The functions f(x) = x^2 – 3 and g(x) = –x^2 + 2 are shown on the graph.
Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified?
y ≤ x^2 – 3
y > –x^2 + 2
Answers
The set of inequalities y ≤ x² - 3 and y > -x² + 2 do not have a solution
How to modify the graphsFrom the graph, we have:
f(x) = x² - 3
g(x) = -x² + 2
Next, we change the equations to inequalities as follows:
y ≤ x² - 3
y > -x² + 2
To modify the graph, we then perform the following transformations:
Shift the function g(x) down by 2 unitsReflect across the x-axisShift the function g(x) down by 3 unitsHow to identify the solution setAfter the modifications in (a), we have:
y ≤ x² - 3 and y > -x² + 2
Substitute y > -x² + 2 in y ≤ x² - 3
-x² - 2 ≤ x² - 3
This gives
2x² ≤ - 1
Divide by 2
x² ≤ - 0.5
The square root of numbers less than 0 is a complex number
Hence, the set of inequalities do not have a solution
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Related Questions
Find the equation of the line that
is parallel to y = -5x – 9 and
contains the point (-3, -3).
=
-
y = [? ]X + [ ]
![Find the equation of the line thatis parallel to y = -5x 9 andcontains the point (-3, -3).=-y = [? ]X](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/GvkdTrO6vApmXQRbonThwsU7u6XrCzUv.png)
Answers
Answer:
see photo attached for detailed information
Step-by-step explanation:
![Find the equation of the line thatis parallel to y = -5x 9 andcontains the point (-3, -3).=-y = [? ]X](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/Y7uBEMLAXNntC7q0aGfREYmrOv5zIAeR.jpeg)
4 divided by 57 please help
Answers
Answer:
0.07017
Step-by-step explanation:
SOMEOne PLS EXPLAIN VERTICAL ASYMPTOTES TO ME IM DYING- i need to know how u get the asymptote(explanation) and answer T^TTTTTTTTT
Answers
In your denominator, you have (x+7)(x-5)(x-3).
What values of x makes (x+7)(x-5)(x-3)=0?
If x = -7, if x = 5, or if x = 3, then that entire expression will equal zero. (Same idea as when you solve equations by factoring.
Now the only place this can get trickier is if one of those factors — one of (x+7), (x-5), or (x-3) — also appears in the numerator. If that happens, then it’s more involved whether you have an asymptote or not. But that doesn’t happen in this example.
So the short version: Asymptotes happen when you try to divide by zero. Dividing by zero is not a good thing. So you just ask yourself, “What will make the denominator 0?”
suppose v is finite-dimensional, t 2 l.v / has dim v distinct eigenvalues, and s 2 l.v / has the same eigenvectors as t (not necessarily with the same eigenvalues). prove that st d ts.
Answers
As, stx = tsx for every eigenvector x of t, and eigenvectors corresponding to distinct eigenvalues are linearly independent, we can conclude that st = ts.
To prove that st = ts, where v is finite-dimensional, t and s are linear operators on v, t has dim v distinct eigenvalues, and s has the same eigenvectors as t (not necessarily with the same eigenvalues), we can use the fact that eigenvectors corresponding to distinct eigenvalues are linearly independent.
Let's consider an eigenvector x of t with eigenvalue λ. We can write this as tx = λx. Now, since s has the same eigenvectors as t, we can write this as sx = λx.
Now, let's consider the product stx. Using the definitions of s and t, we have stx = s(λx) = λ(sx).
Since sx = λx, we can substitute this in the above equation to get stx = λ(λx) = λ²x.
On the other hand, let's consider the product tsx. Using the definitions of s and t, we have tsx = t(λx) = λ(tx).
Since tx = λx, we can substitute this in the above equation to get tsx = λ(λx) = λ²x.
Since stx = tsx for every eigenvector x of t, and eigenvectors corresponding to distinct eigenvalues are linearly independent, we can conclude that st = ts.
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a bus arrives at 2:30 p.m. in Sydney if it left port if it left port Macquarie at 6.15 a.m the trip took
Answers
Answer:
Step-by-step explanation
Left at 6:15 am
How many hours until 2:15pm? 8 hours
How many minutes from 2:15 until 2:30? 15
So it took 8 hours and 15 minutes
What value of x makes this equation true?
15 –
1
2
x = 21
Answers
Answer:
x= -0.5
Step-by-step explanation:
You want to isolate x on one side of the equation
15-12x=21
-15 -15
-12x=6
/-12 /-12
x= -0.5
complete the following proof by dragging and dropping the correct reason in the spaces below
Answers
Two angles are said to be complementary angles if their sum is 90 degrees. Then ∠I ≅ ∠H is proved, below.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
Two angles are said to be complementary angles if their sum is 90 degrees.
