Answers
Answer:
A) (-2, 8), (4, 8)
B) See attachment.
C) 36 square units
Step-by-step explanation:
Part AGiven functions:
[tex]\begin{cases}f(x)=x^2-2x\\g(x)=8\end{cases}[/tex]
To find the x-coordinates of the points where the two functions intersect, set the equations equal to each other and solve for x:
[tex]f(x)=g(x)\\\\x^2-2x=8\\\\x^2-2x-8=0\\\\x^2-4x+2x-8=0\\\\x(x-4)+2(x-4)=0\\\\(x+2)(x-4)=0\\\\\\x+2=0 \implies x=-2\\\\x-4=0 \implies x=4[/tex]
As points on the function g(x) have a y-coordinate of 8, the solutions to f(x) = g(x) are:
[tex]\Large\boxed{(-2,8)\;\textsf{and}\;(4,8)}[/tex]
[tex]\dotfill[/tex]
Part BThe function g(x) is a horizontal line parallel to the x-axis that intercepts the y-axis at (0, 8).
We are given that function f(x) is a concave up parabola with roots at (0, 0) and (2, 0). From Part A, we know that the parabola intersects g(x) at points (-2, 8) and (4, 8).
To help sketch the graph of function f(x), we can find its vertex and y-intercept.
The x-coordinate of the vertex of a quadratic function in the form y = ax² + bx + c is x = -b/2a. In this case, a = 1 and b = -2, so the x-coordinate of the vertex is:
[tex]x = -\dfrac{-2}{2(1)}=\dfrac{2}{2}=1[/tex]
To find the y-coordinate of the vertex, substitute x = 1 into f(x):
[tex]f(1)=(1)^2-2(1)=1-2=-1[/tex]
Therefore, the vertex of f(x) is at point (1, -1). The axis of symmetry of a parabola is the x-coordinate of the vertex, so in this case, the axis of symmetry is x = 1.
To find the y-intercept, substitute x = 0 into the function and solve for y:
[tex]f(0)=(0)^2-2(0)=0-0=0[/tex]
Therefore, the y-intercept of f(x) is the origin (0, 0).
[tex]\dotfill[/tex]
Part CThe area of the region R bounded by f(x) and g(x) on the interval [-2, 4] is given by the integral:
[tex]\displaystyle R = \int_{-2}^{4} \left[ g(x) - f(x) \right] \; dx[/tex]
Substitute g(x) = 8 and f(x) = x² - 2x:
[tex]\displaystyle R = \int_{-2}^{4} \left[8-(x^2-2x)\right] \; dx \\\\\\ R = \int_{-2}^{4} \left[8-x^2+2x\right] \; dx[/tex]
Evaluate the Integral
[tex]\displaystyle R = \left[8x-\dfrac{x^{2+1}}{2+1}+\dfrac{2x^{1+1}}{1+1}\right]^4_{-2} \\\\\\ R = \left[8x-\dfrac{x^{3}}{3}+x^2\right]^4_{-2} \\\\\\ R=\left(8(4)-\dfrac{(4)^{3}}{3}+(4)^2\right)-\left(8(-2)-\dfrac{(-2)^{3}}{3}+(-2)^2\right) \\\\\\ R=\left(32-\dfrac{64}{3}+16\right)-\left(-16+\dfrac{8}{3}+4\right) \\\\\\ R=\dfrac{80}{3}+\dfrac{28}{3} \\\\\\ R=\dfrac{108}{3}\\\\\\ R=36[/tex]
Therefore, the area of the region R bounded by f(x) and g(x) is:
[tex]\Large\boxed{\textsf{$36$ square units}}[/tex]
Related Questions
Which graph shows the solution set for Negative 4.4 greater-than-or-equal-to 1.6 x minus 3.6?
A number line going from negative 3 to positive 3. A closed circle is at negative 0.5. Everything to the left of the circle is shaded.
A number line going from negative 3 to positive 3. A closed circle is at negative 0.5. Everything to the right of the circle is shaded.
A number line going from negative 7 to negative 1. A closed circle is at negative 5. Everything to the left of the circle is shaded.
A number line going from negative 7 to negative 1. A closed circle is at negative 5. Everything to the right of the circle is shaded.
Answers
Answer:
A number line going from negative 7 to negative 1. A closed circle is at negative 5. Everything to the right of the circle is shaded.
