So on solving the provided question, we can say that by unitary method task done of 15 days done = 7/5 X 15hours = 21 hours
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
here,
task done of 5 days done = 7 hours.
task done of 1 days done = 7/5 hours.
task done of 15 days done = 7/5 X 15hours = 21 hours
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try these amc 8 algebra questions and check your knowledge! amc 8,2020 problem 1 luka is making lemonade to sell at a school fundraiser. his recipe requires 4 times as much water as sugar and twice as much sugar as lemon juice. he uses 3 cups of lemon juice. how many cups of water does he need?
He need 12 cup of water.
What is algebra?Algebra is a branch of mathematics that studies the manipulation of symbols in equations. It is used to solve problems involving unknowns, such as finding the solution to equations or determining the unknown value of a variable. Algebra is used in many areas of mathematics, science, and engineering. It is also used to understand and analyze functions, graphs, and other mathematical relationships. Algebra has applications in fields such as finance, physics, chemistry, and engineering.
To solve this problem, we can set up a proportion. Since the ratio of water to sugar is 4 to 1, and the ratio of sugar to lemon juice is 2 to 1, we can write the proportion 4/1 = 2/x, where x is the amount of water. Solving for x, we get x = 4/2 = 2. Multiplying this by the amount of lemon juice, 3 cups, gives us our answer of 12 cups of water.
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Write the equation of this line in slope-intercept form.
Answer:
Step-by-step explanation:
m= 3/1
y-int=-5
A water bottle holds 56oz. Each time Anna takes a sip she drinks 8oz.
a) Write a function to represent the scenario
b) How many sips can Anna take before she needs to refill?
c) Create a graph to represent this situation.
d) What is the domain in set notation of the function?
Answer:
a) The function to represent the scenario would be:
f(x) = 56 - 8x
b) To find out how many sips Anna can take before she needs to refill, we need to find when the water bottle is empty.
To do this, we can set f(x) = 0 and solve for x:
0 = 56 - 8x
8x = 56
x = 7
So, Anna can take 7 sips before she needs to refill.
c) A graph to represent this situation would be a straight line with a slope of -8 and y-intercept of 56.
d) The domain of the function is the set of all possible input values, or in this case, the number of sips Anna takes.
As Anna can take any whole number of sips, the domain of the function is the set of all non-negative integers:
{x | x ∈ Z, x ≥ 0}
We can represent how many sips Anna takes from her water bottle with the function y = 56 - 8x. Anna can take 7 sips before she needs a refill. The graph of this function is a straight line that starts at (0, 56) and ends at (7, 0). The domain in set notation is {x|x is an integer and 0 <= x <= 7}.
Explanation:a) We can represent this scenario with a function, where the amount of water in the bottle depends on how many sips Anna has taken. This is a linear function because each sip Anna takes decreases the amount of water in the bottle by a constant amount. The function could be written as: y = 56 - 8x, where y represents the amount of water in the bottle, and x represents the number of sips Anna has taken.
b) To find out how many sips Anna can take before she needs to refill the bottle, we set y to 0 in our function: 0 = 56 - 8x. Solving for x gives us x = 7. Therefore, Anna can take 7 sips before she needs to refill the bottle.
c) A graph representing this situation would be a straight line starting at (0, 56) on the y-axis, and going down 8 units for each step along the x-axis, until reaching x=7.
d) The domain in set notation for this function would be {x|x is an integer and 0 <= x <= 7}.
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a shipment of 2000 tire pressure gauges arrives at an automotive company warehouse. fifty of the tire gauges are randomly selected from various parts of the shipment and the percent of those that are defective is determined. if this percentage is greater than 5%, the shipment is sent back. which of the following is the population of interest for this example? a. all tire pressure gauges c. the 2000 tire gauges in the shipment b. the 50 randomly selected tire gauges d. 5% of the tire gauges in the shipment
The population mean of interest for this example is all of the tire pressure gauges in the shipment of 2000.
1. The problem states that 2000 tire pressure gauges were shipped to an automotive company warehouse.
2. Fifty of the tire gauges were randomly selected from various parts of the shipment and the percent of those that were defective was determined.
