The two limits when x tends to zero are:
\(\lim_{x \to \ 0^-} f(x) = 1\\\\ \lim_{x \to \ 0^+} f(x) = 0\)
How to get the limits when x tends to zero?Notice that we have a jump at x = 0.
Then we can take two limits, one going from the negative side (where we will go along the blue line)
And other from the positive side (where we go along the orange line).
We will get:
\(\lim_{x \to \ 0^-} f(x) = 1\\\\ \lim_{x \to \ 0^+} f(x) = 0\)
Notice that the two limits are different, that means that the function is not a continuous function.
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Name two transformation sequences that can be done in any order without changing the outcome and explain how you know.
Answer:
There are two different categories of transformations: The rigid transformation, which does not change the shape or size of the preimage. The non-rigid transformation, which will change the size but not the shape of the preimage.
Step-by-step explanation:
yep sorry if you get it wrong it is
B
Can someone pls help me :-(
Answer:
One: x = 3/32
Two: y = 3/10
Step-by-step explanation:
One
y = k*x
1/4 = k* 1/8 Multiply both sides by 8
8(1/4) = 8*k*(1/8)
8/4 = k
k = 2
=======================
3/16 = 2*x Divide by 2
3/32 = x
Two
y = 2/5
x = 1/3
2/5 = k * 1/3 Multiply both sides by 5
2 = 5*k * 1/3
2 = 5/3 * k Multiply both sides by 3
6 = 5 * k Divide both sides by 5
6/5 = k
y = 6/5 * x
x = 1/4
y = 6/5 * 1/4
y = 6/20 = 3/10
Evaluate the function f(x) = x +5x +7 at the given values of the independent variable and simplify. b. f(x+ 4) f(-x) a. f(6) C. f(6) (Simplify your answer.) a. (Simplify your answer.) b. f(x+ 4) . f(-x) =
f(6) = 93.
To answer the question, you need to substitute the given values of the independent variable into the function and simplify.
For a. f(6), substitute 6 for x in the function, giving f(6) = 6 + 5(6) + 7 = 43. To solve b. f(x+ 4) f(-x), substitute x+ 4 for x in the first part of the equation, giving f(x+ 4) = (x+ 4) + 5(x+ 4) + 7, and substitute -x for x in the second part, giving f(-x) = (-x) + 5(-x) + 7. Simplifying these equations, you get f(x+ 4) = x + 9x + 31 and f(-x) = -x - 5x - 7.
Finally, for c. f(6), substitute 6 for x in the equation, giving f(6) = 6 + 9(6) + 31 = 93. Simplifying this equation gives f(6) = 93.
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How would you write the quotient as a simplified fraction
The written form of the quotient as a simplified fraction as required in the task content is; Choice Choice B; 18 1/2.
What is the written form of the quotient as a simplified fraction?It follows from the task content that the quotient as given in the task content is; 851/46.
On this note, it follows that the result of the division is; 18 with a remainder of 23.
Hence, we have; 18 23/46 which is equivalent to 18 1/2.
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At a grocery store, 5 oranges cost $2.00. At this rate, how much would 12 oranges cost?
Answer:
Step-by-step explanation:
2.00/5= 0.40 an orange
12*.40= $4.80
find the exact trigonometric ratios for the angle x whose radian measure is given. (if an answer is undefined, enter undefined.) 27???? 4
The exact trigonometric ratios for the angle x is second quadrant.
Given Radian equals to θ = 27π / 4, we need to find all the Trigonometric ratios for the same -
Lets calculate the value of θ first.
We know π equals 180 degree angle and 2π equals 360 degree, hence with each 2π the radian moves back to zero degree. Which means
θ = 27π / 4 can be reduced to θ = 3π / 4
Hence θ = 135 degree which can be represented as below -
As This lies in second quadrant, hence on x-axis (Value of base , needs to be taken as -1)
sin θ = 1/√2 cosec θ = √2
cos θ = -1/√2 sec θ = - √2
tan θ = -1 cot θ = - 1
What is trigonometric ratios?Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.
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answer easy question quick
Answer:
Step-by-step explanation:
a) 9.80- 98/10
b) 7.3- 73/10
a) 7/100- 0.07
b) 82/10- 8.2
Hope this helps
Fraction:
a) 98/100
b) 73/10
Decimal:
a) 0.07
b) 8.2
Select the correct answer from each drop-down menu.
The table shows the hourly cookie sales by students in grades 7 and 8 at the school's annual bake sale.
Grade 7 Grade 8
20 21
15 29
30 14
24 19
18 24
21 25
The interquartile range for the grade 7 data is
The interquartile range for the grade 8 data is
The difference of the medians of the two data sets is
The difference is about
times the interquartile range of either data set.
Reset Next
The interquartile range for the grade 7 data is 9 (30 – 21).
The interquartile range for the grade 8 data is 10 (29 – 19).
The difference of the medians of the two data sets is 6 (21 – 15).
The difference is about 0.67 times the interquartile range of either data set.
What is interquartile range?It is a measure of the spread of numerical data, which is calculated by subtracting the third quartile (Q3) from the first quartile (Q1). It is used to measure the variability of a data set and is a good indicator of the outliers in the data set.
In the table given, the interquartile range of grade 7 data is 9 and the interquartile range of grade 8 data is 10.
The difference of the medians of the two data sets is 6.
This difference is about 0.67 times the interquartile range of either data set.
This shows that the variability between the two data sets is not significantly different, as the difference between their medians is only two thirds of the IQR of either data set. Thus, the two data sets are relatively similar in terms of their variability.
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I. Will give Brainly to whoever can help meeeeeeeeee
Answer:
(3/2)x - 2 < 11/2
(3/2)x < 15/2
x < 5
number line with a closed circle at 5 and the arrow going to the left
2x - 2 > 8
2x > 10
x > 5
number line with a closed circle at 5 and the arrow going to the right
4x - 7 > 13
4x > 20
x > 5
number line with an open circle at 5 and the arrow going to the right
3x + 4 < 19
3x < 15
x < 5
number line with an open circle at 5 and the arrow going to the left
Here is an identity.
a(4x 10) = 24x + 5b
Work out the values of a and b.
i know a is equal to 6 but im stuck with b
Answer:
b = 12
Step-by-step explanation:
If we substitute a = 6 and simplify the given equation, we get:
6(4x 10) = 24x + 5b
Simplifying the left-hand side, we get:
24x + 60 = 24x + 5b
Subtracting 24x from both sides, we get:
60 = 5b
Dividing both sides by 5, we get:
12 = b
Therefore, the values of a and b are a = 6 and b = 12.
How does the value of the digit 3 in the number 63,297 compared to the value of the digit 3 in the number 60,325?
Answer:
The value of digit 3 in 63,297 is in the thousands place while the digit 3 in the number 60,325 is in the hundreds place
Hope this helps!
Find x and y ( please explain )
Answer:
y = 75°
Step-by-step explanation:
y and 105°
are on a straight line ,
a straight line is 180°
180 - 105 = 75°
y=75 °
I'm not sure about x hope you understand
A piece of string 25 cm long goes exactly once round the edge of a plate in the form of a quadrant. Calculate the area of the quadrant.
Answer:
25 cm
Step-by-step explanation:
If the string is 25 cm and it goes perfectly around the edge of a plate. The plate, is 25 cm.
Help me please ASAP!!!
Which of the following statements implies that limx→−[infinity]f(x)=+[infinity]? A. For every M>0 there exists N>0 so that if x<−N then ∣f(x)∣>M. B. For every M>0 there exists N>0 so that if ∣x∣>N then ∣f(x)∣>M. C. For every M>0 there exists N>0 so that if ∣x∣>N then f(x)>M. D. For every M>0 there exists N>0 so that if x<−N then f(x)
The correct statement that implies limx→-∞f(x)=+∞ is option C.
Option C states: "For every M > 0, there exists N > 0 such that if |x| > N, then f(x) > M." This statement means that as x approaches negative infinity, f(x) becomes arbitrarily large (greater than any positive number M). This aligns with the definition of limx→-∞f(x)=+∞, which states that the function grows without bound as x approaches negative infinity.
