A Confirm that the integral test is applicable and use it to determine whether the series converges Σ 1 5k +2 k=1 B. Determine whether the series converges. k=1
Answers
The integral diverges, the series also diverges. Therefore, the series Σ 1/(5k+2), k=1, does not converge.
The integral test can be applied to a series if the following conditions are met:
1. The terms of the series are positive.
2. The terms of the series are decreasing.
3. The series has a continuous and positive function that can be integrated over the same interval as the series.
For the series Σ 1/(5k+2), k=1, all of these conditions are satisfied since:
1. The terms of the series are positive because the denominator is always greater than 0.
2. The terms of the series are decreasing because as k increases, the denominator increases and the overall fraction becomes smaller.
3. The function f(x) = 1/(5x+2) is continuous and positive on the interval [1, ∞).
Using the integral test, we can evaluate the convergence of the series by comparing it to the integral of the function f(x) over the same interval, as follows:
∫₁^∞ (1/(5x+2)) dx = (1/5) ln|5x+2| |₁^∞
= (1/5) lim┬(b→∞)(ln|5b+2| - ln|7|) = ∞
Since the integral diverges, the series also diverges. Therefore, the series Σ 1/(5k+2), k=1, does not converge.
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Related Questions
How to solve x^4 -10x^2 +9
Answers
Answer:
(x² - 9)(x² - 1)
Step-by-step explanation:
Using Quadratic trinomials
Factor x⁴ - 10x² + 9
Step 1: Find the two integers whose product of 9 and whose sum of -10
Product
-9 × -1 = 9
Sum
-9 + -1 = -10
Step 2: Use -1 and -9 to complete the factors
x⁴ - 10x² + 9 = (x² - 9)(x² - 1)
Step 3: Use the foil method to check the factors
(x² - 9)(x² - 1) = x⁴ - 1x² - 9x² + 9 = x⁴ - 10x² + 9
a testable prediction of what will happen under a specific set of conditions is known as a/an
Answers
A testable prediction of what will happen under a specific set of conditions is known as a hypothesis.
A hypothesis is a tentative explanation or prediction about a phenomenon or relationship between variables, based on limited evidence or prior knowledge. It is often formulated as a statement that can be tested through research or experimentation.
A hypothesis typically includes an independent variable (the variable that is being manipulated or studied) and a dependent variable (the variable that is being measured or observed). The hypothesis also includes a prediction about how the independent variable will affect the dependent variable.
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. A customer at a store paid $42 for 4 pairs of pants and 3 shirts. At the same store, a
second customer paid $2 more for 1 pair of pants and 7 shirts. The price of each pain
of pants is the same, and the price of each shirt is the same.
-Which system of equations can be used to find the price in dollars of each pair of
pants, x, and each shirt, y?
Answers
Answer:
A
Step-by-step explanation:
The waiting time to ride a roller coaster is 1/3 of an hour when 150 people are in line. How
long is the waiting time when 240 people are in line? Write an equation and solve.
Answers
Answer:
\( \frac{66}{125} \)
hours
Hope it helped
PLS mark BRAINLIEST
Use the graph to find the unit rate.
Answers
On solving the question, unit rate by using the given graph could be 2.4 potatoes/pound
What is a graph ?Graph can be defined as the visual representation which is used to represent the data.
The unit rate is the slope of the line.
The slope of the line = (change in y-value)/(change in x-value)
= (36 potatoes - 12 potatoes)/(15 pounds - 5 pounds)
= (24potatoes)/(10 pounds)
= 2.4 potatoes/pound
The relationship here is proportional, so the line goes through the point (0, 0) and the unit rate can be figured from any point:
(12 potates)/(5 pounds)
= (24 potatoes)/(10 pounds)
= (36 potatoes)/(15 pounds) = 2.4 potatoes/pound
Hence, The unit rate by using the given graph could be 2.4 potatoes/pound .
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The correct question is -
Identify the unit rate in the graph.
A. 40mph
B. 75mph
C. 50mph
D. 25mph
Which of the following lists is in order from least
to greatest?
