle add up to 180°.
4x + 20 + 4x + 20 + x + 32 = 180
1. Simplify
9x + 72 = 180
2. Subtract 72 from both sides.
9x = 108
3. Divide both sides by 9.
x = 12
Replace x by 12 in each angle.
- 12 + 32 = 44°
- 4(12) + 20 = 68°
- 4(12) + 20 = 68°
All of the angles are less than 90°, so they aren't obtuse.
What benefits came from the collapse of communism in eastern europe? select three answers.
Greater freedom of movement, growing entrepreneurship, more contact with Western Europe.
three benefits came from the collapse of communism in eastern europe
Entrepreneurship is the creation or receipt of financial rewards. Under this definition, entrepreneurship is generally viewed as a change that involves more risk than is normally incurred when starting a business, and that may also involve value beyond its actual economic value.
An entrepreneur is a person who creates and/or invests in one or more groups while taking maximum risk and enjoying maximum return. [citation needed] The way to start a business is known as entrepreneurship. Entrepreneurs are usually seen as innovators, sources of new ideas, objects, offerings and ventures/technologies.
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identify all the linear functions with a rate of change greater than or equal to 1.5
A student is trying to prove that the triangle XAB is similar to triangle XYZ.
Answer:
Below
Step-by-step explanation:
See image
L side goes from 3 units to 6 units so scale factor is 2
Given the following observation for ortime serie X
t=1,2,3,4,5,6,7,8,9,10
Xt=47,64,23,71,38,64,55,41,59,48
Find
r(2)
Answer:t he autocorrelation of the time series X at lag 2 is approximately -0.018.
Step-by-step explanation:
To find the autocorrelation of the time series X at lag 2, we need to calculate the covariance between X(t) and X(t-2). This can be done using the following formula:
r(2) = cov(X(t), X(t-2)) / var(X(t))
where cov(X(t), X(t-2)) is the covariance between X(t) and X(t-2), and var(X(t)) is the variance of X(t).
To calculate the covariance, we'll use the following formula:
cov(X(t), X(t-2)) = sum((X(t) - mean(X(t))) * (X(t-2) - mean(X(t-2)))) / (n - 1)
where n is the number of observations in the time series. To calculate the variance, we'll use the following formula:
var(X(t)) = sum((X(t) - mean(X(t)))^2) / (n - 1)
First, let's calculate the mean of X(t):
mean(X(t)) = (47 + 64 + 23 + 71 + 38 + 64 + 55 + 41 + 59 + 48) / 10 = 51
Next, let's calculate the covariance between X(t) and X(t-2):
cov(X(t), X(t-2)) = sum((X(t) - 51) * (X(t-2) - 49)) / (10 - 1) = -10.3
Finally, let's calculate the variance of X(t):
var(X(t)) = sum((X(t) - 51)^2) / (10 - 1) = 563.7
Plugging in these values, we can find the autocorrelation at lag 2:
r(2) = cov(X(t), X(t-2)) / var(X(t)) = -10.3 / 563.7 = -0.018
So the autocorrelation of the time series X at lag 2 is approximately -0.018.
Expand and simplify (x + 2)(x + 1)
Answer:
x^2 + 3x + 2
Step-by-step explanation:
(x + 2) * (x + 1) =
= x * x + x * 1 + 2 * x + 2 * 1 =
= x^2 + x + 2x + 2 =
= x^2 + 3x + 2
A certain species of bacteria in a laboratory culture begins with 50 cells and doubles in number every 30 minutes. Write a function
fix) to model the situation where x is the number of 30-minute time periods.
since we know the number is doubling, so if say it was "x" right now so 30 minutes later will be "x" + 100 of "x", namely 2x, so that simply means the rate of growth is 100%.
