Therefore, f(x) = [[x − 2]] is discontinuous at x = k - 2 and x = k + 2. The discontinuities at these points are removable.
The function f(x) = [[x − 2]] is discontinuous at any value of x that is two units away from an integer. That means it is discontinuous at x = k - 2 and x = k + 2, where k is any arbitrary integer.
The discontinuities at x = k - 2 and x = k + 2 are both removable. That is because the discontinuities occur when the left- and right-hand limits of the function are not equal, and the limits can be made equal by redefining the value of the function at the point of discontinuity.
To solve the problem, set the left- and right-hand limits equal to each other and solve for x.
Left-hand limit: lim x→k-2 f(x) = lim x→k-2 [[x − 2]] = [[k - 2 - 2]] = [[k - 4]]
Right-hand limit: lim x→k+2 f(x) = lim x→k+2 [[x − 2]] = [[k + 2 - 2]] = [[k]]
Equating the two limits, we have [[k - 4]] = [[k]]. Solving for x, we get x = k - 2 and x = k + 2.
Therefore, f(x) = [[x − 2]] is discontinuous at x = k - 2 and x = k + 2. The discontinuities at these points are removable.
Hope this helps!
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what is 10+28 divided by 7 (10-9+6)
Answer:
To simplify this expression, we first need to evaluate the expression inside the parentheses:
10 - 9 + 6 = 7
Now we can substitute this value back into the original expression:
10 + 28 ÷ 7 (7) = 10 + 4(7) (since 28 ÷ 7 = 4)
= 10 + 28
= 38
Therefore, 10 + 28 divided by 7 (10-9+6) equals 38.
Hans has scored 79, 89, 80, and 65 on his previous four tests. What score does he need on his next test so that his average (mean) is 77?
yes
im not sure though try it!
The Grade 8 learners decided to start training more. They will either box or grid. There
are 125 Grade 8 learners, and they box and grid in the ratio 3:2. Calculate how many
learners participate in each sport?
Bill's SUV is 6 feet 4 inches tall. If he puts a 2 -foot 9 -inch box on top of his SUV, what is the total height of the SUV and the box (in feet and inches)?
Answer: The total height of the SUV and the box is 9 feet 1 inch.
Step-by-step explanation:
To solve this problem, we first convert the height of the SUV and the box from feet and inches to inches. The height of the SUV is 6 feet 4 inches, which is equal to 76 inches. The height of the box is 2 feet 9 inches, which is equal to 33 inches. We then add the heights of the SUV and the box to get the total height:
76 inches + 33 inches = 109 inches
To convert this back to feet and inches, we divide by 12 to get 9, with a remainder of 1. Therefore, the total height of the SUV and the box is 9 feet 1 inch.
Add or subtract these rational expressions. Show your common denominators and numerators on this sheet or separate paper. Factor denomunators when possible. 1. 5/8 - 3/8x
2. 9/15x + 2/15x
3. 5x/7 - 2x/7
1). 1/4
2). 11/15x
3). 3x/7
1. To add or subtract the rational expressions 5/8 and 3/8x, we need a common denominator. The smallest common denominator is 8x, so we can rewrite each expression with a denominator of 8x:
5/8 = 5x/8x
3/8x = 3/8 * 1/x = 3x/8x
Now we can combine the numerators and simplify:
5x/8x - 3x/8x = (5x - 3x)/8x = 2x/8x = 1/4
Therefore, 5/8 - 3/8x = 1/4.
2. To add or subtract the rational expressions 9/15x and 2/15x, we again need a common denominator. The smallest common denominator is 15x, so we can rewrite each expression with a denominator of 15x:
9/15x = 3/5x
2/15x = 2/15 * 1/x = 2/15x
Now we can combine the numerators and simplify:
3/5x + 2/15x = (9 + 2)/15x = 11/15x
Therefore, 9/15x + 2/15x = 11/15x.
3. To add or subtract the rational expressions 5x/7 and -2x/7, we already have a common denominator of 7. We can simply combine the numerators:
5x/7 - 2x/7 = (5x - 2x)/7 = 3x/7
Therefore, 5x/7 - 2x/7 = 3x/7.
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A baseball team won of its games this season. Which percent is equivalent to ?