Answers
Answer:
B
Step-by-step explanation:
in a random School sampling of 50 middle school students it was found that 18 students bring their lunch to school everyday if there are 942 students in the school predict how many bring their lunch to school each day
Answers
Answer:
340
Step-by-step explanation:
We can see in the sample that 18/50 people bring lunches to school. If we divide 18 by 50 we get 0.36 now we know that 36% of people bring their lunches in the sample. Now we take that number and multiply it by 942.
0.36*942= 339.12 which we can round to 340
Given {(1, 2), (3, 5), (-2, 2), (3,6)}, choose the pair of coordinates that clarify why this
relation is not a function.
Answers
Given:
The relation is:
\(\{(1, 2), (3, 5), (-2, 2), (3,6)\}\)
To find:
The pair of coordinates that clarify why this relation is not a function.
Solution:
A relation is called a function if there exist unique y-value for each x-value. In other words, if a relation has two outputs for a single input, then the relation is not a function.
The given relation is:
\(\{(1, 2), (3, 5), (-2, 2), (3,6)\}\)
This relation has two y-values 5 and 6 for a single x-value 3. Since the y-value is not unique all all values of x, therefore the relation is not a function.
Hence, the pairs of coordinates (3,5) and (3,6) clarify that the given relation is not a function.
Please help I will give brainliest and a lot of points :)
Answers
The inequality shaded in the graph is given as follows:
y ≥ 5x/2 + 3.
How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
In which:
m is the slope.b is the intercept.The graph crosses the y-axis at y = -3, hence the intercept b is given as follows:
b = 3.
When x increases by 2, y increases by 5, hence the slope m is given as follows:
m = 5/2.
Then the equation of the line is given as follows:
y = 5x/2 + 3.
The line is a solid line, and values above it are plotted, hence the inequality is given as follows:
y ≥ 5x/2 + 3.
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Can someone please help me
Answers
Answer:
z
Step-by-step explanation:
It costs Widgeco $2,000 to purchase a machine that produces widgets and $2.75 to produce each widget. If widgets are sold for $4.99 each, which of these represents the profit, P(w), received when Widgeco sells w widgets?
A
P(w) = 2.24w + 2,000
B.
P(w) = 7.74w + 2,000
C.
P(w) = 2.24w – 2,000
D.
P(w) = 7.74w – 2,000
Answers
Answer:
B
Step-by-step explanation:
You would add the 2.75 and 4.99 to get 7.74 and you would add the variable for how much widgets are made and since its the profit you would have to add the 2,000 so the equation would be P(w) = 7.74w + 2,000
Hope this helps
(oﾟvﾟ)ノ
What’s 50.272 to 1 decimal place
Answers
TRUNCATED to one decimal place, it's 50.2
ROUNDED to one decimal place, it's 50.3
The round-off of 50.272 to 1 decimal place using rules of rounding
numbers are 50.3.
Rounding off numbers means making a number simpler by adjusting it to its nearest place according to certain rules.
Rounding a number to one decimal place means keeping only the first digit after the decimal point and neglecting the rest. In this case, the digit in the second decimal place is 7, which is greater than or equal to 5. As per the rounding rules, if the digit is greater than 5, the preceding digit is increased by 1.
So, 50.272 becomes 50.3 when rounded to one decimal place.
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draining 15 gallons of water from a fish tank
(Write your answer as an integer)
Answers
Answer:
-15
Step-by-step explanation:
if its just asking for what number would represent a loss of 15 it would be negative 15
i dont know if there's more to the problem or not
Answer:
-15
Step-by-step explanation:
This is because whatever much water was in the tank is now decreasing by 15, therefore, you can write it as -15,
hope this helps!
The data set below represents the heights (in inches) of students in a particular high school class: 72 67 62 64 59 71 62 66 67 75 67 62 What is the range of the data set? 0 18 inches 16 inches 0 12 inches 0 75 inches
Answers
The range of the data set is 16 inches.
How many inches is the range of the data set?The range of a data set represents the difference between the highest and lowest values in the set. In this case, the data set consists of the following heights (in inches):
59, 62, 62, 62, 64, 66, 67, 67, 67, 71, 72, 75
To find the range, we need to determine the minimum and maximum values in the set. By sorting the data set in ascending order, we can identify the minimum and maximum values more easily:
59, 62, 62, 62, 64, 66, 67, 67, 67, 71, 72, 75
The smallest value in the set is 59, which is the minimum value, and the largest value is 75, which is the maximum value.
