Answer:
To estimate the distance the train traveled in the first 20 seconds using four strips of equal width, follow these steps:
a) Calculate the average velocity for each strip by finding the average height of each strip.
b) Multiply the average velocity of each strip by the width (time) of each strip to obtain the distance covered by each strip.
c) Add up the distances covered by each strip to find the estimated total distance traveled in the first 20 seconds.
Regarding part b), to determine if the estimate is an overestimate or an underestimate, we need to analyze the graph. If the graph shows that the velocity increases during the 20-second period, then the estimate will be an underestimate because the actual distance covered would be greater than the estimation based on a constant velocity assumption. On the other hand, if the graph shows that the velocity decreases during the 20-second period, then the estimate will be an overestimate since the actual distance covered would be less than the estimation based on a constant velocity assumption.
Without seeing the graph, it's difficult to provide a definitive answer.
I need some statistics help (this question got deleted)
A researcher hypothesizes that zylex, a new antidepressant, will affect concentration. It is known that scores on a standardized concentration test is normally distributed with a μ= 50 and a σ= 12. A random sample of n=16 participants, aged 19-35, are chosen from the State of New Jersey. The sample is put on a six month dosage plan of zylex. After six months, all the participants are given a standardized concentration test. The researcher records the data and calculates a sample mean of M=56. Are the data sufficient to conclude that the drug, zylex, does have an effect on concentration?
Based on the above research scenario, please answer the following questions:
1. Name the population: ____________________________________
2. Name the sample: _______________________________
3. What is the independent variable? ________________
4. What is the dependent variable? _
_______________________
5. What is the appropriate hypothesis test? __________________
6. What two means are you comparing in this test? ____________________________
7. Please calculate the appropriate hypothesis test using all four steps:
Step 1:
Step 2:
Step 3:
Step 4: _______________________________
Write the statistical statement for your results: __________________________________
Interpret your results (relating back to the hypothesis): _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________
Is there a probability of Type I error? Yes ______ No ______ If yes, what is the probability of a Type I error? ________
Is yes, how could you have decreased that probability? __________________________________
Is there a probability of Type II error? Yes____ _ No______
If it is appropriate, please calculate effect size: Answer:________
Multiply.
(2x+6)²
NEED ANSWER ASAPP
Answer:
4x² + 24x + 36
Step-by-step explanation:
(2x + 6)² = (2x + 6)(2x + 6) = 4x² + 12x + 12x + 36 = 4x² + 24x + 36
Answer the equation n + 3/4 = 5/8
N = ??
Answer:
n = -1/8
Step-by-step explanation:
n + 3/4 = 5/8
n = 5/8 - 3/4
n = 5/8 - 6/8
n = -1/8
So, n = -1/8
really need help with is problem if any math wizards are on
Answer:
2
DNE
-3
3
Step-by-step explanation:
(1) DNE because it is not continuous
(2) DNE because it is not continuous
(3) -3 because at 4, f(x) = -3
(4) x can be any value of -5-2k (where k is a positive integer) or 3. So you can just put 3.
The midpoint of AB is M(1,2). If the coordinates of A are (8,-4), what are the coordinates of B?
The midpoint of AB is M(1,2). If the coordinates of A are (8,-4), The coordinates of point B are (-6, 8).
To find the coordinates of point B, we can use the midpoint formula, which states that the midpoint between two points (x₁, y₁) and (x₂, y₂) is given by:
Midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
We are given the midpoint M(1, 2) and the coordinates of point A (8, -4). Let's denote the coordinates of point B as (x, y).
Using the midpoint formula, we can set up the following equations:
1 = (8 + x) / 2 (equation 1)
2 = (-4 + y) / 2 (equation 2)
Let's solve these equations to find the values of x and y.
From equation 1:
2 = 8 + x
x = 2 - 8
x = -6
From equation 2:
4 = -4 + y
y = 4 + 4
y = 8
Therefore, the coordinates of point B are (-6, 8).
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Answer:
B = (-6, 8)
Step-by-step explanation:
To find the coordinates of B, given the coordinates of A and the coordinates of the midpoint of AB, use the Midpoint formula.
