What would be the point of discontinuity in the following function f(x)=x^2+5x+6/x+3
Answers
For the expression f(x)=x^2+5x+6/x+3, you see that there is a term 6/x. Therefore, the expression can be continuous when x=0 because 6/0 or any number divided by zero is undefined. To verify this, let's see the graph by assigning values of x and plotting them against their values of y. As you can see, the curves only approach zero but never touches zero. These are called asymptotes.
Related Questions
One number exceeds another by 11. the sum of the numbers is 3535. what are the numbers?
Answers
2x + 11 = 3535
2x = 3524
x = 1762
1762 and 1773
Probability of a lightbulb failing question? If the probability is .001 that a light bulb will fail on any given day, then what is the probability that it will last at least 30 days?
Answers
The midpoint of A (-4, 2) and B(8, 5) is
Answers
Answer: The midpoint of the points A(-4, 2) and B(8, 5) is M(2, 3.5).
Step-by-step explanation: We are given to find the midpoint of the points A(-4, 2) and B(8, 5).
We know that
the co-ordinates of the midpoint of the points (a, b) and (c, d) are given by
[tex]M=\left(\dfrac{a+c}{2},\dfrac{b+d}{2}\right).[/tex]
Therefore, the co-ordinates of the midpoint of the points (-4, 2) and B(8, 5) will be
[tex]M=\left(\dfrac{-4+8}{2},\dfrac{2+5}{2}\right)=\left(\dfrac{4}{2},\dfrac{7}{2}\right)=(2,3.5).[/tex]
Thus, the midpoint of the points A(-4, 2) and B(8, 5) is M(2, 3.5).
what must be done to the expression x + 108 to make it equal x?
Answers
To make the expression x + 108 equal to x, subtract 108 from both sides of the equation.
Explanation:To make the expression x + 108 equal to x, we need to subtract 108 from both sides of the equation. This will give us:
x + 108 - 108 = x - 108
Simplifying the equation, we get:
x = x - 108
However, if we are not solving an equation and simply need to simplify the expression x + 108 to make it equal to x, then the answer is that nothing can be done. The expression cannot be simplified to make it equal to x without additional information or context.
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Which point is a solution of x + 2y ≤ 4?
A. (2,4)
B. (1,1)
C. (3,5)
D. (-1,5)
Answers
Can you use matrix multiplication with a matrix with three rows and a matrix with two columns
Answers
A fast typist can type 120 words in 100 seconds. In 180 seconds, how many words could be typed?
Answers
180 seconds --- x words
[tex]x= \cfrac{180*120}{100}=18*12=216 \ \text{words}[/tex]
Answer:
216
Step-by-step explanation:
i think
the distance across the center of a circle is called the?
Answers
The distance from one side of a circle to the other going through the center is called the Diameter.
I hope that helps!
A candy factory made 54 boxes of chocolates. Each box weighs 2 pounds. They packed the boxes in 6 cases with the same number of boxes in each case. How many pounds of chocolates were there in each case?
Answers
The number of pounds of chocolates in each case is 18 pounds
How to find the number of pounds in each case?
The candy factory made 54 boxes of chocolates.
Each box weighs 2 pounds
Therefore,
each box = 2 pounds
They packed the boxes in 6 cases with the same number of boxes in each case. Therefore,
Boxes in each case = 54 / 6 = 9 boxes
Therefore,
pounds of chocolates in each case = 9 × 2 = 18 pounds
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The table below shows the surface area y, in square feet, of a shrinking lake in x days: Time (x) (days) 5 10 15 20 Surface area (y) (square feet) 90 85 70 61 Part A: What is the most likely value of the correlation coefficient of the data in the table? Based on the correlation coefficient, describe the relationship between time and surface area of the lake. [Choose the value of the correlation coefficient from −1, −0.98, −0.5, −0.02.] (4 points) Part B: What is the value of the slope of the graph of surface area versus time between 15 and 20 days, and what does the slope represent? (3 points) Part C: Does the data in the table represent correlation or causation? Explain your answer. (3 points)
Answers
Given the table below showing the surface area y, in square feet, of a shrinking lake in x days.