A. 55%
B. 55.5%
C. 55%
D. 59%
55.5% is equivalent to 5/9.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
A baseball team won of its games of 5/9 this season.
We need to find the equivalent percentage of 5/9.
To convert 5/9 to a percentage, we can multiply it by 100.
(5/9) x 100 = 55.5%
So, the percentage equivalent to 5/9 is 55.5%.
Therefore, 55.5% is equivalent to 5/9.
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The__________of an angle is the point where the sides of the angle intersect
Help please<3
If f(x)=-7x-13 what is the value of f(-4)
Answer:
f(-4) = 15
Step-by-step explanation:
A function is notated as f(x), because the x is the value you are putting in. For example. In f(x) = x + 5, the value you are putting in is x, and the output would be x + 5.
So in this case, we have f(x) = -7x-13. We are to figure out f(-4), so we can simply put in -4 as the x-value;
-7(-4) - 13
28 - 13
15
And so the value of f(-4) = 15
if you liked this answer please mark brainliest!
Answer:
9
Step-by-step explanation:
f times 9 = 7x - 13 = 9 pls make me brianlist
need someone to help me understand how to do an Exponential Equation
Answer: p = (3.6 x 10^4)(0.03)^2
Step-by-step explanation:
How many times as great as the value of 4 in 4,670 is the value of 4 in 5,040
The value of the digit 4 in 5,040 is 100 times more than that of the digit 4 in 4,670.
At the unit place of both numerals, there is a digit 4. The place value of a digit determines how valuable it is in a number. The position of the digit from the number's rightmost side determines its place value.
The value of the digit 4 in the tens place of the number 4,670 is 4 x 10 = 40.
The value of the digit 4 in the thousands position of the number 5,040 is 4 x 1000, or 4000.
Therefore, As 4000/40 = 100, the value of the digit 4 in 5,040 is 100 times more than that of the digit 4 in 4,670.
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Mr. Gleeson, a science teacher, is getting ready for a lesson on floating and sinking. For the lesson, he grabs a glass container shaped like a rectangular prism that is 60 centimeters long, 20 centimeters wide, and 45 centimeters tall. Mr. Gleeson knows that 1,000 cubic centimeters is the same as 1 liter, and he wants to figure out how many liters of water will fill the container before it overflows.
Answer:
To find the volume of the container in cubic centimeters, we multiply its length, width, and height:
Volume = 60 cm x 20 cm x 45 cm = 54,000 cubic centimeters
To convert cubic centimeters to liters, we divide by 1,000:
54,000 cubic centimeters ÷ 1,000 = 54 liters
Therefore, the container can hold 54 liters of water before it overflows.
Step-by-step explanation:
For a given rational function, n < m. what does this mean about the graph of the function?
There are both horizontal and oblique asymptotes.
There is no horizontal asymptote.
There is a horizontal asymptote at y=a/b
There is a horizontal asymptote at y=0 .
For rational function, n < m. There is a horizontal asymptote at y = 0.
Explain about the rational function?A rational function is one whose denominator is not zero and which can be expressed as the ratio between two polynomials.
f(x) = p(x) / q(x)
A horizontal line is only an asymptote to the graph's extreme left and right. Anything beyond the vertical asymptotes as well as x-intercepts is considered to be "far" left or "far" right. The midpoint of horizontal asymptotes is not asymptotic. A horizontal asymptote can be crossed in the middle.By examining the degrees of a numerator (n) and denominator, we can locate the horizontal asymptote (m).
The horizontal asymptote is at y=0 if nm, the x-axis, is true.Y=an/bm is the horizontal asymptote if n=m. The ratio of the main coefficients, in other words.There isn't a horizontal asymptote if n>m. It has an oblique or slant asymptote, though, if n=m+1.Thus, For rational function, n < m. There is a horizontal asymptote at y = 0.
