How do I write the interval(s) for which f(x) is greater than or equal to 0 (interval notation)
Answers
-2. This could be expressed as (-infinity, -2). Also, all x values greater than 0 also lead to a y-value greater than 0. Thus, another interval would be (0, infinity). Thus, the answer is (-infinity, -2) and (0, infinity).
To write intervals where f(x) is greater than or equal to 0, solve the equation f(x) >= 0 for x. The solutions are then expressed in interval notation. For instance, x >= 3 is written as [3, infinity).
To write the interval for which f(x) is greater than or equal to 0 in interval notation, you first need to establish where the function is above or touching the x-axis. With algebraic functions, you simply solve the equation f(x) >= 0 for x to find where the function is non-negative. You then write these solutions in interval notation. For example, if your solution was x >= 3, you would write this in interval notation as [3, infinity). Also, keep in mind that round brackets ( ) are used when the number is not included in the interval while square brackets [ ] are used when the number is included.
Learn more about Interval Notation here:
https://brainly.com/question/31413502
#SPJ3
Related Questions
A) choose the linear model that passes through the most data points on the scatterplot.
a. true. choose the linear model that passes through the most data points on the scatterplot.
b. false. the line usually touches none of the points. minimize the sum of the squared errors.
c. false. all of the data points either touch the line or fall below the line.
d. false. the linear model line usually passes through exactly half of the data points.
Answers
Explanation:
The line of best fit to a scattergram is obtained in linear regression analysis by minimizing the sum of the squared errors.
For example, in the diagram shown below, there are n data points in the scattergram.
The error for the i-th data point is [tex]e_{i}[/tex].
The coefficients (a and b) for the line of best fit are determined using calculus, to minimize [tex]\sum_{i=1}^{n} e_{i}^{2}[/tex].
Final answer:
The correct statement relating to the selection of a linear model is that the line of best fit is found using the least-squares method to minimize the sum of squared errors. This involves plotting data points, calculating the least-squares regression line, and determining if the linear model fits the data appropriately.
Explanation:
The question pertains to the selection of a linear model based on a provided scatterplot. The correct choice is b. false. the line usually touches none of the points. minimize the sum of the squared errors. This statement refers to the concept of least-squares regression, a mathematical method used to find the line of best fit by minimizing the squared differences (errors) between the observed values and the values predicted by the model. This line is intended to predict the dependent variable based on the independent variable. The process includes plotting the data, calculating the least-squares line, and determining if the linear model is appropriate for the data set.
After plotting the data points on a scatter plot, we use a calculator or statistical software to compute the least-squares regression line, represented as ŷ = a + bx, where a is the y-intercept, b is the slope, and ŷ is the predicted value of the dependent variable for any given value of the independent variable. The line may not pass through the most data points, but instead represents the trend of the data points in a way that minimizes the overall error of the model.
The line passing through the points (-7,4) and (-23,y) is parallel to a line that has a slope of -5/8. What is the value of y?
Answers
so if this line is parallel to another with a slope of -5/8, the slope of this line is also -5/8 then. We also know that it passes through -7, 4 and -23, y, let's do some checking.
[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -7}}\quad ,&{{ 4}})\quad % (c,d) &({{ -23}}\quad ,&{{ y}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{y-4}{-23-(-7)}\implies \cfrac{y-4}{-23+7} \\\\\\ \cfrac{y-4}{-16}=\boxed{-\cfrac{5}{8}}\implies 8y-32=80\implies 8y=112 \\\\\\ y=\cfrac{112}{8}\implies y=14[/tex]
Use your calculator to evaluate the limit of x equals 1 to 3 of e raised to the x squared power, dx. Give your answer to the nearest integer.
Numerical Answers Expected!
Answers
∫1-3 e^(X^2) dx.
Solving using scientific calculator, we have 1443.082471 or simply 1443.