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Midpoint formula}\\\\$M(x,y)=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints.\\\end{minipage}}[/tex]
Let A = (x₁, y₁) = (8, -4)
Let B = (x₂, y₂)
Given M is (1, 2), substitute the points into the midpoint formula:
[tex](1,2)=\left(\dfrac{x_2+8}{2},\dfrac{y_2-4}{2}\right)[/tex]
[tex](1,2)=\left(\dfrac{x_2}{2}+4,\dfrac{y_2}{2}-2\right)[/tex]
Equate the x-coordinates and solve for x₂:
[tex]\begin{aligned}1&=\dfrac{x_2}{2}+4\\\\1-4&=\dfrac{x_2}{2}+4-4\\\\-3&=\dfrac{x_2}{2}\\\\-3\cdot 2&=\dfrac{x_2}{2}\cdot 2\\\\-6&=x_2\\\\x_2&=-6\end{aligned}[/tex]
Equate the y-coordinates and solve for y₂:
[tex]\begin{aligned}2&=\dfrac{y_2}{2}-2\\\\2+2&=\dfrac{y_2}{2}-2+2\\\\4&=\dfrac{y_2}{2}\\\\4\cdot 2&=\dfrac{y_2}{2}\cdot 2\\\\8&=y_2\\\\y_2&=8\end{aligned}[/tex]
Therefore, the coordinates of B are (-6, 8).
Select the expression that is equivalent to (n²-25)
A. n² +10n - 25
B. n²-10-25
C. (n+5)(n-5)
D. (n-5) ²
Answer:
C. (n+5)(n-5)
Step-by-step explanation:
Select the expression that is equivalent to (n²-25)
Let's check each option. A and B are wrong, so we only check C & D.
C. (n + 5) (n - 5)
n² - 5n + 5n - 25
n² - 25
D. (n - 5)²
(n - 5) (n - 5)
n² - 5n - 5n + 25
n² - 10n + 25
So, the correct answer is C. (n+5)(n-5)
Identify the value of x. Give your answers in simplest radical form.
The figure shows right triangle A B C. Angle A B C is a right angle. Angle A C B measures 45 degrees. Side A B has a length of 3 units. Hypotenuse A C has a length of x units.
The value of x, representing the length of the hypotenuse AC, is 3√2 units.
In a right triangle ABC, with angle ABC measuring 45 degrees and side AB having a length of 3 units, we can use trigonometric ratios to find the length of the hypotenuse AC, represented by x.
Since angle ABC is 45 degrees, we know that it is a special right triangle, specifically a 45-45-90 triangle.
In such a triangle, the lengths of the sides are in a specific ratio: 1:1:√2.
In this case, side AB is 3 units, which represents the length of one of the legs. By the ratio mentioned earlier, the hypotenuse AC (x) will be √2 times the length of AB.
Therefore, we have:
AC = AB [tex]\times[/tex] √2
AC = 3 [tex]\times[/tex] √2
AC = 3√2 units
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Sales at Glover's Golf Emporium have been increasing linearly. In their second business year, sales were $160,000
. This year was their seventh business year, and sales were $335,000
. If sales continue to increase at this rate, predict the sales in their eleventh business year.
The predicted sales in Glover's Golf Emporium's eleventh business year are $475,000.
To predict the sales in Glover's Golf Emporium's eleventh business year, we can use the concept of linear growth. We have two data points: sales in the second year ($160,000) and sales in the seventh year ($335,000).
Let's first find the annual increase in sales:
Increase in sales = Sales in the seventh year - Sales in the second year
Increase in sales = $335,000 - $160,000
Increase in sales = $175,000
Next, we need to determine the rate of increase per year. Since we have a linear growth pattern, we can calculate the average annual increase by dividing the total increase in sales by the number of years:
Average annual increase = Increase in sales / Number of years
Average annual increase = $175,000 / (7 - 2) years
Average annual increase = $175,000 / 5 years
Average annual increase = $35,000 per year
Now, we can predict the sales in the eleventh business year by adding the average annual increase to the sales in the seventh year:
Predicted sales in the eleventh year = Sales in the seventh year + (Average annual increase * Number of additional years)
Predicted sales in the eleventh year = $335,000 + ($35,000 * (11 - 7))
Predicted sales in the eleventh year = $335,000 + ($35,000 * 4)
Predicted sales in the eleventh year = $335,000 + $140,000
Predicted sales in the eleventh year = $475,000
Therefore, the predicted sales in Glover's Golf Emporium's eleventh business year are $475,000.
