Answer:
Step-by-step explanation:
lim x -> +oo -2x³ - 13x² + 8x + 52
x³ (-2 -13/x + 8/x² + 52/x³)
+oo³ (-2 - 13/+oo + 8/+oo² + 52/oo³)
+oo(-2 + 0 + 0 + 0)
-oo
lim x -> -oo -2x³ - 13x² + 8x + 52
x³ (-2 -13/x + 8/x² + 52/x³)
-oo³ (-2 - 13/-oo + 8/-oo² + 52/-oo³)
-oo(-2 + 0 + 0 + 0)
+oo
Which of the following is an example of discrete data?
a.The volume of the pencil case.
b.The length of the pencil case.
c.The length of the pencil.
d.The number of pencils in a pencil case.
e,The time taken to close the pencil case.
An example of discrete data is the number of pencils in a pencil case. Option D
What is discrete data?Discrete data can be defined as a numerical type of data including concrete or whole numbers with fixed and specific data values determined by counting.
Some features of discrete data are;
They are finiteNumericCountableNon-negative integersExamples of discrete data are;
The number of customers The number of computers in an officeThe number of items bought per weekHence, the correct option is the number of pencils in a pencil case.
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Write an equation of a line
passing through the point
(-6, -3) and perpendicular to JK
with J(-2, -7) and K(6, 5).
A) y = -2/3x – 4 the airport
B) y = -2/3x – 7 the library
C) y = 2/3x + 1 the park
D) y = 2/3x + 9 the zoo
E) y = -3/2x – 4 the police station
The equation of the line passing through the point (-6, -3) and perpendicular to JK with J(-2, -7) and K(6, 5) is y = -2 / 3x - 7, so option B is correct.
What is line?
An object having an endless length and no width, depth, or curvature is called a line. Since lines can exist in two, three, or higher-dimensional environments, they are one-dimensional things.
Given:
A line passing through the point (-6, -3) and perpendicular to JK with J(-2, -7) and K(6, 5)
Calculate the slope of the line,
m = 5 - (-7) / 6 - (-)
m = 12 / 8
m = 3 / 2
The slope of a line perpendicular to JK, M = - 1 / 3 / 2 = -2 / 3
Calculate the equation of the line as shown below,
y - (-3) = -2 / 3[x - (-6)]
y + 3 = -2 / 3x - 4
y = -2 / 3x - 7
Therefore, the equation of the line passing through the point (-6, -3) and perpendicular to JK with J(-2, -7) and K(6, 5) is y = -2 / 3x - 7.
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A hallway has a length of 450 inches (in) and width of 80 inches (in). What are the
dimensions for the hallway in meters (m)? Round to the nearest tenth if necessary.
Answer:
2.5 feet = 30 inches.
Step-by-step explanation:
Let L = length not carpeted
L = 400/30
L = 13.3333333333
L = 13.33 inches
Graph the following function by moving the points to match two ordered pairs, including the x-intercept:
f(x) = log 1/8(x)
The two points, along with the [x] - intercept are joined are joined.
What is logarithmic function? What is a exponential function?In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number [x] to the base [b] is the exponent to which [b] must be raised, to produce [x]. We can write -[tex]y =log_{e} x[/tex]
In mathematics, an exponential function is a function of form f(x) = aˣ, where [x] is a variable and [a] is a constant which is called the base of the function and it should be greater than 0. Examples of exponential function : f(x) = 4ˣWe have the following function -
y = log (1/8)x
We can write -
y = log (1/8)x
y = log(x/8)
y = log(x) - log(8)
Refer to the graph attached. The two points, along with the [x] - intercept are joined.
Therefore, the two points, along with the [x] - intercept are joined are joined.
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Simplify 2(3+d-1) pls
Answer:
6+d-1
Step-by-step explanation:
Answer:
2d+4
Step-by-step explanation:
2(3+d-1)
2(3)+2(d)+2(-1)
6+2d-2
2d+4
hopes this helps
Line A contains the points (2, 6) and (4, 10). Line B contains the
points (-2, 3) and (3, 13).