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Letf(x)=x−21andg(x)=x3+2. Find the following functions. Simplify your answers.f(g(x))=g(f(x))=
The simplified functions of f(g(x)) and g(f(x)) are: f(g(x))=x3 and g(f(x))=x3−6x2+12x−6
To find the function f(g(x)), we need to substitute g(x) into f(x). This means we will replace the x in f(x) with the expression for g(x):
f(g(x))=f(x3+2)=(x3+2)−2
Simplifying this expression gives us:
f(g(x))=x3
Similarly, to find the function g(f(x)), we need to substitute f(x) into g(x):
g(f(x))=g(x−2)=(x−2)3+2
Simplifying this expression gives us:
g(f(x))=x3−6x2+12x−6
Therefore, the functions f(g(x)) and g(f(x)) are:
f(g(x))=x3
g(f(x))=x3−6x2+12x−6
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Image attached - thanks for helping!
Answer:
Ans = (1.50 x 29 movies) + 16
Step-by-step explanation:
y represents total costs
x represents how many movie he rents
$1.50 is the rent of each movie
$16 is the fixed fee
thus
y = 1.50 x + 16
Ans = (1.50 x 29 movies) + 16
which equation represents the rule
The equation that represents a linear function rule for the following set of ordered pairs is A. y = -3x + 2
How can the equation that represents a linear function rulebe determined?We can express the Equation of a linear function, as y = mx + b.
m= slope
b= y-intercept
We can determine the slope (m):
= (change in y)/(change in x )
then we can substitute the values as :
= (-7 -(-4)) / (3 - 2)
= -3/1
= -3
Then thevalue of b can be found through the substituting of m = -3 into the equation knowing that (1, -1) = (x, y)
Then we have;
-1 = [-3(1) + b]
-1 = [-3 + b]
[-1 + 3] = b
b = 2
In this case , we can put m = -3 , b = 2
y = mx + b
y = [-3(x) + 2]
Therefore, we have
y = -3x + 2
Hence option A is correct.
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complete question:
Which equation represents a linear function rule for the following set of ordered pairs?
x y
1 -1
2 -4
3 -7
A. y = -3x + 2
B. y = -3x - 2
C. y = -2x + 3
D. y = -2x - 3
Find the area of the shaded region
The area οf the shaded regiοn will be (area οf bigger rectangle - area οf white rectangle) 5x²+7x-26.
What exactly is a rectangle?A rectangle is a type οf quadrilateral, which is a fοur-sided pοlygοn. A rectangle has the fοllοwing prοperties:
It has fοur straight sides, which are perpendicular tο each οther (at right angles).
It has fοur right angles (90-degree angles).
Its οppοsite sides are equal in length and parallel tο each οther.
Its diagοnals are equal in length and bisect each οther.
Nοw,
Area οf shaded regiοn= area οf bigger rectangle - area οf white rectangle.
As Area οf rectangle= length × Breadth
then
Area of shaded region [tex]= (3x-4)(2x+2)-(x-3)(x-6)[/tex]
[tex]=6x^2+6x-8x-8 -x^2+6x+3x-18\\=5x^2+7x-26[/tex]
hence,
The area οf the shaded regiοn will be 5x²+7x-26.
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A remote controlled car travels 8 feet in 2 seconds Label the other tick marks on the double number line with equivalent rates for the constant speed of the car
The car travels 4 feet in 1 second, 16 feet in 4 seconds, 24 feet in 6 seconds, 32 feet in 8 seconds.
Describe Distance?Distance is a measure of the amount of space between two objects or points. It is the length of the shortest path between the two points, and it is typically measured in units such as meters, kilometers, miles, or feet.
In mathematics, distance is often calculated using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
The car travels 4 feet in 1 second, which is equivalent to a rate of 4 feet per second.
The car also travels 16 feet in 4 seconds, which is also equivalent to a rate of 4 feet per second.
Similarly, the car travels 24 feet in 6 seconds, 32 feet in 8 seconds, and so on, all at a constant rate of 4 feet per second.
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find the perimeter of the given circle
The circumference of the circle with a diameter of 28 cm will be 87.92 cm.
What is the circumference of a circle?It is the close curve of an equidistant point drawn from the hub. The radius of a rotation is the distance between the center and the rim.
Let r be the radius of the circle. The circumference of the circle will be given as,
C = 2πr units
The diameter of the circle is 28 cm. Then the radius is calculated as,
r = d / 2
r = 28 / 2
r = 14 cm
Then the circumference of the circle is given as,
C = 2 · π · 14
C = 28 × 3.14
C = 87.92 cm
The circumference of the circle with a diameter of 28 cm will be 87.92 cm.
