-a/b=-5/3 is the slope of the line 5x 3y 15
for
ax+by=c
the slope is -a/b
the slope of paralell lines are the same
find slope
5x+3y=15
-a/b=-5/3
paralell as same slope
the slopes are:
L1: slope 3
L2: slope -3
L3: slope -1/3
So now multiply the slopes of each pair of lines:
L1 and L2: 3 * (-3) = - 9 => No, they are not perpendicular
L2 and L3: (-3) * (-1/3) = 1 => No, they are not perpendicular
L1 and L3: (3) * (-1/3) = -1 => Yes, they are penpendicular.
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What is base in math formula?
The base in math formula is the sum that is multiplied when an exponent is used.
In mathematics, a base is a group of digits that are used to represent numbers. Different number systems employ various digit combinations as their base.
Depending on the situation, the word "base" can signify many things. The word "base" typically refers to the first component, core component, or base layer of a supporting structure.
The total number of digits a number system uses to express numbers is known as base in mathematics. The term "radix" is sometimes used to describe a number system's base.
Examples: In the expression 62, the base is 6, and the answer is 6 × 6 = 36.
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Which table represents exponential growth? a 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 6, 8. A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 8, 16.
The table that represents exponential growth is the second table.. The second column is labeled y with entries 2, 4, 6, 8. A 2-column table has 4 rows.
What is exponential growth?
Exponential growth simply means a process that increases quantity over time. It occurs when the instantaneous rate of change of a quantity with respect to time is proportional to the quantity itself.
Exponential growth is the pattern of data which shows sharper increases over time. In finance, compounding creates exponential returns and the savings accounts with a compounding interest rate can show exponential growth.
In this case, the second table described represents an exponential function. It has a common ratio of 4, meaning that each y-value is multiplied by 4 to get to the next value. Here, every time the Xs increase by 1, the Ys increase by a multiple of 4.
One of the best examples of exponential growth is observed in bacteria. Here, it takes bacteria roughly an hour to reproduce through prokaryotic fission. This illustrates exponential growth.
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Step-by-step explanation:
Carter is ordering a taxi from an online taxi service. The taxi charges $2.50 just for
the pickup and then an additional $2 per mile driven. How much would a taxi ride
cost if Carter is riding for 7 miles? How much would a taxi ride cost that is m miles
long?
Answer:
$16.50
Step-by-step explanation:
y=mx+b
y is total cost, m is the miles, x is the cost per mile driven, and b is the pickup charge.
y=(7 miles x $2) + $2.50
y= $16.50
Answer:
Step-by-step explanation:
y=(7 miles x $2) + $2.50
y= $16.50
If a1 = 3, an+1 = 2an, find a2.
Answer:
a2=0Step-by-step explanation:
a=2
n=0.5
2a=0
2.2=0
4=0
2a=0
how do you simplify 75 65/1000
In a survey of students about favorite sports, the results include 34 who like tennis, 37 who like football, 17 who like tennis and football, 21 who like tennis and baseball, 25 who like football and baseball, 9 who like all three sports, and 7 who like none of the sports. How many students like only tennis and football?
please help me on this ;-;
8 students like only tennis and football. When, In a survey of students about favorite sports, the results include 34 who like tennis, 37 who like football, 17 who like tennis and football, 21 who like tennis and baseball, 25 who like football and baseball, 9 who like all three sports, and 7 who like none of the sports.
Define algebra.One of the earliest areas of mathematics that deals with number theory, geometry, and analysis is algebra. Algebra is also defined as the study of mathematical rules and symbols through the manipulation of those mathematical symbols. The area of mathematics known as algebra is used to portray situations or problems using mathematical expressions. In algebra, we utilize integers with fixed or definite values, such as 2, 7, 0.068, etc. In algebra, we combine integers with variables like x, y, and z.
