Please explain for what values of x is function g(x) continuous if it is defined by.
Answers
Using the continuity concept, it is found that the function is continuous for all real values.
What is the continuity concept?A function f(x) is continuous at x = a if it is defined at x = a, and:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
In this problem, we are given a piece-wise function, hence we have to look at the points where the definition of the function changes. In this problem, it can only be discontinuous at x = 0, which we have to verify.
Then:
[tex]f(0) = 0^2 - 1 = -1[/tex].[tex]\lim_{x \rightarrow 0^-} = \lim_{x \rightarrow 0} x^2 - 1 = 0^2 - 1 = -1[/tex].[tex]\lim_{x \rightarrow 0^+} = \lim_{x \rightarrow 0} \frac{1}{x - 1} = \frac{1}{0 - 1} = -1[/tex].The 3 values are equal, hence the function is continuous at x = 0 and for all real values.
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Related Questions
Which graph represents the relationship?
In the following questions, look at different ways to represent the relation given by the
equation y = x2 - 1.
The table below shows some values for the given equation. Find the values of a and b.
a =
b =
A 2-column table with 4 rows. The first column is labeled x with entries negative 2, negative 1, b, 1. The second column is labeled y with entries a, 0, negative 1, 0.
Answers
From the values in the table, we can say that the first graph is the correct one that shows some values for the given equation.
How to draw the graph of quadratic functions?We are given the quadratic equation as;
y = x² - 1
From the given table;
At x = -2, y = (-2)² - 1 = 3
At x = -1, y = 0
At x = 0, y = -1
At x = 1, y = 0
Now, from the values above, we can say that the first graph is the correct one that shows some values for the given equation.
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Find the value of x for which the lines I and m are parallel.
5x+13
11x-73
14.3
15
16.6
10
Answers
Answer:
15
Step-by-step explanation:
5x+13+11x-73=180°( co-interior angles sum is 180)
5x+11x+13-73=180°
16x-60=180
16x=180+60
16x=240
x=15
21. Find the measure of angle A.
40
20
80
160
160°
Answers
Answer:
m<A = 20°
Step-by-step explanation:
360 160 = 200
m<A = (1/2)(200° - 160°)
m<A = 20°
Bag A contains 7 blue discs, 4 red discs and 1 yellow disc.
Bag B contains 3 blue discs and 6 red discs.
A disc is drawn at random from Bag A and placed in Bag B.
A disc is then drawn at random from Bag B.
Find the probability that the disc drawn from Bag B is red.
Answers
Answer:
75% or 65%
Step-by-step explanation: that's what I did at lest
4/3 ÷21/5 what is this answer
Answers
20/63
Step-by-step explanation:
Use Keep Change Flip so your question would become 4/3 multiplied by 5/21
Answer:
20/63
Step-by-step explanation:
[tex]\frac{4}{3} /\frac{21}{5} =\frac{(4)(5)}{(3)(21)} =\frac{20}{63}[/tex]
Hope this helps
The proof is converted to paragraph form.
Which parts of the paragraph proof are incorrect?
AMC is a right angle is given. BMD is a right angle is also given. Since XAMC is a right angle, BMC and XCMD are
complementary. Since BMD is a right angle, AMB and BMC are complementary. By the Congruent Complements Theorem,
AMB CMD.
Answers
The part of the proof regarding the triangle that is incorrect is By the Congruent Complements Theorem AMB CMD.
How to illustrate the information?From the information given, it should be noted that AMC is a right angle and also that BMD is a right angle.
Therefore, it illustrates that AMC and BMD are equal.
Therefore, by the Congruent Complements Theorem AMC and BMD are equal.
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Isn't the series here divergent? doesn't that mean it cannot be represented as a riemann sum
Answers
No issues with convergence here. If you actually expand the summand you can use the well-known Faulhaber formulas to compute the sum.
[tex]\displaystyle \sum_{i=1}^n 1 = n[/tex]
[tex]\displaystyle \sum_{i=1}^n i = \frac{n(n+1)}2[/tex]
[tex]\displaystyle \sum_{i=1}^n i^2 = \frac{n(n+1)(2n+1)}6[/tex]
[tex]\displaystyle \sum_{i=1}^n i^3 = \frac{n^2(n+1)^2}4[/tex]
and so on. You would end up with
[tex]\displaystyle L_n = \frac2n \times \frac{96-8796n^2+40283n^3-49458n^4}{n^3}[/tex]
As [tex]n\to\infty[/tex], we have [tex]L_n\to-98916[/tex].
Now, when [tex]i=1[/tex], the first term of the sum is
[tex]7(5+0)^3 - 6(5+0)^5[/tex]
so the left endpoint of the first subinterval is [tex]a=5[/tex].