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(BRAINLIEST AND 95 PTS TO CORRECT ANSWER!! PLS HELP!!) Part B: A student would like to show their teacher that they have practiced long enough for the day. Which measure of center should the student give to their teacher? Explain your answer. (2 points)
The measure of center that the student should give to their teacher is the median.
What is median, in statistics?In statistics, the median is a measure of central tendency that represents the middle value in a dataset when it is ordered from least to greatest. It divides the dataset into two equal halves, where half the values are smaller than the median and half are larger.
The median is useful because it is not influenced by extreme values or outliers in the dataset, unlike the mean (average). It provides a representative value that indicates the central position of the data.
The median is a better measure of center in this case since the data is skewed. The value of median is not affected by skewness
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LU In a class of y children, n mathematics books, each costing p shillings, were lost. The teacher decided that the cost of the lost books be shared equally among the children. How much money did each child pay?
In the class , each child needs to pay (n * p) / y shillings to cover the cost of the lost books.
In the given scenario, there is a class of "y" children, and "n" mathematics books were lost, each costing "p" shillings. The teacher decides to distribute the cost of the lost books equally among all the children.
To find out how much money each child needs to pay, we need to divide the total cost of the lost books by the number of children in the class.
The total cost of the lost books can be calculated by multiplying the number of lost books ("n") by the cost of each book ("p").
Total cost = n * p
To distribute the cost equally among all the children, we divide the total cost by the number of children ("y"):
Cost per child = Total cost / Number of children
Substituting the values, we get:
Cost per child = (n * p) / y
Therefore, each child in the class needs to pay (n * p) / y shillings to cover the cost of the lost books.
It's important to note that this calculation assumes that the total cost is evenly distributed among all the children, regardless of whether they were responsible for losing the books or not.
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The following data set shows the number of books checked out from a library
during the first two weeks of the month:
19, 10, 15, 99, 12, 18, 15, 16, 12, 13, 18, 17, 19, 13
Which of the following statements is true based on the data set?
O There is one outlier, indicating very few books were checked out on that day.
O There is one outlier, indicating an abnormally large number of books were checked
out on that day.
O There are two outliers, indicating very few books were checked out on those two
days.
O There are two outliers, indicating an abnormally large number of books were checked
out on those 2 days.
The statement "There is one outlier, indicating an abnormally large number of books were checked out on that day" is true based on the data set.
To determine if there are any outliers in the given data set of the number of books checked out from a library during the first two weeks of the month, we can examine the values and look for extreme values that deviate significantly from the rest of the data.
The data set is as follows:
19, 10, 15, 99, 12, 18, 15, 16, 12, 13, 18, 17, 19, 13
To identify outliers, we can use different methods, such as the interquartile range (IQR) or z-scores. Let's calculate the IQR to determine if there are any outliers:
Arrange the data set in ascending order:
10, 12, 12, 13, 13, 15, 15, 16, 17, 18, 18, 19, 19, 99
Calculate the first quartile (Q1) and third quartile (Q3):
Q1 = 13 (median of the lower half)
Q3 = 18 (median of the upper half)
Calculate the interquartile range (IQR):
IQR = Q3 - Q1 = 18 - 13 = 5
Define the lower and upper boundaries for outliers:
Lower bound = Q1 - 1.5 * IQR = 13 - 1.5 * 5 = 5.5
Upper bound = Q3 + 1.5 * IQR = 18 + 1.5 * 5 = 25.5
Based on these calculations, any value below 5.5 or above 25.5 would be considered an outlier.
Looking at the data set, we can see that there is indeed one outlier, which is the value 99. It is significantly larger than the rest of the values and falls above the upper bound.
Therefore, the statement "There is one outlier, indicating an abnormally large number of books were checked out on that day" is true based on the data set.
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A gaming system costs $600 and is on sale for 15% off. After the discount, there is a 5% tax. What is the final price of the gaming system?
Answer$535.50
Step-by-step explanation:
15% is equal to .15
So, multiply 600.00x .15=90
600.00 - 90.0=510.
510. 00x .05=25.50
510.00+25.50=535.50
Your answer is $535.5
find the midpoint of the line segment with endpoints (-9,-1) and (7,0)
Answer:
Midpoint = (-1, -1/2)
Step-by-step explanation:
We can find the midpoint using the midpoint formula which is given by:
M = (x1 + x2) / 2, (y1 + y2) / 2, where
M is the coordinates of the midpoint,(x1, y1) are one point on the line segment,and (x2, y2) are another point on the line segment.Thus, we can plug in (-9, -1) for (x1, y1) point and (7, 0) for (x2, y2) in the midpoint formula:
M = (-9 + 7) / 2, (-1 + 0) / 2
M = (-2) / 2, (-1) / 2
M = -1, -1/2
Thus, (-1, -1/2) is the midpoint of the line segment with endpoints (-9, -1) and (7, 0).