Step-by-step explanation:
-4.4 ≥ 1.6 x - 3.6
Solving for the value of x,
1.6 x ≤ -4.4 + 3.6
1.6 x ≤ - 0.8
Dividing 1.6 from both sides to know value of x
x ≤ - 0.5
Answer:
the answer is a
Step-by-step explanation:
Edenuity
A triangle with a base of 10 units and height of 8 units. Find the area of the triangle. The area of the triangle is square units.
Answers
Answer: 40 units
Step-by-step explanation: just did got it right.
Let the abbreviation PSLT stand for the percent of the gross family income that goes into paying state and local taxes. Suppose one wants to estimate the mean PSLT for the population of all families in New York City with gross incomes in the range $35.000 to $40.000. If sigma equals 2.0, how many such families should be surveyed if one wants to be 90% sure of being able to estimate the true mean PSLT within .5?
Answers
Answer:
Number of families that should be surveyed if one wants to be 90% sure of being able to estimate the true mean PSLT within 0.5 is at least 43.
Step-by-step explanation:
We are given that one wants to estimate the mean PSLT for the population of all families in New York City with gross incomes in the range $35.000 to $40.000.
If sigma equals 2.0, we have to find that how many families should be surveyed if one wants to be 90% sure of being able to estimate the true mean PSLT within 0.5.
Here, we will use the concept of Margin of error as the statement "true mean PSLT within 0.5" represents the margin of error we want.
SO, Margin of error formula is given by;
Margin of error = [tex]Z_(_\frac{\alpha}{2}_ ) \times \frac{\sigma}{\sqrt{n} }[/tex]
where, [tex]\alpha[/tex] = significance level = 10%
[tex]\sigma[/tex] = standard deviation = 2.0
n = number of families
Now, in the z table the critical value of x at 5% ( [tex]\frac{0.10}{2} = 0.05[/tex] ) level of significance is 1.645.
SO, Margin of error = [tex]Z_(_\frac{\alpha}{2}_ ) \times \frac{\sigma}{\sqrt{n} }[/tex]
0.5 = [tex]1.645 \times \frac{2}{\sqrt{n} }[/tex]
[tex]\sqrt{n} =\frac{2\times 1.645 }{0.5}[/tex]
[tex]\sqrt{n} =6.58[/tex]
n = [tex]6.58^{2}[/tex]
= 43.3 ≈ 43
Therefore, number of families that should be surveyed if one wants to be 90% sure of being able to estimate the true mean PSLT within 0.5 is at least 43.
What is the median of this data set 14,18,31,34,44,50
Answers
Because:
14 + 18 + 31 + 34 + 44 + 50 = 191
191 / 6 = 31.83 (the median)
what is the length of the diameter of the circle
Answers
Answer:
6 cm
Step-by-step explanation:
3 is the radius
the radius is half of the diameter
to find the diameter from the radius you have to multiply it by 2
3×2
=6
"A sample of 64 hotels in Atlanta was selected in order to determine whether or not the average room price is significantly different from $110. The average price of the rooms in the sample was $112. The population standard deviation is known to be $16. Use a 0.05 level of significance. Use this information to answer Questions 16 to 19. What should be the appropriate null and alternative hypotheses for the purpose of your analysis?"
Answers
Answer:
The null and alternative hypothesis are:
[tex]H_0: \mu=110\\\\H_a:\mu\neq 110[/tex]
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the average room price in Atlanta is significantly different from $110 (P-value=0.317) .
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the average room price in Atlanta is significantly different from $110.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=110\\\\H_a:\mu\neq 110[/tex]
The significance level is 0.05.
The sample has a size n=64.
The sample mean is M=112.
The standard deviation of the population is known and has a value of σ=16.
We can calculate the standard error as:
[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{16}{\sqrt{64}}=2[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{112-110}{2}=\dfrac{2}{2}=1[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as:
[tex]P-value=2\cdot P(z>1)=0.317[/tex]
As the P-value (0.317) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the average room price in Atlanta is significantly different from $110.
Which statement correctly describes the diagram? On a coordinate plane, triangle A is reflected across the x-axis to form triangle B. Triangle A is rotated to form triangle C. Triangle B is a reflection of triangle A across the x-axis. Triangle C is not a reflection of triangle A.. Triangle B is a reflection of triangle A across the y-axis. Triangle C is a reflection of triangle A across the line y = x + 3. Triangle B is a reflection of triangle A across the y-axis. Triangle C is not a reflection of triangle A. Triangle B is a reflection of triangle A across the x-axis. Triangle C is a reflection of triangle A across the line y = x + 3.