At the other end, when [tex]i=n[/tex], the last term of the sum is
[tex]7\left(5+\dfrac{2(n-1)}n\right)^3 - 6\left(5+\dfrac{2(n-1)}n\right)^5[/tex]
which converges to
[tex]7(5+2)^3 - 6(5+2)^5[/tex]
so the left endpoint of the last subinterval converges to [tex]b=5 + 2 = 7[/tex].
From here it's quite clear that [tex]f(x)=7x^3-6x^5[/tex]. So, the Riemann sum converges to the definite integral
[tex]\boxed{\displaystyle \int_5^7 (7x^3 - 6x^5) \, dx}[/tex]
her the
Use the figure for exercises 13-14. Rewrite each sum using a single angle.
13. mLLMN + mLNMP
14. mLNMP
mLOMP
Given that x = 3 + y and that -2y + 3 < -1, provide
reasons for each step in the following solution for x.
STATEMENTS
15. x = 3 + y and -2y + 3 < -1
16. x > y
17. -2y<-4
18. y> 2
19. x > 2
15.
16.
17.
18.
19.
REASONS
M
Answers
Answer:
13. m∠MN + m∠NMP = m∠MP.
14. m∠NMP - m∠OMP = m∠NMO.
~
15. x = 3 + y and -2y + 3 < -1 : Given
16. x > y : x = 3 + y
17. -2y < -4 : -2y < -4
18. y > 2 : y > 2
19. x > 2 : x = 3 + y and y > 2
------------------------------------------
Part B: In complete sentences, explain how a circle can be used to find the circumcenter of the triangle graphed below.
Part C: Use a circle to locate the circumcenter of the triangle. Provide the location of the circumcenter.
Answers
Answer:
Step-by-step explanation:
Part B:
The center of the circumscribed circle around a triangle is equidistant from vertices of that triangle. To find the circumcenter need to draw at least two perpendicular bisectors to the sides of the given triangle. Point of intersect of them is center of the circumscribed circle.
Part C:
Coordinates of the midpoint of line BC ( y = - 1 ) are
( [tex]\frac{-6+2}{2}[/tex] , [tex]\frac{-1-1}{2}[/tex] ) = ( - 2 , - 1 ) and the equation of the line ⊥ to BC is x = - 2
Because BC is ║ to x-axis and m∠A is 90° , the center of the circle is midpoint of BC and r = [tex]\frac{BC}{2}[/tex] = 4
Schweser Satellites Inc. produces satellite earth stations that sell for $115,000 each. The firm's fixed costs, F, are $3 million, 50 earth stations are produced and sold each year, profits total $600,000, and the firm's assets (all equity financed) are $4 million. The firm estimates that it can change its production process, adding $3 million to assets and $500,000 to fixed operating costs. This change will reduce variable costs per unit by $12,000 and increase output by 15 units. However, the sales price on all units must be lowered to $110,000 to permit sales of the additional output. The firm has tax loss carryforwards that render its tax rate zero, its cost of equity is 13%, and it uses no debt.
What is the incremental profit? Enter your answer in dollars. For example, an answer of $4 million should be entered as 4,000,000, not 4. Round your answer to the nearest dollar.
$
To get a rough idea of the project's profitability, what is the project's expected rate of return for the next year (defined as the incremental profit divided by the investment)? Round your answer to two decimal places.
%
Should the firm make the investment?
-Select-
Would the firm's break-even point increase or decrease if it made the change?
The change would
-Select-
the break-even point.
Would the new situation expose the firm to more or less business risk than the old one?
I. The new situation would obviously have more business risk than the old one.
II. The new situation would obviously have less business risk than the old one.
III. It is impossible to state unequivocally whether the new situation would have more or less business risk than the old one.
-Select-
Answers
The incremental profit is $175,000 and the new situation would obviously have less business risk than the old one.
Incremental profitFirst step
Profit $600,000
Add Fixed cost $3,000,000
Contribution $3,600,000
Variable Cost=Total Sales−Contribution
Variable Cost=$115,000×50-$3,600,000
Variable Cost=$2,150,000
Second step
Profit at revised cost
Sales $8,625,000
(75x $115,000)
Less: Variable cost $4,350,000
[75×($3,000,000+$500,000/50-$12,000)]
Contribution $4,275,000
Less Fixed cost $3,500,000
($3,000,000+$500,000)
Profit $775,000
Incremental profit=Profit at revised cost-Existing profit
Incremental profit=$775,000-$600,000
Incremental profit=$175,000
Expected rate of return=Incremental profit/Investment
Expected rate of return=$175,000/$4,000,000×100
Expected rate of return=$4.375%
2. Break-even point
Existing
Break-even point=Fixed cost/Contribution
Break-even point=$3,000,000/[($115,000-($3,000,000+$500,000/50)]
Break-even point=$3,000,000/[($115,000-$70,000)
Break-even point= 66.67
Revised
Break-even point=Fixed cost/Contribution
Break-even point=$3,500,000/[($110,000-($3,000,000/50)]
Break-even point=$3,000,000/[($110,000-$60,000)
Break-even point=60
II. The new situation would obviously have less business risk than the old one.
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What is the solution, if any, to the inequality |3x|≥0?
all real numbers
A.all real numbers
B.no solution
C.x20
D.x≤0
Answers
The inequality is all real numbers.
