Consider the function f (x) = StartLayout Enlarged left-brace first row negative StartFraction 4 x Over x minus 3 EndFraction, x less-than 5 second row negative 7 x + 25, x greater-than 5 EndLayout. Which type of discontinuity occurs at x = 5? mixed infinite endpoint removable
Answers
Answer:
Its removable
Step-by-step explanation:
yes
this is a removable discontinuity
Here we have the piecewise function:
[tex]f(x) = \frac{-4x}{x - 3}[/tex] if x < 5
[tex]f(x) = -7x + 25[/tex] if x > 5.
We want to see which type of discontinuity we have at x = 5.
Remember that:
If we have two asymptotes, then is an infinite discontinuity
if just one point is missing, then it is a removable discontinuity
If the value drastically changes after the discontinuity, then its a jump discontinuity
Mixed case is when two of these happen.
Because we have a piecewise function, we need to evaluate both parts in x = 5.
If both parts give the same value, then we will have a removable discontinuity
if the values are different, then we have a jump discontinuity.
first part:
f(5) = -4×5/(5 - 3) = -20/2 = -10
second part:
f(5) = -7×5 + 25 = -35 + 25 = -10
So we got the same value, which means that this is a removable discontinuity
in the image below you can see the graph of the piecewise function, and see that as x tends to 5, both sides of the function tend to the same value.
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Related Questions
An investment of $100 is now valued at $149.18 the interest rate is 8% compounded continuously about how long has the money been invested
Answers
question: An investment of $100 is now valued at $149.18 the interest rate is 8% per year, compounded continuously about how long has the money been invested
Answer:
5.2 years
Step-by-step explanation:
Applying
A = P(1+R/100)ⁿ.......................... Equation 1
Where A = amount, P = principle, R = rate, n = time.
From the question,
Given: A = $149.18, P = $100, R = 8%
Substitute these values into equation 1 and solve for n
149.18 = 100(1+8/100)ⁿ
149.18/100 = (1+8/100)ⁿ
1.4918 = (1+0.08)ⁿ
1.4918 = (1.08)ⁿ
Taking the Logarithm of both side
Log(1.4918) = Log(1.08)ⁿ
Log(1.4918) = nLog(1.08)
n = Log(1.4918)/Log(1.08)
n = 0.1737/0.0334
n = 5.2 years.
Please help me with full calculations
Answers
Answer:
use formula,
P(x,y)=P'(-y,x)
so.
R(-2,-2)=R'=(2,-2)
S(1,1)=S'(-1,1)
T(-1,-3)=T'(3,-1)
Step-by-step explanation:
plot R,S,T and R',S',T' in the graph
I just need help with this
Answers
Answer:
z = 4.5
Step-by-step explanation:
∠B = ∠B ∠BAD = 90° - ∠B = ∠C
ΔBAD ~ ΔBCA
AB / z = BD / AB
z = AB * AB / BD = 3*3 / 2 = 4.5
In a high school high jump contest, the height of clearing the bar ranged from 71 inches to 84 inches. The mean height was 76 inches and the standard deviation was 3.5 inches. What percent of the jumpers were in the group jumping below 79.5 inches
Answers
Step-by-step explanation:
Given data:
Range of jumps = 71 to 84 inches
Mean of jumps = 76 inches
standard deviation = 3.5
To calculate the percent of jumpers in the group jumping below 79.5 inches
Let us calculate the number of standard deviation in 79.5 inches
= 79.5/3.5
= 22.71 times
Answer:
84.1%
Step-by-step explanation:
Please help me with this. And my teacher said to show your work so what do I have to do and she said on paper please help thank you!
Answers
Answer:
Step-by-step explanation:
V=H x W x L so 11.25= H (1.5) (2); 3H=11.25 so the height of one box is 3.75’
To find the volume of 5 stacked boxes multiply the volume of one box by 5.
5(3.75 x 1.5 x 2) which is 20.25 cubic feet.
Help me with my ixl please?!?
Answers
Answer:
funding a stuggling
Step-by-step explanation:
Complete the following sentence. x = x' cosθ - y'sinθ where x’ and y’ are _____.
rotated points
original points
translated points
vertex points
Answers
Answer:
ROTATED POINTS
Step-by-step explanation:
HOPE IT HELP MHUW
Can someone please show me how to do this, I know the answer is 125 a^3 b^2.
The question is shown below in a picture I’m not sure how to do it please explain!