Answers
Answer:
Your answer would be Triangle B is a reflection of triangle A across the x-axis. Triangle C is not a reflection of triangle A.
Explanation
B is a reflection of the x-axis.
But triangle C is not a reflection because if you fold the image with the y-axis line in the middle then you would see that triangle C doesnt match the placement of triangle A.
hope this helps
give brainliest if you please
Answer:
Without the picture of diagram, based on your description:
Triangle A is reflected across the x-axis to form triangle B.
Triangle A is rotated to form triangle C.
Option A: Triangle B is a reflection of triangle A across the x-axis.
It is correct because "Triangle A is reflected across the x-axis to form triangle B" => Triangle B is a reflection of triangle A across the x-axis
Option B: Triangle C is not a reflection of triangle A
It is correct because "Triangle A is rotated to form triangle C"
Option C: Triangle B is a reflection of triangle A across the y-axis
It is incorrect, because "Triangle A is reflected across the x-axis to form triangle B" => Triangle B is a reflection of triangle A across the x-axis, not y-axis.
Option D: Triangle C is a reflection of triangle A across the line y = x + 3
It is incorrect, because "Triangle A is rotated to form triangle C" => triangle C is a result of rotation, not reflection.
Hope this helps!
:)
A recipe calls for 3 teaspoons of orange juice. A can of orange juice is 20 fluid ounces. How many teaspoons of juice are in the can? My child needs help and I don't get it. Help!
Answers
Answer:
Step-by-step explanation:
You have to look up (google) the number of ml in a fluid ounce. It equals 29.57 ml approximately.
Next you must look up the number of mL in a teaspoon. The conversion factor turns out to be 4.93 mL = 1 teaspoon.
1 fluid ounce = 29.57 mL
20 fluid ounces = x mL
1/20 = 29.57 /x
x = 20*29.57
x = 591.4 mL
1 teaspoon = 4.93 mL
x teaspoons = 591.4
4.93 * x = 591.4
4.93 * x/4.93 = 591.4 / 4.93
x = 119.96
Which best describes the clusters in the data set? Number of Fish in Each Tank at the Pet Store A dot plot going from 10 to 15. 10 has 6 dots, 11 has 8 dots, 12 has 0 dots, 13 has 4 dots, 14 has 2 dots, 15 has 3 dots.
Answers
Answer:
C
Step-by-step explanation:
Option D is correct, There are two clusters, at 10 and 11, and at 13, 14, and 15.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Data is a collection of discrete values that convey information, describing quantity, quality, fact, statistics, other basic units of meaning
Clustering is the task of dividing the population or data points into a number of groups such that data points in the same groups are more similar to other data points in the same group than those in other groups.
There are two clusters, at 10 and 11, and at 13, 14, and 15 is best describes the clusters in the data set
Hence, Option D is correct, There are two clusters, at 10 and 11, and at 13, 14, and 15.
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what is the best estimate for the length of a baseball bat?
Answers
Answer:
42 inches
By regulation it may be no more than 2.75 inches (7.0 cm) in diameter at the thickest part and no more than 42 inches (1.067 m) in length.
Step-by-step explanation:
baseball bat - is a smooth wooden or metal club used in the sport of baseball to hit the ball after it is thrown by the pitcher.
length- a measure of distance.
Answer:
30 inches
Step-by-step explanation:
1. Find the Length of Line AD A(6, 2) D(-3, -2)
Answers
Answer:
5
Step-by-step explanation:
[tex]\sqrt{(2-(-2))^{2} + (6-(-3))^2}[/tex]
=[tex]\sqrt{4^{2} + 3^{2} } \\[/tex]
=[tex]\sqrt{25}[/tex]
=5
The base of a triangular prism has a base of 5 cm and a height of 8 cm. The prism itself has a height of 7 cm. What is its volume?