What is inequality?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Given:
|3x|≥0
3x = 0
Divide both sides of the equation by the coefficient of variable
x= 0/3
x=0 = RHS
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HELP ME ANSWER THIS PLEASE
Answers
The table does not represent a function.
What is a function?
A function is a relationship that maps elements of the domain into elements of the range. Such that each element of the domain can be mapped into only one element of the range.
Here we have a table.
If you look at the table, you can see that the element of the domain:
x = -18
Is being mapped into two different values in the range.
Into y = -10 and y = 21.
From that, we conclude that this table does not represent a function.
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The diameter of a proton is about 1.9 cross times 10 to the power of short dash 15 end exponent meters. A hydrogen atom has an overall length of 100,000 times (or 1 cross times 10 to the power of 5 times) the diameter of a proton.
What is the length of the hydrogen atom, in meters, if it were written in scientific notation?
A. 1.9 x 10 (15 exponent)
B. 1.9 x 10 (-15 exponent)
C. 1.9 x 10 (-8 exponent)
D. 1.9 x 10 (-12 exponent)
Answers
Using scientific notation, the measure is given as follows:
[tex]1.9 \times 10^{-10}[/tex]
What is scientific notation?A number in scientific notation is given by:
[tex]a \times 10^b[/tex]
With the base being [tex]a \in [1, 10)[/tex].
The diameter of a proton, in scientific notation, is given by:
[tex]1.9 \times 10^{-15}[/tex].
The hydrogen atom has an overall length of 100,000 = 10^5 times the diameter of the proton, hence the length is given by:
[tex]L = 100000 \times 1.9 \times 10^{-15} = 10^5 \times 1.9 \times 10^{-15} = 1.9 \times 10^{5 - 15} = 1.9 \times 10^{-10}[/tex]
For the above length, I applied the multiplication of factors with the same base and different exponents, where we keep the base and add the exponents.
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Simplify
b^10/b^2
OA. b^-8
OB. b^5
O c. b^-5
O D. b^8
Answers
Step-by-step explanation:
The answer is D)
b^10/b^2
= b^10-b^2 = b^8
hope this helps.pls like and follow if you understand.
thanks:-):-)
2y + 5 =
solve for the correct answer
Answers
let the value of y be 2
Now,
2y+5
2x2+5
4+5
9
Hence,proved
20 points/ Brainliest!!
What set of transformations are applied to parallelogram ABCD to create A”B”C”D?
Answers
Answer:
A) Reflected over the x axis and reflected over the y-axisStep-by-step explanation:
ABCD moves 2 quadrants, so has to move over 2 axes.
So, the only option that would work is A).
Hope this helps.
A pizza place has pizzas in 2 different sizes, with 8 different flavors for the crust, and 8 different toppings.
How many one-topping pizzas can be ordered?
Answers
Use multiplication:
[tex]2\text{ sizes}*8\text{ flavors}*8\text{ toppings}=\large\boxed{128\text{ pizzas}}[/tex]
This question is basically the same as the other question of yours that I answered, so the explanation is very similar:
You can imagine the possibilities as leaves on a tree. Your tree has 2 large branches to represent the two possible sizes. Each of those branch off into 8 smaller branches, each representing a crust flavor. Each one of the smaller branches has 8 leaves to represent a different topping. Each leaf is a combination of a size, a crust flavor, and a topping, so it represents a complete pizza. Your job is to calculate the number of leaves.
If $200 is put in the bank and each year the account earns 5% simple interest,
then how much interest will be earned in two years?
$10
$20
$30
$100
Answers
Work Shown:
i = P*r*t
i = 200*0.05*2
i = 20
A quick mental shortcut is to double the 5% interest to get 10%, since this occurs over 2 years. Then taking 10% of something is the same as moving the decimal point one spot to the left. So we go from 200 to 20
1. What are opposites?
a) Give an example of opposites.
b) Describe a real world situation using opposites.
please make it simple
Answers
Answer:A person or thing that is different from other people or things.
Like me and you we might like different things like I like playing games you dont your the opposite of me.
A real world situation would be looking at maybe plants see how different they look or if they look the same study them and realize one is poison the other is fresh.
