which of the following functions is continuous between x=-3 and x=0? choices on attachment
Answers
A: f(x) = (-x + 1)/(x + 2)
Now we don't actually need to know what the graph of this function looks like to see which values it is continuous for, instead we should look at which values of x will make this function undefined - in this case that would be x = -2. The reasoning behind this is that a number divided by 0 would be undefined, so when we search for which value of x would make the denominator of the equation 0, we get:
x + 2 = 0
x = -2
Since x = -2 is within the interval [-3, 0] we cannot say the function is continuous over this interval
B: f(x) = -2/(x + 1)
Using the same method as above we get:
x + 1 = 0
x = -1
x = -1 is again within the interval [-3, 0] and so the function is not continuous within this interval
C: f(x) = 3x/(x - 2)
x - 2 = 0
x = 2
x = 2 is outside the interval of [-3, 0] and so the function is continuous within this interval and C is the correct answer.
Just for the sake of it however we can look at D as well:
D: f(x) = 1/(2x + 1)
2x + 1 = 0
x = -1/2
-1/2 is within [-3, 0] and so D is not continuous over this interval
Related Questions
Which expressions result in a rational number?
Answers
C+D
A*B
C*D
A*A
A+B does not give a rational number answer; √3+2√3 = 3√3
C+D is a rational number; √25=5 and √16=4; 5+4=9.
A+D is not a rational number; √3+√16 = √3+4
A*B is a rational number; √3*2√3 = 2√9 = 2*3 = 6
B*D is not a rational number; 2√3*√16 = 2√3*4 = 8√3
C*D is a rational number; √25*√16 = 5*4 = 20
A*A is a rational number; √3*√3 = √9 = 3
Rational numbers are those that can be expressed as a fraction of two integers. Examples of expressions that result in rational numbers include simple calculations or operations that result in whole numbers or decimal numbers that can be written as a fraction.
Explanation:In mathematics, a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, with the denominator not being zero. If an expression results in such a number, then it is considered a rational number.
Let's consider some examples from the given information:
106 (6-3): This equates to 10^3 which will result in the number 1000, a rational number as it can be expressed as 1000/1. 4.5 × 10⁹: The result of this multiplication also gives a rational number as it can be written in a fraction form. 0.3333: This number is also rational as we can write it as 3333/10000. 0.6: This can be written as 6/10 or 3/5, so it's also a rational number.
However, numbers resulting from certain trigonometric functions like sine and cosine, logarithms, or exponential functions may not always be rational. These functions require pure numbers as inputs and outputs.
Learn more about Rational Numbers here:https://brainly.com/question/24398433
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A bicycle and a bicycle helmet cost 240 dollars. How much did each cost, if the bicycle cost 5 times as much as the helmet?
Question 8 options:
bike = $200 and helmet = $40
bike = $160 and helmet = $80
bike = $120 and helmet = $60
bike = $100 and helmet = $90
Answers
Avenue A is perpendicular to North Street. What is the relationship between Avenue A and South Street?
Answers
Final answer:
Avenue A is perpendicular to North Street, and it would also be perpendicular to South Street since they run parallel. The concept of vector components Ax and Ay, being perpendicular and analogous to these streets, helps illustrate the perpendicular relationship between Avenue A and South Street.
Explanation:
Given that Avenue A is perpendicular to North Street, we can infer that Avenue A is also perpendicular to South Street because in a typical city grid, north and south streets run parallel to each other. When two lines are perpendicular to a third line, they are parallel to each other and form a 90° angle with the perpendicular line.
The relationships among vectors can help further illustrate this idea. If we look at the components of a vector, Ax and Ay, where Ax is the movement in the east-west direction (like Avenue A) and Ay is the movement in the north-south direction (like North Street), they form a right angle with each other. If you walk along Avenue A (the Ax component), then along North Street (the Ay component), you construct a path that is the resultant vector A with its own magnitude and direction.