∠G and ∠H are complementary angles and ∠G and ∠I are complementary angles.
Then show that ∠I ≅ ∠H
∠G + ∠H = 90° ...1
∠G + ∠I = 90° ...2
Then from equation 1 and 2, we ahve
∠G + ∠I = ∠G + ∠H
∠I = ∠H
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write a function for the graph in the form y=mx+b help fast worth 73 points i will give you brainlest
Answers
Answer:
y = 1.5x + 4.5-------------------
Use two points on the line:
(-1, 3) and (1, 6)Find the slope using slope equation:
m = (y₂ - y₁)/(x₂ - x₁)m = (6 - 3)/(1 - (-1)) = 3/2 = 1.5Find the y-intercept using the point-slope equation and one of the points, (1, 6):
y - y₁ = m(x - x₁)y - 6 = 1.5(x - 1)Convert it into slope-intercept form:
y - 6 = 1.5x - 1.5y = 1.5x + 4.5Question 5 Rocko paid $12.50 for 25 game tickets. Louisa paid $17.50 for 35 game tickets. What is the constant of proportionality? Express your answer in decimal form.
Answers
Answer: k = $0.50
Step-by-step explanation:
The data that we have is:
Rocko paid: $12.50 for 25 tickets.
Louisa paid: $17.50 for 35 tickets.
Now, the question asks to find the constant of proportionality.
A proportional relation can be written as:
y = k*x
where k is the constant, and in this case, y is the price and x the number of tickets bought.
Then replacing with the values above, we have:
$12.50 = k*25
then:
k = $12.50/25 = $0.50
And the other data:
$17.50 = k*35
K = $17.50/35 = $0.50
So we have the same k in both cases, this means that the constant of proportionality is k = $0.50
plsss HELP ANYONE PLSSS !
Answers
Answer:
can be fourth one cause it starts at 2 on y axis. ( fourth option)
Step-by-step explanation:
can't be the first one cause it starts at origin
can't be second one cause it starts at -2 on x axis
can't be third on cause it starts on 2 on x axis
can't be fifth cause it starts on -2 on y axis.
evaluate the integral. 1 (7 − 8v3 16v7) dv 0
Answers
The evaluated integral is: ∫₀¹ (7 - 8v³ + 16v⁷) dv = 7.
To clarify, the integral we are evaluating is:
∫₀¹ (7 - 8v³ + 16v⁷) dv
To evaluate this integral, follow these steps:
Step 1: Break the integral into smaller integrals for each term:
∫₀¹ 7 dv - ∫₀¹ 8v³ dv + ∫₀¹ 16v⁷ dv
Step 2: Integrate each term separately:
For the first integral: ∫₀¹ 7 dv = 7v | evaluated from 0 to 1
For the second integral: ∫₀¹ 8v³ dv = (8/4)v⁴ | evaluated from 0 to 1
For the third integral: ∫₀¹ 16v⁷ dv = (16/8)v⁸ | evaluated from 0 to 1
Step 3: Evaluate each term at the bounds (1 and 0) and subtract:
7(1) - 7(0) = 7
(8/4)(1)⁴ - (8/4)(0)⁴ = 2
(16/8)(1)⁸ - (16/8)(0)⁸ = 2
Step 4: Combine the results:
7 - 2 + 2 = 7
So the evaluated integral is:
∫₀¹ (7 - 8v³ + 16v⁷) dv = 7
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in a situation where the sample size was 28 while the population standard deviation was increased, what would be the impact on the confidence interval?
Answers
if the population standard deviation is increased while the sample size is 28, the confidence interval will become wider. This is because there is more variability in the sample mean, and therefore more uncertainty in the estimate of the population parameter.
If the sample size is 28 and the population standard deviation is increased, there will be a direct impact on the confidence interval. This is because the confidence interval is calculated based on the sample mean and the standard deviation. If the population standard deviation is increased, it means that there is more variability in the population. This increase in variability will lead to wider confidence intervals.
A confidence interval is a range of values that is likely to contain the true population parameter with a certain level of confidence. The width of the confidence interval is determined by the sample size, the standard deviation, and the level of confidence.
In this case, if the population standard deviation is increased, it means that the sample standard deviation will also increase. The sample mean will be relatively more variable than it would be if the population standard deviation was lower. This increase in variability will cause the confidence interval to become wider, as there is more uncertainty in the estimate of the population parameter.
In summary, if the population standard deviation is increased while the sample size is 28, the confidence interval will become wider. This is because there is more variability in the sample mean, and therefore more uncertainty in the estimate of the population parameter. It is important to note that increasing the sample size can help to reduce the impact of increased population standard deviation on the confidence interval, as a larger sample size provides more accurate estimates of the population parameter.