Step-by-step explanation:
two siblings are 55 years old combined the youngest sibling is 9 years younger than the oldest sibling how old is the youngest sibling
Answers
To solve systems of equations word problems, we can delegate certain variables to subjects mentioned in the word problem. From there, we can form equations based on the given values.
Solving the QuestionLet a be the older sibling's age and b be the younger sibling's age.
We're given:
a + b = 55 years oldb + 9 years = aAll we've done so far is translate the given sentences into equations. Now, we have to solve for b, which is the age of the youngest sibling. Solve using substitution:
[tex]a+b=55\\(b+9)+b=55\\b+9+b=55\\2b+9=55\\2b=46\\b=23[/tex]
Therefore, the younger sibling is 23 years old.
Answer23 years old.
Aamir wants to add 894 and 76. He first adds 890 and 80. What should he do next to get the correct answer?
O add 4
O add 8
O subtract 4
O He has already calculated the correct answer in the first step
Answers
Really need help on this one!!
Answers
Select the correct answer.
To solve this system of equations using substitution, what could be substituted in place of y in the first equation?
4x=5-2y
y-2x=7
A 7-2x
B. 4x-5
C. 5-4x/2
D. 2x + 7
Answers
C
when doing substitution,you must make one a subject,which is y in this case.To make y the subject,you must move -2y to 4x to make the y positive,that leaves us with 2y+4x=5.Now move the 4x to 5 to make 2y=5-4x.Lastly,to make y the subject,divide both side by 2 to remove the 2 from the y, which leaves us with y=5-4x/2
Edgar records the time that it takes his school bus to take him from the bus stop
to school each day. This is a
______ random variable.
A. continuous
B. infinite
C. discrete
D. intervalled
Answers
Answer: I'm pretty sure it is D. intervalled
explanation: Because it can never be exact each and every time
line segment SU is a diameter at Circle V what is the measure of arc ST?
Answers
The measure of ST based on the diagram regarding the circle is 56°.
How to calculate the value?Fron the information given, angle S is equal to 34°. Also, the triangle is inscribed in a circle.
Therefore, the measure of the angle will be:
= 180 - 90 - 34
= 56°
Therefore, the measure of angle ST is 56°.
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Predict what will happen to the coordinates of a point (x, y) as the point translates to produce point (x′, y′). Assume that the point translates a units to the left or right and b units up or down. Express your answers in terms of x, y, a, and b. Be sure to watch your signs.
Answers
Answer:
(x' , y') = ( (x ± 1) , (y ± b) )
Step-by-step explanation:
(object vector) = (x', y')
(translation vector) = ( ±1 , ±b ) ==> Since horizontal movement (x) is right/ or left meaning ±1 , and vertical movement(y) is up or down meaning ±b
Notice that : (image vector) = (object vector) + (translation vector)
therefore (x' , y') = ( (x ± 1) , (y ± b) )
New topic please help
Answers
Answer:
2262.9cm squared
Step-by-step explanation:
That's all I could do.Hope it helps.
40. Noor is packing chocolates into boxes. The boxes come in small, medium and large sizes. A large box holds twice as many chocolates as a medium box and three times as many chocolates as a small box. Noor fills three times as many small boxes as medium boxes and twice as many medium boxes as large boxes. Altogether she packs 1296 chocolates. In total, how many chocolates does she pack into the small boxes.
Answers
The number of chocolate which goes into the small boxes is 100 chocolate
EquationChocolate in small boxes = xChocolate in medium boxes = 3xChocolate in large boxes = 3x + 2(3x)= 3x + 6x
= 9x
Total chocolate = 1296x + 3x + 9x = 1296
13x = 1296
x = 1296/13
x = 99.6923076923076
Approximately,
x = 100 boxes
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Which the most accurate statement about progress monitoring?
a. Progress monitoring is a useful way to ensure children are participating in targeted, purposeful, and meaningful math instruction and allows for the teacher to identify the skills children may need additional support in.
b. Incorporating children's individual differences into lesson planning is not necessary since the curriculum includes all the skills children need to learn in the order they need to learn them.
c. Progress monitoring is about administering formal assessments at the beginning and end of the year.
Answers
Answer:
progress monitoring is used to access students academic and social emotional behaviour as EB progress examine rate of improvement and evaluate effectiveness of introduction are invention it is typical use with both individual students and small groups
Which function is a quadratic function?
y - 3x² = 3(x² + 5) + 1
y²-7x = 2(x² + 6) + 7
y-2x² = 6(x3 + 5)-4
y - 5x = 4(x + 5) + 9
Answers
Answer:
y – 3x2 = 3(x2 5) 1 is correct
Step-by-step explanation:
hope this helps this may be wrong