To calculate the range, we subtract the minimum value from the maximum value:
Range = Maximum value - Minimum value
Range = 75 - 59
Range = 16 inches
Therefore, the range of the given data set is 16 inches. This means that the difference between the tallest and shortest student in the class is 16 inches.
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Sydnie scored 74 points in Round Two of a talent competition. This is 7 points less than three times her score in Round One. Which equation should be used to find Sydnie’s score in Round One?
Answers
What is the probability of spinning pink and rolling an odd number?
Answers
Answer:0.625 for pink and 50% for an odd number
Step-by-step explanation:
Patricia and her brother Ian help themselves to a pitcher of lemonade on the kitchen counter. Patricia takes a glass and fills it with p ounces of lemonade. Ian takes a bigger glass and pours himself 20% more lemonade than Patricia poured in her glass. Write an expression to represent the quantity of lemonade(in ounces) in Ian’s glass in terms of the quantity in Patricias glass (p).
Part A- Write an expressionism terms of p that shows how many more ounces Ian poured in his glass than Patricia poured in hers.
Part B-Write an expression in terms of p to represent the amount of lemonade (in ounces) Ian poured in his glass. Include two terms in your expression.
Part C- combine the like terms in the expression from part B to create an equivalent expression.
Part D- using the simplified expression you wrote in part C, and domain what it means to have 30% more of a given quantity.
Part E- suppose that Patricia drinks one-fourth of the lemonade in her glass. Write an expression in terms of p that represents the number of ounces Patricia drank.
Part F- in part E, Patricia drank one-fourth of the lemonade in her glass. Write and expression in terms of p that represents the number of ounces Patricia has left in her glass. Include two terms in your expression.
Part G- combine the like terms in the expression from part F to create an equivalent expression.
Part H- using the simplified expression you wrote in part G, explain what it means to have 1/4 less of given quantity.
Please help me I’m struggling on this!
Answers
Answer:
Part A: 0.20p or 0.2p (doesn't matter which one you use)
Part B: p + 0.2p
Part C: p + 0.2p = 1p + 0.2p =
1.2p
Part D: increasing a quantity by 20% is the same as multiplying the quantity by 1.2
Part E: 1/4p ounces
Part F: p - 1/4p
Part G: = 3/4p
Part H: decreasing a quantity by 1/4 is the same as multiplying the quantity by 3/4
Step-by-step
Maya is playing a trivia game with multiple choice questions. Each question has 2 22 correct answers among 5 55 answer choices. Maya has no idea what the answers to a certain question are, so she needs to choose two different answers at random. What is the probability that maya's first guess is correct and her second guess is incorrect?.
Answers
Answer:
0.3 or 3/10
Step-by-step explanation:
First guess:
chance it is right: 2/5
chance it is wrong: 3/5
Second guess, if first is right:
chance it is right: 1/4
chance it is wrong: 3/4
therefore we multipy 2/5 and 3/4 and get a simplified answer of 3/10
Is the function even,odd, or neither
Answers
Answer:
even I think
Step-by-step explanation:
Answer:
Neither
Step-by-step explanation:
If f (–x) = f (x), then the function is even. if f (–x) = –f (x), (all the signs are flipped) the it is odd.
To apply this to the function here, simply replace the x in \((x-2)^{2}\) with -x.
\((x-2)^{2}\) = \(x^{2}\) - 4x + 4, and \((-x - 2)^{2}\) = \(x^{2}\) +4x + 4.
Since \(x^{2}\)+4x + 4 doesnt equal \(x^{2}\) - 4x + 4 (even) or \(-x^{2}\)+4x -4 (odd), the function is neither even nor odd.
help my little sister
Answers
Answer:
The answer would be 48 cm^2
Step-by-step explanation:
You have to do 9x4 and then add 6x2 to that.
9x4 is 36 and 6x2 is 12.