The sum of these vectors is represented as Ax + Ay = A. This combination holds only for vector quantities, which include both magnitude and direction. This principle does not apply when we're summing up the magnitudes alone, as in the example where if Ax is 3 m east and Ay is 4 m north, the direct path A would not simply be their sum in magnitudes but would instead be a diagonal 5 m northeast according to the Pythagorean theorem.
the quotient of 7.3 divided by -7.3
Answers
Answer:
-1
Step-by-step explanation:
7.3
------ = -1
-7.3
You are reading a book with 120 pages if you want to read the same number of pages each night how many would you have to read each night to finish in 10 days
Answers
[tex]120 / 10 = 12[/tex]
If you want to read the same number of pages each night for 10 days, you will read 12 pages every night.
If you wanted to finish an 120 paged book in 10 days you would have to read 12 pages. You can ether divided 10/12 and you confirm your answer by 10•12.
Can you please answer for 30 points Thanks
Answers
Find m∠2.
90 - 72 = 18
m∠2 = 18°
Now ∠2 + ∠3 must equal 180° because they are on a straight line.
Subtract 18 from 180.
180 - 18 = 162
m∠3 = 162°
Answer:
Step-by-step explanation:
To find angle 3, we need to first find angle 2.
-It is given that it's a square. The full angle is 90°. Angle 2 would be 90-72, which is 18°.
Now that we have angle 2, we can find angle 3 because angle 2 and 3 are linear pairs.
180°-18°
162°
m<3=162°
g={(-9,6),(-6,4),(2,-6),(6,-5)}
h(x)=3x-4
find the following
g^-1(-6)=
h^-1(x)=
(h^-1·h)(3)=
Answers
g^-1(-6) = 2
b) Swap x and y and solve for y.
x = 3y -4
x +4 = 3y
(x +4)/3 = y
Then the inverse function can be written as
h^-1(x) = (x +4)/3
c) You have shown the product of h^-1(x) and h(x). We have to assume that is what you intend.
h^-1(3) = (3 +4)/3 = 7/3
h(3) = 3×3 -4 = 5
(h^-1·h)(3) = h^-1(3)·h(3) = (7/3)·5
(h^-1·h)(3) = 35/3
If you intend (h^-1◦h)(3), that value is 3.
if sec theta equals negative 5/3, such that 180° <thata<270° then determine what is tan theta ?
Answers
Different sizes of ribbon need to be cut to go around various shapes. All of the following sizes are in inches.
π , √5 ,√8 ,2√5
a.) Without using your calculator, approximate the decimal equivalent of each number to the nearest tenth.
b.) Order the ribbon sizes from least to greatest.
PLEASE SHOW YOUR WORK
Answers
The square root of 5 is about 2.2
The square root of 8 is about 2.8
pi is about 3.14
2 square roots of 5 are about 4.4
The numbers are also placed in order from least to greatest.
Simplify the expression insert
Answers
[tex] \frac{96}{8} =12[/tex]
So, we can rewrite our radical as follows:
[tex] \sqrt{ \frac{96}{8}} = \sqrt{12} [/tex]
Now, we are going to decompose 12 into prime factors:
[tex]12=2^2*3[/tex]
So, we can rewrite our fraction as follows:
[tex] \sqrt{12} = \sqrt{2^2*3} [/tex]
Since 2 has the same exponent as the index of the radical, we can take it out:
[tex]\sqrt{2^2*3}=2 \sqrt{3} [/tex]
We can conclude that the simplified form of the expression is: [tex]2 \sqrt{3}[/tex]
40% of the flowers in the garden are roses the rest of the flowers are daiseis if 8 flowers are roses how many flowers are there altoghether draw a model to justify your anwser
Answers
2/5 of the garden is 8 roses, 1/5 of the garden is 4 flowers, 3/5 is 12 flowers, so if 2/5 is 8 roses, 3/5 is 12 daisies.
8+12=20
There are 20 flowers in total.
Let j = 16. What is the value of k in the equation k = 2 × j + 4?
Answers
You put 16 in for j
k = 2 * 16 + 4
Multiply
k = 32 + 4
Add
k = 36
The answer is 36
Hope this helps!
That equals:
-------↓-------
k = 2 × 16 + 4
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
Multiplication comes before addition
2 × 16 = 32
32 + 4 = 36
k = 36
Hope this helps :)
What is 50,935 divided by 5?
Answers
Which choice shows a correct way to solve 8•13?
Answers
Answer:
Step-by-step explanation:
8 x(10+3)
if if f(x)=x-6 and g(x)=x, what is if f(x) times g(x)?