1. Are the lines parallel? Explain your reasoning.
Answer:
It is not possible to determine whether the lines are parallel based on the information given. To determine whether two lines are parallel, we need to calculate the slope of each line and compare them. The slope is calculated as the change in the y-coordinate divided by the change in the x-coordinate, or (y2-y1)/(x2-x1). Since we only have the coordinates of the endpoints of the lines and not the equations of the lines, we cannot calculate the slope and therefore cannot determine whether the lines are parallel.
Answer: lines are parallel
Step-by-step explanation:
Lines are parallel if they have the same slope
[tex]\boxed {The\ slope\ m=\frac{y_2-y_1}{x_2-x_1} }[/tex]
1) (2,6) (4,10)
x₁=2 x₂=4 y₁=6 y₂=10
Hence,
[tex]\displaystyle\\m=\frac{10-6}{4-2} \\\\m=\frac{4}{2}\\\\m=2[/tex]
2) (-2,3) (3,13)
x₁=-2 x₂=3 y₁=3 y₂=13
Hence,
[tex]\displaystyle\\m_1=\frac{13-3}{3-(-2)} \\\\m_1=\frac{10}{3+2} \\\\m_1=\frac{10}{5}\\\\m_1=2[/tex]
m=m₁=2
Hence, lines are parallel
a pool can be filled by one pump in 50 minutes and by another pump in 60 minutes. a third pump can drain the pool in 75 minutes. if all 3 pumps go into operation at the same time, how long will it take to fill the pool?
In 42 6/7 minutes the pool will get filed when all 3 pumps work together.
Given,
Time taken by the pump 1 to fill a pool = 50 minutes
Time taken by pump 2 to fill the same pool = 60 minutes
The time taken by pump 3 to drain the pool = 75 minutes
When all the 3 pumps work together, we have to find the time taken to fill the pool;
Here,
In every minute,
Pump 1 fills 1/50 of pool
Pump 2 fills 1/60 of pool
Pump 3 drains 1/75 of pool
That is,
1/50 + 1/60 - 1/75 = 6/300 + 5/300 - 4/300 = 11 - 4 / 300 = 7/300
The time taken = 300/7 minutes = 42 6/7 minutes
Therefore,
When the 3 pumps work together, it will take 42 6/7 minutes to fill the pool.
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Describe and correct the error in solving the
system of linear equations.
y = 3x -8
y = 3x - 12
The lines have the same slope. So, the system
has infinitely many solutions.
Answer:
it’s no solution
Step-by-step explanation:
karen is going to rent a truck for one day. there are two companies she can choose from, and they have the following prices. company a charges and allows unlimited mileage. company b has an initial fee of and charges an additional for every mile driven. for what mileages will company a charge less than company b? use for the number of miles driven, and solve your inequality for .
Company B charges a $55 initial price plus an extra $0.90 for every mile traveled. For 70 miles, Company A will charge less than Company B.
The occurrence of an unfair and/or uneven distribution of opportunities and resources among the people that make up a society is referred to as inequality. To different individuals and in various settings, the word "inequality" may indicate different things.
$118 in change and unrestricted mileage
B affects the initial $550 and the cost per mile traveled.
Let m stand for the distance covered.
So inequality is
118 < 55 + 0.90 m
= 0.90 m > 118 - 55
= m > 63/0.90
= m > 70
So for 70 miles above company A changed less than company B.
Complete question:
Karen is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices. Company A charges $118 and allows unlimited mileage. Company B has an initial fee of $55 and charges an additional $0.90 for every mile driven. For what mileages will Company A charge less than Company B? Use m for the number of miles driven, and solve your inequality for m.
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PLS HELP 15 POINTS!!!!!!