Answers
Answer:
140
Step-by-step explanation:
The volume of a triangular prism with a base of 5 cm and height of 8cm and the height of the prism as 7cm is 140 cm³
Volume of a triangular prismvolume of triangular prism = 1 / 2 bhl
where
b = base of the triangular baseh = height of the triangular basel = height of the triangular prismTherefore,
base = b = 5 cm
height = h = 8 cm
l = 7cm
Hence,
volume of the triangular prism = 1 / 2 × 5 × 8 × 7
volume of the triangular prism = 280 / 2
volume of the triangular prism = 140 cm³
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An inequality represents an infinite amount of numbers larger than-5. Which inequality represents the situation?
OX<-5
Ox>-5
O x>-4
OX<-4
Answers
Answer:
b) x > - 5
Step-by-step explanation:
x > - 5
x ∈ (- 5 ; + oo)
Answer:
B
Step-by-step explanation:
Edge2022
A light bulb consumes 600 watt hours per day. How many Watt hours? Does it consume in 3 days and 12 hours?
Answers
Answer:
2100 Watt Hours
Step-by-step explanation:
600 Watt hours is consumed by the bulb every day.
3 Days and 12 Hours = 3 1/2 Days
To find how many Watt hours was consumed in 3 1/2 days we must multiply both of the numbers.
600 x 3 1/2 = 2100
Therefore, we can conclude that 2100 Watt Hours are consumed in 3 Days and 12 Hours.
what is 250 divided by 17
Answers
An insurance company is interested in conducting a study to to estimate the population proportion of teenagers who obtain a driving permit within 1 year of their 16th birthday. A level of confidence of 99% will be used and an error of no more than .04 is desired. There is no knowledge as to what the population proportion will be. The size of sample should be at least _______. 289
Answers
Answer:
The size of the sample should be at least 1037.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error of the interval is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
A level of confidence of 99% will be used and an error of no more than .04 is desired. There is no knowledge as to what the population proportion will be. The size of sample should be at least
We need a sample size of at least n.
n is found when [tex]M = 0.04[/tex]
We don't know the proportion of the population, so we use [tex]\pi = 0.5[/tex]
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 2.575\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.04\sqrt{n} = 2.575*0.5[/tex]
[tex]\sqrt{n} = \frac{2.575*0.5}{0.04}[/tex]
[tex](\sqrt{n})^{2} = (\frac{2.575*0.5}{0.04})^{2}[/tex]
[tex]n = 1036.03[/tex]
Rounding up
The size of the sample should be at least 1037.
Which expression is equal to 5x(m-n)
1. (m-5)x(n-5)
2. 5m-5n
3. m-5n
Answers
Multiply each term in the parentheses by 5
Olive's garden is only 10 yd to the second power and the watermelon plants she wants to grow requires 2.5 yd to the second power each, how many watermelon plants can she grow
Answers
Answer:
4
Step-by-step explanation:
Garden area: 10 yd²
Each watermelon plant area: 2.5 yd²
No. of plants:
10/2.5 = 4
Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 11. Use the empirical rule to determine the following. (a) What percentage of people has an IQ score between 67 and 133? (b) What percentage of people has an IQ score less than 89 or greater than 111? (c) What percentage of people has an IQ score greater than 111?
Answers
Answer:
(a) The percentage of people having an IQ score between 67 and 133 is 99.73%.
(b) The percentage of people having an IQ score less than 89 or greater than 111 is 31.73%.
(c) The percentage of people having an IQ greater than 111 is 15.87%.
Step-by-step explanation:
The random variable X can be defined as the scores of an IQ test.
The random variable X is normally distributed with parameters μ = 100 and σ = 11.
(a)
Compute the probability of people who has an IQ score between 67 and 133 as follows:
[tex]P(67<X<133)=P(\frac{67-100}{11}<\frac{X-\mu}{\sigma}<\frac{133-100}{11})\\\\=P(-3<Z<3)\\\\=P(Z<3)-P(Z<-3)\\\\=0.99865-0.00135\\\\=0.9973[/tex]
The percentage is, 0.9973 × 100 = 99.73%.
Thus, the percentage of people having an IQ score between 67 and 133 is 99.73%.
(b)
Compute the probability of people having an IQ score less than 89 or greater than 111 as follows:
[tex]P(X<89\ \cup\ X>111)=1-P(89<X<111)\\\\=1-P(\frac{89-100}{11}<\frac{X-\mu}{\sigma}<\frac{111-100}{11})\\\\=1-P(-1<Z<1)\\\\=1-[P(Z<1)-P(Z<-1)]\\\\=1-[0.84134-0.15866]\\\\=0.31732\\\\\approx 0.3173[/tex]
The percentage is, 0.3173 × 100 = 31.73%.