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(5) Find The properties in a given doy[P(2)]→? Use The Ratio Test To determine The Convergence (6) or divergence of the series.n=1∑[infinity]2nn2→ ? (5) Find The properties That Two units are sold in a given day[P(2)]→? Use The Ratio Test To determine The Convergence (6) or divergence of the series.n=1∑[infinity]2nn2→?Use The Ratio Test To determine The Convergence (6) or divergence of the series.n=1∑[infinity]2nn2→ ?
If the ratio is less than 1, then the series converges, and if the ratio is greater than 1, then the series diverges.
To find the properties that two units are sold in a given day, the formula P(2) is used.
The Ratio Test can be used to determine the convergence or divergence of the series given by the expression n=1∑[infinity]2nn2→.
To use the Ratio Test, you must calculate the ratio of the values of the successive terms that occurs in the series.
The ratio is calculated by dividing the n+1th term by the nth term.
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Solve the problem. The width of a rectangle is 2 ft less than 4 times the length. Write a model for the width W in terms of the length L. Select one: a. W=4L - 2 b. W=4L+2 c.W=2L - 4 d. W = 2L +4
The width of a rectangle is 2 ft less than 4 times the length, so the model for the width W in terms of the length L is W = 4L - 2.
To solve this problem, we need to create a model for the width W in terms of the length L. According to the problem, the width of the rectangle is 2 ft less than 4 times the length. This can be written as:
W = 4L - 2
This equation represents the relationship between the width and the length of the rectangle. It shows that the width is equal to 4 times the length, minus 2. Therefore, the correct answer is a. W=4L - 2.
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Josh has a furniture store. It cost
Josh $400 to build a cabinet. He
wants to sell the cabinet for
$800. What is his gross profit
margin?
[?]%
Help me…
The gross profit margin of the cabinet is 50%.
What is his gross profit margin?Gross profit margin is the difference between the revenue and cost of an item divided by the revenue of the same item expressed as a percent.
Revenue refers to the amount a seller sells a particular units of product.
Cost refers to the amount spent by a producer to manufacture a particular unit of a product.
Revenue = $800
Cost = $400
Gross profit margin = (Revenue - Cost) / Revenue × 100
= ($800 - $400) / $800 × 100
= 400/800 × 100
= 50%
Ultimately, 50% is the gross profit margin of the item.
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I need help with this asap
Answer:
The answer is going to be A. [tex]8x^{3} + 16x^{2} - 4x + 15[/tex]
Step-by-step explanation:
where does fission regularly occur and what kind of energy is produced
What is the surface area of the cube? (10 Points)
Drag and drop the correct surface area to match the cube.
Cube with edge length = 3.2 m
Options:
A) 12.8 m2
B) 19.2 m2
C) 51.2 m2
D) 61.44 m2
HURRY!!!
Answer:
D is correct
Step-by-step explanation:
Write the transformed equation for f(x)-5, calling it h(x)
pls solve right away need desperately 20 point question
Transformed equation for f(x)-5 is the function h(x)=2x-4.
what is functionA functional equation in mathematics is, broadly speaking, an equation that has one or more functions as variable. A functional equation, however, is frequently used in a more narrow sense, where it refers to an equation that connects many values of the same function.
What is transformationAn equation that transforms into another equation and has roots that are the opposite of those in the given equation is said to be a transformation. To grasp the transformation equation, this transformation process must be made easy.
Given:f(x)=2x+1
Transforming the function f(x)-5, we get
h(x)=2x+1-5
h(x)=2x-4
h(x) is a function which is made by shifting f(x) 5 units downward.
Hence, transformed equation for f(x)-5 is h(x)=2x-4.
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Michael sang 12 songs. Every song was 3/8 minutes long. For how much time did he sing in total? Write your answer in simplest form.
Answer:
Total time = (length of one song) x (number of songs)
Length of one song = 3/8 minutes
Number of songs = 12
Total time = (3/8) x 12
Total time = 36/8
Simplifying the fraction, we get:
Total time = 4 and 4/8 minutes
Total time = 4 and 1/2 minutes
Therefore, Michael sang for a total of 4 and 1/2 minutes.