Answers
Answer:
Step-by-step explanation:
5^4 = 625. I hope your calculator will do this.
625 / 5 = 125
There is a more general way to do this which will be in harmony with the rest of the question.
5^4 / 5^1 = 5^(4 - 1) = 5^3 = 125
b^4 / b2 = b^(4 - 2) = b^2
a remains as it is at a^3
So the answer is 125 a^3 b^2
The owner of a flower shop on H street sells 28 roses for $140. What is the cost in dollars per rose?
Answers
Answer:
$5 ( sorry if it is incorrect)
Step-by-step explanation:
What is m∠BAC.
............
Answers
Answer:
37 degrees
Step-by-step explanation:
1. m∠CBA = 71+45 = 116 degrees
2. m∠CBA = m∠CDA because of the quadrilateral property of opposite sides.
3. m∠CBA + m∠CDA = 2*116 = 232.
4. Total angle measure of a quadrilateral is 360 degrees, so m∠BAD + m∠BCD = 360-232 = 128 degrees.
5. m∠BAD = m∠BCD = 128/2 = 64 degrees
6. m∠BAC = m∠BAD - m∠CAD = 64 - 27 = 37 degrees
Im being asked to put this in simplest form can anyone help me?
What is 0.57 (7 repeating) expressed as a fraction in simplest form?
Answers
Answer:
57/100
Step-by-step explanation:
look it up
A car lot has both used and new cars. If 86% of the cars on the lot are new and 45% of the cars are new and have a sunroof, find the probability of randomly choosing a car with a sunroof, given that it is a new car
Answers
Answer:
0.523
Step-by-step explanation:
Let :
New car = N
Sunroof = S
P(N) = 0.86
P(N n S) = 0.45
Recall :
P(A|B) = p(AnB) / p(B)
Therefore ;
P(S|N) = P(SnN) / p(N)
P(S|N) = 0.45 / 0.86
P(S|N) = 0.523
Emma bought a pair of earrings, a dress and a coat. The dress cost 6 times as much as the earrings, and the coat cost 13 times as much as the earrings. If the three items cost a total of $3200, how much did each of them cost?
Answers
Answer:cost of earring=$160
cost of dress= $960
cost of coat =$2,080
Step-by-step explanation:
Let cost of earring be represented as x
so that the cost of dress =6x
And the cost of coat =13x
Since the three items cost a total of $3200, we can develop an equation which can be represented as
cost of earring+cost of dress +cost of coat =3200
x +6x+13x=3200
20x =3200
x=3200/20=160
THerefore cost of earring=$160
cost of dress= 6x =$160 x 6=$960
cost of coat = 13x = $160 x 13=$2,080
The average of the first 3 numbers was 28. The average of the next 12 numbers was 38. What was the overall average of the numbers?
***NO SPAM, PLEASE!!!!!!***
Answers
Answer:
ther overall average would be 36
Step-by-step explanation:
NEED HELPPPPP LOL XDDDDD OH MY GODDD
Answers
Answer:
yo w t f is thisssssss
Step-by-step explanation:
b c idek im so cluless rn im in 7th grade XD
What is the distance between the two points? (Round to the nearest tenth)
8.6 units
6.1 Units
2.8 units
9.2 units
Answers
Ayuda plis contesten los que saben porfis
Answers
Answer:
13 c
Step-by-step explanation:
15+6=21
21+3=24
24-7=17
17-4=13
FREEEE POINTS REALLY
Answers
Answer:
x is less than 46
x<46°
Step-by-step explanation:
............
Based on equation of the line of best fit how much money should Millie expect to earn if he works a five hour shift?
Answers
Answer:
See Explanation
Step-by-step explanation:
Given
[tex]x = 5[/tex] ---- 5-hour shift
Required
The expected earnings
The question is incomplete, as the equation is not given. A general way to solve this, is to substitute the value of x in the equation, then solve for the y variable.
Take for instance, the equation is:
[tex]y = 10x + 2[/tex]
The expected earnings will be:
[tex]y = 10*5 + 2[/tex]
[tex]y = 50 + 2[/tex]
[tex]y = 52[/tex]
Expected Earnings = $52
A frosting is made of cream cheese and powdered sugar in the ratio 3:2. If you use 120g or cream cheese, how much powdered sugar should you use
Answers
Answer: 80 g
Step-by-step explanation:
Given
The frosting is made of cream cheese and Powdered sugar in the ratio of 3:2.