Time (x) (hours): 5 10 15 20
Surface area (y) (square inches): 90 85 70 61
We can find the correlation coeficient of the data using the table below:
[tex]\begin{center} \begin{tabular} {|c|c|c|c|c|} x & y & x^2 & y^2 & xy \\ [1ex] 5 & 90 & 25 & 8,100 & 450\\ 10 & 85 & 100 & 7,225 & 850\\ 15 & 70 & 225 & 4,900 & 1,050\\ 20 & 61 & 400 & 3,721 & 1,220\\ [1ex] \Sigma x=50 & \Sigma y=306 & \Sigma x^2=750 & \Sigma y^2=23,946 & \Sigma xy=3,570 \end{tabular} \end{center}[/tex]
Recall that the correlation coefitient is given by the equation:
[tex]r= \frac{n(\Sigma xy)-(\Sigma x)(\Sigma y)}{ \sqrt{(n\Sigma x^2-(\Sigma x)^2)(n\Sigma y^2-(\Sigma y)^2)} } \\ \\ = \frac{4(3,570)-(50)(306)}{ \sqrt{(4(750)-(50)^2)(4(23,946)-(306)^2)} } \\ \\ = \frac{14,280-15,300}{ \sqrt{(3,000-2,500)(95,784-93,636)}} = \frac{-1,020}{ \sqrt{500(2,148)}} \\ \\ = \frac{-1,020}{ \sqrt{1,074,000} } = \frac{-1,020}{1,036} =-0.98[/tex]
From the value of the correlation coeffeicient, it can be deduced that the surface area of the lake has a strong negative relationship with the time.
Recall the for the value of the correlation coeficient closer to +1, the relationship is strong positive, for the value closer to -1, the value is strong negative and for the values closer to zero, either way of zero is a weak positive if it is positive and weak negative if it is negative.
PART B:
Recall that the slope of a straight line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
is given by
[tex]m= \frac{y_2-y_1}{x_2-x_1}[/tex]
Thus, the slope of the graph of surface area versus time between 15 and 20 days, [i.e. the line passes through points (15, 70) and (20, 61)] is given by
[tex]m= \frac{61-70}{20-15}= \frac{-9}{5} =-1.8[/tex]
The value of the slope means that the surface area y, in square feet, of the shrinking lake, shrinks by 1.8 square feet every day between the day 15 and day 20.
PART C:
We can say that the data above represent both correlation and causation.
Recall that correlation expresses the relationship between two variables while causation expresses that an event is as a result of another event.
From the information above, we have seen that there is a relationship (correlation) between the passing of days and the shrink in the surface area of the lake.
Also we can conclude that the shrink in the surface area of the lake is a function of the passing of days, i.e. the shrink in the surface area of the lake is as a result of the passing of days.
Therefore, the data in the table represent both correlation and causation.
Which of the following is FALSE? The diagonals of a parallelogram bisect each other. The diagonals of a rhombus bisect each other. The diagonals of a square bisect each other. The diagonals of a kite bisect each other
Answers
Answer:
The diagonals of a kite bisect each other
Step-by-step explanation:
Let analyse all possible answer:
a. The diagonals of a parallelogram bisect each other
True, it is one of the properties of a parallelogram
b. The diagonals of a rhombus bisect each other
True, In any rhombus, the diagonals (lines linking opposite corners) bisect each other at right angles (90°). That is, each diagonal cuts the other into two equal parts, and the angle where they cross is always 90 degrees.
c. The diagonals of a square bisect each other.
True, it is one of the properties of a square
d. The diagonals of a kite bisect each other
Wrong, because we do not know what shape of the kite is, it can have a really strange shape that we can not identify where the diagonals are as you can see in the attached photo.
There were 490 people at play. The admission price was $3.00 for adults and $1.00 for children. The admission receipts were $990. How many adults and children attended
Answers
3a + c = 990
3(490 - c) + c = 990
1470 - 3c + c = 990
-3c + c = 990 - 1470
-2c = - 480
c = -480 / -2
c = 240 <=== there were 240 children
a + c = 490
a + 240 = 490
a = 490 - 240
a = 250 <== there were 250 adults
How can you rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations?
Answers
Make a the subject of the formula
b^2 = 2as + c
subtract c from both sides:-
b^2 - c = 2as
Now divide both sides by 2s ( to isolate a):-
a = (b^2 - c) / 2s
You can rearrange formulas to highlight a specific quantity of interest by identifying it and isolating it using inverse operations.
Explanation:In mathematics, you can rearrange formulas to highlight a specific quantity of interest using the same reasoning as in solving equations. The goal is to isolate the variable or the quantity you want to highlight on one side of the formula. Here are the steps to do it:
Identify the quantity of interest you want to highlight.
Apply inverse operations to isolate that quantity on one side of the equation/formula.
Simplify or solve for the highlighted quantity if needed.
For example, if you have the formula for the area of a rectangle, A = L * W, and you want to solve for the length of the rectangle, you can rearrange the formula as L = A / W, highlighting the length as the quantity of interest.