Please show the graph with correct points in x and y. Please specify if it’s a hollow dot or solid dot for each point. I’ll give good rating! Thank you!
The graph of the solution to the inequality is attached as image to this answer.
Understanding Piece-Wise FunctionThe piece-wise defined function h(x) represents different values of y (the output) depending on the value of x (the input). Each interval of x has a different value assigned to it.
In this particular case, the inequality statements define the intervals for x and their corresponding output values.
Let's break it down:
- For values of x that are greater than -3 and less than or equal to -2, h(x) is assigned the value of -1.
- For values of x that are greater than -2 and less than or equal to -1, h(x) is assigned the value of 0.
- For values of x that are greater than -1 and less than or equal to 0, h(x) is assigned the value of 1.
- For values of x that are greater than 0 and less than or equal to 1, h(x) is assigned the value of 2.
Any values of x outside of these intervals are not defined in this piece-wise function and are typically represented as "not a number" (NaN).
For example, if you were to evaluate h(-2.5), it falls within the first interval (-3 < x ≤ -2), so h(-2.5) would be equal to -1. Similarly, if you were to evaluate h(0.5), it falls within the fourth interval (0 < x ≤ 1), so h(0.5) would be equal to 2.
The graph of the piece-wise function h(x) consists of horizontal line segments connecting the specified values of y for each interval, resulting in a step-like pattern.
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x = 13, ¿cuál ecuación es verdadera?
3(18 - x) = 67
4(9x) = 23
2(x-3)=7
5(x-9) = 20
When x = 13, the equation that is true is option D) 5(x - 9) = 20.
To determine which equation is true when x = 13, we can substitute the value of x into each equation and see which equation holds true. Let's go through each option:
A) 3(18 - x) = 67
Substituting x = 13:
3(18 - 13) = 67
3(5) = 67
15 = 67
The equation is not true when x = 13. Therefore, option A is false.
B) 4(9x) = 23
Substituting x = 13:
4(9*13) = 23
4(117) = 23
468 = 23
Again, the equation is not true when x = 13. Therefore, option B is also false.
C) 2(x - 3) = 7
Substituting x = 13:
2(13 - 3) = 7
2(10) = 7
20 = 7
Once again, the equation is not true when x = 13. Therefore, option C is false as well.
D) 5(x - 9) = 20
Substituting x = 13:
5(13 - 9) = 20
5(4) = 20
20 = 20
Finally, the equation is true when x = 13. Therefore, option D is true.
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Note: the translated questions is
X = 13, which equation is true?
Solve this system of by rewriting the statements into a set of 2 equations. Then solve the equations using the addition method The surm of two numbers is 21. The difference of the two numbers is 19. What are the two numbers?
Answer:
the two numbers are 20 and 1.
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Find the average rate of change of each function over the interval (0, 3). Match each representation with its respective average rate of change.
-1
-2
X
0
6
= 2² + 2x - 5
1
3
2
3 4
-3
The correct matches are:
-1: 0
-2: 0
X: 14/3
0: 0
6: Not used
= 2² + 2x - 5: Not used
To match the representations with their respective average rates of change, we need to calculate the average rate of change for each function over the interval (0, 3) and compare it to the given values.
Let's calculate the average rate of change for each function:
Function: 2² + 2x - 5
To find the average rate of change, we need to calculate the difference in function values divided by the difference in x-values:
Average rate of change = (f(3) - f(0)) / (3 - 0)
Average rate of change = ((2² + 2(3) - 5) - (2² + 2(0) - 5)) / 3
Average rate of change = (13 - (-1)) / 3
Average rate of change = 14 / 3
Match: X = 14/3
Function: -1
Since the function is constant, the average rate of change is 0.
Match: 0
Function: 2
Since the function is constant, the average rate of change is 0.
Match: 0
Function: 3
Since the function is constant, the average rate of change is 0.
Match: 0
Function: -2
Since the function is constant, the average rate of change is 0.
Match: 0
Function: -3
Since the function is constant, the average rate of change is 0.