15. What is the solution to the system of equations below?
y=4x+2
y=1/2x-5
A. (2,6)
B (6,2)
C. (-6,-2)
D. (-2,-6)
which represents the lowest degree of certainty? group of answer choices conclusion theory fact hypothesis
Theory is the correct answer, theory represents the lowest degree of certainty.
What is certainty?
The epistemic attribute of beliefs that one cannot rationally reject is certainty, often known as epistemic certainty or objective certainty. Epistemic certainty is commonly defined as a belief being certain if and only if the person holding it could not be wrong in holding it. Other popular definitions of certainty refer to the beliefs' incontrovertibility or describe certainty as a characteristic of those beliefs with the strongest foundation. Although certainty and knowledge are closely related, modern philosophers frequently treat knowledge as having less conditions than certainty.
The rest of the options given in the questions which are conclusion, fact, hypothesis are evidence based and they provides comparatively higher degree of certainty than theory.
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How do you find the range of a quadratic graph?
The range is all real integers bigger than or equal to the range's y-coordinate if a quadratic function opens up. All real integers less than or equal to the range's y-coordinate are in the range if a quadratic function opens downward.
In the given question we have to explain, how we can find the range of a quadratic graph.
Because it is the most fundamental quadratic function, all quadratic functions collectively can be referred to as a family, with this particular function serving as the parent (i.e., not transformed in any way). This function can be used to start broadly generalising the domains and ranges of quadratic functions.
The range is partly determined by the pivotal point, or vertex. The parabola's opening direction is the other. The range is all real integers bigger than or equal to the range's y-coordinate if a quadratic function opens up. All real integers less than or equal to the range's y-coordinate are in the range if a quadratic function opens downward.
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the margin of error of a confidence interval is the error from biased sampling methods. True or False
In triangle def, m∠d = (4x 15)°, m∠e = (5x 32)°, and m∠f = 70°. determine the degree measure of the exterior angle to ∠d. 137° 113° 67° 43°
The degree measure of the exterior angle triangle is ∠D = 137°.
What is Triangle ?Having three vertices and three angles that add up to 180 degrees, a triangle is a three-sided polygon.
given this, the angles D, E, and F in the triangle DEF are (4x + 15), (5x + 32), and 70 respectively.
The sum of the angles of a triangle is now 180°.
Therefore, we may write: m ∠D m∠ E m ∠F = 180
When all the numbers are substituted, we obtain the following results: (9x + 117 = 180) 9x
= 180 -117 (4x + 15) + (5x + 32) + 70
⇒ 9x = 63
⇒ x = 7
As a result, we obtain m∠ D = (4x + 15)°,
m∠ D = (4 x 7 + 15)°,
m ∠D = (28 + 15)°, and m∠ D = (43)°.
Furthermore, m∠ E = (5x + 32)°
m ∠E = (5 x 7 + 32)°
m ∠E = (35 + 32)°
m ∠E = 67°
Since, The measure of the exterior angle to ∠D = m ∠E + m ∠F
= 67° + 70
= 137°
Thus, The measure of the exterior angle ∠D will be 137°.
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What are the x- and y- coordinates of point e, which partitions the directed line segment from j to k into a ratio of 1:4? x = (startfraction m over m n endfraction) (x 2 minus x 1) x 1 y = (startfraction m over m n endfraction) (y 2 minus y 1) y 1 (–13, –3) (–7, –1) (–5, 0) (17, 11)
Point E's coordinates are (-7, -1).
The formulas for our new x and y are provided to us. We must first establish our points 1 and 2 before applying this formula. Due to the fact that the issue was sole with the point E that divides the line segment "from J to K,"
the following formula: point 1 = point J = (x1, y1)
Points 2 and K are equal (x2, y2)
The partition segments JE and EK take up a certain amount of the original segment, as indicated by the variables m and n. Given that the ratio is 1:1, then
JE = m = 1
EK = n = 4
Consequently, using the above formulas to calculate for x and y:
x = [1 / (1 + 4)] (25 – (-15)) + (-15) (-15)
x = -7
y = [1 / (1 + 4)] (15 – (-5)) + (-5) (-5)
y = -1
Consequently, point E's coordinates are (-7, -1)
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Part B: Fill out the Problem-Solving boxes to talk yourself through the problem.