ANSWER: 1443
HELP WITH SOLVING SYSTEMS WITH THREE VARIABLES, WILL MEDAL
-x -y -z = -8
-4x + 4y + 5z = 7
2x + 2z = 4
I'm not sure how to work this out.
Answers
Equation 2) -4x + 4y + 5z = 7
Equation 3) 2x + 2z = 4
Solving for three variables is quite similar to solving for two variables. Just like when solving for two variables, you look for like variables & solve them one-by-one. So, let's get started! :)
Multiply ALL of equation 1 by four.
1) 4(-x - y - z = -8)
Simplify.
1) -4x - 4y - 4z = -32
Both equations 1 & 2 have the same three variables (x, y, z), so, we must look at these equations together.
1) -4x - 4y - 4z = -32
2) -4x + 4y + 5z = 7
Add these equations together, and create a fourth equation.
4) -8x - z = -25
Now, notice how both equations 3 & 4 have the same two variables (x, z).
So, we must look at these equations together.
3) 2x + 2z = 4
4) -8x - z = -25
Multiply ALL of equation 4 by 2.
4) 2(-8x - z = -25)
Simplify.
4) -16x - 2z =-50
3) 2x + 2z = 4
Now, add the equations together, so that we can solve for x.
-14x = -42
Divide both sides by -14.
x = 3
Now, plug in 3 for x into our 3rd equation.
3) 2x + 2z = 4
3) 2(3) + 2z = 4
Simplify.
6 + 2z = 4
Subtract 6 from both sides.
2z = 4 - 6
Simplify.
2z = -2
Divide both sides by 2.
z = -1
Now, plug in -1 for z & 3 for x in our 1st equation.
1) -x - y - z = -8
-(3) - y - (-1) = -8
Simplify.
-3 - y + 1 = -8
Simplify.
-2 - y = -8
Add 2 to both sides.
-y = -8 + 2
Simplify.
-y = -6
Divide both sides by -1.
y = 6
SO :
x = 3, y = 6, z = -1
~Hope I helped!~
Point F is on circle C.
What is the length of line segment GF?
a.12.5 units
b.15.0 units
c.17.5 units
d.20.0 units
Answers
Answer:
GF = 20 units .
Step-by-step explanation:
Given : A circle ,Point F is on circle C.
To find : What is the length of line segment GF.
Solution : We have given A circle ,Point F is on circle C.
In circle we can see in triangle GCE
EC = CF = 7.5
GE = 10.
By the Pythagorean theorem :
GC² = EG²+ EC².
Plugging the values
GC² = 10²+ 7.5².
GC² = 100 + 56 .25.
GC² = 156.25.
Taking square root.
GC = 12.5 units.
Radius of circle CF = 7.5 units .
GF = GC +CF.
GF = 12.5 + 7.5
GF = 20 units .
Therefore, GF = 20 units .
One third of the sum of two consecutive odd integers is five less than the smaller integer
Answers
Your answer is 17, 19
Which ordered pairs are solutions to the inequality y−4x≥−5 ?
Select each correct answer.
(5, −2)
(1, −1)
(−4, 2)
(4, 0)
(−2, 1)
Answers
The ordered pairs that satisfy the given inequality is required.
The points that are solutions are [tex](-4,2),(-2,1),(1,-1)[/tex]
The given inequality is [tex]y-4x\geq -5[/tex]
Let us substitute each point in the inequality
[tex](5,-2)[/tex]
[tex]y-4x\\ =-2-4\times 5\\ =-22\ngeq -5[/tex]
[tex](1,-1)[/tex]
[tex]-1-4\times 1\\ =-5\geq -5[/tex]
[tex](-4,2)[/tex]
[tex]2-4\times -4\\ =18\geq -5[/tex]
[tex](4,0)[/tex]
[tex]0-4\times 4=-16\ngeq -5[/tex]
[tex](-2,1)[/tex]
[tex]1-4\times -2=7\geq -5[/tex]
The points that are solutions are [tex](-4,2),(-2,1),(1,-1)[/tex]
Learn more:
https://brainly.com/question/20872996
https://brainly.com/question/12503952
Trisha needs 4 yards of fabric to do a project. If she already has of a yard of fabric, what is the minimum amount of fabric she must buy to be able to complete her project? A. 3 5/6 B.4 1/12 C.4 1/6
Answers
Answer:
The answer is A. OR 3 5/6
What is the greatest common factor of 125, 50, and 275?