3. If the percentage of defective tire gauges was greater than 5%, the shipment was sent back.
4. Therefore, the population of interest for this example is all of the tire pressure gauges in the shipment of 2000.
This example involves an automotive company warehouse receiving a shipment of 2000 tire pressure gauges. Fifty of the tire gauges were randomly selected from various parts of the shipment and the percent of those that were defective was determined. If the percentage of defective tire gauges was greater than 5%, the shipment was sent back. Therefore, the population of interest for this example is all of the tire pressure gauges in the shipment of 2000 since this is the sample from which the percentage of defective gauges was determined.
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if you went to college and earned a four-year degree, how much more money would you expect to earn each year than if you did not graduate from high school?
If you went to college and earned a four-year degree, then 70% more money would you expect to earn each year than if you did not graduate from high school.
The pursuit of a college education is such a crucial life goal that it has taken center stage in the "American Dream." Attend college, secure a career, purchase a home, and start a family. Even if it isn't usually that easy, it all begins with your college education.
According to a study conducted across the country and released by the State Higher Education Executive Officers Association (sheeo.org), the average pay for high school graduates is close to $30,000. Graduates with a bachelor's degree typically make a little over $50,000 per year.
The average annual salary for those with higher level degrees (master's, doctoral, or professional) is also close to $70,000. This results in a sizable wage discrepancy over the course of a person's lifetime.
Hence, if you went to college and earned a four-year degree, then 70% more money would you expect to earn each year than if you did not graduate from high school.
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At what points do the graphs of y=2x+1 and y=-(x-1)^2+3 intersect?
A. (-3,5) and (1,3)
B. (-2,-6) and (2,2)
C. (-1,-1) and (1,3)
D. (1,3) and (3,7)
Answer:
D. (1,3) and (3,7)
Step-by-step explanation:
The graphs of y = 2x + 1 and y = -(x-1)^2 + 3 intersect at the points where they have the same y-coordinate. To find these points, we can set the two equations equal to each other and solve for x.
y = 2x + 1 = -(x-1)^2 + 3
2x + 1 = -x^2 + 2x + 2
x^2 - 4x + 1 = 0
(x-1)^2 = 0
x = 1
Now we can substitute this value of x into either of the given equations to find the corresponding y-coordinate.
y = 2x + 1 = 2(1) + 1 = 3
so the point of intersection is (1,3)
So the answer is D. (1,3) and (3,7)
Please note that the solution is valid only if the two equations y=2x+1 and y=-(x-1)^2+3 are defined for the same domain.
does part 95.987 mean i can use my 10 meter radio on cb, so long as i follow the rules on frequency, and power?
No, You cannot use your 10 meter radio on CB (citizen’s band), so long as you follow the rules on frequency, and power.
What is Citizen's Band?A public, two-way personal radio service is the Citizen's Band (CB) Radio Service, usually abbreviated as CB. There are various categories for CB operating. The most popular CB method is voice communication, which rose to popularity in the 1970s. Mobile CB operating is still common, particularly in automobiles and trucks. The majority of CB operating occurs in a constrained range of frequencies around 27 MHz. This band contains 40 channels. There is excessive channel saturation.
A CB (citizen’s band) radio must be FCC type approved. Of course, I have no idea where you are, so maybe, where you are, it is ok. In the US however, CB radios are not to be “easily modified” neither to increase power out nor to allow operation outside the citizen’s band frequencies. Even as an extra class amateur radio licensee, I may not use a modified radio on the CB band. I am allowed, however to modify a CB radio to operate on amateur radio bands.
You cannot use your 10 meter radio on CB (citizen’s band), so long as you follow the rules on frequency, and power.
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How many days is 18,000 seconds?
That's 0.20833 of one day./
(5/24 of a day)
x² - 4x-20 = 0 pls help
Answer:
Step-by-step explanation:
x=2+2[tex]\sqrt{6}[/tex] or x=2-2[tex]\sqrt{6}[/tex]
I really need help with a math problem please look in the photo and help
f(g(7))
First look at the g(x) table:you can see that f(7) = 4, so plug in f(7) = 4 in the equation
Left with f(4)Now look for f(x) table:you can see that f(4) = 9
Answer to this function is 9 A)
Hope it helps!
Suzie has $9,126 in an account. The interest rate is 10% compounded annually.