Two mountain bikers leave from the same parking lot and head in opposite directions on two different trials. The first rider goes 8km due East, then rides due south for 15km. The second rider goes 8km due West, then changes direction and rides 20 degrees west due North for 15km. (See the picture below.) Both riders have been traveling for 23km, but when they stopped, which one was further away from the parking lot?
Understand & Think (1 point): What is being asked in the problem? What do I know and what does it mean? What plan am I going to try?
Do/Answer (2 points): I will write out my response to the question, explaining my answer and what it means. I will explain why my answer makes sense.
Explanation of my answer why it makes sense:
PLEASE HELP AND TRY NOT TO MAKE IT SOUND SO COMPLICATED… THANKS AND MUCH APPRECIATED!!!
The first rider the displacement is, 17 km.
And the 2nd river the displacement is 20.22 km.
What is right triangle?
A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and other angles of the right triangle.
It is asked in this problem is who's displacement is greater (not distance) it means that the shortest distance of starting and ending point with direction from start and end.
Here we have two triangle with two arm know for both.
So we have to find the 3rd arm for both triangle.
Now we have for a right triangle
a^2 + b^2 = c^2
For other triangle we know the cosine law of triangle is,
a^2 + b^2 - 2ab cosθ = c^2
θ is the opposite angle of c
For the first rider the displacement is,
c = [tex]c = \sqrt{a^2 + b^2} = \sqrt{8^2 + 15^2} = 17 km\\[/tex]
For the 2nd river the displacement is
[tex]c = \sqrt{a^2-b^2 -2abcosheta}[/tex], θ = 120°
[tex]c = \sqrt{8^2 + 15^2 - 2ab cos(120)} \\c = \sqrt{289 - 240cos(120)} \\c = \sqrt{289 - (-120)} \\c = \sqrt{289 + 120}\\ c = \sqrt{409} \\c = 20.22km[/tex]
Hence, the first rider the displacement is, 17 km.
And the 2nd river the displacement is 20.22 km.
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Find the value of x. A. Square root 3, B.3 square root 2 over 2
The value of x is 3√2/2.
What is a right-angled triangle?A triangle with one angle being a right angle is called a right-angled triangle.
Given a right-angled triangle, with both acute angles equal to 45°
Since, acute angles = 45°
Therefore, both the legs of the triangle are equal.
Applying Pythagoras theorem,
x²+x² = 3²
2x² = 9
x² = 9/2
x = 3/√2
Rationalizing the denominator,
x = 3√2/√2x√2
x = 3√2/2
Hence, The value of x is 3√2/2.
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Find the least common multiple of 3, 8 and 12
The least common multiple(LCM) of 3, 8, and 12 is 24.
What is the least common multiple(LCM)?
The smallest positive integer that is divisible by both a and b is known as the least common multiple (lcm), lowest common multiple (lcm), or smallest common multiple of two numbers a and b in mathematics and number theory.
We have,
3, 8 and 12
and least common multiple of 3, 8, and 12?
LCM of 3, 8, and 12 is the smallest number among all common multiples of 3, 8, and 12.
The smallest number that can be divisible by 3, 8, and 12 exactly is the LCM.
Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, ….
Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, …..
Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, …..
Hence, the least common multiple(LCM) of 3, 8, and 12 is 24.
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A group of students take a test. The group consists of 8 girls and 12 boys. The mean mark for the girls is 18. The mean mark for the boys is 16. 5. Calculate the mean mark for the whole group.