Answers
Answer:
25 is the greatest common factor.
Step-by-step explanation:
We are given the following information in the question:
We have t find the greatest common factor of 125, 50 and 275.
We can use the method of prime factorization.
[tex]125 = 5\times 5\times 5\\50 = 5\times 5\times 2\\275 = 5\times 5\times 11[/tex]
Hence, the common factor of the the three numbers are:
[tex]5\times 5 = 25[/tex]
Hence, the greatest common factor 125, 50, 275 is 25.
Simplify the expression x^2+3x-28/x^2-7x+12
Answers
X^2 - 7X + 12 factors to (X-4)(X-3)
Now we see that the equation is [(X+7)(X-4)]/[(X-4)(X-3)]
By dividing the top and bottom by (X-4), we see that the equation equals (X+7)/(X-3).
Answer:
[tex]\frac{x+7}{x-3}[/tex].
Step-by-step explanation:
We have been given an expression. We are asked to simplify our given expression.
[tex]\frac{x^2+3x-28}{x^2-7x+12}[/tex]
Let us factor numerator and denominator by splitting the middle term.
[tex]\frac{x^2+7x-4x-28}{x^2-4x-3x+12}[/tex]
[tex]\frac{(x^2+7x)+(-4x-28)}{(x^2-4x)+(-3x+12)}[/tex]
Factor out GCF of each group:
[tex]\frac{x(x+7)-4(x+7)}{x(x-4)-3(x-4)}[/tex]
[tex]\frac{(x+7)(x-4)}{(x-4)(x-3)}[/tex]
Cancel out common factor [tex](x-4)[/tex]:
[tex]\frac{(x+7)}{(x-3)}[/tex]
Therefore, the simplified form of the given expression would be [tex]\frac{x+7}{x-3}[/tex].
Express terms in i square root -40
Answers
As Marta built a square fence around her garden, she wondered how much she would have to pay if she increased the length of each side of the fence by the same number of meters. Each meter of fence costs 3 dollars. Which of the following functions best describes the additional amount of money Marta will have to spend, in dollars, if she increases each side of the fence by m meters?
Answers
Suppose the she increases each side of the fence by m meters, then the total increase to the four sides of the square is given by 4m.
Given that each meter of fence costs 3 dollars, therefore, the function that best describes the additional amount of money Marta will have to spend, in dollars, if she increases each side of the fence by m meters is given by C = 12m.
Describe the translation from AB TO AB
Answers
Answer: I got A.
Step-by-step explanation:
When writing the slope as a fraction which numner goes on top?
Answers
The number goes on top tells line changes in the y direction and how much it rises.
what is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx
where, m is the slope
As, The top number indicates how much the line rises or moves in the y direction.
Given that the number is a 1 and is positive, we can infer that the line rises or moves up by one.
Hence, line changes in the y direction and how much it rises.
Learn more about slope here:
https://brainly.com/question/3605446
#SPJ5
It takes 69 pounds of seed to completely plant an 8 -acre field. how many acres can be planted per pound of seed? math
Answers
In this you simply need to divide both sides by 69:
69/69 = 1
8/69 = 0.1159...
There is no whole number for this answer.
Therefore, your answer is the value for 8/69.
Hope This Helps You!
Good Luck :)
- Hannah ❤
HELP! A daycare purchases two type of snacks, granola bars and fruit rolls. One week, they purchase 10 packs of granola bars and 6 packs of fruit rolls for a total of 152 snacks. The next week, they purchase 7 packs of granola bars and 12 packs of fruit rolls for a total of 200 snacks. How many snacks are in one pack of granola bars and one pack of fruit rolls?