Thus, the percentage of people having an IQ score less than 89 or greater than 111 is 31.73%.
(c)
Compute the probability of people having an IQ score greater than 111 as follows:
[tex]P(X>111)=P(\frac{X-\mu}{\sigma}>\frac{111-100}{11})\\\\=P(Z>1)\\\\=1-P(Z<1)\\\\=1-0.84134\\\\=0.15866\\\\\approx 0.1587[/tex]
The percentage is, 0.1587 × 100 = 15.87%.
Thus, the percentage of people having an IQ greater than 111 is 15.87%.
The % of people having an IQ score between the 67 and the 133 is 99.73%. The % of people having an IQ score less than the 89 or greater than 111 is 31.73%. The % of people having an IQ greater than 111 is 15.87%.
What is the percentage of the scope of the IQ test.?As per the IQ test which is done to check the intelligent quotient of a score that s derived from a standard sets of tests. They are made to test human intelligence. The IQ score falls in a bell-shaped curve with the distortion of 100 and SD of 11.
The percentage of the people having a score between the 67 and 133 was 099.7% and those between the 89 of more 111 is 31.7% and those having a greater IQ of 111 are 15.8 % that is declining to the top.
Find out more information about the IQ test.
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Which image shows a translation of the green quadrilateral JKLM three units to the right and one unit down?
Answers
Answer:
The second option shows the correct translation of 3 units to the right and 1 unit down.
g A realtor is trying to predict the selling price of houses in Greenville (in thousands of dollars) as a function of Size (measured in thousands of square feet) and whether or not there is a fireplace (FP is 0 if there is no fireplace, 1 if there is a fireplace). Part of the regression output is provided below, based on a sample of 20 homes. Some of the information has been omitted. hh Which statement is supported by the regression output? Select one: At α = .05, FP is not a significant predictor in a two-tailed test FP is a more significant predictor than Size A large house with no fireplace will sell for more than a small house with a fireplace a fireplace adds around $6476 to the selling price of the average house
Answers
Answer:
size=13.80966
Step-by-step explanation:
Missing information:
size=13.80966
Since p-value of FP is less than 0.05 so it is significant to the model.
If all other things remain constant then a fire place add approximately $6476 to the selling price of the average house. So statement "A fireplace adds around $6476 to the selling price of the average house." is supported by the model.
It is impossible to definitively determine the correct statement without the actual regression output. While we can make educated guesses about the significance of the 'Fireplace' variable and its impact on the house's selling price, further information like t-values, p-values, and standard errors is required to make a detailed and accurate estimate.
Explanation:With the information provided, it is impossible to definitively determine which of the four options are correct without the actual regression output. However, if it were provided and the p-value for the Fireplace's coefficient is higher than 0.05, we could say at α = .05, FP is not a significant predictor in a two-tailed test. If the regression coefficient for the Fireplace is $6,476 and it is significant, then a fireplace adds around $6476 to the selling price of the average house is correct. However, declaring that FP is a more significant predictor than Size or that a large house with no fireplace will sell for more than a small house with a fireplace, would require further information that goes beyond the coefficients themselves, including the standard errors, t-values, and p-values associated with each coefficient.
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Which scenarios have a negative correlation? Check all that apply. the number of calories consumed and the amount of weight lost by a person the temperature outside and the number of pool guests the number of children assigned to a class and the number of desks the price of rice and the number of penguins at the South Pole the thickness of the ice on a lake and the likelihood of falling through the ice
Answers
answer:
the first one and the last one
The correlation coefficient helps us to know how strong is the relation between two variables. The situations in which there exists a negative relationship are A and E.
What is the correlation coefficient?The correlation coefficient helps us to know how strong is the relation between two variables. Its value is always between +1 to -1, where, the numerical value shows how strong is the relation between them and, the '+' or '-' sign shows whether the relationship is positive or negative.
1 indicates a strong positive relationship.-1 indicates a strong negative relationship.A result of zero indicates no relationship at all, therefore, independent variable.A negative correlation is a relation in which as one variable increases the other decreases, therefore, there exists an inverse relationship between the two varibles.