If 120 g of cheese is used
Assume the quantity of powdered sugar is x
So, we can write the ratio as
[tex]\Rightarrow \dfrac{3}{2}=\dfrac{120}{x}\\\\\Rightarrow x=\dfrac{2}{3}\times 120\\\\\Rightarrow x=\dfrac{2}{3}\times 3\times 40\\\\\Rightarrow x=80\ g[/tex]
So, 80 g of powdered sugar is used.
Answer: 80grams
Step-by-step explanation: pretty simple 120/3=40. 40x2=80 grams. Sorry for explanation not being really clear.
the sum of two numbers is 19 and their diffrence is 3
Answers
Answer:
8 and 11
Step-by-step explanation:
Amy is baking her famous pies to sell at the Town Fall Festival. She 1 point
uses 32 /4 cups of flour for every 1/2 batches of pie that she makes. How
many cups of flour would Amy use for 7 batches of pie?
A. 21 1/2 cups
B. 112 7/8 cups
C. 150 72 cups
D. 225 34 cups
Answers
Answer:
Step-by-step explanation:
A
. Which of the following is the correct algebraic representation of the translation below?
a. (x – 6, y – 5)
b. (x – 5, y – 6)
c. (x + 5, y + 6)
d. (x + 6, y + 5)
Answers
Answer:
D) (x+6, y+5)
Step-by-step explanation:
You can start with the top corner of triangle A
Then count up 5 units and right 6 units
Because you count vertically 5 units that means you're using the y-axis, And because you're counting up, than means the values are positive.
And because you count horizontally 6 units you're using the x-axis, And you are counting to the right so the values are positive.
Down vertically=Negative Y-axis Values. Up vertically=Positive Y-axis Values
Right horizontally=Positive X-axis values. Left horizontally=Negative X-axis Values
Suppose that there were a strong correlation between the variables n and a
Which of these is a true statement?
A. n must cause p.
B. n must not cause p.
C. p must cause n.
D. n may cause p.
Answers
Answer:
D
Step-by-step explanation:
correlation does not= causation
i really need help on this i’m confused
Answers
Solve for m.
3m = 15
A. m = 45
B. m = 35
C. m = 12
D. m = 5
Answers
Answer:
D.
Step-by-step explanation:
Have a Nice Day
Answer:
it's D.
Step-by-step explanation:
NO LINKS The circumference of a circle is 36 feet. What is the length of the radius of this circler
O 9 ft
18 ft
36 ft
O 72 ft
Thank you so much for your help! :)
Answers
Answer:
18ft
Step-by-step explanation:
Formula of circumference * r x r x 3.14* or d x 3.14*
:DDD And ye glad I could help!
Find the mode, median, mean and range for this set of data.
Number of Hours Slept: 8.5, 7,6.75,5.75, 8.75,6.25,7,7.5, 4.25
Answers
Central Tendency is the statistical measure that can be used to represent all the distribution or a dataset using a single value. The most common measures of central tendency are the mode, median, and mean.
How to determine this
Mode is the value that has the highest frequency in a given data set.
So,
8.75 the highest frequency in the data set
Mode = 8.75
Median is the middle of a sorted list of numbers when arranged in ascending order.
So,
4.25, 5.75, 6.25, 6.75, 7, 7, 7.5, 8.5, 8.75 in ascending order
Median = 7
Mean is the average or the most common value in a given set of values.
Mean = 8.5 + 7 + 6.75 + 5.75 + 8.75 + 6.25 + 7 + 7.5 + 4.25/9
Mean = 61.75/9
Mean = 6.8611
Mean = 6.86 to 2 decimal place
Range is the difference between the highest value and lowest values.
Range = Maximum value - Minimum value
Range = 8.75 - 4.25
Range = 4.5
Read more about Central Tendency
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Tell if the number is rational or irrational. 3.65028
Answers
Answer:
Irrational
Step-by-step explanation:
Answer: YES
Explanation: 3.65028 is a terminating decimal, or decimal that ends, and all terminating decimals are rational numbers.
can 5,7 and 13 make a triangle
Answers
Answer:
No
Step-by-step explanation:
5+7=12
12>13 X
13+5=18
18>13 YES
13+7=20
20>5 YES
If all equations were true, it would make a triangle, but since only 2 are true, it doesn't make a triangle.
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hope it helps