Options A, B, and D do not necessarily imply that f(x) goes to positive infinity as x approaches negative infinity. These options may indicate boundedness or other behaviors of the function, but they do not specifically capture the concept of f(x) going to positive infinity as x approaches negative infinity.
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Han made some hot chocolate by mixing 4 cups of milk with 6 tablespoons of cocoa.
How many tablespoons of cocoa per cup of milk is that?
How many cups of milk per tablespoon of cocoa is that?
Answer:
1.5 ( tablespoons per cup) and 0.68 for the second one
Step-by-step explanation:
your just trying to find the unit rate
what is the answer to this question -11+8(6k-17) ?
Answer:
\(\huge\boxed{\sf 48k - 147}\)
Step-by-step explanation:
Given expression:= -11 + 8(6k - 17)
Distribute 8 to 6k and 17= -11 + 48k - 136
Combine like terms= 48k - 11 - 136
= 48k - 147\(\rule[225]{225}{2}\)
Answer:
48k - 147
Step-by-step explanation:
Now we have to,
→ Simplify the given expression.
The expression is,
→ -11 + 8(6k - 17)
Major steps we use are,
→ Rearranging the expression.
→ Combining the like terms.
Let's simplify the expression,
→ -11 + 8(6k - 17)
→ 8(6k - 17) - 11
→ 8(6k) - 8(17) - 11
→ 48k - 136 - 11
→ 48k - (136 + 11)
→ 48k - 147
Hence, the answer is 48k - 147.
Question 4 13 points)
COMPARING METHODS
Solve the triangle with the given information. Round decimal answers to the nearest tenth:
m ZB = 98°
m ZC = 37°
a = 18
The solutions to the triangle are given as follows:
m < A = 45º.b = 25.2.c = 15.3. What is the law of sines?We consider a triangle with side lengths and angles related as follows:
Side length of a is opposite to angle A.Side length of b is opposite to angle B.Side length of c is opposite to angle C.Then the lengths and the sines of the angles are related as follows:
sin(A)/a = sin(B)/b = sin(C)/c.
The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of angle A is given as follows:
m < A + 98 + 37 = 180
m < A = 180 - 135
m < A = 45º.
Hence the relations from the law of sines are given as follows:
sin(45º)/18 = sin(98º)/b = sin(37º)/c.
Hence the length b is given as follows:
sin(45º)/18 = sin(98º)/b
b = 18 x sine of 98 degrees/sine of 45 degrees
b = 25.2.
The length c is given as follows:
sin(45º)/18 = sin(37º)/c.
c = 18 x sine of 37 degrees/sine of 45 degrees
c = 15.3.
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Given the following table, compute the mean of the grouped data. Class Midpoint [1, 6) 3.5 [6, 11) 8.5 [11, 16) 13.5 [16, 21) 18.5 [21, 26) 23.5 26, 31) 28.5 [31, 36) 33.5 Totals What is the mean of the grouped data? 20.016667 What is the standard deviation of the grouped data? What is the coefficient of variation? percent 30 Frequency 2 1 5 7 10 3 2
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnn
The mean of the grouped data is approximately 13.5. To compute the mean of grouped data, we need to consider the midpoints of each class interval and their corresponding frequencies.
The mean of the grouped data is calculated by summing the products of each midpoint and its frequency, and then dividing the sum by the total frequency.
Using the provided table, we have the following midpoints and frequencies:
To compute the mean, we need the missing frequencies for each class interval. Once we have the frequencies, we can multiply each midpoint by its frequency, sum up the products, and then divide by the total frequency to get the mean.
To compute the mean of grouped data, we need the midpoints and frequencies of each class interval. Once we have the complete table, we multiply each midpoint by its frequency, sum up the products, and divide by the total frequency to obtain the mean.
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The silence of a triangle are 9 12 and 15 is this a right triangle
Answer:
Yes because 9 + 12 = 15
Step-by-step explanation:
What is the solution to the system of equations y equals 1.5 x minus 4y equals negative x?
The solution to the system of equations is (1.6,-1.6).
What is the system of equations?
Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.