36+12 is 48. Hope this helps! :)
Answer:
The answer would be 48 cm^2
cards and 20% with debit cards. The transaction fees charged by the credit and debit card issuers are as follows: Credit cards: $0.50 per transaction +2% of the amount charged Debit cards: $0.30 per transaction +1% of the amount charged Read the Requirement 1. How much of the total sales revenue is expected to be paid in cash? The total sales revenue expected to be paid in cash is Requirement 2. How many customer transactions does the company expect in January? In January, the number of transactions the company expects is Requirement 3 . How much of the total sales revenue is expected to be paid with credit cards? The total sales revenue expected to be paid with credit cards is Requirement 4. How many customer transactions will be paid for by customers using credit cards? The number of customer transactions paid for using credit cards is Requirement 5. When budgeting for January's operating expenses, how much should the restaurant expect to incur in credit card transaction fees? In January, the restaurant should expect to incur transaction fees of Requirement 6 . How much of the total sales revenue is expected to be paid with debit cards? The total sales revenue expected to be paid with debit cards is Requirement 7. How many customer transactions will be paid for by customers using debit cards? The number of customer transactions paid for by customers using debit cards is Requirement 8 . When budgeting for January's operating expenses, how much should the restaurant expect to incur in debit card transaction fees? In January, the restaurant should expect to incur debit card transaction fees of the funds on the same day the transactions occur at the restaurant (there is no processing delay). The amount that will be deposited in the restaurant's bank account during the month of January related to credit and debit card sales is Requirement 10. What is the total amount of money that the restaurant expects to deposit in its bank account during the month of January from cash, credit card, and debit card sales? Again assume the credit and debit card issuers deposit the funds on the same day that the transaction occurs. The amount that will be deposited in the restaurant's bank account during the month of January from cash, credit card, and and debit card sales is
Answers
The total amount expected to be deposited in the restaurant's bank account during the month of January from cash, credit card, and debit card sales is equal to the total sales revenue, which is $X.
Cash sales: 40%
Credit card sales: 40%
Debit card sales: 20%
Requirement 1: How much of the total sales revenue is expected to be paid in cash?
Assuming the total sales revenue for January is $X, the amount expected to be paid in cash is 40% of X.
Cash sales = 0.4 × X
Requirement 2: How many customer transactions does the company expect in January?
The number of customer transactions can vary, and the information provided doesn't specify a particular value. You would need to have additional data or assumptions to determine the number of transactions.
Requirement 3: How much of the total sales revenue is expected to be paid with credit cards?
Assuming the total sales revenue for January is $X, the amount expected to be paid with credit cards is 40% of X.
Credit card sales = 0.4 × X
Requirement 4: How many customer transactions will be paid for by customers using credit cards?
Similar to Requirement 2, the number of customer transactions paid for by credit cards would require additional data or assumptions to determine.
Requirement 5: When budgeting for January's operating expenses, how much should the restaurant expect to incur in credit card transaction fees?
To calculate the credit card transaction fees, we need to consider two components: a fixed fee per transaction and a percentage fee based on the amount charged.
Assuming the number of credit card transactions is Y, and the average amount charged per transaction is Z, the credit card transaction fees can be calculated as:
Credit card transaction fees = (0.50 × Y) + (0.02 × Z × Y)
Requirement 6: How much of the total sales revenue is expected to be paid with debit cards?
Assuming the total sales revenue for January is $X, the amount expected to be paid with debit cards is 20% of X.
Debit card sales = 0.2 × X
Requirement 7: How many customer transactions will be paid for by customers using debit cards?
Similar to Requirement 2 and Requirement 4, the number of customer transactions paid for by debit cards would require additional data or assumptions to determine.
Requirement 8: When budgeting for January's operating expenses, how much should the restaurant expect to incur in debit card transaction fees?
Similar to Requirement 5, the debit card transaction fees can be calculated using the same formula but with different values for the fixed fee per transaction and the percentage fee based on the amount charged.
Requirement 10: What is the total amount of money that the restaurant expects to deposit in its bank account during the month of January from cash, credit card, and debit card sales?
Assuming the total sales revenue for January is $X, the total amount expected to be deposited in the bank account is the sum of cash sales, credit card sales, and debit card sales.
Total deposits = Cash sales + Credit card sales + Debit card sales
= 0.4 × X + 0.4 × X + 0.2 × X
= X
Therefore, the total amount expected to be deposited in the restaurant's bank account during the month of January from cash, credit card, and debit card sales is equal to the total sales revenue, which is $X.