Given
Number of student who only likes tennis and football
= number of student likes only tennis and football - who like all three sports
= 17 - 9
= 8
8 students like only tennis and football. When, In a survey of students about favorite sports, the results include 34 who like tennis, 37 who like football, 17 who like tennis and football, 21 who like tennis and baseball, 25 who like football and baseball, 9 who like all three sports, and 7 who like none of the sports.
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2. The total surface area of a square based pyramid is 900 sq. cm. If the lateral surface area of the pyramid is three times the base area, find the length of the base. Also find the volume of the pyramid.
Answer:
Length of the base = 15 cm
Volume = 1125√2 cm³ = 1590.99 cm³ (2 d.p.)
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.6cm}\underline{Lateral Surface Area of a square pyramid}\\\\$LSA=a \sqrt{a^2+4h^2}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the base edge \\\phantom{ww}$\bullet$ $h$ is the height\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{6.6cm}\underline{Base Area of a square pyramid}\\\\$BA=a^2$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the base edge \\\end{minipage}}[/tex]
If the lateral surface area (LSA) of the pyramid is three times the base area (BA):
[tex]\implies a \sqrt{a^2+4h^2}=3a^2[/tex]
Rearrange the equation to isolate h²:
[tex]\implies \sqrt{a^2+4h^2}=3a[/tex]
[tex]\implies (\sqrt{a^2+4h^2})^2=(3a)^2[/tex]
[tex]\implies a^2+4h^2=9a^2[/tex]
[tex]\implies 4h^2=8a^2[/tex]
[tex]\implies h^2=2a^2[/tex]
[tex]\boxed{\begin{minipage}{6.6cm}\underline{Total Surface Area of a square pyramid}\\\\$SA=a^2+a \sqrt{a^2+4h^2}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the base edge \\\phantom{ww}$\bullet$ $h$ is the height\\\end{minipage}}[/tex]
Given:
SA = 900 cm²h² = 2a²Substitute these values into the formula for the total surface area and solve for a:
[tex]\implies a^2+a\sqrt{a^2+4(2a^2)}=900[/tex]
[tex]\implies a^2+a\sqrt{a^2+8a^2}=900[/tex]
[tex]\implies a^2+a\sqrt{9a^2}=900[/tex]
[tex]\implies a^2+a(3a)=900[/tex]
[tex]\implies a^2+3a^2=900[/tex]
[tex]\implies 4a^2=900[/tex]
[tex]\implies a^2=225[/tex]
[tex]\implies a=15[/tex]
Therefore, the length of the base of the square based pyramid is:
a = 15 cmTo find the height (h), substitute the found value of a into the formula for h² and solve for h:
[tex]\implies h^2=2(15)^2[/tex]
[tex]\implies \sqrt{h^2}=\sqrt{2(15)^2}[/tex]
[tex]\implies h=\sqrt{2}\sqrt{(15)^2}[/tex]
[tex]\implies h=15\sqrt{2}[/tex]
Therefore, the height of the square based pyramid is:
h = 15√2 cm[tex]\boxed{\begin{minipage}{5cm}\underline{Volume of a square pyramid}\\\\$V=\dfrac{1}{3}a^2h$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the base edge \\\phantom{ww}$\bullet$ $h$ is the height\\\end{minipage}}[/tex]
Given:
a = 15h = 15√2Substitute the values into the formula and solve for volume:
[tex]\implies V=\dfrac{1}{3}(15)^2 \cdot 15\sqrt{2}[/tex]
[tex]\implies V=\dfrac{225}{3} \cdot 15\sqrt{2}[/tex]
[tex]\implies V=75\cdot 15\sqrt{2}[/tex]
[tex]\implies V=1125\sqrt{2}[/tex]
[tex]\implies V=1590.99[/tex]
Therefore, the volume of the square based pyramid is:
1590.99 cm³ (2 d.p.)May I ask what’s the answer to this MC question because what I've calculated is 36 to the power 222 which giant matched the above choices
Answer:
B
Step-by-step explanation:
16 = 2⁴
9 = 3²
(2⁴)¹¹¹ × (3²)²²² = 2⁴⁴⁴ × 3⁴⁴⁴ = (2×3)⁴⁴⁴ = 6⁴⁴⁴
you can only combine the exponents of the same bases, or the bases of the same exponent.
in our case here the latter is used.
and indeed
6⁴⁴⁴ = (6²)²²² = 36²²²
so, essentially you were right. but you still needed to transform this into the form of the given answer option.
A new bank customer with $2,500 wants to open a money market account. The bank is offering a simple interest rate of 1.6%.
a. How much interest will the customer earn in 20 years?
b. What will the account balance be after 20 years?
a) The customer will earn $800 as interest in 20 years.
b) The account balance after 20 years will be - $ 3300.
Principle = $2500
Rate of simple interest = 1.6%
Time = 20 yrs
The simple interest is expressed as :
S.I = [tex]\frac{PRT}{100}[/tex]
⇒ S.I = [tex]\frac{2500 * 1.6 * 20}{100}[/tex]
⇒ S.I = 25 * 20 *1.6
⇒ S.I = 800
The simple interest after 20 years = $800
The account balance after 20 years is -
= principle + simple interest
= 2500 + 800
= 3300
a) The customer will earn $800 as interest in 20 years.
b) The account balance after 20 years will be - $ 3300.
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1/3x-3+4=10 solve for x
Answer:
x = 27
Step-by-step explanation:
[tex] \frac{1}{3}x - 3 + 4 = 10[/tex]
[tex] \frac{1}{3}x + 1 = 10 [/tex]
multiply both sides by (3)
[tex]3 \times \frac{1}{3}x + 3 \times 1 = 3 \times 10[/tex]
x + 3 =30
x = 30–3
x = 27
i hope i helped
does the residual plot support the appropriateness of a linear model? responses yes, because there is a clear pattern displayed in the residual plot. yes, because there is a clear pattern displayed in the residual plot. yes, because about half the residuals are positive and the other half are negative. yes, because about half the residuals are positive and the other half are negative.
Answer:
Step-by-step explanation:
Yes, the residual plot supports the appropriateness of a linear model because it displays a clear pattern and has roughly equal amounts of positive and negative residuals.
Is the residual plot relatively symmetrical around the centerline?
Yes, if the residual plot is relatively symmetrical around the centerline, it suggests that the linear model is appropriate because it is capturing the variance in the data evenly. If the residual plot is skewed or has outliers, it may indicate that the linear model is not accurately representing the data and a different model may be needed.
A residual plot is a graph that plots the residuals (the differences between the observed values and the predicted values) on the y-axis and the independent variable on the x-axis. The residual plot is used to assess the appropriateness of a linear model. If the residual plot displays a clear pattern and has roughly equal amounts of positive and negative residuals, it suggests that the linear model is appropriate. On the other hand, if the residual plot is scattered randomly or displays a clear pattern, it suggests that the linear model is not appropriate. In this case, the residual plot supports the appropriateness of a linear model because it displays a clear pattern and has roughly equal amounts of positive and negative residuals. This suggests that the linear model is able to accurately predict the dependent variable based on the independent variable.
Therefore, the residual plot supports the appropriateness of a linear model.
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Yes, because it displays a clear pattern and has roughly equal amounts of positive and negative residuals.
What is a residual plot and how does it support the appropriateness of a linear model?
A residual plot is a graphical representation of the residuals (prediction errors) of a regression model. It can be used to assess the appropriateness of a linear model by examining the pattern of the residuals and the presence of any unusual points or trends.
If the residual plot shows a clear pattern, such as a trend or curvature, it suggests that the linear model may not be appropriate for the data. On the other hand, if the residual plot appears random and shows roughly equal amounts of positive and negative residuals, it supports the appropriateness of a linear model.
The residual plot is used to judge whether a linear model is suitable. The linear model may be useful if the residual plot exhibits a distinct pattern and contains nearly equal numbers of positive and negative residuals. On the other hand, it indicates that the linear model is inappropriate if the residual plot is dispersed randomly or exhibits a distinct pattern. The residual plot shows a distinct pattern and about equal numbers of positive and negative residuals, which in this instance confirms the suitability of a linear model. This suggests that the dependent variable may be accurately predicted by the linear model utilising the independent variable.
Therefore, the residual plot confirms that a linear model is adequate.
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s = ut + 1/2 at2
u = 10 a = -2 t= 1/2
Answer:
Step-by-step explanation:
What is the discriminant of the quadratic equation 2x 5x² 1?
The Discriminant of the quadratic equation "2x + 5x² = 1" is 24 .
The Discriminant(D) of the Quadratic Equation ax² + bx + c can be calculated using the formula ; D = b² - 4ac .
the quadratic equation is given as 2x + 5x² = 1 ;
after rearranging the terms ,
the equation can be written as :
⇒ 5x² [tex]+[/tex] 2x - 1 = 0 ;
Substituting the values in the discriminant formula ,
we get ;
D = (2)² - 4×5×(-1)
Simplifying further ,
we get ;
D = 4 + 20
D = 24 .
Therefore , the value of the Discriminant is 24 .
The given question is incomplete , the complete question is
What is the discriminant of the quadratic equation 2x + 5x² = 1 ?
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A 12 -foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 10 feet from the base of the building. How high up the wall does the ladder reach?
The height of the wall where the ladder reaches will be 6.33 feet.
What is a Pythagoras theorem?It communicates that the area of the square whose side is the hypotenuse is identical to how much the locale of the squares on the other various sides.
The Pythagoras theorem formula is given as
H² = P² + B²
A 12-foot ladder is set against a vertical mass of construction, with the lower portion of the ladder staying on level ground 10 feet from the underpinning of the design.
The height of the wall where the ladder reaches will be calculated as,
12² = P² + 10²
144 = P² + 100
P² = 44
P =6.33 feet
The level of the wall where the stepping stool arrives freely will be 6.33 feet.
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Graph the line through the given point with the given slope.
(0, 5), m = - 5
(basically what coordinate points would there be?)
Answer:
The equation would be
y =-5x + 5
Step-by-step explanation:
Use the x of 0 from the point given (0,5)
Use the y of 5 from the point given (0,5)
Use the slope that is given: -5
Use all of the above to solve for the y-intercept (b).
y = mx + b
5 = -5(0) + b
5 = 0 + b
5 = b
y =mx + b
y = -5x + 5
In the graph, the line crosses the y axis at (0,5) . The is the y -intercept or the "b" of the equation.
From that points move down 5 and one to the right. This is the slope. Once we have two points we can draw a line.
How can I verify my SSS number?
The process to verify SSS number is to submit your printed records together with the required documentary requirements
The term documentary is referred as document reality, primarily for the purposes of instruction, education or maintaining a historical record
Here we need to find the process to verify the SSS number.
In order to find that we must know the definition of SSS,
The term SSS refers an independent federal agency that administers compulsory military service.
In order to verify the SSS number, you must have the following documentaries,
Last name
Social Security Number
Date of Birth
Now, we have to do the following steps to verify the SSS number, now you have to submit these to the appropriate department to do the verification.
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Is a rhombus a 2 D shape?
Answer: yes
Step-by-step explanation: it is a 2 dimensional shape if it was 3d it would end up being a prism
If sinA + sin² A = 1, then the value of the expression (cos²A + cos¹A) is
(a) 1 (6) 1/2 (c) 2 (d) 3
Using trigonometric identities, If sinA + sin² A = 1, then the value of the expression (cos²A + cos⁴A) is; 1
How to solve trigonometric identities?We are told that sinA + sin² A = 1.
Now, we want to find (cos²A + cos⁴A).
From trigonometric identities, we know that;
cos²A = 1 - sin² A
Thus;
cos²A + cos⁴A = 1 - sin² A + cos⁴A
Similarly, using trig identities on the given expression;
From sinA + sin² A = 1, we can say that;
sinA = 1 - sin² A
Since cos²A = 1 - sin² A, then we can say that;
sinA = cos²A
Thus;
sin²A = cos⁴A
Thus;
cos²A + cos⁴A = 1 - sin² A + sin²A
= sinA + sin²A= 1
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Correct question is;
If sinA + sin² A = 1, then the value of the expression (cos²A + cos⁴A) is
9. Find the measure of angle B. Round to the nearest tenth. (show work)
The measure of angle 55 degrees Celsius
What is the explanation?In order to get the measure of the unknown angle A, we are given a right-angled triangle with two known side lengths for the perpendicular and base.
To do that, we may use the tan formula, which uses the two provided side lengths.
the nearest tenth:
To get the solution in this case, we must apply the tan ratio.
tan = Adjacent or Opposite
tan = Opposite / Adjacent
Given: Opposite equals 4, adjacent equals 13.
Given: Adjacent = 13, opposite = 12.
tan θ = 12/13
θ = tan^-1 (12/13)
55 degrees.
55 degrees, please.
The measure of angle 55 degrees Celsius
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Just need help with 21-23 missed lessons and it’s not making any sense
Evaluate the quantity of x cubed minus 2x squared plus 3x minus 7 end quantity divided by the quantity of x minus 1 end quantity period.
Our final resulting answer will be -5.
To calculate the remainder, first divide the polynomials.
Set up the polynomials to be divided. if there is not a term for every exponent, insert one with a value of 0.
[tex]\sqrt[x-1]{x^{3}-2x^{2} +3x-7 }[/tex]
Divide the highest order term in the dividend [tex]x^{3}[/tex] by the highest order term in divisor x.
Multiply the new quotient term by the divisor.
The expression needs to be subtracted from the dividend, so change all the signs [tex]x^{3}[/tex]+[tex]x^{2}[/tex].
After changing the signs, add the last dividend from the multiplied polynomials to find the new dividend.
Pull the next terms from the original dividend down into the current dividend.
Divide the highest order term in the dividend -[tex]x^{2}[/tex] by the highest order term in divisor x.
Multiply the new quotient term by the divisor.
The expression needs to be subtracted from the dividend, so change all the signs in -[tex]x^{2}[/tex]-x.
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
Pull the next terms from the original dividend down into the current dividend.
Divide the highest order term in the dividend 2x by the highest order in divisor x.
Multiply the new quotient term by the divisor.
The expression needs to be subtracted from the dividend, so change all the signs in -2x+2.
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
The final answer is the quotient plus the remainder over the divisor.
[tex]x^{2}[/tex]-x+2-[tex]\frac{5}{x-1}[/tex]
Since the last term in the resulting expression is a fraction, the numerator of the fraction is the remainder.
So, our final answer will be -5.
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Select all that are equal to 5^3 x 5^-7
1/5^-4
1/5^4
5^-4
5^4
1/-625
Answer:
5^-4
1/-625
Step-by-step explanation:
5^3 x 5^-7
They have the same base is 5, which means we just need to add the root, so 3 + (-7) = -4, so the answer is 5^-4
5^ -4
5 times 5 times 5 times 5 = -625
Because it is a negative exponent, means it is a fraction. So, the answer is
1/ -625
Farmer Pisquet put grain into bins Y, A and P. The ratio of weight of
flour in bin Y to weight of flour in bin A was 9:3. The ratio of weight of
flour in bin A to weight of flour in bin P was 4:3. If there were 36
pounds of grain in bin A, how many pounds of grain were there
altogether?
The weight of Y = 108 pound and weight of P is 27 pound
What does the math ratio mean?
Definitions: An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)
Given that :
A = 36 pound
A:P =4:3
so when A is 36 = 4*9
then P is 3*9 = 27
Hence the weight of P is 27 pound
Now we have Y:A = 9:3
when A = 36 = 3*12
Then Y is 9*12 = 108
Hence weight of Y is 108 pound
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How do we get negative infinity?
Negative infinity is obtained by taking the limit of a decreasing sequence of negative real numbers as they approach negative infinity.