Answers
5x+3y=76
7x+12y=200
-20x-12y=-304
-13x=-104
x=8
40+3y=76
3y=36
y=12
There are 8 granola bars in a pack and 12 fruit rolls in a pack
Answer: The number of granola bars in one pack = 8
The number of fruit rolls in one pack = 12
Step-by-step explanation:
Let x be the number of granola bars in each pack and y be the number of fruit rolls in each pack .
Then according to the question we have the following system of equations :
[tex]10x+6y=152.....................(1)\\7x+12y=200.......................(2)[/tex]
Multiply equation (1) by 2 we get
[tex]20x+12y=304......................(3)[/tex]
Subtract equation (2) from equation (3), we get
[tex]13x=104\\\\\Rigtarrow x=8[/tex]
Substitute x=8 in (1), we get
[tex]10(8)+6y=152\\\\\Rightarrow6y=152-80\\\\\Rightarrow\ 6y=72\\\Rightarrow y=12[/tex]
Hence, the number of granola bars in one pack = 8
The number of fruit rolls in one pack = 12
Hadlee got 18 out of 20 questions correct on her math quiz. What percent of the questions did she get right?
Answers
First divide -----> 18/20 = 0.9
Then multiply by 100 or move decimal 2 places to the right.
----> 0.9 * 100 = 90
Answer: 90%
During a certain period of time, a car can cover the distance of 120 miles, going at an average speed of 55 mph. What distance over the same period of time would cover a truck, going at an average speed of 44 mph?
Answers
Here, we're looking for the distance traveled by a truck, given only its rate, 44 mph. We're also given that both of the vehicles travel for is the same. This lets us use the car's information to find that time, which we can then use to find the distance traveled by the truck.
For the car, our distance is 120 miles, our rate is 55 mph, and our time is unknown; let's call that value [tex]t[/tex]. We have:
[tex]120=55t[/tex]
Dividing both sides by 55, we find:
[tex] \frac{120}{55}=t\\\\ \frac{24}{11}=t[/tex]
So our time is 24/11 hours - roughly 2 hours and 13 minutes. We'll use the 24/11 value to get as exact an answer as we can, though.
For the truck, we know its rate and its time (24/11 hours), but we don't know its distance. We'll call it [tex]d[/tex]. Putting in our new value for time, we have:
[tex]d=44 \big(\frac{24}{11}\big) \\ d=4(24)\\ d=96[/tex]
So, in 24/11 hours, the truck will have traveled 96 miles traveling at its average speed.
Which of the following phrases could represent the expression k - 4?
A.a number subtracted from four
B.four less a number
C.a number decreased by four
D.a number less than four
Answers
There are two phrases that can represent the expression [tex]k - 4[/tex]
→ Four less a number
or
→ A number decreased by four.
Bot option B and C are correct.
Hope I helped (:
Have a great day!
Helpp me with this word problem number one
Answers
4 1/3 x 6 1/2 =
13/3 x 13/2 = 169/6
169 divided by 6 = 28 1/6
What is the expression phrase of the sum of a number x and 4, all divided by 3?
Answers
Then you divide that sum by 3.
(x + 4)/3
Estimate the unit rate
Answers
You must have a number of miles traveled in a number of hours, or a number of items bought for so many dollars, etc.
Which of the following expressions represents the value, in dollars, of a certain number of dimes, d, and pennies, p?
0.01d + 0.10p
0.10d + 0.01p
0.11dp
0.11d + p
Answers
Then 0.10d + 0.01p is the expression
If it took eight men ten hours to build a wall, how many hours would it take four men to build it?