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What is the domain of the relation: (0, 7), (8, -1), (2, 3), (-4, 6)?
A. (-4, 0, 2, 8)
B. (-1, 3, 6, 7)
C. (1, 7, 8, -1)
D. (2, 3, -4, 6)
Answers
When asked for the domain and given a set of ordered pairs, the domain is always all of the x values ordered from least to greatest.
What does "a"equal to?
Answers
7.4a+22.2=3.2a+43.2
Subtract 3.2a from both sides
4.2a+22.2=43.2
Subtract 22.2 from both sides
4.2a=21
Divide both sides by 4.2
a=5
What is the 12th term of the arithmetic sequence where a1 = 5 and a6 = 20?
Answers
an=nth term
a1=first term
d=common differnce
n=which term
alrighty, a1=5
neat
an=5+d(n-1)
given a6=20
20=a6=5+d(6-1)
20=5+d(5)
20=5+5d
minus 5 both sides
15=5d
divide both sides by 5
3=d
so
an=5+3(n-1) is the formula for the nth term
12th term
a12=5+3(12-1)
a12=5+3(11)
a12=5+33
a12=38
the 12th term is 38
Melissa has three different positive integers. she adds their reciprocals together and gets a sum of 1. what is the product of her integers?
Answers
First let us assign the three positive integers to be x, y, and z.
From the given problem statement, we know that:
(1/x) + (1/y) + (1/z) = 1
Without loss of generality we can assume x < y
< z.
We know that:
1 = (1/3) + (1/3) + (1/3)
Where x = y = z = 3 would be a solution
However this could not be true because x, y, and z must all be different integers. And x, y, and z cannot all be 3 or bigger than 3 because the sum would then be less than 1. So let us say that x is a denominator that is less than 3. So x = 2, and we have:
(1/2) + (1/y) + (1/z) = 1
Therefore
(1/y) + (1/z) = 1/2
We also know that:
(1/4) + (1/4) = (1/2)
and y = z = 4 would be a solution, however this is also not true because y and z must also be different. And y and z cannot be larger than 4, so y=3, therefore
(1/2) + (1/3) + (1/z) = 1
Now we are left by 1 variable so we calculate for z. Multiply both sides by 6z:
3z + 2z + 6 = 6z
z = 6
Therefore:
(1/2) + (1/3) + (1/6) = 1
so {x,y,z}={2,3,6}
Final answer:
The product of Melissa's integers is 120.
Explanation:
The product of Melissa's integers is 120.
Let the integers be a, b, and c.
According to the given information, 1/a + 1/b + 1/c = 1.
By finding common denominators and simplifying, you can determine that a * b * c = 120.
Graph the hyperbola with equation quantity x plus four squared divided by sixteen minus the quantity of y plus three squared divided by twenty five = 1.
Answers
(x-h)²/a² - (y-k)²/b² = 1, where
(h,k) is the center
a is the semi-major axis
b is the semi-minor axis
The given equation is
(x+4)²/16 - (y+3)²/25 = 1
So, from the general form we can deduce that,
Center(-4,-3)
a = 4
b = 5
So, the first point we can plot is the centerpoint. Next, you draw the two intersecting lines. Their slopes are +/- b/a. Thus, it corresponds to +/- 5/4. Using this slope, we can find the equation of the two lines by using the slope and the center.
-3 = +5/4 (-4) + b ---> b= 2
-3 = -5/4 (-4) + b ---> b= -8
So, you plot the equations y=5/4x + 2 and y = -5/4 x -8 by assigning values of x and plotting them against y. Then, the vertex of the hyperbolas are 4 units from the center, denoted by the green dots. The hyperbola is shown in the next picture.
A.) How many ways can you select 1 flavor of ice cream, 1 topping and 1 drink if there are 5 flavors of ice cream, 3 toppings and 4 drinks to choose from?
B.) How many ways can you select a 4-digit passcode without repeating any digit?
C.) How many ways can you select 3 toppings for a pizza with 8 toppings to choose from?
D.) What is the probability of rolling a single die and it landing on a prime number? (Remember, the number 1 is not considered prime.)
E.) How many items are in the sample space for rolling a die and spinning a spinner with 4 different colored sections (red, yellow, green and blue)?
F.) What is the probability of rolling the die and spinning the 4-sectioned spinner described in part E, and getting the number 5 and the color red?
G.) If you wanted to purchase a size T-shirt that "most" people could wear, would you purchase the mean size, the median size or the mode size?
Answers
This means a total of 5*3*4=60 ways.