First, let's calculate the total number of marks for each group:
Girls: 8 students * 18 marks/student = 144 marksBoys: 12 students * 16 marks/student = 192 marksThen, we can calculate the mean mark for the whole group by adding up the total number of marks for each group and dividing by the total number of students:
(144 marks + 192 marks) / (8 students + 12 students) = 336 marks / 20 students = 16.8 marks/student
Therefore, the mean mark for the whole group is 16.8.
The mathematical mean is a measure of central tendency that is calculated by adding up all the values in a data set and dividing by the number of values in the set. It is also commonly known as the "average."
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Answer:
34.5
Step-by-step explanation:
Someone help with Literal equations
Solve for R
a=nr2h
[tex]\displaystyle\\Answer:\ r=\sqrt{\frac{a}{nh} }[/tex]
Step-by-step explanation:
a=nr^2h
Divide both parts of the equation by nh:
[tex]\displaystyle\\\frac{a}{nh} =r^2\\[/tex]
Extract the square root of both parts of the equation:
[tex]\displaystyle\\\sqrt{\frac{a}{nh} } =\sqrt{r^2} \\\\\sqrt{\frac{a}{nh} } =r\\\\Thus,\ r=\sqrt{\frac{a}{nh} }[/tex]
(PLUS 2) Instead suppose the contest always starts with $100 and adds $20 to the pot when people give wrong answers. How many people would have to guess incorrectly for the winner to get $1360? Show your work. (You'll need to know the 'starting value' and 'rate of change' Once you create the equation, substitute the 1360 into the correct position) pelt i
Answer:
63
Step-by-step explanation:
trial and error aint that hard
Andres needed to get his computer fixed. He took it to the repair store. The technician at the store worked on the computer for 5. 25 hours and charged him $116 for parts. The total was $719. 75. Which equation could be used to determine cc, the cost of labor per hour?.
Answer:
5.25c + 116 = 719.75
Step-by-step explanation:
Let c = cost of labor per hour
He worked for 5.25 hours, so the part of the cost due to the hourly rate is
5.25c
You must the add the cost of the parts.
5.25c + 116
Now you set the total cost expression equal to the actual total cost.
5.25c + 116 = 719.75
How do I solve this?
By using the fact that the sum of the internal angles must be equal to 360°, we will see that x = 18
How to find the value of x?Suppose we have a figure of N sides, the sum of the internal angles of that figure will be equal to:
S = (N - 2)*180°
In this case, we have 4 sides, then:
S = (4 - 2)*180° = 360°
Also notice that the figure is symmetrical around the two vertical vertices, then the angle at the left side (the only one that we don't know) also measures 101°, like the one in the right side.
Then we can write the linear equation:
100° + 101° + 101° + (4 + 3x)° = 360°
Now we can try to solve this for x.
(100° + 101° + 101°) + (4 + 3x)° = 360°
302° + (4 + 3x)° = 360°
(4 + 3x)° = 360° - 302°
4 + 3x = 58
3x = 58 - 4 = 54
x = 54/3
x = 18
That is the value of x in the kite.
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what is the area of a parallelogram with a base of 8. meters and a height of 12 meters
Answer:
96 m²
Step-by-step explanation:
area = base × height
area = 8 m × 12 m
area = 96 m²
Question 7 pls help!!!!!!!
The given ray is a bisector of a given angle.
So, the option (b) is the correct answer.
What is bisector?
Bisection in geometry is the division of an object into two equal or congruent parts, typically by a line, which is then referred to as a bisector. The segment bisector and the angle bisector are the two types of bisectors that are most frequently used.
An angle is divided into two equal parts by a ray known as an angle bisector or angle bisector. For instance, if ray AX divides a 60 degree angle into two equal parts, each measurement will be 30 degrees.
Consider, the given angle.
The given angle is bisects by a ray equally.
Hence, the given ray is a bisector of a given angle.
So, the option (b) is the correct answer.
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which suggests that failure to meet a higher-order need may trigger regression to an already fulfilled lower-order need.
According to ERG theory, frustration over not being able to satisfy a higher-order need may cause regression to a lower level.
What is ERG theory?ERG theory is a psychological theory put forth by Clayton Alderfer.
ERG concept, An individual will put more effort into the higher category once needs in the lower category are met. An individual will put more effort into the lower category if needs in the higher category are not met.
Maslow's hierarchy of needs was further developed by Alderfer by being categorised into his ERG theory (Existence, Relatedness and Growth). The necessity of meeting the essential material needs of people falls under the existence category. Concerned in the relatedness category is the desire to uphold significant interpersonal connections.
The desire for personal growth is addressed in the growth category. These include the self-actualization traits and the intrinsic component from Maslow's esteem category.
in a simple manner we define the three stages of ERG theory
1. Existence - what we need from a physiological point of view .
examples- a house , healthcare, etc.
2- Relatedness - our social needs.
examples - friendship, social connectivity, national identity, etc.
3-growth - Self-realization needs.
examples- feelings , success, failure ,etc.
Hence, ERG Theory suggests that failure to meet higher-order need may trigger regression to an already fulfilled lower-order need.
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What is the solution to the compound inequality in interval notation?
4(z +1) > -4 or 2z - 4 < -10
Answer:
(-infinity, -2) ∪ (-3, infinity).
Step-by-step explanation:
To solve this compound inequality, we need to first solve each inequality separately. For the first inequality, 4(z+1) > -4, we can distribute the 4 to get 4z + 4 > -4. Then, we can subtract 4 from both sides to get 4z > -8. Finally, we can divide both sides by 4 to get z > -2.
For the second inequality, 2z - 4 < -10, we can add 4 to both sides to get 2z < -6. Then, we can divide both sides by 2 to get z < -3.
Now that we have solved both inequalities, we need to consider their intersection. Since the inequalities are joined by the "or" operator, the solution is the union of the solutions to each inequality. In interval notation, this is represented as the union of the intervals (-infinity, -2) and (-3, infinity).
Therefore, the solution to the compound inequality in interval notation is (-infinity, -2) ∪ (-3, infinity).
larry's lazertag park charges $50 flat fee for birthday partly rental and $5.50 per person. Sam has no more than $100 to spend on his birthday party. How many friends can he invite without going over his limit?
The maximum number of friends that he can invite without going over his limit is 9.
What is inequality?A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.
In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.
As per the given,
Fixed fee = $50
Suppose the number of people is x.
Total fee = 50 + 5.50x
Total fee ≤ budget
50 + 5.50x ≤ 100
5.50x ≤ 50
x ≤ 9.09 thus, x = 9
Hence "The maximum number of friends that he can invite without going over his limit is 9".
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What are the 4 ways to find slope?
Let us discuss the 4 ways to find the slope:
1. The first case is where, you have two points (x1,y1) and (x2,y2)
These points often may be intercepts of the x and/or y axes.
The equation of the slope is given by-
m= (y2−y1) / (x2−x1).
2. The second condition is where you are given the linear equation that is either in the form or can be manipulated into the form y=mx+b.
Here, the slope is m(the coefficient of x).
3. The third case is when you have a line that is a tangent to another function, you may have (or be able to determine) the slope of the tangent as the derivative of the function. Normally in such cases, the derivative is a function expressed in terms of x and all you need to do is substitute the value of x into this function for the required equation.
4. The fourth case is when you are given a graph as follows-
Here , the slope m = Δy/Δx
Also, note that tan θ = Δy/Δx
Hence, this tan θ is considered as the slope of the line.
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What is the y-intercept of the line on the graph?
b=
Point form: ( , )
The y-intercept of the line on the graph is -60.
How to find y-intercept of a graph?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slope of a lineb = y-interceptTherefore, the y-intercept is the point where the graph intersects the y-axis. The y-intercept is the value of y when x = 0.
Therefore, on the graph the value of y when x is equals to zero is -60.
Hence,
y-intercept = -60
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