Answers
Hope this helps have a nice day
Now,
4men= ? hours
Since there are lesser number of men, the amount of time needed will be greater.. Thus, you need to multiply the amount of hours by 2! If you are thinking why, look at the following steps
8/2=4 (men)
10 x 2= 20(time)
Thus the answer is 20
Hope this helped :))
What is a 401(k) plan? an investment plan offered by an insurance company a retirement plan offered by employers a personal retirement plan
Answers
factor completely: x^3+8x^2+7x
Answers
x(x^2 + 8x + 7)
now it's x multiplied by a typical parabolic equation. factor this normally by seeing what multiplies to give 7 and adds to give 8.
x(x + 7)(x + 1)
20 POINTS!
Alana is writing a coordinate proof to show that the diagonals of a rectangle are congruent. She starts by assigning coordinates to a rectangle as shown. Then she uses the coordinates to write and simplify expressions for the lengths of the diagonals.
What is the length of one of the diagonals of the rectangle?
Answers
(6r^3s^5)(-2rs^3)(-r^2s)
Answers
What is 6 * (-2) * (-1) ?
Hint: negative times negative = positive.
Now multiply the variable r.
What is r^3 * r * r^2?
Hint: r alone is the same as r^1; add the exponents.
Now multiply the variable s.
What is s^5 * s^3 * s?
Hint: s alone is the same as s^1; add the exponents.
Now put it ll together.
What do you get?
Child development
What have researchers learned about the relationship between longer childhoods and brain development?
Answers
Longer childhoods are closely linked to brain development, enhancing cognitive abilities by allowing more complex neuronal connections and greater adaptation to environmental stimuli. Extended brain development is also associated with increased brain plasticity, leading to better adaptability and higher complex problem-solving skills.
Explanation:Research has found a significant relationship between longer childhoods and brain development. Humans have one of the longest childhoods among species, a period during which our brains continue to develop and mature significantly. This extended period of growth allows for more complex neuronal connections and adaptation to environmental stimuli, thus enhancing cognitive abilities.
A long childhood provides ample opportunities for learning and skill acquisition, and it is during this period that the brain is especially receptive to picking up new information. More prolonged brain development during childhood also tends to be associated with increased brain plasticity, meaning the brain's ability to change and adapt as a result of experiences. This plasticity aids in the formation of our identities and equips us to handle complex tasks and challenges as we grow.
Learn more about Long Childhoods & Brain Development here:https://brainly.com/question/32732228
#SPJ3
the diagram below shows a rectangle inside a regular hexagon . the apothem of the hexagon is 19.05 units . to the nearest square unit . what is the area of the shaded region
A. 1257
B.861
C.442
D.1653
Answers
Answer:
B. 861.Step-by-step explanation:
In the figure attached, you can observe that the shaded area can be found by calculating the difference between the area of the regular hexagon and the area of the rectangle inside.
The area of a regular hexagon is defined as
[tex]A_{hexagon} =\frac{Pa}{2}[/tex]
Where [tex]P[/tex] is the perimeter and [tex]a[/tex] is the apothem.
By given, we know that the side of the hexagon is 22 units.
Remember that the perimeter is the sum of all sides, in this case would be
[tex]P_{hexagon}=22(6) =132[/tex].
The perimeter of the hexagon is 132 units.
Therefore, the area is
[tex]A_{hexagon} =\frac{132(19.05)}{2}=\frac{2514.6}{2}=1257.3 u^{2}[/tex]
On the other hand, the area of the rectangle is defined as
[tex]A_{rectangle}=bh[/tex], where [tex]b[/tex] is the base and [tex]h[/tex] is the height. We know, by given
[tex]b=22\\h=18[/tex]
Replacing these values, we have
[tex]A_{rectangle}=bh=22(18)=396 u^{2}[/tex]
As we said before, the shaded are is defined by the following difference
[tex]A_{shaded}=A_{hexagon}-A_{rectangle}[/tex]
Replacing each area, we have
[tex]A_{shaded}=A_{hexagon}-A_{rectangle}\\A_{shaded}=1257.3u^{2} -396u^{2}=861.3 u^{2}[/tex]
Therefore, the right answer is B. 861.