Here, we have
Given equations:
y = 1.5x - 4....(1)
y = -x....(2)
Substitute y = -x in the first equation
-x = 1.5x - 4
Collect like terms
-1.5x - x = -4
This gives
-2.5x = -4
Divide both sides by -2.5
x = 1.6
Substitute x = 1.6 in y = -x
y = -1.6
Hence, the solution to the system of equations is (1.6,-1.6)
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SOMEBODY!!! HEELLLLLLP if you can help me with one question that's fine!
Step-by-step explanation:
Question 1The 20° angle is equal to the angle next you friend.
since they are interior alternate angles
The height of the ballon is 600 feet
Let x be the missing distance we are looking for
sin20° = 600/x switch x and sin 20° x = 600/ sin 20° x=1754.28≈ 1754 ftso the missing distance is 1754 feet
Question 2Here I represented the situation to visualize the problem
Let h be L be the length of the ladder
sin 30° = 7/L switch L and sin 30°L= 7/sin 30° = 14L = 14 ftso the ladder is 14 ft
Which value of x would make the expression fourth root of 7 to the fifth power all to the x power equal to 5? a) 3 b) 12 c) four fifths d) five fourths
The correct answer for this question is option d). four fifths.
What does root imply?
The terms origin, source, inception, and root all refer to the starting place of anything. The term "origin" refers to the things or people from which something ultimately derives, and it frequently refers to the factors present before the thing itself manifests.
This type of question looks tricky at first by breaking them into parts we can handle .
This question is all about \(x^{7^{\frac{5}{4} } }\) we have to find the value of x put the value of x=3 we will get
\(x^{7^{\frac{5}{4} } }\) = 11.38 ≅ 12 so the value
a) 3 = > \(3^{12}\) = 531441
b) 12 = > \(12^{12}\) = 8916100448256
c) Four fifths => \((\frac{4}{5}) ^{12}\) = 0.068
d) Five fourths => \((\frac{5}{4}) ^{12}\) = 14.55 which is the nearest value to the required solution.
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If anyone knows how to do this please help, its for a test and I have to finish the course by 11:59 tonight
Answer: The answer to this inequality is C.
what is 2(3x+2)=2x+28
Answer:
x=6
Step-by-step explanation:
6x+4=2x+28
4x=24
x=6
Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
Answer:
Rise is vertical, run is horizontal
Step-by-step explanation:
Please help i need a explanation and what one, its due tmmr
Answer:
what do u need it on there is nothing there
Evaluate the expression. Will choose brainliest
Answer:
-213
Step-by-step explanation:
3|3-5|^2-(-15)^2
3(4)-225
=12-225= -213
Answer:
-213
Step-by-step explanation:
=3|x+y|²-(xy)²
Subtitute value of x and y above:
=3(|3+-5|)²-(3×-5)²
=3(|-2|)²-(-15)²
=3(2)²-(225)
=3(4)-225
=12-225
=-213
Note: If you need to ask question,I'll gladly give you answee.Thanks
The dot plot shows the numbers of text message received by students over the weekend .
Can someone help me answer and explain with all them ???
Answer:
basdasidw buga
Step-by-step explanation:
Answer:
Part A: The amount of students represented is around 68-69
Part B: You Can collect the data by using the dot plot, the units are text messages
Part C: How many students receive text messages over the weekend? This is a statical question because there’s more than one answer.
I’m not sure by the way, I hope it helps anyway. If this doesn’t work out then sorry :)
true or false: there are arbitrarily manydifferent mathematical functions that interpolatea given set of data points.
the statement "there are arbitrarily many different mathematical functions that interpolate a given set of data points" is false.
Interpolation is the process of constructing a mathematical function that passes through a given set of data points. However, not every set of data points can be interpolated by a unique function. For example, if we have two data points (x1, y1) and (x2, y2) where x1 ≠ x2, then there exists a unique linear function f(x) = mx + b that passes through these two points.
However, if we have three or more data points, there may be multiple functions that interpolate the data. Nevertheless, there are some conditions that can guarantee the uniqueness of the interpolating function, such as if the data points are the values of a polynomial of degree n or less, then there exists a unique polynomial of degree n or less that interpolates the data.
Therefore, the statement "there are arbitrarily many different mathematical functions that interpolate a given set of data points" is false. The number of possible interpolating functions depends on the properties of the data points and the type of function used for interpolation.
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