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Two mechanics, Martin and Gordon, are working on your car. Martin can complete the work in 4 hours, while Gordon can complete the work in 2 hours. How many hours does the maintenance take if they work together?
Answers
Answer: 4/3 hours or 1 1/3 hours
Step-by-step explanation:
From the question, we are told that two mechanics, Martin and Gordon, are working on your car. Martin can complete the work in 4 hours, while Gordon can complete the work in 2 hours.
Since Martin can complete the work in 4 hours, that means in 1 hour, he will do 1/4 of the work.
Since Gordon can complete the work in 2 hours, that means in 1 hour, he'll do 1/2 of the job.
When they both work together, we will add their fraction of work done in one hour together. This will be:
= 1/4 + 1/2
= 3/4
This means that both of them will do 3/4 of the job in one hour. Then to get the time taken to get the whole job done, we divide 1 by 3/4. This will be:
= 1 ÷ 3/4
= 1 × 4/3
= 4/3 hours
= 1 hour 20 minutes.
In one
someone help me quickly
Answers
A factory makes 23 fear of rope
per minute. How mary text of rope
will the factory make in 7 minutes,
Answers
Answer: 2346
Step-by-step explanation:
Evaluate
7/8
×
16/35
Give your answer in its simplest form.
Answers
Answer:
2/5 thats the answer i think
Answer:
2/5
Step-by-step explanation:
\(\frac{7}{8}\)×\(\frac{16}{35}\)
7×16=112
8×35=280
Simplify:
\(\frac{112}{280}\) 112÷4=28 280÷4=70
\(\frac{28}{70}\) Continue simplifying → 28÷2=14 70÷2=35 14/35 continue simplifying 14÷7=2 35÷7=5 2/5 You cannot continue simplifying.
So, \(\frac{2}{5}\) is the answer.
Express 1.2, 2.25, 3.5, 4.06 as a fraction in its simplest form
Answers
Answer:
1.2 = 12/10 = 6/5
2.25 = 225/100 = 9/4
3.5 = 35/10 = 7/2
4.06 = 406/100 = 203/50
Which techniques can be used to evaluate the expression 12.75 = 1.5? Select all that apply.
Answers
The evaluation of the expression 12.75 ÷ 1.5 is 51 / 6.
How to evaluate expression?To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.
Therefore, let's evaluate the expression as follows:
Hence,
12.75 ÷ 1.5
Let's convert each decimal to fractions for easy evaluation
Therefore,
12.75 = 1275 / 100
1.5 = 15 / 10
Therefore,
1275 / 100 ÷ 15 / 10
Let's change the division sign to multiplication sign.
1275 / 100 × 10 / 15
1275 / 150
Therefore,
255 / 30 = 51 / 6
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-21.5%, 1/3, -4/5, 1.3, 4.5%, -0.04
Pls help I need order from greatest to least
Answers
Answer:
Sure, here are the numbers arranged from greatest to least
Step-by-step explanation:
Order from greatest to least
1.3, 4.5%, 1/3, -4/5, -0.04, -21.5%
Answer:
From the greatest to least
Step-by-step explanation:
1.3, 4.5%, 1/3, -4/5, -0.04, -21.5%
You can identify which number is greater than other by using a number line.
What is a number line?
A number line is what a math student can use to find the answer to addition and subtraction questions. A straight line, theoretically extending to infinity in both positive and negative directions from zero, that shows the relative order of the real numbers.
Hope this helps :)
Pls Brainliest...
plot the raw data for anulli and mass for all turtles as well as each of these new models on the same plot.
Answers
To plot the raw data for annuli and mass for all turtles, as well as each of the new models, you can use a scatter plot. The x-axis will represent the annuli, while the y-axis will represent the mass. Each point on the scatter plot will represent a turtle's data point. To differentiate between the different models, you can use different colors or markers for each model's data points. This will allow you to visually compare the raw data with the different models on the same plot.
In the scatter plot, the x-axis represents the annuli, which are the rings found on a turtle's shell. The y-axis represents the mass, which is the weight of the turtle. Each point on the scatter plot represents the annuli and mass data for a specific turtle. By plotting the raw data for all turtles and the new models on the same plot, you can compare how well the models fit the actual data. Using different colors or markers for each model's data points will make it easier to differentiate between them. This plot will help you visually analyze the relationship between annuli and mass for the turtles and evaluate the performance of the models.
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Bridget has swimming lessons every fifth day and diving lessons every third day. If she had a swimming lesson and a diving lesson today, how many days will be till the next date on which she has both swimming and diving lessons?