A.) The number of calories consumed and the amount of weight lost by a person
It is known that if a person consumes more calories then he will gain more weight, therefore, the number of calories consumed and the amount of weight lost by a person have a negative correlation.
B.) The temperature outside and the number of pool guests.
If the temperature outside is more, more people will come to visit the pool. Thus, there exists a positive correlation.
C.) The number of children assigned to a class and the number of desks
The more the number of students, the more desk will be needed for them. Thus, there exists a positive correlation.
D.) The price of rice and the number of penguins at the South Pole.
The price of rice and the number of penguins at the south pole are two completely independent variables, therefore, there exists zero correlation.
E.)The thickness of the ice on a lake and the likelihood of falling through the ice.
If the thickness of the ice on a lake is more, there will be less likelihood of falling through the ice. Therefore, there exists a negative correlation.
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Answer the questions below about the function whose derivative is f prime (x )equalsStartFraction (x minus 2 )(x plus 8 )Over (x plus 1 )(x minus 5 )EndFraction , xnot equalsminus1, 5. a. What are the critical points of f? b. On what open intervals is f increasing or decreasing? c. At what points, if any, does f assume local maximum and minimum values?
Answers
Answer:
Step-by-step explanation:
a) you have that:
[tex]f'(x)=\frac{(x-2)(x+8)}{(x+1)(x-5)},\ \ x\neq -1,5[/tex]
The derivative of a function equals to zero allows you to find the critical points:
[tex]f'(x)=0\\\\(x-2)(x+8)=0\\\\x_1=2\\\\x_2=-8[/tex]
x=2,8 are the critical points
b) To know the behavior if f it is necessary to know where are f is indeterminated. The derivative give to you information about the slope of f. For x=-1,5 you have an infinite slope. Hence, for that values of x you have two indetermination s of f(x.)
However, if you see the atacched images you can obser that the original function (that is obtained with the intgegral) does not have available values for x<5 due to the logrithms. Hence, there are no critical points
The function only increases after x=5 from -infinity to +infinity
c) there are no local maximum neither local minimum
What is the slope for y= -1/2x -3
Answers
Answer:
-1/2
Step-by-step explanation:
Note the slope intercept form:
y = mx + b
y = (x , y)
m = slope
x = (x , y)
b = y-intercept.
In this case, the number that replaces the m (slope) is -1/2, which is your answer.
~
Answer:
m= -1/2
Step-by-step explanation:
This equation is in slope intercept form:
y=mx+b
where m is the slope and b is the y intercept
We have the equation:
y= -1/2x -3
If we compare the 2 equations:
y=-1/2x -3
y=mx+b
The slope must be -1/2, since x is being multiplied by -1/2
If f(x) = 3/x+2 - sqrtx-3 , complete the folowing statement f(19)=____
Answers
Answer:-27/7
Step-by-step explanation:
f(x)=3/(x+2) -√(x-3)
f(19)=3/(19+2)-√(19-3)
f(19)=3/21 - √(16)
f(19)=1/7-4/1
f(19)=(1 x 1 - 7 x 4)/7
f(19)=(1-28)/7
f(19)=-27/7
To calculate f(19), we would substitute x with 19 in the function f(x) and simplify. However, the function provided is incomplete or incorrect, and therefore, a solution cannot be confidently provided.
To solve the problem f(19), we have to substitute the value of x with 19 into the provided function f(x). However, based on the question provided, the function seems to be incomplete or incorrectly stated.
If we had a correct form of the function f(x), the process would involve replacing any instance of x with 19 and simplifying the resulting expression according to the rules of arithmetic and algebra.
Example Process with Hypothetical Function
Let's assume the function is given correctly as f(x) = 3/(x+2) - √{x-3}. Then, we would calculate:
Step 1: Substitute x with 19: f(19) = 3/(19+2) - √{19-3}
Step 2: Simplify the expression: f(19) = 3/21 - √{16}
Step 3: Complete the calculations: f(19) = 1/7 - 4
Step 4: Find the common denominator and subtract: f(19) = -27/7
However, since we do not have the correct function, I am unable to confidently provide the solution to f(19).
Please, answer, I need help.
Answers
Answer:
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Andres is offered a job as manager of a health club. The job will pay $3,100 per month, paid semimonthly. Along with the base salary, the company offers to pay half the cost of medical insurance and will match Andres' contribution to a retirement plan up to a total of $3,500. If the full cost of the medical insurance is $450 per month and Andres plans to contribute the full $3,500 every year to a retirement plan, what is the actual annual value of this job to Andres?