Match: 0
Therefore, the correct matches are:
-1: 0
-2: 0
X: 14/3
0: 0
6: Not used
= 2² + 2x - 5: Not used
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Dora's bowling score this week where 152 170 and 161
question below what is Dora mean score
The mean score of Dora's bowling for this week would be = 161.
How to calculate the mean score for the week?To calculate the mean score for the week the following would be carried out as follows;
The formula that is used to calculate mean = summation of the score/ number of scores recorded.
That is;
The weeks scores = 152+170+161
= 483/3
= 161
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f(x) = 8x – 2
g(x) = 9x + 2
What is h(x) = f(x) – g(x)?
h(x) = 17x + 14
h(x) = x + 4
h(x) = –x – 4
h(x) = –x + 14
Answer:
h(x) = -x - 4
Step-by-step explanation:
Given:
f(x) = 8x - 2
g(x) = 9x + 2
Substituting these values into the equation h(x) = f(x) - g(x)
h(x) = (8x - 2) - (9x + 2)
Simplify
h(x) = 8x - 2 - 9x - 2
Combining like terms
h(x) = (8x - 9x) - (2 + 2)
h(x) = -x - 4
Hope this helps.
3
2
пал
2 4
6 8 10
1
-1
Determine the period.
-2
-3
14/
The period of the function in this problem is given as follows:
5 units.
How to obtain the period of the function?A periodic function is a function that has the behavior repeating over intervals in the domain of the function.
Then the period of the function has the concept defined as the difference between two points in which the function has the same behavior.
Two consecutive peaks of the graph of the function in this problem are given as follows:
Input of 1 and input of 6.
Hence the period of the function is given as follows:
6 - 1 = 5 units.
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The sum of three numbers is 71. The third number is 2 times the first. The second number is 5 less than the first. What are the numbers?
Answer:
19, 14, 38
Step-by-step explanation:
Let x, y, and z be each number respectively:
[tex]x+y+z=71\\z=2x\\y=x-5\\\\x+y+z=71\\x+(x-5)+2x=71\\2x-5+2x=71\\4x-5=71\\4x=76\\x=19\\\\y=x-5\\y=19-5\\y=14\\\\z=2x\\z=2(19)\\z=38[/tex]
Therefore, the three numbers are 19, 14, and 38.
there are 50 people in a coffee shop fourteen are tourist.what percent of people in the shop are tourist and non tourist
Answer:
tourist: 28%
non-tourist: 72%
Step-by-step explanation:
total: 50
tourists: 14
non-tourists:50 - 14 = 36
tourist percentage: 14/50 × 100% = 28%
non-tourist percentage: 36/50 × 100 = 72%
Find the critical value t Subscript c for the confidence level c=0.99 and sample size n=22.
tc=?
The critical value tₕ for a confidence level of 0.99 and a sample size of 22 is approximately 2.831.
To find the critical value tₕ for a given confidence level and sample size, we can use a t-distribution table or a statistical software.
For a confidence level of 0.99, we need to determine the critical value tₕ such that the area under the t-distribution curve to the right of tₕ is equal to (1 - c) / 2. In this case, (1 - c) / 2 = (1 - 0.99) / 2 = 0.005.
Since the sample size is 22, we have n - 1 degrees of freedom, which is 22 - 1 = 21. We need to find the critical value tₕ with 21 degrees of freedom that corresponds to an area of 0.005 in the upper tail of the t-distribution.
Using a t-distribution table or a statistical software, we find that the critical value tₕ is approximately 2.831.
Therefore, the critical value tₕ for a confidence level of 0.99 and a sample size of 22 is approximately 2.831.
It is important to note that the critical value may vary slightly depending on the specific t-distribution table or statistical software used. However, the value obtained above is a reasonable approximation based on commonly used tables or software.
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Assume that Canes customer would buy. A maximum of 82000. Units of Alpha and62000 of beta assume that the raw material availability for production is limited to 162000 pounds how many units of each product should Cane produce to maximize profits
The units of each product that Cane should produce to maximize profits will be 62000 units of Beta and 7600 units of
Alpha.
Contribution margin per poundAlpha Beta
Selling price 130 90
Variable cost 78 48
Contribution margin 52 42
Pound per unit 5 2
Contribution margin per pound 10.4 21
Pound Unit
Beta 62000*2 = 124000 62000
Alpha 38000 38000/5 = 7600
Total 162000
Maximum contribution margin = (38000*10.4+124000*21) = 2999200
Highest price = 10.4+5 = 15.40 per pound
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The ordered pair (2, 10) is a point on a direct variation equation. Write the direct variation equation.
Answer:
Y=KX so its 10=K2
Step-by-step explanation:
Plug in the Number OR K=y/x
If mLEFD=2x -3 and mZDFG= x+12, find mLEFD.
If mLEFD=2x -3 and mZDFG= x+12, the measure of angle LEFD (mLEFD) is 27.
To find the measure of angle LEFD (mLEFD), we need to equate it to the given expressions mLEFD = 2x - 3 and mZDFG = x + 12.
Since angle LEFD and angle ZDFG are alternate interior angles, they are congruent.
Therefore, we have:
mLEFD = mZDFG
Substituting the expressions for mLEFD and mZDFG:
2x - 3 = x + 12
Next, we solve the equation for x by isolating the variable:
2x - x = 12 + 3
x = 15
Now that we have the value of x, we can substitute it back into the expression for mLEFD to find the measure of angle LEFD:
mLEFD = 2(15) - 3
mLEFD = 30 - 3
mLEFD = 27
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PLEASE HELP ASAP
solve -1/6[3-15(1/3)2]
Answer:
C) -2/9
Step-by-step explanation:
[tex]\displaystyle -\frac{1}{6}\biggr[3-15\biggr(\frac{1}{3}\biggr)^2\biggr]\\\\=-\frac{1}{6}\biggr[3-15\biggr(\frac{1}{9}\biggr)\biggr]\\\\=-\frac{1}{6}\biggr[3-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{27}{9}-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{12}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{4}{3}\biggr]\\\\=-\frac{4}{18}\\\\=-\frac{2}{9}[/tex]
Answer:
Hence, Option (C) - 2/9 is the Answer:
Step-by-step explanation:
-1/6 [3 -15(1/3)^2]
-1/6(3 -15)(1/9))
-1/6(3 - 5/3)
-1/6 (4/3)
Hence, Option (C) - 2/9 is the Answer:
I hope it helps!
what are the steps to solve this
Answer:
The equation of this line is y = -4.
Answer:
y=-4
Step-by-step explanation:
zero slope m=0
y-y1=m(x-x1)
y-(-4)=0(x-(-9))
y+4=0
y=-4
If f(x)=/x-7 and g(x) - 4x - 8
which statement is true
1 is in the domain
1 isnt in the domain of f(0) g
ANSWERED: 1 is NOT in the domain.
The statement "1 is NOT in the domain" is true because for the function f(x), the expression x - 7 results in division by zero when x equals 1, which makes 1 not a valid input for the function.
To determine if a value is in the domain of a function, we need to consider any restrictions or limitations on the input values.
For the function f(x) = √(x - 7), the square root function is defined only for non-negative values.
Therefore, the expression (x - 7) inside the square root must be greater than or equal to zero. In other words, x - 7 ≥ 0.
Solving this inequality, we find x ≥ 7.
This means that any value of x that is greater than or equal to 7 is in the domain of f(x).
However, the statement is asking specifically about the value 1.
Since 1 is less than 7, it does not satisfy the inequality x ≥ 7 and is therefore not in the domain of f(x).
Similarly, for the function g(x) = 4x - 8, there are no restrictions on the domain.
Any real number can be substituted into the function, including the value 1.
Therefore, the statement "1 isn't in the domain of f(0) g" is not accurate.
It is true that 1 is not in the domain of f(x), but it is in the domain of g(x).
In summary, the correct statement is that "1 is not in the domain."
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Triangle DEF has vertices at D(−3, 5), E(−10, 4), and F(−11, 8). Triangle D′E′F′ is the image of triangle DEF after a reflection. Determine the line of reflection if D′ is located at (3, 5).
y = 5
x = −3
y-axis
x-axis
The line of reflection for the image of triangle DEF is the y-axis.
To determine the line of reflection for the image of triangle DEF, we need to find the axis along which the reflection occurred. We can do this by examining the coordinates of the corresponding points before and after the reflection.
Given that D' is located at (3, 5) after the reflection, we can compare the x-coordinates of D and D'. The x-coordinate of D is -3, and the x-coordinate of D' is 3. We notice that there is a change in sign, indicating a reflection across the y-axis.
Therefore, the line of reflection for the image of triangle DEF is the y-axis.
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