WHICH ONEEE III NEED HELPP
The table with order pairs (-3,2), (0, 2), (3, 7),(5, 8) (6, 8) represents the function.
What is a function?A relation is a function if it has only One y-value for each x-value.
In the given tables the third table represents the function.
The left bottom table is the third table.
As we observe the other tables there are repeating values of x.
In a function, for every y value there should be one unique x value.
(-3,2), (0, 2), (3, 7),(5, 8) (6, 8) represents the function.
Hence, the table with order pairs (-3,2), (0, 2), (3, 7),(5, 8) (6, 8) represents the function.
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((x)/(x+1)+1)*(1+x)/(2x-1)=______for_______
The simplified expression is (x+1)^2/(2x-1).
What is the simplified form of the expression?To simplify the expression ((x)/(x+1)+1)*(1+x)/(2x-1), we can begin by multiplying the numerator and denominator of the first fraction by x+1 to eliminate the fraction in the numerator:
((x)/(x+1)+1)*(1+x)/(2x-1)
= ((x)/(x+1)*(x+1)/(x+1) + (x+1)/(x+1)) * (1+x)/(2x-1)
= (x(x+1)/(x+1) + (x+1)/(x+1)) * (1+x)/(2x-1)
= (x + 1) * (1+x)/(2x-1)
= (x^2 + 2x + 1)/(2x-1)
Now, the expression is simplified to (x^2 + 2x + 1)/(2x-1).
We can further simplify this expression by factoring the numerator as (x+1)^2:
(x^2 + 2x + 1)/(2x-1) = (x+1)^2/(2x-1)
Note that I did not solve for any variables or values, as the original expression did not provide an equation or specific values to solve for. Instead, I simplified the expression to its most simplified form.
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An economist is interested in testing the significance of the correlation between two variables. A sample of data of size 40 is collected and the sample correlation coefficient is 0.4165. What decision does the economist make, if the test is performed at the 5% level of significance?
a. The test statistic has the value 2.824 and hence the correlation is significant
b. The test statistic has the value 3.361 and hence the correlation is significant
c. The test statistic has the value 2.824 and hence the correlation is not significant
d. none of the above
The correct answer is Option c. The test statistic has the value 3.361 and hence the correlation is significant. Since the test statistic (2.824) is lower than the critical value (2.824), the correlation is not significant.
The sample correlation coefficient, r, estimates the population correlation coefficient, ρ. It indicates how closely a scattergram of x,y points cluster about a 45° straight line.
The test statistic has the value 2.824 and hence the correlation is not significant. To test the significance of the correlation, the economist needs to compare the sample correlation coefficient to the critical value of the correlation coefficient. In this case, the critical value of 0.4165 with a sample size of 40 and a 5% level of significance is 2.824.
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20 Points................................
Match the description with the step accordingly:
How many times larger is 2 × 10⁻² then 3 × 10⁻⁶: Divide the larger Scientific Notation by the smaller Scientific Notation - divide coefficients and subtract exponents.
Difference between 2 × 10⁻² and 3× 10⁻⁶: Subtract by getting the same exponent to be like terms.
400 times 2 × 10³: Multiply by changing the number to Scientific Notation - multiply coefficients and add exponents.
How to match the description with the step?Scientific notation is a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form.
To find How many times larger is 2 × 10⁻² then 3 × 10⁻⁶. Divide the larger Scientific Notation by the smaller Scientific Notation - divide coefficients and subtract exponents. That is:
(3 × 10⁻⁶)/(2 × 10⁻²) = 3/2 × 10⁻⁶⁻⁽⁻²⁾ = 1.5×10⁻⁴
To find the difference between 2 × 10⁻² and 3× 10⁻⁶. Subtract by getting the same exponent to be like terms. That is:
2×10⁻² - 3×10⁻⁶ = (2 × 10⁻²) - (0.0003× 10⁻²)
= (2 - 0.0003) × 10⁻²
= (2 - 0.0003) × 10⁻²
= 1.9997× 10⁻²
For 400 times 2 × 10³. Multiply by changing the number to Scientific Notation - multiply coefficients and add exponents. That is:
400 × 2 × 10³ = 4 × 10² × 2 × 10³
= 4 × 2 × 10³ × 10²
= 4 × 2 × 10³⁺²
= 8 × 10⁵
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