To the nearest cent, how much will she have in 5 years?
Answer: $14697.51
Step-by-step explanation:
[tex]9126(1+0.10)^{5} \approx \$14697.51[/tex]
help me please!!! i will give brainliest
The linear equation on the graph is the one in the last option, it is:
y = 6x
Which equation is the graphed one?A general linear equation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
First, we can see that the line passes through the point (0, 0), thus the y-intercept is b = 0.
We can write:
y = a*x
We also can see that the line passes through the point (1, 6)
Replacing these values we will get:
6 = a*1
6/1 = a
6 = a
Then the linear equation is:
y = 6x
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The graph shows the population y of a certain city over the course of 10 years x. The equation of the trend line shown is y=1.9x+21. Answer parts a and b. Click the icon to view the scatter plot. Question content area bottom. The population will reach 52,900 during year 16. Part 2 b. In the tenth year, the population was actually 2,000 people from what the trend line shows. What could the actual number of people be in 10 years?
The actual number of people could be _ or _
(Use ascending order. Round to the nearest thousand as needed.)
The actual number of people in 10 years could be 57,000 or 56,000. The equation of the trend line is y=1.9x+21, so for any year x, the population y can be found using this equation. To find the population in 16 years, when the population is 52,900, we can plug in x=16 and solve for y to find y=52,900. To find the population in 10 years, when the population is 2,000 people from what the trend line shows, we can plug in x=10 and solve for y to find y=50,900. Since the population should be 2,000 more, the actual population in 10 years is either 57,000 (50,900 + 2,000) or 56,000 (50,900 + 1,000).
Answer:
Part A is 16
Step-by-step explanation:
for the line segment below, the ratio of the length of mn to the length of no is 3:7. if it can be determined, what is the ratio of the length of mn to the length of mo ?
For the line segment MO, the ratio of the length of MN to length of NO is 3 : 7. The ratio of the length of MN to length of MO is 3 : 10.
Ratio or proportion is the relation describing the size, quantity, or the amount of two or more variables.
For example, the ratio of sugar and flour in a cake dough is 1 : 2. It means, if there is 200 grams of sugar in the dough, the amount of flour is 2 x 200 = 400 grams.
In the given problem, the ratio of length MN to the length NO is 3 : 7.
Notice that:
MO = MN + NO
Hence, the ratio of the length of MN to the length of MO is:
MN : MO = MN : (MN + NO)
MN : MO = 3 : (3 + 7)
MN : MO = 3 : 10
The picture in your question is missing. Most likely it was like the one in the attached picture.
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449 students were surveyed about their preferences of sports. 146 students like football, 107 students like baseball, and 49 students like both sports. how many students like exactly one of the two sports?
449 students were surveyed about their preferences for sports. 146 students like football, 107 students like baseball, and 49 students like both sports. there are 293 students like exactly one of the two sports.
This can be determined by subtracting the number of students who like both sports (49) from the total number of students surveyed (439). This leaves us with 390 students who like either football, baseball, or both. To find the number of students who like exactly one of the two sports, we will need to subtract the number of students who like both sports from the number of students who like either football or baseball.
To do this, we add together the number of students who like football (146) and the number of students who like baseball (107). This gives us 253 students who like either football or baseball. Subtracting this number (253) from the number of students who like either sport (390) gives us the number of students who like exactly one of the two sports (293).
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find the vectors t, n, and b at the given point. r(t) = (t^2, 2/3 t^3, t), (4, 16/3 , -2)
At the given point, (4, 16/3 , -2), the vectors t, n, and b are (2, 4, -1), (16, -8, 4), and (-32, 8, 8), respectively.
What is vector?Vector is a mathematical element that has both magnitude and direction. It is used to represent quantities such as velocity, force, acceleration, and displacement. Vector is used in physics and engineering for computing physical quantities. Vector is also used in computer graphics for representing shapes, lines, and curves. Vector can also be used in economics for representing stocks and bonds.