Answers
Andres' job has an actual annual value of $43,400. This figure was obtained by summing his base salary, the company's health insurance contribution, and the company's retirement plan contribution.
Explanation:To calculate the actual annual value of the job offer to Andres, we need to take into account his base salary, the company's contribution towards medical insurance, and the company's matching contribution to his retirement plan. Andres receives a base salary of $3,100 per month and gets paid semimonthly, which equates to an annual salary of $3,100 x 12 = $37,200.
The company pays half of Andres' $450 monthly medical insurance expense. So, that will be $450/2 = $225 per month, and over a year, that's $225 x 12 = $2,700.
Lastly, the company matches Andres' contribution to his retirement plan up to $3,500 annually.
To get the total value, add all these figures up: $37,200 (base salary) + $2,700 (health insurance contribution) + $3,500 (retirement contribution) = $43,400.
So, the actual annual value of Andres' job is $43,400.
Learn more about salary calculation here:https://brainly.com/question/35989197
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Adelia ate lunch and wanted to leave her waitress a 15% tip. her meal cost $8.95. How much money should Adeila leave for the tip?
Answers
Answer:
15% of 8.95 is 1.3425
Step-by-step explanation:
Answer:
$1.34
Hope this helped :)
which linear function has the steepest slope?
Answers
Answer:
Option A is correct.
Step-by-step explanation:
The linear function that has the steepest slope is,
Explanation:
Slope intercept form: The general formula is, where m is the slope and b is the y-intercept.
Option A:
According to slope intercept form:
Slope is -8
Similarly, for
Option B :
Slope is -2
Option C:
Slope is 7
Option D :
Slope is 6
Steepest slope defined as that is closest to being vertical.
This could be a line that is positive or negative slope respectively.
Therefore, the linear function that has the steepest slope is, option A
The steepest slope is in Option 4 with a slope of -4. Therefore, Option 4 has the steepest slope.
To determine which linear function has the steepest slope, we need to compare the slopes of the given options.
The slope of a linear function can be calculated using the formula:
[tex]\[ \text{Slope} = \frac{\text{change in } y}{\text{change in } x} \][/tex]
We will calculate the slopes for each option and compare them.
Option 1:
[tex]\[ \text{Slope} = \frac{-2 - 4}{1 - (-1)} = \frac{-6}{2} = -3 \][/tex]
Option 2:
[tex]\[ \text{Slope} = \frac{13 - 10}{6 - 3} = \frac{3}{3} = 1 \][/tex]
[tex]\[ \text{Slope} = \frac{16 - 10}{9 - 3} = \frac{6}{6} = 1 \][/tex]
[tex]\[ \text{Slope} = \frac{19 - 13}{12 - 9} = \frac{6}{3} = 2 \][/tex]
Option 3:
[tex]\[ \text{Slope} = \frac{-4 - 2}{-1 - 2} = \frac{-6}{-3} = 2 \][/tex]
Option 4:
[tex]\[ \text{Slope} = \frac{-12 - (-4)}{4 - 2} = \frac{-8}{2} = -4 \][/tex]
[tex]\[ \text{Slope} = \frac{-20 - (-12)}{6 - 4} = \frac{-8}{2} = -4 \][/tex]
[tex]\[ \text{Slope} = \frac{-28 - (-20)}{8 - 6} = \frac{-8}{2} = -4 \][/tex]
Comparing the slopes:
- Option 1: Slope = -3
- Option 2: Slopes = 1, 1, 2
- Option 3: Slope = 2
- Option 4: Slopes = -4, -4, -4
The steepest slope is the largest magnitude of slope, regardless of whether it's positive or negative. In this case, the steepest slope is in Option 4 with a slope of -4. Therefore, Option 4 has the steepest slope.
(a) What is the matrix representation of G, with vertices in numerical (ascending) order? (b) Consider using the Greedy Coloring Algorithm to color G, where the randomly generated vertex order is [4,3,1,6,7,5,2] and a randomly generated color order is [red, blue, green, purple, onyx, heather, fuchsia]. What color is the vertex 2 at the end of the algorithm?
Answers
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image below to see the step by step explanation to the question above.