Answers
Need help on this please
Answers
So "C"
Lizzie played tennis for 2 2/3 hours. Andrew played tennis for 1 1/3 hours. How much longer did Lizzie play tennis than Andrew?
Answers
Lizzie played for 2 hours and 40 minutes
Andrew played for half as long as Lizzie did, so Lizzie played for 1 1/3 hours longer than Andrew did. Hope this helps!
[tex]2 \frac{2}{3} -1 \frac{1}{3} [/tex]
For simpler subtraction, we can convert the mixed numbers into improper fractions:
[tex]\frac{8}{3} -\frac{4}{3} = \frac{4}{3}= 1\frac{1}{3} [/tex]
Lizzie played tennis [tex]1\frac{1}{3}[/tex] hours, or 1 hour and 20 minutes, longer than Andrew.
please I need help and I dont get it..
Answers
40*3=120 total cakes
120*.15=18 chocolate cakes
SOMEONE HELP ME OUT PLEASE WILL MARK BRAINLIEST
Answers
Which angle in the image corresponds to ∠X in the pre-image?
∠L
∠M
∠N
Answers
The angle that corresponds to angle X would be the angle on the opposite figure that is in the same position as angle X.
Your answer is Angle L.
Bella is making button barrettes. She allows each of her friends to reach into her bag of buttons and randomly select a color. Then she replaces it with the same color button and shakes the bag before letting another friend pick a color. Bella’s bag of buttons contains the colors below. Which model shows the probability of randomly selecting each color button from her bag?
Answers
Answer: Pink 12 %, Orange 40%, Green 28%, Blue 20%
Step-by-step explanation:
Given, Total number of,
Pink button = 300
Green button = 700
Orange button = 1000
Blue button = 500
Thus, total button = 300 + 700 + 1000 + 500 = 2500
Now, the probability of getting pink button = [tex]\frac{300_C_1}{2500_C_1} = \frac{300}{2500} = 0.12=12\%[/tex]
The probability of getting green button = [tex]\frac{700_C_1}{2500_C_1} = \frac{700}{2500} = 0.28=28\%[/tex]
The probability of getting orange button = [tex]\frac{300_C_1}{2500_C_1} = \frac{1000}{2500} = 0.40=40\%[/tex]
The probability of getting blue button = [tex]\frac{300_C_1}{2500_C_1} = \frac{500}{2500} = 0.20=20\%[/tex]
⇒ Third Option is correct.
Answer:
the third one
Step-by-step explanation:
i got 100
Please need help on this
Answers
you are u on online school y
rate 5 stars plz
The letter E would be for stock increasing
Letter D for Stock decreasing
and Letter C for it remaining constant
Hope this helped!!
Veronique has a spinner with three sections of equal size, red (r), green (g), and blue (b).The spinner is spun twice. The sample space for the possible outcomes is S = {rr, rb, rg, gr, gg, gb, br, bg, bb}. If the number of times red is spun is the random variable, X, which graph represents the probability distribution?
Answers
Answer:
a, the first graph
Step-by-step explanation:
The probability distribution represents the likelihood of each possible value of a random variable. In this case, the random variable X represents the number of times red is spun. The graph that represents this probability distribution would have the values 0, 9/33, and 24/33 plotted for X=0, X=1, and X=2.
Explanation:The probability distribution represents the likelihood of each possible value of a random variable. In this case, the random variable X represents the number of times red is spun. The sample space S consists of nine outcomes with one red spin and twenty-four outcomes with two red spins.
To find the probability distribution, we calculate the probability of each possible value of X. The probability of X=0 (no red spins) is 0, the probability of X=1 (one red spin) is 9/33, and the probability of X=2 (two red spins) is 24/33.
The graph that represents this probability distribution would have the values 0, 9/33, and 24/33 plotted on the y-axis for the corresponding values of X=0, X=1, and X=2 on the x-axis.
the area of a circle is 452.39 ft^2 . Why would the diameter have to be?
Answers
Find the radius.