The vector t is the direction vector of the parametric function r(t). It is found by taking the derivative of the parametric equation:
t = (2t, 2t^2, 1)
The normal vector n is found by taking the cross product of the curvature vector and the direction vector. The curvature vector is found by taking the second derivative of the parametric equation.
k = (2, 4t, 0)
n = (4t, -2, 2)
The binormal vector b is found by taking the cross product of the direction vector and the normal vector.
b = (-8t, 4, -4t)
At the given point, (4, 16/3 , -2), the vectors t, n, and b are (2, 4, -1), (16, -8, 4), and (-32, 8, 8), respectively.
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DEDUCTIVE OR INDUCTIVE?
1. 2, 4, 6, 8. The next number is 10.
A. Inductive Reasoning
B. Deductive Reasoning
2. All plants need water. Water Hyacinth is a plant. Therefore, Water Hyacinth need water.
A. Inductive Reasoning
B. Deductive Reasoning
3. The next square has 16 dots.
A. Inductive Reasoning
B. Deductive Reasoning
4. A child’s teacher in pre-school is a female. In his grade 1 and 2, his teacher were both female. The child may say that her/his next teacher is female.
A. Inductive Reasoning
B. Deductive Reasoning
5. All football players are muscular. Peter is muscular. Therefore, Peter is a football player.
A. Inductive Reasoning
B. Deductive Reasoning
The answer to the first, third and fourth part is inductive reasoning and the answer to the second and fifth part is deductive reasoning.
The first example is an example of Inductive reasoning because it is based on a pattern or trend of a sequence of numbers (2, 4, 6, 8) and uses that pattern to make a prediction or generalization about the next number in the sequence (10). This is a common use of inductive reasoning, where observations or data are used to make generalizations about future events or situations.
The second example is an example of Deductive reasoning because it starts with a general statement (all plants need water) and applies it to a specific case (Water Hyacinth) to reach a logical conclusion (Water Hyacinth needs water). This is the classic form of deductive reasoning, where the conclusion follows logically from the premises and can be proven to be true if the premises are true.
The third example is an example of Inductive reasoning because it is based on a pattern or trend of a sequence of numbers (dots in squares) and uses that pattern to make a prediction or generalization about the next number in the sequence (16 dots in the next square).
The fourth example is an example of Inductive reasoning because it is based on a pattern or trend of a sequence of events (pre-school, grade 1, grade 2) and uses that pattern to make a prediction or generalization about the next event in the sequence (the child's next teacher will be female).
The fifth example is an example of Deductive reasoning because it starts with a general statement (all football players are muscular) and applies it to a specific case (Peter) to reach a logical conclusion (Peter is a football player). This is the classic form of deductive reasoning, where the conclusion follows logically from the premises and can be proven to be true if the premises are true.
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write an expression to represent the sum of three consecutive odd integers in which n is the least number.
An expression to represent the sum of three consecutive odd integers is 3n + 3
The term expression in math is known as a sentence with a minimum of two numbers or variables and at least one math operation.
Here we have given that an expression to represent the sum of three consecutive odd integers in which n is the least number.
As here we have given that since the smallest integer is n,
And then it can be written as n+1 and n + 2 are the consecutive integers after that.
And then finally here we have to know that if you add them all up, then it becomes (n) + (n+1)+(n + 2) or simply 3n+3.
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PART 2 : Show your work for the equation gives the exact answer do not approximate :)
The value of x is equal to 0.660441.
what is the logarithmic function?In mathematics, the logarithmic function is an inverse function to exponentiation. The logarithmic function is defined as For x > 0, a > 0, and a ≠1, y= logₐ x if and only if x = a^y Then the function is given by f(x) = logₐ x The base of the logarithm is a. This can be read it as log base a of x.
Given here: The exponential function 2(3e)ˣ=8
Simplifying further we get, (3e)ˣ=4
Taking log both sides we get x (ln3+1)=ln4
x×2.0986=1.386
x=0.660441
Hence, The value of x is equal to 0.660441.
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given rectangular grid nxm starting at position (x1,y1) you are trying to reach (x2,y2) return number of steps it takes to get there. code signal
Given an infinite grid, initial cell position (x, y) and a sequence of other cell position which needs to be covered in the given order.
The task is to find the minimum number of steps needed to travel to all those cells.