B) assuming that the first digit can be 0, we have 10 choices for the 1. digit, 9 for the 2., 8 for the third and 7 choices for the fourth digit.
In total, there are 10*9*8*7=5040 passwords we can create.
C) Selection of 3 objects out of 8, can be done in
C(8, 3)=8!/(3!5!)=(8*7*6)/3!=8*7=56 many ways.
D.
P(prime)=n(prime)/n{1, 2, 3, 4, 5, 6}=n{2, 3, 5}/6=3/6=1/2=0.5
E.
any of the 6 outcomes of rolling a die, can be combined with any of the 4 colors.
for example (1, red), (1, yellow), (1, green), (1, blue).
so in total, there are 6*4=24 items in the sample space.
F.
(5, red) is just one of the 24 items in the sample space, so its probability is 1/24= 0.0417
G.
the mode, as it is the size which appears the most.
Answers:
A.60
B.5040
C.56
D. 0.5
E.24
F.1/24= 0.0417
G.mode
Which regular polygon can be drawn by using rotations in geometry software?
Answers
Since we can draw a Hexagon because 360/6 = 60 degree.So we can draw a hexagon using 60 degree rotation(where result will be your exterior angle. So in this we can say 60 degree will be exterior angle.)
Similarly we can draw a 12 - gon. because 360/12 = 30 degree.So we can draw a 12 gon using 30 degree rotation.
Answer:
n- regular polygon
Step-by-step explanation:
In order to draw n- regular polygons, 360 must be divisible by n.
Therefore, there are many regular polygons such as 12- polygon using 30° rotations and 15-polygon using 24° rotations.
The mean incubation time for a type of fertilized egg kept at 100.2100.2â°f is 2323 days. suppose that the incubation times are approximately normally distributed with a standard deviation of 11 dayday. â(a) what is the probability that a randomly selected fertilized egg hatches in less than 2121 âdays? â(b) what is the probability that a randomly selected fertilized egg hatches between 2222 and 2323 âdays? â(c) what is the probability that a randomly selected fertilized egg takes over 2525 days toâ hatch?
Answers
To solve this problem, what we have to do is to calculate for the z scores of each condition then find the probability using the standard normal probability tables for z.
The formula for z score is:
z = (x – u) / s
where,
x = sample value
u = sample mean = 23 days
s = standard deviation = 1 day
A. P when x < 21 days
z = (21 – 23) / 1
z = -2
Using the table,
P = 0.0228
Therefore there is a 2.28% probability that the hatching period is less than 21 days.
B. P when 23 ≥ x ≥ 22
z (x=22) = (22 – 23) / 1 = -1
P (z=-1) = 0.1587
z (x=23) = (23 – 23) / 1 = 0
P (z=0) = 0.5
P = 0.5 - 0.1587 = 0.3413
Therefore there is a 34.13% probability that the hatching period is between 22 and 23 days.
C. P when x > 25
z = (25 – 23) / 1
z = 2
P = 0.9772
This is not yet the answer since this probability refers to the left of z. Therefore the correct probability is:
P true = 1 – 0.9772
P true = 0.0228
Therefore there is a 2.28% probability that the hatching period is more than 25 days.
A box contains seven green marbles, six blue marbles and eight orange marbles. Without looking, you choose two marbles out of the bag. What is the probability that the first two picked will both be green if you don’t replace the marble after the first pick?
Answers
The probability is 0.1 (or 10%).
It is required to find the probability.
What is probability?probability is the ratio of the number of favorable outcomes and the total number of possible outcomes.
Given that:
The favorable count is determined as follows: considering Green marbles. There are 7 of them in the box, so 7 possible picks at the first draw.
Since you don't replace the pick, at the next drawing there are only 6 Green ones. So for each of the 7 possible first picks, there are 6 possible second picks: number of possibilities is 7 by 6 = 42.
The total number of possible drawings, irrespective of color is determined as follows: there are 21 marbles in total at first drawing, and 20 at second. So, for each first pick there are 20 possibilities, i.e., total number is 21 by 20 = 420
The probability is P = 42 / 420 = 1 / 10 = 0.1 (or 10%)
So, the probability is 0.1 (or 10%).
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How many days are between march the 15th and august the 15th?
Answers
August the 15 is 15 days into the month.
You add 16+15 which equals 31 days.
Answer:21 weeks and 6 days
Step-by-step explanation:
lol im late its 2021
What is the length of the diagonal of a cube with a side length of 5 cm? Round to the nearest tenth. 7.1 cm 8.7 cm 21.3 cm 26.7 cm
Answers
D = 5√3 ≈ 8.7 cm.