[tex]\textit{Periodic/Cyclical Exponential Growth} \\\\ A=P(1 + r)^{\frac{t}{c}}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &50\\ r=rate\to 100\%\to \frac{100}{100}\dotfill &1.00\\ t=minutes\\ c=period \dotfill &30 \end{cases} \\\\\\ A=P(1 + 1.00)^{\frac{t}{30}}\implies A=P(2)^{\frac{t}{30}}\hspace{5em}f(x)=P(2)^{\frac{x}{30}}[/tex]
A statistics professor gives a survey to each of the 10 students in an introductory statistics course. The survey asks the students how many text messages they think they sent yesterday. The data are included below. Use a TI-83, TI-83 Plus, or TI-84 to calculate the population standard deviation and the population variance. Round your answers to one decimal place . Texts sent yesterday 29 211 130 21 21 19 67 60 O Help Copy to Clipboard Open Provide your answer below: Standard Deviation Variance- FEEDBACK Content attribution
Using a TI-83, TI-83 Plus, or TI-84 Population standard deviation is 56.4 and Population variance is 3178.5 .
To calculate the population standard deviation and variance using a TI-83, TI-83 Plus, or TI-84 calculator, we can use the following steps:
Enter the data into a list on the calculator. To do this, press the STAT key, then select Edit. Enter the data into L1.
Calculate the sample mean by pressing STAT, then CALC, then 1-Var Stats. Make sure L1 is selected as the list, then press ENTER.
Find the population variance by pressing STAT, then CALC, then 2-Var Stats. Make sure L1 is selected as the list, then press ENTER. The variance will be displayed as sX².
Take the square root of the population variance to find the population standard deviation. To do this, press the MATH key, then select PRB, then select 5:√(. Enter the population variance, then press ENTER.
Using this method, we find that the population standard deviation is approximately 56.4 and the population variance is approximately 3178.5.
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Complete question is:
A statistics professor gives a survey to each of the 10 students in an introductory statistics course. The survey asks the students how many text messages they think they sent yesterday. The data are included below. Use a TI-83, TI-83 Plus, or TI-84 to calculate the population standard deviation and the population variance. Round your answers to one decimal place .
Texts sent yesterday: 29 211 130 21 5 21 19 67 60 95
please help me with intersections i’ll give you brainlist
Answer:
(-3,-1)
Step-by-step explanation:
The two lines intersect at that point. -3 is in the x axis and -1 is in the y axis.
Answers for this photo?
The slope for:
1 = 1/2 (Option E)
2 = 2 (Option C)
3 = -1/2 (Option H)
4 = -2 (Option A)
What is slope in Maths?The slope or gradient of a line in mathematics is a quantity that specifies both the direction and the steepness of the line.
The formula for slope (m) is given as:
m = Rise/Run = y2-y1/x2-x1
(x1,y1) = Coordinates of the first point in the line
(x2,y2) = Coordinates of the second point in the line.
1) The points are:
x1= -2
y1 = 2
x2 =2
y2 = 4
m = (4 - 2) / (2 - (-2))
m = 2 / 4
m = 1/2
Thus, Δy/Δx = 1/2
2) The points are:
x1= -1
y1 = -12
x2 =5
yx = 0
m = (y2 - y1) / (x2 - x1)
Substituting the given values, we get:
m = (0 - (-12)) / (5 - (-1))
m = 12 / 6
m = 2
Thus, Δy/Δx = 2
3) Where the points are:
x1= 2
y1 = -6
x2 = - 4
y2 = -3
Substituting the given values, we get:
m = (-3 - (-6)) / (-4 - 2)
m = 3 / (-6)
m = -1/2
Thus, Δy/Δx = -1/2
4) Where the points are:
x1= 0
y1 = 3
x2 = 1.5
y2 = 0
Substituting the given values, we get:
m = (0 - 3) / (1.5 - 0)
m = -3 / 1.5
m = -2
Thus, Δy/Δx = -2
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What is the vertex for the graph below?
Answer:B
Step-by-step explanation: the graph moves x vertically -1 while y is moved vertically to 4