Note: Movement can be done in any of the eight possible directions from a given cell that is from cell (x, y) you can move to any of the following eight positions:(x-1, y+1), (x-1, y), (x-1, y-1), (x, y-1), (x+1, y-1), (x+1, y), (x+1, y+1), (x, y+1) is possible
Examples:
Input: points[] = [(0, 0), (1, 1), (1, 2)]
Output: 2
Move from (0, 0) to (1, 1) in 1 step(diagonal) and
then from (1, 1) to (1, 2) in 1 step (rightwards)
Input: points[] = [{4, 6}, {1, 2}, {4, 5}, {10, 12}]
Output: 14
Move from (4, 6) -> (3, 5) -> (2, 4) -> (1, 3) ->
(1, 2) -> (2, 3) -> (3, 4) ->
(4, 5) -> (5, 6) -> (6, 7) ->
(7, 8) -> (8, 9) -> (9, 10) -> (10, 11) -> (10, 12)
Since all the given points are to be covered in the specified order.
Find the minimum number of steps required to reach from a starting point to next point, then the sum of all such minimum steps for covering all the points would be the answer.
One way to reach from a point (x1, y1) to (x2, y2) is to move abs(x2-x1) steps in the horizontal direction and abs(y2-y1) steps in the vertical direction, but this is not the shortest path to reach (x2, y2).
The best way would be to cover the maximum possible distance in a diagonal direction and remaining in horizontal or vertical direction.
If we look closely this just reduces to the maximum of abs(x2-x1) and abs(y2-y1).
Traverse for all points and summation of all diagonal distance will be the answer.
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Vertical and Adjacent Angles. What is the value of x?
120°
(6x)
Answer: x=10
Step-by-step explanation:
120=6x
120+6x=+180=360
300+6x=360
6x=60
x=10
Can anyone help me please
Answer:
2
Step-by-step explanation:
-4+6=2
A sports marketing company is interested in how many hours teenagers in a town spend watching sports. They randomly select 40 teenagers in this town and ask how many hours per week they spend watching sports. The mean amount is 6.25 hours with a standard deviation of 4.33 hours. Which of the following is the 90% confidence interval for the true mean amount of time teenagers from this town watch sports
(5.097, 7.404) is the 90% confidence interval for the true mean amount of time teenagers from this town watch sports. This can be solved using the concept of standard deviation.
What is standard deviation?Data dispersion in regard to the mean is quantified by a standard deviation, or "σ". Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.
Because it makes measures easier to comprehend when the data is spread, standard deviation is significant. The data's standard deviation will increase as the data's distribution becomes more widely scattered. The deviation of each observed value from the mean is measured using this metric. The majority of data in any distribution will fall within a 2 standard deviation range of the mean.
Thus, (5.097, 7.404) is the 90% confidence interval for the true mean amount of time teenagers from this town watch sports.
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The complete question is as follows:
A sports marketing company is interested in how many hours teenagers in a town spend watching sports. They randomly select 40 teenagers in this town and ask how many hours per week they spend watching sports. The mean amount is 6.25 hours with a standard deviation of 4.33 hours. Which of the following is the 90% confidence interval for the true mean amount of time teenagers from this town watch sports?
Find the t-table here.
(4.396, 8.104)
(4.865, 7.635)
(5.097, 7.404)
(5.245, 7.256)
In the figure below, which term best describes point W?
A. Incenter
B. Centroid
C. Orthocenter
D. Circumcenter
Answer:
a is the correct answer because it is in the center of the shape
Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2, and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold.
Graph the function. On the graph, make sure to label the intercepts. You may graph your equation by hand on a piece of paper.
The graph of 2x + 3y = 1470 have a y intercept of 490
What is an equation?An equation is a expression that shows the relationship between numbers and variables.
The standard form of a linear equation is:
y = mx + b
Where m is the rate of change and b is the y intercept
Let x represent the number of sandwich and y represent the number of wraps.
The profit on every sandwich is $2, and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. Hence:
2x + 3y = 1470
The graph is attached
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what is the end behavior of:
1. [tex]\sqrt{6x}[/tex]
2. [tex]\sqrt{x-5}-6[/tex]
3. [tex]-3\sqrt{x+3}+7[/tex]
In the given question, none of the function exhibits an end behavior
What is End Behavior of a PolynomialThe end behavior of a polynomial is the way the graph of the polynomial behaves as the input values become very large or very small. Generally, the end behavior of a polynomial is either up, down, or a combination of both. If the highest degree term has a positive coefficient, the end behavior is up; if the highest degree term has a negative coefficient, the end behavior is down. If the highest degree term has a coefficient of zero, the end behavior is a combination of up and down.