Answers
Answer:
15 days
Step-by-step explanation:
Take LCM of 3 and 5 and u get your answer
A triangular pane of glass has a height of 48 inches and an area of 576 square inches. What is the length of the base of the pane?
URGENT
Answers
Answer:
12
Step-by-step explanation:
Solution:
We know that:
Area of triangular pane = 576 in²Height of triangular pane = 48 inArea of triangle formula = 1/2 x Base x AltitudeSubstituting the height and the area of the pane in the formula
Area of triangle = 1/2 x Base x Altitude = 576 in²1/2 x Base x 48 = 576 in²Simplifying the LHS:
1/2 x Base x 48 = 576 in²Base x 24 = 576 in²Dividing 24 both sides
(Base x 24)/24 = 576/24Base = 576/24 = 24 inThus, the measure of the base is 24 inches.
How can you represent writing a check of$10 as an integer
Answers
Answer:
Step-by-step explanation:
La cantidad numérica es donde escribes la cantidad del cheque con números/dígitos. Escribe los dólares en forma numérica y luego indica los centavos después del punto decimal. En el ejemplo a continuación, los dólares son ciento veinticinco (125) y los centavos son setenta y cinco (. 75).
ezra determined that the graph shown below is vertically compressed by a factor of 1/3 from the graph of y=|x| do you agree or disagree? why?
Answers
Answer:
Step-by-step explanation:
no graph was shown
A bookstore had 70 copies of a magazine. Yesterday, it sold 1/5 of them. Today, it sold 5/7 of what remained. How many copies does the bookstore have left?
Answers
Answer: 16
Step-by-step explanation:
1/5 x 70 = 14
70 - 14 = 56
5/7 x 56 = 40
56 - 40 = 16
Answer:
16
Step-by-step explanation:
Yesterday, the bookstore sold 1/5 of the 70 copies, which is 70 * 1/5 = 14 copies.
After selling 14 copies, the bookstore was left with 70 - 14 = 56 copies.
Today, the bookstore sold 5/7 of what remained, which is 5/7 * 56 = 40 copies.
So, the bookstore has 56 - 40 = 16 copies left.
The main idea behind statistical inference is that: a. without statistics we would have no way of determining if an effect is taking place in any given experiment. b. through the transformation of data we can derive many conclusions about our sample.
c. through the use of sample data we are able to draw conclusions about the population from which the data was drawn. d. when generalizing results to a population you must make sure that the correct statistical procedure has been applied.
Answers
The main idea behind statistical inference is that through the use of sample data, we are able to draw conclusions about the population from which the data was drawn (option c).
Statistical inference allows us to make inferences and draw conclusions about a larger population based on the analysis of a smaller representative sample.
By collecting data from a sample, we can use statistical methods to analyze and summarize the information. These methods include estimating population parameters, testing hypotheses, and making predictions.
The key assumption underlying statistical inference is that the sample is representative of the larger population, allowing us to generalize the findings to the population as a whole.
Statistical inference provides a way to make reliable and informed decisions, identify patterns and relationships, and make predictions about future observations based on the available data. It allows researchers, scientists, and decision-makers to make evidence-based conclusions and draw meaningful insights from limited observations.
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Find the slope passing the line (3,4) and (8, -3)
Answers
Answer: -1 2/5 i think im not sure (check explaination)
Step-by-step explanation:
slope formula= y2-y1/x2-x1
-3-4/8-3=-7/5,-1 2/5
help for 50 points!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
The slope of the line given the information in the table is 1.
What is the slope?The slope is found in linear functions. The slope measures the rate of change of the dependent variable with respect to the independent variable. In this question, the independent variable is x and the dependent variable is y.
Slope = change in the value of y / change in the value of x
Slope = (0 - - 1) / (1 - 0) = 1
Slope = (1 - 0) / (2 - 1) = 1
Slope = (2 -1 ) / (3 - 2) = 1
Based on the value of the slope, it means that for every one percent change in the value of x, the value of y changes by 1%.
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Answer:
Step-by-step explanation:
look at the x and axis and the irrational fractions and you should find your slope
plz help me with this math questionnnnn
Answers
Answer:
n ≤ 4
Step-by-step explanation:
Which means you should start at four (make sure it's a close circle) pointing to the left. I hope it helps.
The length of the highway is 600 miles. If 2 inches represent 75 miles, what is the length of the highway on the map?
Answers
Answer:
16 inches
Step-by-step explanation:
The variables in this equation are miles and inches. You're given the ration 2 inches: 75 miles. Take the other factor that you are given, which for this problem would be 600 miles, and divide it by the number with the same variable, which would be 75 miles. This comes out to be 8, to which you then multiply that by the number with the variable that you are trying to find, which is two. Therefore, the length of the highway on the map would be 16 inches.