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Which vectors represent the reflection of the vector <3, -7> across the x-axis? A. [3/7} B. [-3/7] C. <-3, 7> D. <3, 7> E. [7/-3] F. <7, -3>
Answers
Answer:
D) < 3, 7)>
Step-by-step explanation:
Explanation:-
Given that the vector < 3 , -7 >
Given the vector reflection across the x-axis
(x,y) → (x , -y)
The vector < 3,-7> →< 3, -(-7)>
< 3,-7> →< 3, 7)>
convert million gallons per day to cubic feet per second
Answers
The flow rate of 5 MGD is equivalent to 7.73615 cfs
To convert million gallons per day (MGD) to cubic feet per second (cfs), we need to use the conversion factor between the two units. The conversion factor is 1 MGD = 1.54723 cfs.
Therefore, to convert MGD to cfs, we can multiply the given value of MGD by the conversion factor. For example, if we have a flow rate of 5 MGD, we can convert it to cfs as follows:
5 MGD x 1.54723 cfs/MGD = 7.73615 cfs
So, the flow rate of 5 MGD is equivalent to 7.73615 cfs. Similarly, we can convert any given flow rate in MGD to cfs by using the same conversion factor.
It is important to note that these units are commonly used in the context of water supply and distribution systems, where flow rates are a crucial factor in the design and operation of such systems. Therefore, knowing how to convert between different flow rate units is essential for engineers and technicians working in this field.
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Use the vertical line test to determine if the graph is a function or not a function.
Answers
Answer:
Use the vertical line test to determine if the graph is a function or not a function.
On a coordinate plane, a graph decreases to a minimum point, and then increases.
✔ function
On a coordinate plane, a graph increases to a maximum, decreases to a minimum, increases to the maximum, and decreases again to the minimum.
✔ function
On a coordinate plane, a graph decreases to the right, then decreases to the left, then decreases to the right.
✔ not a function
Step-by-step explanation:
As per the concept of the vertical line test, the third graph is not a function.
But the First and Second graphs represent a function.
The vertical line test is a method used to determine if a graph represents a function. It involves visually inspecting the graph and checking if any vertical line intersects the graph at more than one point.
Let's apply the vertical line test to the given graphs:
First graph:
For the first graph, if we draw any vertical line, it will intersect the graph at most once. Hence, the graph passes the vertical line test, indicating that it represents a function.
Second graph:
For the first graph, if we draw any vertical line, it will intersect the graph at most once. Hence, the graph passes the vertical line test, indicating that it represents a function.
Third graph:
The vertical line test is given in the image below.
In conclusion:
The third graph is not a function.
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WILL GIVE BRAINLIEST
1. A department store kept records of how many fans were sold each day and the high temperature for that day. The results are shown in the scatterplot. Answer the questions about the scatterplot.
a. What is the explanatory variable (independent variable)? (1 point)
b. What is the response variable (dependent variable)? (1 point)
c. Circle the best range for the correlation coefficient. (1 point)
(–1 to –0.7) (–0.7 to –0.3) (–0.3 to 0) (0 to 0.3) (0.3 to 0.7) (0.7 to 1.0)
d. Based on this scatterplot, does a rise in temperature cause more fans to be sold? Why or why not? (3 points)
2. This scatterplot shows the relationship between a player's level in a game and the point total in the level. Answer the questions about the scatterplot.
a. The best model for these data would be (linear / exponential / quadratic). (Circle the correct answer.) (1 point)
b. This table shows the values from the scatterplot. Find the regression equation for the model that you chose in Part a. Round your answer to the nearest hundredth. (3 points)
x
Level
y
Point total
1
124
2
156
3
194
4
240
5
305
6
380
7
477
8
596
9
745
c. Using the equation that you found in Part b, predict the point total in the 10th level. Round your answer to the nearest integer. (2 points)
3. Maria is a veterinarian. She wants to know how the weight of a puppy is related to its length. To find out, Maria randomly selected 10 puppies that are two months old. She recorded the length and weight of each puppy in the table below.