The required length of the diagonal of a cube with a side length of 5 cm is approximately 8.7 cm.
What is diagonal?A diagonal is a straight line that connects two non-adjacent corners of a polygon, such as a square, rectangle, or any other shape with four or more sides. For a given quesiton, the diagonal of a cube with side length s is given by the formula d = s√3.
Here,
As mentioned in the question, we have given a cube with a length of its side is 5 cm.
We know that the diagonal of a cube with side length s is given by the formula d = s√3.
Substituting s=5 into this formula, we get:
d = s√3.
d = 5√3
Rounding to the nearest tenth, we get d = 8.7 cm.
Therefore, the length of the diagonal of a cube with a side length of 5 cm is approximately 8.7 cm.
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NEED HELP!!!!!!!!!!!!!!!
Which factorizations can be used to identify the real zeros of the function f(x)=-20x^2+23x-6 ?
A. (-10x+2)(2x+3)
B. -(10x+2)(2x-3)
C. -(4x-3)(5x+2)
D. -(4x-3)(5x-2)
Answers
Answer:
Option D. [tex]-(4x-3)(5x-2)[/tex]
Step-by-step explanation:
we have
[tex]f(x)=-20x^{2}+23x-6[/tex]
Equate the function to zero
[tex]-20x^{2}+23x-6=0[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]-20x^{2}+23x=6[/tex]
Factor the leading coefficient
[tex]-20(x^{2}-(23/20)x)=6[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex]-20(x^{2}-(23/20)x+(529/1,600))=6-(529/80)[/tex]
[tex]-20(x^{2}-(23/20)x+(529/1,600))=-(49/80)[/tex]
[tex](x^{2}-(23/20)x+(529/1,600))=(49/1,600)[/tex]
Rewrite as perfect squares
[tex](x-(23/40))^{2}=(49/1,600)[/tex]
[tex](x-(23/40))=(+/-)(7/40)[/tex]
[tex]x=(23/40)(+/-)(7/40)[/tex]
[tex]x=(23/40)(+)(7/40)=30/40=3/4[/tex]
[tex]x=(23/40)(-)(7/40)=16/40=2/5[/tex]
therefore
[tex]-20x^{2}+23x-6=-20(x-(3/4))(x-(2/5))[/tex]
[tex]-20x^{2}+23x-6=-(5)(4)(x-(3/4))(x-(2/5))[/tex]
[tex]-20x^{2}+23x-6=-(4x-3)(5x-2)[/tex]
How do you find the vertex of this parabola? I just plotted the points down on a graphing calculator, but I figure there's a better way.
Answers
Jonathan deposits $2000 into a bank account that pays 7% annual interest compounded annually. This means the bank pays him 7% of his account balance as interest at the end of each year, and he leaves the original amount and the interest in the account.
1. Write a recursive formula to model the situation described above. Use A0 to represent the initial amount invested. Then describe An, the next year’s balance, in terms of the current year’s balance, An-1.
Answers
A=p(1+r/100)^n
where;
A=future amount=An
p=current amount=A0
r=rate=7%
n=time= 1 year
thus rewriting our formula we shall have:
An=A0(1+r)^n
The above is the model describing the information given for future cash flow;
hence, the amount in 1 year will be:
An=A0(1+0.07)^1
An=2000(1.07)^1
An=$2,140
What is the difference between discrete vs continuous data
And can someone please help me with 1-5
Answers
On the other hand, discrete data can't be treated the same way (eg: if n = number of people, then there is no midpoint between n = 3 and n = 4).
-------------------------------------
With that in mind, we have the following answers
1) Continuous data. Time values are always continuous. Any two distinct time values can be averaged to find the midpoint
2) Continuous data. Like time values, temperatures can be averaged as well.
3) Discrete data. Place locations in a race or competition are finite and we can't have midpoints. We can't have a midpoint between 9th and 10th place for instance.
4) Continuous data. We can find the midpoint and it makes sense to do so when it comes to speeds.
5) Discrete data. This is a finite number and countable. We cannot have 20.5 freshman for instance.
no idea. please help:)
Answers
Find the GCF of the first two terms and the GCF of the last two terms of the polynomial. 5h^3+20h^2+4h+16
Answers
The GCF of the last two terms: 4
5h³ and 20h²
Both of these terms are divisible by 5. (constant)
Both of these terms also have at least 2 h's. (variable)
4h and 16
Both of these terms are divisible by 4.
Only one term has a variable, so that has to be left out.