Area=πr^2
plug in the known numbers
452.39= (3.14)r^2
divide both sides by 3.14
452.39 ÷ 3.14= r^2
144.07= r^2
take the square root of 144.07 and r^2
12 feet= r
STEP 2:
multiply radius by 2 to equal diameter
Diameter= Radius * 2
Diameter= 12 feet * 2
Diameter= 24 feet
ANSWER: The diameter would be 24 feet.
Hope this helps! :)
The Delucci family traveled on the highway for two hours at 70 miles per hour, and then three hours at 35 miles per hour. How far did they travel in the five hours? How do you know? Explain (write a prportion)
Answers
which equations are equal to 1/4 (8x+56) =20
Answers
if u solve for x; 20-14=6 , 2x=6; x=3
Following are the calculation to the given equation:
Given:
[tex]\to \frac{1}{4}(8x+56)=20[/tex]
To find:
x=?
Solution:
[tex]\to \frac{1}{4}(8x+56)=20\\\\\to \frac{8x}{4} + \frac{56}{4}=20\\\\\to 2x + 14=20\\\\\to 2x = 20-14\\\\\to 2x= 6\\\\\to x=\frac{6}{2}\\\\\to x= 3[/tex]
Therefore, the final answer is "3".
Learn more:
brainly.com/question/23248705
a right triangle has a legs measuring 16 in and 28 in
What is the length of the hypotenuse?
Round your answer to the nearest tenth.
a. 23.0 in.
b. 32.2 in.
c. 44.0 in.
d. 1040.0 in.
URGENT
WILL MARK BRAINLEIST
Answers
To solve this, let's use apply the Pythagorean Theorem.
Formula: [tex]a^2 + b^2 = c^2[/tex]
For a and b, we would plug in the values for the two known legs.
[tex]16^2 + 28^2 = c^2[/tex]
[tex]16^2 = 256 28^2 = 784 256 + 784 = 1,040[/tex]
Now we take the square root of 1,040
[tex] \sqrt{1,040} = 32.2[/tex]
Your answer is 32.2 :)
Jaden buys a raffle ticket. Each ticket has a 1% chance of being drawn. How likely is it that Jaden's ticket will be drawn? It definitely will be drawn.
It likely won't be drawn.
It likely will be drawn.
It definitely won't be drawn.
Answers
Your answer would be
It likely won't be drawn.
The answer is - It likely won't be drawn. The likelihood of Jaden's ticket being drawn is 1%, so it is unlikely that his ticket will be selected.
The likelihood that Jaden's ticket will be drawn depends on the probability of his ticket being selected. In this case, each ticket has a 1% chance of being drawn, which means there is a 1 in 100 chance that Jaden's ticket will be selected. Therefore, it is likely that Jaden's ticket won't be drawn.
Jaden's raffle ticket has a 1% chance of being drawn, making it much more likely that it won't be drawn than it will. The concept of 'being due to win' is a common fallacy as each draw is an independent event with a constant probability.
The table contains data on the admission price (in dollars) for one-day tickets to 10 theme parks in the United States. Find the interquartile range for this data set. The numbers are 60 60 42 43 25 52 65 43 42 40
Answers
To find the IQR, the data was first sorted and then split into two halves to find Q1 (42) and Q3 (60). The IQR of the theme park ticket prices is the difference between Q3 and Q1, which is 18 dollars.
Explanation:To find the interquartile range (IQR) of the admission price for one-day tickets to 10 theme parks in the United States, first, we need to arrange the data in ascending order: 25, 40, 42, 42, 43, 43, 52, 60, 60, 65. With the data sorted, we find the median (the middle value) to divide the data set into two halves. However, since there are an even number of observations, the median will fall between the two middle numbers. The two middle numbers are the 5th and 6th values, which are 43 and 43, so their average is also 43.
Next, we find the first quartile (Q1) and the third quartile (Q3). Q1 is the median of the first half of the data (25, 40, 42, 42, 43), which is 42. Q3 is the median of the second half of the data (43, 52, 60, 60, 65), which is 60. The IQR is then found by subtracting Q1 from Q3, which is 60 - 42 = 18.
will give crown to best answer!!!!!!
\Which of these pairs of points defines a line with a slope of -1?
A. (3, 10) and (3, 5) B. (3, 10) and (5, 3) C. (10, 3) and (15, -2) D. (10, 3) and (3, 5)
Answers
Answer:
c
Step-by-step explanation: