Answer:
To make f continuous at [tex]x=2[/tex], [tex]f(2)[/tex] should be defined [tex]x = 2.[/tex]
Step-by-step explanation:
A function, let say [tex]f(x)[/tex], is defined at [tex]x = c[/tex] is continuous at [tex]x = c[/tex]
If the limit of [tex]f(x)[/tex] as [tex]x[/tex] approaches [tex]c[/tex] is equal to the value of [tex]f(x)[/tex] at [tex]x = c[/tex].
Mathematically it is written as:
if
[tex]\lim _{x\to c}\:f\left(x\right)=f\left(c\right)[/tex]
then
[tex]f(x)[/tex] is continuous at [tex]x = c[/tex].
So from the above definition, we conclude that:
To make f continuous at [tex]x=2[/tex], [tex]f(2)[/tex] should be defined [tex]x = 2.[/tex]
i.e.
if
[tex]\lim _{x\to 2}\:f\left(x\right)=f\left(2\right)[/tex]
then
[tex]f(x)[/tex] is continuous at [tex]x = 2[/tex].
To make f continuous at x=2, define f(2) to be equal to 4. This makes the left-hand limit, right-hand limit, and function value at x=2 all equal to 4, which satisfies the definition of continuity.
To make a function continuous at a point, the left-hand limit and right-hand limit at that point must be equal to the function's value at that point. In other words, if a function is continuous at x=a, then
[tex]\lim_{x \to a^+} f(x)=f(a)[/tex]
Therefore, to make f continuous at x=2, we must define f(2) to be equal to the limit of f(x) as x approaches 2 from both the left and the right.
We can see that the limit of f(x) as x approaches 2 from the left is 4. This is because f(x) approaches 4 as x approaches 2 from the left, even though f(2) is undefined.
We can also see that the limit of f(x) as x approaches 2 from the right is 4. This is because f(x) approaches 4 as x approaches 2 from the right, even though f(2) is undefined.
Therefore, to make f continuous at x=2, we must define f(2) to be equal to 4.
For similar question on continuity
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For homework, Anya had to find the width of a bedroom after the scale changed from 1 inch : 4 feet to 1 inch : 7 feet. Her work is shown below.
Answer:
The correct answer is A!!
Step-by-step explanation:
Answer:
the first one
Step-by-step explanation:
a
What scale factor did Salome use to go from Triangle R to Triangle T?
Answer:is there a picture included in this promblem
Step-by-step explanation:
Answer:
1/2
Step-by-step explanation:
Determine if the expression 7r - 6r3 - 10r4 is a polynomial or not.
Answer:
A polynomial is a combination of terms separated by + or - signs. A polynomial does not contain variables raised to negative or fractional exponents, variables in the denominator or under a radical, or any special features such as trigonometric functions, or logarithms.
The expression 7r - 6r^3 - 10r^4 is a polynomial because it consists of terms with variables raised to non-negative integer exponents.
Explanation:The expression 7r - 6r3 - 10r4 is a polynomial because it is a mathematical expression consisting of terms with variables raised to non-negative integer exponents.
A polynomial is an algebraic expression made up of one or more terms, where each term has a coefficient and a variable raised to a non-negative integer exponent. In this case, the expression has three terms: 7r, -6r3, and -10r4. The variable in the expression is 'r', and each term is raised to a non-negative integer exponent.
Therefore, the expression 7r - 6r3 - 10r4 is a polynomial.
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HELP WILL MARK BRAINLIEST!!
Solve.
Answer:
[tex]-\frac{11}{12}[/tex]
Step-by-step explanation:
[tex]\frac{5}{8} +\frac{3}{4} =\frac{11}{8} \\\\\frac{11}{8}=1.375\\\\\frac{-2}{3} -\frac{5}{6} =-\frac{3}{2} \\\\-\frac{3}{2}=-1.5\\\\\frac{1.375}{-1.5} =-\frac{11}{12}[/tex]
We'll split this up between the numerator and denominator.
Numerator:
5/8 + 3/4
Step 1) Make all of the denominators the same
5/8 + 6/8
Step 2) Add the numerators together
11/8
Denominator:
-2/3 - 5/6
Step 1) Make all of the denominators the same
-4/6 - 5/6
Step 2) Subtract the numerators
-9/6
Now we have (11/8) / (-9/6). Dividing fractions is the same as multiplying by the reciprocal.
11/8 x -9/6
-99/48
-2 3/48
-2 1/16
Hope this helps! :)
What is the probability that you will get a 3-digit combination correct if no digits in the combination can be repeated?
110
1504
1720
MERT QUESTION
ASK FOR HELP
TURN IT IN
Answer:
i believe its 1/6
Step-by-step explanation:
The probability of guessing a 3-digit combination correctly, with no repetition, is 1 out of 720 option C.
To calculate the probability of getting a 3-digit combination correct where no digits can be repeated, you can use the concept of permutations.
For the first digit, you have 10 options (0 through 9). For the second digit, since no digit can be repeated, you have 9 options left. For the third digit, you have 8 options left.
So the total number of possible combinations is [tex]\(10 \times 9 \times 8 = 720\).[/tex]
Therefore, the probability of getting the correct combination is:
[tex]\[\frac{1}{720}\][/tex]
So, the correct answer is option C) 1/720.
Complete Question:
What is the probability that you will get a 3-digit combination correct if no digits in the combination can be repeated?
A) 1/10
B) 1/504
C) 1/720
Use the distributive property to write an equivalent expression:
Example: 24n + 32 = 4 (6n+ 8)
(Look at the first expression. What factor goes into BOTH 24 and 32? (4 does!) So the number 4 goes on the outside of the parenthesis. 4 times what number will give me 24? (6 Does!). Then we do the same for 32...4 times what number gives me 32? (8 does!). Do you see the pattern? This means that both of these expressions are EQUIVALENT!
48x + 24
18n + 36
15 + 12k
Answer:
1. 48x + 24= 24(2x + 1)
2. 18n + 36= 18(n + 2)
3. 15 + 12k= 3(5+4k)
Step-by-step explanation:
1. What factor both goes into 24 and 48? 24 does!
so, 48x + 24= 24(2x + 1).
2. What factor both goes into 18 and 36? 18 does!
so, 18n + 36= 18(n + 2).
3. What factor both goes into 15 and 12? 3 does!
so, 15 + 12k= 3(5+4k).
Final answer:
The distributive property allows us to create equivalent expressions by factoring out a common factor from each term, resulting in expressions like 24(2x + 1), 18(n + 2), and 3(5 + 4k) for 48x + 24, 18n + 36, and 15 + 12k respectively.
Explanation:
To use the distributive property to write equivalent expressions for each of the following:
48x + 24: Both terms are divisible by 24. Therefore, the equivalent expression using the distributive property is 24(2x + 1).
18n + 36: Both terms are divisible by 18. Therefore, the equivalent expression using the distributive property is 18(n + 2).
15 + 12k: Both terms are divisible by 3. Therefore, the equivalent expression using the distributive property is 3(5 + 4k).
In each case, identifying the common factor and using it to factor out the original expression creates an equivalent expression where the terms inside the parenthesis are the results of dividing the original terms by the common factor.
Can someone please give me the right answer to this question please???
Answer:
x=87 degrees
Step-by-step explanation:
Answer:
The answer is 87 degrees.
Step-by-step explanation:
All angles in a triangle add up to 180 degrees
37 + 56 = 93
180 - 93 = 87
Tomás is enlarging a square with a side length of 15 cm using this scale factor and scale drawing.
Scale factor = 2 centimeters: 7 meters. A square with side lengths of 15 centimeters.
Which proportion would Tomás use to solve for the side length (x) of the enlarged square in meters?
Answer:
[tex]\frac{2 CM}{7 M} = \frac{15 CM}{X M}[/tex]
Step-by-step explanation:
I did the assignment.
The side length (x) of the enlarged square in meters has a scale factor will be 52.5 meters.
What is dilation?Dilation means the changing of the size of the object without changing the shape. The size of the object may be increased or decreased based on the scale factor.
Tomás is enlarging a square with a side length of 15 cm using this scale factor and scale drawing.
Scale factor = 2 centimeters: 7 meters. A square with side lengths of 15 centimeters.
Let x be the dilated length.
Then we have
[tex]\rm \dfrac{15}{x} = \dfrac{2}{7}\\\\x \ \ = 52.5[/tex]
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The total weight of the golf balls from Julio's golf bag was 273 grams. If each golf ball weighed 45.5 grams, which graph
shows the weight of golf balls as it relates to the number of golf balls?
Weight of Golf Balls
Number of Golf Balls
Weight (in grams)
45.5
273
Answer:
Attached graph
Step-by-step explanation:
Since all the six balls have same weight and the total weight is given as 273g, then weight of one ball will be
273/6=45.5 g
1 ball=45.5 g
2 balls =2*45.5=91 g
3 balls =3*45.5=136.5 g
4 balls=4*45.5=182 g
5 balls =5*45.5=227.5 g
6 balls =6*45.5=273 g
Since the graph to select is not given, I attached ny own sketch. Any other graph with these corresponding figures in x and y axis as indicated will be correct.
Answer:
A
Step-by-step explanation:
Since all the six balls have same weight and the total weight is given as 273g, then weight of one ball will be
273/6=45.5 g
1 ball=45.5 g
2 balls =2*45.5=91 g
3 balls =3*45.5=136.5 g
4 balls=4*45.5=182 g
5 balls =5*45.5=227.5 g
6 balls =6*45.5=273 g
Since the graph to select is not given, I attached ny own sketch. Any other graph with these corresponding figures in x and y axis as indicated will be correct.
The area of a rectangle is 84 square inches. Its length and width are both whole numbers.
31. What is the minimum perimeter of the rectangle?!
32. What is the maximum perimeter of the rectangle?
31. the minimum perimeter of the rectangle is ( 38 ) inches.
32.the maximum perimeter is ( 170 ) inches.
To find the minimum and maximum perimeter of the rectangle, we need to consider all possible combinations of length and width that yield an area of 84 square inches.
Given that the area of the rectangle is 84 square inches, we can find all the pairs of factors of 84. These pairs will represent the possible combinations of length and width.
The pairs of factors of 84 are:
1. [tex]\( 1 \times 84 \)[/tex]
2. [tex]\( 2 \times 42 \)[/tex]
3. [tex]\( 3 \times 28 \)[/tex]
4. [tex]\( 4 \times 21 \)[/tex]
5. [tex]\( 6 \times 14 \)[/tex]
6. [tex]\( 7 \times 12 \)[/tex]
Now, we calculate the perimeter for each pair:
1. [tex]\( \text{Perimeter} = 2 \times (1 + 84) = 2 \times 85 = 170 \)[/tex]
2. [tex]\( \text{Perimeter} = 2 \times (2 + 42) = 2 \times 44 = 88 \)[/tex]
3. [tex]\( \text{Perimeter} = 2 \times (3 + 28) = 2 \times 31 = 62 \)[/tex]
4.[tex]\( \text{Perimeter} = 2 \times (4 + 21) = 2 \times 25 = 50 \)[/tex]
5.[tex]\( \text{Perimeter} = 2 \times (6 + 14) = 2 \times 20 = 40 \)[/tex]
6.[tex]\( \text{Perimeter} = 2 \times (7 + 12) = 2 \times 19 = 38 \)[/tex]
Therefore, the minimum perimeter of the rectangle is ( 38 ) inches, and the maximum perimeter is ( 170 ) inches.
PLEASE ANSWER!!! I NEED HELP!!!
Answer:
Third Option
Step-by-step explanation:
sqrt(13 = 3.6055512754639893
3.6
The volume of a cube is 64 inches cubed what is the measure of each side of the cube please help ASAP
Answer:
4
Step-by-step explanation:
a≈4
A geologist has 10 rocks of equal weight. If 6 rocks and a 10-ounce weight balance on a scale with 4 rocks and a 22-ounce weight , what is the weight of one of these rocks in ounces ?
Weight of each rock is 14.8 ounces.
Step-by-step explanation:
Given,
Total number of rocks = 10
6 rocks weigh 10 ounce each
4 rocks weigh 22 ounce each.
To find the the weight of each rock.
Now,
Weight of 6 rocks = 10×6 ounces = 60 ounces
Weight of 4 rocks = 22×4 ounces = 88 ounces
So,
Weight of 10 rocks = 88+60 = 148 ounces
Hence,
Weight of each rock = 148÷10 = 14.8 ounces.
Answer: 6 oz.
Step-by-step explanation:
Just did it.
Before soccer practice Allyson jogs around the field that measures 100 yards by 65 yards twice. How far will she jog?
Answer:
she will jog 660
Step-by-step explanation:
(100+65)×2=1 lap
330×2=2 laps (660yards)
Final answer:
Allyson will jog around the perimeter of the soccer field twice, which totals 660 yards.
Explanation:
Allyson is jogging around a soccer field that has dimensions of 100 yards long and 65 yards wide. To find out how far she will jog, we need to calculate the perimeter of the field and then multiply it by the number of times she jogs around it.
Calculating the Perimeter:
The perimeter P of a rectangle is given by P = 2(length + width). In this case:
Length (L) = 100 yardsWidth (W) = 65 yardsSo the perimeter of the soccer field is:
P = 2(100 yards + 65 yards) = 2(165 yards) = 330 yards.
Total Distance Jogged:
Since Allyson jogs around the field twice, the total distance she will jog is:
Total Distance = Perimeter × Number of Laps = 330 yards × 2 = 660 yards.
Therefore, Allyson will jog a total distance of 660 yards.
Find the value of x.
Answer:
x = 12
Step-by-step explanation:
By property of intersecting secants outside of a circle:
[tex]x \times 15 = 20 \times 12 \\ x = \frac{20 \times 12}{15} \\ x = \frac{20 \times 3}{5} \\ x = 4 \times 3 \\ x = 12[/tex]
What’s the square root of -16?
Answer:
It can`t be -4 because -4² = +16 and it can`t be 4² because 4² = +16
In other words, there is nothing you can square to get -16.
Step-by-step explanation:
It izz wat it izzzz!!!
Find the circumference of both circles. Use 3.14 for pi
Answer:
Larger Circle:Radius: 12 in.
Circumference =
[tex]2\pi \: r[/tex]
= 2 x 3.14 x 12
= 75.36 in.
Smaller Circle:Radius: (12 - 4) in. = 8 in.
Circumference = 2 x 3.14 x 8
= 50.24 in.
Pls help i am so confused
Answer:
A 13
Step-by-step explanation:
8 families own 2 pets
4 families own 3 pets
1 family owns 4 pets
8+4+1 = 13
13 families owns between 2 and 4 pets
What is y+6=1/3(x-9) written in slope-intercept form?
Slope intercept form is y = mx + b.
y + 6 = 1/3(x - 9)
y + 6 = 1/3x - 3
y = 1/3x - 9
Hope this helps!! :)
Answer:
[tex]y = 1/3x - 9[/tex]
Step-by-step explanation:
Step 1: Rewrite in slope-int form
[tex]y + 6 = 1/3(x - 9)[/tex]
[tex]y + 6 = 1/3x - 3[/tex]
[tex]y + 6 - 6 = 1/3x - 3 - 6[/tex]
[tex]y = 1/3x - 9[/tex]
Answer: [tex]y = 1/3x - 9[/tex]
I need The answers for U,V and W
Answer:
U=30
W=2.25
tho I’m not sure about v
Answers:
U: 5 + 13 + 12 = 30 cm
V: 8 + 7 + 4 + 3,5 = 22,5 ft
W: 2 1/8 + 6 3/4 + 2 = 2 + 0,125 + 6 + 0.75 + 2 = 10,875 mm
Match the angle measures with the value of x in each triangle. i!mages below!
145°
33°
46°
124°
60°
Step-by-step explanation:
left side X°=33(i.e 75+72+x=180)
left side down x°= 60°
right side=145°
right side down= 124
For PLATO Users here is the correct matching
Using a scale of 2in: 45 miles
The distance between Troy City and Ben City is 315 miles. How far apart are they on the map? (numerical answer)
set Up a ratio:
2 inches / 45 miles = x inches / 315 miles
Solve for x
Cross multiply:
45x = 630
Divide both sides by 45
X = 630 /45
X = 14 inches apart
Combine the like terms to create an equivalent expression: -4q - (-8q) + 10
Like terms are terms that have the same variable and power/exponent.
-4q - (-8q) + 10 (two negative signs cancel each other out and become positive)
-4q + 8q + 10 The only like terms you can combine are -4q and 8q, because they have the same variable of q and an exponent of 1.
4q + 10 (this is as far as you can simplify)
Please help!
I'm having a tuff time figuring this out.
Answer:
x = 17
Step-by-step explanation:
Since the triangles are congruent
<I = <P
3x+4 = 72-x
Add x to each side
3x+4+x = 72-x+x
4x+4 = 72
Subtract 4 from each side
4x+4-4 = 72-4
4x = 68
Divide each side by 4
4x/4 = 68/4
x = 17
The segment JK has coordinates at point J(1, 4) and point K(-6, -8). The segment DE has coordinates at point D(3, 3) and point E(-4, -9). Is segment JK congruent to segment DE? Explain why.
Segment JK is congruent to segment DE because they have the same length.
Explanation:To determine if segment JK is congruent to segment DE, we need to compare their lengths. We can use the distance formula to find the length of each segment.
For segment JK, the coordinates are J(1, 4) and K(-6, -8). Using the distance formula, we have:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((-6 - 1)^2 + (-8 - 4)^2)
= sqrt((-7)^2 + (-12)^2)
= sqrt(49 + 144)
= sqrt(193)
For segment DE, the coordinates are D(3, 3) and E(-4, -9). Using the distance formula, we have:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((-4 - 3)^2 + (-9 - 3)^2)
= sqrt((-7)^2 + (-12)^2)
= sqrt(49 + 144)
= sqrt(193)
Since the lengths of segment JK and segment DE are both sqrt(193), they are congruent.
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Name all segments parallel to GH.
All the segments that are parallel to GH in the given shape are, BC, AD and FI. Option A
How to identify all segments parallel to GH
To identify all segments parallel to GH, understand the basic structure of a cuboid and its faces.
A cuboid is a three-dimensional shape with six rectangular faces. Each face of the cuboid is parallel to the opposite face. This property allows us to identify segments that are parallel to each other within the cuboid.
To identify segments parallel to a specific segment in a cuboid, follow these steps:
Understand the orientation of the cuboid:
Visualize the cuboid and identify its three pairs of opposite faces. These faces are parallel to each other.
Identify the given segment:
Determine the specific segment in the cuboid to which you want to find parallel segments.
In this case GH
Locate the faces that contain the given segment:
Identify the faces that contain the given segment. These faces will be parallel to each other.
Based on the highlighted steps above, by visualization,
Segment BC is parallel to GH
Segment AD is parallel to GH
Segment FI is parallel to GH
Therefore, all the segments that are parallel to GH are, BC, AD and FI. Option A
The graph below shows the average daily temperatures on January 1 from 1900 to 1934 for city A.
Average Daily Temperature
Jan. 1 - 1900-1934
City A
Number of Years
20
22 24 26 28
Average Daily Temperature
The mean of the temperatures in the chart is 24° with a standard deviation of 4° Which temperature is within one standard
deviation of the mean?
Save and Fxit
25 years had temperatures within one standard deviation of the mean.
What is standard Deviation?The term "standard deviation" (or σ) refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
Given:
Data for the average daily temperature on January 1 from 1900 to 1934 for city A.
Mean u = 24°C
standard deviation σ = 4°C
Now, Interval for 1 standard deviation ( σ ):
[ u - σ , u + σ ]
[ 24 - 4 , 24 + 4 ]
[ 20 , 28 ] °C
Now, determine the number of years the temperature T lied in the above calculated range: [ 20 , 28 ].
T1 = 20 , n1 = 2 years
T2 = 21 , n2 = 3 years
T3 = 22 , n3 = 2 years
T4 = 23 , n4 = 4 years
T5 = 24 , n5 = 3 years
T6 = 25 , n6 = 3 years
T7 = 26 , n7 = 5 years
T8 = 27 , n8 = 2 years
T5 = 28 , n9 = 1 years
and, The total number of years:
∑ni = n1 + n2 + n3 + n4 + n5 + n6 + n7 + n8 + n9
= 2 + 3 + 2 + 4 + 3 + 3 + 5 + 2 + 1
= 25 years
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Which measure of center should you use to describe two data sets that are both symmetric?
Answer:
im pretty sure its median
Step-by-step explanation:
Mean and median can be used to describe two data sets that are both symmetric.
What is Outlier?An observation that differs abnormally from other values in a population-based random sample is referred to as an outlier. In a way, this definition defers to the analyst's (or a consensus process') judgement as to what constitutes aberrant behaviour.
Given:
Two symmetric data sets are described by the following measure of centre:
The mean and median are two numerical measures of centre that, if the distribution is symmetric, can determine the centre as the average value; otherwise, the median can be employed because it is not robust against outliers.
For example : Height of 3 students in 70, 72, 74
Mean of students= (70 +72+ 74)/ 3 = 72
and, median = 72
Hence, mean and median can be used.
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9/(70X-10) =1/(70x-10)
Joan draws a bar chart to show the temperatures at midday
on March 1st in five cities.
Joan has made four mistakes
in her diagram.
Write down any three of them.
Possible mistakes in Joan's bar chart could be incorrect scale, inaccurate labeling, and inconsistent bar lengths. Correcting these errors would make the chart a more accurate representation of the temperature data.
Explanation:Without the specific bar chart, it is difficult to identify Joan's mistakes, but possible errors in a bar chart depicting temperatures could be the following:
Incorrect scale: The scale of the bar chart must correspond to the range of temperatures. For example, if temperatures vary from 15 degrees Celsius to 35 degrees Celsius, the scale should encompass this range.Incorrect labeling: Each city and corresponding temperature should be accurately labeled on the chart.Inconsistent bar lengths: The length of the bars should represent the actual data accurately. A higher temperature should have a longer bar and a lower temperature a shorter one.Learn more about Bar Chart Mistakes here:https://brainly.com/question/32121650
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