Part A. The data from the table are shown on the scatterplot. Draw an estimated line of best fit through the data points. (3 points)
Part B. Use the scatterplot to answer these questions.
a. What kind of correlation exists between the length and weight of the puppies? Explain. (2 points)
b. Identify two points on the line of best fit that you drew in Part A. Use the two points to find the equation of the line. Write the equation of the best fit line in slope-intercept form. Show your work. (4 points: 1 point for identifying the coordinates of two points, 1 point for slope, 1 point for b-value, and 1 point for showing work)
4. Maria also wants to study the relationship between the weight of puppies at birth and their adult weight (at two years old). She collected data from five randomly selected small-breed dogs and displayed the data in the table.
Birth weight
(pounds)
Adult weight
(pounds)
1.5
10
3
17
1
8
2.5
14
0.75
5
Part A. Use the data in the table to create a scatterplot. (5 points)
Part B. Look at the scatterplot that you drew in Part A. Which regression equation (linear, exponential, or quadratic) do you think would be the best model for these data? To help you decide, think about the adult weight you would expect if the birth weight were larger — say, 10 pounds. Would you expect the pattern in the scatterplot to continue? To grow exponentially? To change direction? Explain your answer. (2 points)
Part C. Perform a linear regression and interpret the results.
a. Use a calculator to perform a linear regression. Round the values your calculator gives you for a and b to the nearest hundredth. (2 points)
y = _______x + _______
b. What is the slope of the regression equation? What does this mean in terms of the birth weight and adult weight? (2 points)
c. What is the value of the correlation coefficient? (1 point)
d. Describe the correlation in terms of strength (weak or strong) and direction (positive or negative). (2 points)
Part D. Analyze the residuals.
Birth weight
(pounds)
Adult weight
(pounds)
Predicted
adult weight
Residual
1.5
10
3
17
1
8
2.5
14
0.75
5
a. Use the linear regression equation from Part C to calculate the predicted adult weight for each birth weight. Round to the nearest hundredth. Enter these in the third column of the table. (2.5 points)
b. Find the residual for each birth weight. Round to the nearest hundredth. Enter these in the fourth column of the table. (2.5 points)
c. Plot the residuals. (3 points)
d. Based on the residuals, is your regression line a reasonable model for the data? Why or why not? (2 points)
5. Decide whether each statement is true or false. (1 point each)
a. T/F: If there is a strong correlation between two variables, the correlation coefficient will be close to –1 or 1.
b. T/F: If there is a negative correlation between two variables, the slope of the regression line will be positive.
c. T/F: If there is a strong correlation between two variables, there is a cause-and-effect relationship.
d. T/F: The best model for data that change direction is a linear model.
e. T/F: A regression line is useful for predicting unknown values within the range of the observed data values.
Answers
Answer:
Step-by-step explanation:
Answer to #5: is T, F, F, F, T I'm pretty sure that's correct.
HELP ME PLEOPLE THIS IS SO CONFUSING HELP ME I WILL GET SUSPENDED IF I DON"T ANSWER THIS HELP ME PLEASE HELP I WILL GET A 0 AND SUSPENDED HELP HELP
Answers
B) distribute once again but instead of multiplying , divide the factors
(3.6/1.8) + (3.6/10^2) + (10^-5/1.8) + (10^-5/10^2) =
2 + 0.36 + 0.00005555555555 + 0.000001 = should be around 2.36
If a and b are whole numbers such that a x b = 2027, find the value of a + b. Explain your answer.
Answers
Answer:
2028
Step-by-step explanation:
2027 is a prime number, so a = 2027 and b = 1, then a + b = 2028
what is the sum of -3a + 2 + 5a -3
Answers
Answer:
2a - 1
Step-by-step explanation:
I can only simplify
-3a + 2 + 5a - 3
2a + 2 - 3
2a - 1
Answer:
2a-1
Step-by-step explanation:
-3a+2+5a-3
Add like terms
-3a+5a+2-3
2a-1
(+ turns into minus because +2-3 equals a negative number)
A parabola is the set of all points in the plane that are equidistant from a fixed point called the ____ and a fixed line called the ____ of the parabola.
Answers
Need help need help need help lol
Answers
Answer:
Max value is 9 because that's the highest value of y, and the y intercept is 8 because (0,8) is where the graph intersects the y axis
Step-by-step explanation: