Review the graph of f(x). What is the function’s behavior close to the vertical asymptote x = 2? Limit of f (x) as x approaches 2 minus = infinity and limit of f (x) as x approaches 2 plus = infinity Limit of f (x) as x approaches 2 minus = infinity and limit of f (x) as x approaches 2 plus = negative infinity Limit of f (x) as x approaches 2 minus = negative infinity and limit of f (x) as x approaches 2 plus = infinity
Answers
The function's behavior at vertical asymptote x = 2 is (b) [tex]\mathbf{ \lim_{x \to 2^-} f(x) = \infty\ and \ \lim_{x \to 2^+} f(x) = -\infty}[/tex]
How to determine the function's behavior?The attached graph represents the missing information in the question.
From the attached graph, we have the following highlights:
At x = 2, a curve points upwardAt x = -2, another curve points downwardThis means that the limit of f(x) approaches negative infinity and positive infinity at this value of x
Hence, the function's behavior is (b) [tex]\mathbf{ \lim_{x \to 2^-} f(x) = \infty\ and \ \lim_{x \to 2^+} f(x) = -\infty}[/tex]
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Related Questions
Andrei wants to fill a glass tank with spherical marbles and then fill the remaining space with water.
The variable "w" models the amount of water (in liters) Andrei uses if he uses n marbles.
w = 32 - 0.05n
What is the volume of each marble?
Answers
The volume of each marble is 0.05 liter
How to determine the volume?The volume function is given as:
w = 32 - 0.05n
The variable n represents the number of marbles.
This means that 0.05n represents the volume of n marbles and 32 represents the total volume of the glass tank
To get the volume of each marble, we divide 0.05n by n
i.e.
Volume = 0.05n/n = 0.05
Hence, the volume of each marble is 0.05 liter
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What is the range of the function
Answers
Answer:
should be the first one -inf < y < inf
period of f(x)=cos(x)+2
Answers
Answer:
The period is 2π
Explanation:
The period is 2 times pi because 2 is the standalone-term multiplied by pi to get the period.
50 POINTS HELP ME PLEASE ITS GEOMETRY
Answers
Answer:
x is the midpoint of a segment in the diahram
Answer:
x is mid point
Step-by-step explanation:
I hope it's helpful for
Allison earned a score of 95% on a test where the mean was only an 82%. How far above average was her score?
Answers
Answer:
The correct answer is 13%.
Step-by-step explanation:
We can easily put in the equation:
95 - 82 = 13
Hope this helps:) Goodluck!
Kayla drew a right triangle. Which could be the lengths of the triangle's sides?
A. 12 cm, 25 cm, 37 cm B. 9 cm, 16 cm, 25 cm
C. 8 cm, 14 cm, 17 cm D. 7 cm, 24 cm, 25 cm
Answers
Answer:
A triangle has side lengths 10 feet, V205 feet, and V105 feet
Step-by-step explanation:
1. Which shows the factoring pattern for the sum of cubes?
1. (a+b)(a2–ab+b2)
2. (a+b)(a2–ab–b2)
3. (a–b)(a2–ab+b2)
4. (a+b)(a+b)(a+b)
2. Select all the solutions of x3+2x2−9x=18.
1. x=2
2. x=−3
3. x=3
4. x=−2
3. If x=−1 is a root of the polynomial 0=x3+2x2−5x−6, what are the other roots?
1. x=3, x=−2
2. x=−3, x=2
3. x=−1, x=−3, x=2
4. x=0, x=−3, x=2
4. Subtract: (x2–1)–(x3–2x+1)
1. –x^3 – x^2 + 2x
2. –x^3 – x^2 + 2x + 2
3. –x^3 + x^2 + 2x – 2
4. –x^3 + x^2 – 2x – 2
5. What is the largest multiplicity in the factored polynomial y=(x2−1)(x+2)(x+4)?
1. 4
2. 1
3. 0
2. 0
Answers
The solution to the questions are:
The expression that represents the factoring pattern is (a + b)(a² - ab + b²)The solutions of the equation x³ + 2x² - 9x = 18 are x = -3, x = 3 and x = -2The other roots are x = -3 and x = 2The result of subtracting the expressions is - x³ + x² + 2x - 2The largest multiplicity is 1Factoring pattern for the sum of cubesAs a general rule, the sum of cubes x³ and y³ is:
x³ + y³= (x+y)(x² - xy + y²)
Replace x with a and y with b
a³ + b³= (a + b)(a² - ab + b²)
Hence, the expression that represents the factoring pattern is (a + b)(a² - ab + b²)
The solutions of the polynomialThe equation is given as:
x³ + 2x² - 9x = 18
Subtract 18 from both sides
x³ + 2x² - 9x - 18 = 0
Factorize the expression
x²(x + 2) - 9(x + 2) = 0
Factor out x + 2
(x²- 9)(x + 2) = 0
Express x²- 9 as a difference of two squares
(x + 3)(x - 3)(x + 2) = 0
Split
(x + 3) = 0 or (x - 3) = 0 or (x + 2) = 0
Remove brackets
x + 3 = 0 or x - 3 = 0 or x + 2 = 0
Solve for x
x = -3, x = 3 and x = -2
Hence, the solutions of the equation x³ + 2x² - 9x = 18 are x = -3, x = 3 and x = -2
The other roots of the polynomialThe polynomial equation is given as:
0 = x³ + 2x² - 5x - 6
Rewrite as:
x³ + 2x² - 5x - 6 = 0
Factorize the expression on the left-hand side
(x + 3)(x + 1)(x - 2) = 0
Split
x + 3 = 0 or x + 1 = 0 or x - 2 = 0
Solve for x
x = -3 or x = -1 or x = 2
Hence, the other roots are x = -3 and x = 2
Subtract the expressionsThe expression is given as:
(x² - 1) - (x³ - 2x + 1)
Expand
x² - 1 - x³ + 2x - 1
Collect like terms
- x³ + x² + 2x - 1 - 1
Evaluate the like terms
- x³ + x² + 2x - 2
Hence, the result of subtracting the expressions is - x³ + x² + 2x - 2
The largest multiplicity of the polynomialThe polynomial is given as:
y = (x² - 1)(x + 2)(x + 4)
Express x² - 1 as a difference of two squares
y = (x - 1)(x + 1)(x + 2)(x + 4)
The power of each factor in the above expression is 1.
This means that the largest multiplicity is 1
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Given: ABCD is a parallelogram. Prove: ∠A ≅ ∠C and ∠B ≅ ∠D Parallelogram A B C D is shown. By the definition of a ▱, AD∥BC and AB∥DC. Using, AD as a transversal, ∠A and ∠ are same-side interior angles, so they are . Using side as a transversal, ∠B and ∠C are same-side interior angles, so they are supplementary. Using AB as a transversal, ∠A and ∠B are same-side interior angles, so they are supplementary. Therefore, ∠A is congruent to ∠C because they are supplements of the same angle. Similarly, ∠B is congruent to ∠ .
Answers
A parallelogram is a quadrilateral with four sides. The opposite sides of the parallelogram are equal and parallel.
How to illustrate the parallelogram?The parallelogram is a quadrilateral with equal and parallel sides, such that the interior angles present on the same side of the transversal are supplementary.
The sum of supplementary angles is equal to 180-degrees. From the theorem of same-side interior angles, the supplementary angles present on the parallel lines must be intersected by a transversal.
From the property of transversal, the interior angles on the same side of the transversal are supplementary. Therefore, ∠A and ∠D are supplementary and their sum is equivalent to 180-degrees.
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Answer:
D Supplementary BC D
Step-by-step explanation:
did on edgu 2022 !!
answer asap!!! please
Answers
Answer:
D.
Step-by-step explanation:
You can see it in the graphs after you plot it.
Ariana has 4 posters she wants to hang on the wall how many different ways can the posters be arranged
Answers
Answer:
4 different ways
Step-by-step explanation:
there are four different ways she can post it because there are four posters she want to hang on the wall.
which of the following is located over the center of the base of a regular pyramid
A vertex
B slant height
C face
D edge
Answers
Vertex is located over the center of the base of a regular pyramid.
What is Vertex Angle?
Vertex angle is defined as the angle formed by two lines or rays that intersect at a point. These two rays make the sides of the angle.
Here, Vertex is the point which is located over the center of the base of a regular pyramid.
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Erica buys a package of note cards costing $1.44. She gives the cashier
$5.00. The cashier gives her her change using the least number of coins and
bills possible. How many of each coin or bill does she receive?
Answers
Answer:
See below.... several options
Step-by-step explanation:
Change is $3.56
3 dollar bills one 50 c piece one nickel one penny
(though 50 cent pieces are uncommon.....this may be 2 quarters)
[For a while , there was $ 2 bills
so it could be one 1 dollar bill and one $ 2 bill instead of three dollar bills]
Use the given information to determine which of the following relationships
can be proved and why.
ZL= 20
ZME P
M
Answers
Answer:
C. ∆LMN ~ ∆OPQ, because of AA
Step-by-step explanation:
All of the triangle congruence postulates require at least one pair of corresponding sides be congruent (in addition to other requirements). Triangle similarity can be proved if there are two pairs of congruent corresponding angles.
__
congruenceNo sides are given as congruent, so no congruences can be proved.
similarityTwo pairs of corresponding angles are said to be congruent, so we can say ...
∆LMN ~ ∆OPQ, because of AA
High school geometry. help is needed, please and thank you.
Answers
I need help please help me and thank you :))
Answers
Answer:
see explanation
Step-by-step explanation:
∠ CZD = 90° , then
∠ CZF = 90° - ∠ FZD = 90° - 40° = 50°
∠ FZD and ∠ AZG are vertically opposite angles and are congruent , so
∠ AZG = 40°
∠ CZF and ∠ GZE are vertically opposite angles and are congruent , so
∠ GZE = 50°
E
∠ AZB + ∠ BZC = 90° , that is
3x - 2 + 32 = 90
3x + 30 = 90 ( subtract 30 from both sides )
3x = 60 ( divide both sides by 3 )
x = 20
Please don’t lie to me and tell the right answer and if you do get it correct I will give you a shout out thanks
Answers
Answer:
Part A = 7
Part B = 1
I hope this is right, sorry if it isn't
Answer:
See below
Step-by-step explanation:
5 cups cheese / ( 2/3 cup cheese/plate ) =
5 * 3/2 = 15/2 = 7 1/2 or 7 full plates
2/3 cup cheese / plate * 9 plates =
2/3 * 9 = 6 cups cheese total
she has 5 cups to start.....she will need 1 cup more
Please help! This is a problem that is relatively easy but I still need help!
Answers
Answer:
Hi,
Step-by-step explanation:
The triangles CBA and DEA are equals ( 3 sides 2 to 2 equals), angles CAB and DAE are also equals:
6t-12=18-4t
10t=30
t=3(°)
angle CAB=6t-12=6*3-12=6(°)=angle(DAE)
angle BCA=(180-6)/2=87(°)=angle CBA=angle (ADE)=angle(DEA)
Which is the graph of f(x)?
Answers
Answer: [tex]fx[/tex]
The slope is 0, and
the y-intercept is (0, 0)
[tex]\left[\begin{array}{ccc}x&y\\0&0\\1&0\end{array}\right][/tex]
In order to find the graph of "f(x)", we need to graph the line using the slope and y-intercept, or two points.
the quotient of a number and three is four. what is the number
Answers
Answer:
12
Step-by-step explanation:
12/3=4
4*3=12
Hope this helps!
If not, I am sorry.
Answer:
12
Step-by-step explanation:
The quotient of a number and three is four. What is the number?
The word problem can be written as:
[tex]\sf{\dfrac{x}{3}=4}[/tex]
1. Multiply both sides by 3:
[tex]\sf{3\left(\dfrac{x}{3}\right)=4(3)}\\\\\implies x=12[/tex]
2. Check your work:
[tex]\sf{\dfrac{12}{3}=4}\\\\\implies 4=4 \ \checkmark[/tex]
Therefore, the number is 12.
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What is the length of st given s (-3, 4) and t (1, 0)
Answers
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{0})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[1 - (-3)]^2 + [0 - 4]^2}\implies d=\sqrt{(1+3)^2 +(-4)^2} \\\\\\ d=\sqrt{32}\implies d\approx 5.66[/tex]
A group of 50 mothers were asked how many children they have. the
table shows the results.
number of children
number frequency
1
8
2
12
3
10
4.
14
5
6
what is the experimental probability of a mother having 1
child?
Answers
Answer:
4/25
Step-by-step explanation:
total no of children-15
total no of mothers-50
probability that a mother has i child
1/50
=8/50
=4/25
Answer:
0.16
Step-by-step explanation:
A group of 50 mothers were asked how many children they have. the
table shows the results.
number of children 1 2 3 4 5
number frequency 8 12 10 14 6
What is the experimental probability of a mother having 1
child?
Total number of mothers = 8 + 12 + 10 + 14 + 6 = 50
Number of mothers with 1 child = 8
p(1 child) = 8/50 = 0.16
The measure of angle is 0 is 7pi/4. The measure of its reference angle is ___ °, and tan 0 is ____
Answers
Answer: pi/4 and -1
Step-by-step explanation:
Which expression is equivalent to
4^sqrt 6 / 3^sqrt2
Answers
Answer: Choice C
[tex]\frac{\sqrt[12]{55,296}}{2}[/tex]
==========================================================
Explanation:
Recall the process to rationalize the denominator is to multiply top and bottom by the denominator expression. This only works if we have a square root in the denominator.
For cube roots, we'll need to multiply two copies of the denominator to top and bottom. This will get us three copies of [tex]\sqrt[3]{2}[/tex] so that the cube root goes away.
Check out the steps below to see what I mean:
[tex]\frac{\sqrt[4]{6}}{\sqrt[3]{2}}\\\\\\\frac{\sqrt[4]{6}\sqrt[3]{2}\sqrt[3]{2}}{\sqrt[3]{2}\sqrt[3]{2}\sqrt[3]{2}}\\\\\\\frac{6^{1/4}*2^{1/3}*2^{1/3}}{\left(\sqrt[3]{2}\right)^3}\\\\\\\frac{6^{3/12}*2^{4/12}*2^{4/12}}{2}\\\\\\\frac{\left(6^3*2^4*2^4\right)^{1/12}}{2}\\\\\\\frac{\left(55,296\right)^{1/12}}{2}\\\\\\\frac{\sqrt[12]{55,296}}{2}\\\\\\[/tex]
In short,
[tex]\frac{\sqrt[4]{6}}{\sqrt[3]{2}}=\frac{\sqrt[12]{55,296}}{2}[/tex]
We have the 12th root of 55,296 all over top the integer 2. The "2" is not part of the 12th root. This shows why choice C is the final answer.
Answer:
C
Step-by-step explanation:
Is LMN = OPQ? If so, name the congruence postulate that applies. N Given: LM = OP PQ = MN P M = 00 O A. Congruent - SAS O B. Congruent - SSS O C. Might not be congruent O D. Congruent - ASA
Answers
Based on the sides of LMN and OPQ, the congruence postulate that applies is B. Congruent - SSS.
When is the SSS rule used?It is used when the two triangles given have three equal corresponding sides which also have equal angles.
All three sides of LMN and OPQ are equal sides and have equal angles and so the SSS rule applies.
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this is due today. help please
Answers
In the triangle represented in the diagram, The value of X is: 23°
Meaning of a TriangleA triangle can be defined as a plain shape that has three sides, three edges and three angles.
A triangle is majorly defined as a shape that possesses three angles and their interior angles sum up to 180°
In conclusion, in the triangle represented in the diagram, The value of X is: 23°
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Considering the sum of the internal angles of a triangle, it is value that the value of x is of x = 23º.
What is the sum of the internal angles of a triangle?A triangle has three angles, and their sum is of 180º.
In this problem, the angles are:
x, 67º, 90º.
Hence:
x + 67º+ 90º = 180º.
x = 23º.
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find the value of x and y
Answers
Answer:
x= 131
y = 49
Step-by-step explanation:
X and 49 form a straight line so they add to 180
x+49 = 180
x = 180-49
x =131
49 and y are alternate interior angles and alternate interior angles have the same value
y = 49
Step-by-step explanation:
please mark me as brainlest
I need help on this. & I'll give brainlyest to anyone who can solve it for me. Thank's!!!!
Answers
Answer:
I can helpyou with that but im not sure with it
A new amusement park presold discounted tickets for the opening day as well as upon arrival at the park. the opening day ticket sales for the park, including presales, is represented by this function, where is the number of tickets sold h hours after opening at 7:00 a.m. what is the approximate rate of change in the number of tickets sold between 10:00 a.m. and 1:00 p.m.? a. tickets per hour b. tickets per hour c. tickets per hour d. tickets per hour
Answers
The approximate rate of change in the number of tickets sold between 10:00 a.m. and 1:00 p.m. -21 tickets per hour
How to determine the rate of change?The missing part of the question is represented by the following function:
[tex]T(h) = \frac{386 + 110h}{h}[/tex]
10:00 a.m is 3 hours after 7:00 am and 1:00 p.m is 6 hours after 7:00 am.
This means that:
h = 3 at 10:00 am
h = 6 at 1:00 pm
Next, we calculate T(3) and T(6)
[tex]T(3) = \frac{386 + 110*3}{3} =238.7[/tex]
[tex]T(6) = \frac{386 + 110*6}{6} =174.3[/tex]
The average rate of change is then calculated as:
[tex]T'(h) = \frac{T(3) - T(6)}{3 - 6}[/tex]
This gives
[tex]T'(h) = \frac{238.7 - 174.3}{-3}\\[/tex]
Evaluate
T'(h) = -21
This means that the approximate rate of change in the number of tickets sold between 10:00 a.m. and 1:00 p.m. -21 tickets per hour
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Corrine wrote temperatures in degrees Celsius and the equivalent temperatures in degrees Fahrenheit.
Equivalent Temperatures
Celsius
–10
5
10
20
Fahrenheit
14
41
50
68
Which explains how Corrine could determine if the temperatures vary directly?
Compare the equivalent temperatures as a ratio; if the ratios are equivalent, then the temperatures vary directly.
Draw a graph of the temperatures; if the points form a straight line, then the temperatures vary directly.
Write an equation that converts one temperature to another; if the temperatures satisfy the equation, then they vary directly.
Look for a pattern in the table; if the pattern is consistent, then the temperatures vary directly.
Answers
Draw a graph of the temperatures; if the points form a straight line, then the temperatures vary directly , Option B is the correct answer.
What is Direct Variation ?When a quantity of one variable is increased and the value of the other also increases then they are said to be in direct variation.
For the data to be in direct variation
Draw a graph of the temperatures; if the points form a straight line, then the temperatures vary directly.
The points in any linear equation can only fluctuate directly, therefore all points will lie on the same line.
Option B is the correct answer.
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Answer:
ez b
Step-by-step explanation:
Helen purchased 3 copies of a book online at a 20% discount. She also paid $10 for shipping that was not discounted. How much was the original price of one copy of the book if her total ended up being $40?
Answers
Answer:
The original price of the book was $12.50
Step-by-step explanation:
3x - 0.2(3x) + 10 = 40
30x - 2(3x) + 100 = 400
30x - 6x + 100 = 400
24x + 100 = 400
24x = 300
x = 12.50