Negative infinity is an abstract concept that is used to represent a value that is less than the lowest possible number. To get negative infinity, one must take the limit of a decreasing sequence of negative real numbers. This means that the sequence of numbers must get closer and closer to negative infinity as it continues to decrease. For example, if you take the sequence of numbers -1, -2, -3, -4, -5, -6, and so on, the limit of this sequence is -∞. As the sequence continues to decrease, it eventually reaches a point where the numbers become so small that they cannot be measured. At this point, the limit of the sequence is -∞.
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Describe a real world situation that could be modeled by the expression Y equals 1/20 XP transcribe what is
The required real-world situation has been written in the solution part which could be modeled by the expression Y equals 1/20 XP.
A real-world situation that could be modeled by the expression Y = 1/20XP is the relationship between the distance a person runs and the number of calories they burn.
In this situation, Y represents the number of calories burned and X represents the distance run in miles. The constant 1/20 represents the rate at which calories are burned per mile.
For example, if a person runs 5 miles, we can substitute 5 for X in the expression to find the number of calories they burn:
Y = 1/20 × 5X
Y = 1/4
Thus, the person burns 1/4 calorie for every mile they run.
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The price of an apple is $1.25. If you get 20% discount, how much do you have to pay?
Why is the use of 0 and necessary in a measuring instrument?
In order for measuring devices to produce correct findings, they must have zero error. Zero error also makes it possible to determine if an instrument is functioning properly or not.
what is measuring instrument?Instruments used by researchers and practitioners to assist in the assessment or evaluation of subjects, clients, or patients are known as measurement tools. From physical functioning to psychosocial welfare, the tools are used to assess or gather data on a number of aspects.
Electrical instruments are one of three categories for measuring devices. Instrument for electronics. a mechanical instrument.
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I need the answer to the second question in the picture, but can you also say if the one above it is correct or not?
The area of shaded region of standard normal distribution is 0.1292
what is standard normal distribution?
A unique type of normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution, or z-distribution.
Any normal distribution can be transformed into the common normal distribution by converting the individual values into z-scores. Z-scores indicate the number of standard deviations that each value in a z-distribution is from the mean.
solution:
For - 3.39 to 0
The standard deviation value is : 0.00035
For 0 to 1.13
The standard deviation value is : 0.3708
Then for - 3.39 to + 1.13 :
The area of the given shaded area is 0.1292
Hence,the area of shaded region of standard normal distribution is 0.1292
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What type of discontinuity is a hole?
A removable discontinuity is when a function has an isolated point where it is not defined, and the function can be made continuous by removing that point. A hole is an example of a removable discontinuity.
In mathematics, a discontinuity is a point or set of points where a function does not behave as expected or fails to exist. There are three types of discontinuities: removable discontinuities, jump discontinuities, and infinite discontinuities. A removable discontinuity is when a function has an isolated point where it is not defined, and the function can be made continuous by removing that point. In other words, the function can be made continuous by “filling in” the discontinuity. An example of a removable discontinuity is a hole, where the graph has a gap that can be filled in. Jump discontinuities occur when the left-hand and right-hand limits of the function do not agree at a point, and the function “jumps” from one value to another at that point. An example of a jump discontinuity is a cusp, where the graph has a sharp point. Finally, an infinite discontinuity is when the function does not exist at a point, such as a vertical asymptote. In all three cases, the discontinuity can be easily identified by looking at the graph of the function.
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What is 3 divided by 6 as a fraction
Answer: [tex]\frac{3}{6}[/tex]
Step-by-step explanation:
[tex]Three\ divided\ by\ 6\ is\ \ \frac{3}{6} \ or\ simplified\ to\ \frac{1}{2}[/tex]
Answer: 3/6 = 0.5
Step-by-step explanation: Divide 3 divided by 6 as a fraction and that should give you 0.5 if your teacher tells you the answer cannot be a decimal then the answer will be 12 or if he tells u to simplify then the answer wil be 1/2