In the functions given, we can find the end behavior of each of these functions.
1)
y = √x
The leading coefficient test requires a polynomial and this function is not a polynomial.
2)
y = √(x - 5) - 6
The leading coefficient test requires a polynomial and this function is not a polynomial.
3)
y = -3√(x + 3) + 7
The leading coefficient test requires a polynomial and this function is not a polynomial
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Please answer my question.
The solution is Option B , Option D.
The equations are z/6 + w = 11 and 5y + 4 = 16 + y
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
a)
( 10 + a ) / ( 3a + 1 )
Now , it is an expression because the "=" sign and terms on both sides must always be present when writing an equation.
b)
z/6 + w = 11 be equation (1)
Now , the equation is having = sign along with coefficients and variables
c)
( z-2 ) / 3 < 15
The < sign represents an inequality relation
So , it is not an equation
d)
5y + 4 = 16 + y be equation (2)
Now , the equation is having = sign along with coefficients and variables
e)
x² + 3x + 7
Now , it is an expression because the "=" sign and terms on both sides must always be present when writing an equation.
f)
5y + 1 ≤ y
The ≤ sign represents an inequality relation
So , it is not an equation
Hence , the equations are solved
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What is a 1/2 percentage?
Answer:
50%
1 2 = 1 × 50 2 × 50 = 50 100 . . So the answer is 50%
please mark me as a brainalist
If $m$ is a real number and $2x^2 mx 8$ has two distinct real roots, then what are the possible values of $m$
The possible values of [tex]$m$[/tex] are all real numbers greater than [tex]$\frac{2}{x^2}$[/tex]
A quadratic equation is an equation of the form ax² + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. It is called a quadratic equation because the highest degree of its unknown variable (x) is two. The solutions of a quadratic equation can be found by solving the equation using the quadratic formula, factoring, or graphing. Quadratic equations are used in many areas of mathematics, from basic algebra to differential equations.
Let [tex]$y = 2x^2mx8$[/tex]
The two distinct real roots of the equation imply that y is a quadratic equation with two distinct real roots.
So,[tex]$y = 0 = 2x^2mx8 \implies 2x^2mx - 8 = 0$[/tex]
Using the quadratic formula , [tex]$m = \frac{8}{2x^2x}$[/tex]
The two distinct real roots of the equation imply that the discriminant of the quadratic equation, [tex]$\Delta = b^2-4ac$[/tex] is greater than 0.
So, [tex]$\Delta = (2x^2)^2-4(2)(-8) > 0 \implies 4x^4 + 64 > 0$[/tex]
[tex]$4x^4 > -64 \implies x^4 > -16$[/tex]
So, [tex]$m > \frac{8}{2x^2x} \implies m > \frac{8}{2x^2(-4)} = \frac{2}{x^2}$[/tex]
Hence, the possible values of m are all real numbers greater than [tex]$\frac{2}{x^2}$[/tex]
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How do you write an absolute value inequality from a line graph?
To write an absolute value inequality from a line graph, we need to identify the inequality sign and determine the interval(s) of x-values that make the inequality true.
Here are the steps to write an absolute value inequality from a line graph:
Identify the inequality sign: If the graph is a solid line, the inequality is "equals to", if the graph is dashed, the inequality is "not equal to", if the graph is a solid line to one side and a dashed line to the other side, the inequality is "greater than or equal to" or "less than or equal to".
Determine the interval(s) of x-values that make the inequality true: The x-values for which the graph is above the x-axis represent the solution set of the inequality when the inequality sign is "greater than" or "greater than or equal to", and the x-values for which the graph is below the x-axis represent the solution set of the inequality when the inequality sign is "less than" or "less than or equal to"
Write the inequality: Using the information from step 1 and 2, we can write the inequality in the form of |x-h| operator k, where h is the x-coordinate of the vertex, k is the distance of the vertex to the x-axis and operator is the inequality sign determined in step 1.
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