Answers
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Work Shown:
[tex]\displaystyle \lim_{x \to 3} \frac{f^2(x)-4}{f^2(x)-f(x)-2}\\\\\\\displaystyle \lim_{x \to 3} \frac{(f(x)-2)(f(x)+2)}{(f(x)-2)(f(x)+1)}\\\\\\\displaystyle \lim_{x \to 3} \frac{f(x)+2}{f(x)+1}\\\\\\\displaystyle \frac{f(3)+2}{f(3)+1}\\\\\\\displaystyle \frac{2+2}{2+1}\\\\\\\displaystyle \frac{4}{3}\\\\\\[/tex]
Notes:
In step 2, I used the difference of squares rule to factor the numerator. The denominator can be factored through trial and error. The key here is the f(x)-2 terms that show up in each. Those factors cancel in step 3.
Afterward, we apply the substitution rule, [tex]\displaystyle \lim_{x \to a} f(x) = f(a)[/tex], so basically I plugged in x = 3. Then evaluated f(3) = 2 due to the point (3,2).
Related Questions
Find the smallest positive four-digit number that is divisible by each of the four smallest prime numbers.
Answers
Answer:
It might be 1,050. Also can't believe thats a college question-
It was very easy to solve! Help from an 8th grader here.
Step-by-step explanation:
The smallest four-digit number that is divisible by each of the four smallest prime numbers is 1050.
What is the divisibility rule?The divisibility rule states that " Divisible By, implies that when two numbers are divided, the result would be a whole number.
The four smallest prime numbers are 2, 3, 5, and 7.
To find the smallest four-digit number that is divisible by each of these numbers, we can start by finding the least common multiple (LCM) of these numbers. The LCM of a set of numbers is the smallest number that is divisible by all of the numbers in the set.
To find the LCM of 2, 3, 5, and 7, we can start by listing the prime factorization of each number:
2 = 2 x 1
3 = 3 x 1
5 = 5 x 1
7 = 7 x 1
Then, we can find the LCM by taking the highest power of each prime that appears in any of the numbers:
LCM(2, 3, 5, 7) = 2¹ x 3¹ x 5¹ x 7¹ = 210
Since we want the "smallest 4-digit number", then it is:
210 x 5 =1050
Therefore, each of the four lowest prime numbers may be divisible by the smallest four-digit number, which is 1050.
Learn more about the divisibility rule here:
brainly.com/question/10703980
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Use mental math to solve the equation.
5) C-(-15) = 38
7) Write a pairs of negative intogoro
Answers
sophias car wash llc specializes in detaling cars. For a pick up truck, sophia charges 30 dollars she also charges a rate of 4 dollars per hour. if sophia charged you 42 dollars how many hours did it take for her to detail your truck
Answers
Answer:
3 Hours
Step-by-step explanation:
If we subtract 30 dollars from the initial 42, we are left with 12 dollars. Then all we have to do is do 12/4 to get 3 hours of work :D
hellllllllllllllllp points if you answeer correctly
Answers
Answer:
the answer will be [-3/4,1/2]
Step-by-step explanation:
I need help asap thx
Answers
Answer:
with what lol
Step-by-step explanation:
Answer:
Theres no question
Step-by-step explanation:
The length of segment AE is 5 centimeters. What is the length of segment CD?
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(Find the distance between each of the following complex numbers. Give your answers in simplified radical form, and show all your work.)
1.) -1+i and -3-4i
2.) 1+i and 7-2i
3.) -3+4i and -6-i
4.) -2+3i and 2-2i
5.) 3 and 5+i
6.) -4+5i and 2-i
Thank you!
Answers
Answer:
I) √29
ii) 3√5
iii) 5√5
iv) √41
v) √5
vi) 6√2
Step-by-step explanation:
1)
Given complex numbers -1+i and -3-4i
The points are ( -1 , 1) and (-3 , -4 )
Distance formula
[tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^2 }[/tex]
= [tex]\sqrt{(-4-(1) )^{2} +(-3 -(-1) )^2 } = \sqrt{25+4} =\sqrt{29}[/tex]
2)
Given complex numbers 1+i and 7-2i
The points are ( -3,4) and (-6,-1)
Distance formula
[tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^2 }[/tex]
[tex]\sqrt{(-2-1 )^{2} +(7-1)^2 } = \sqrt{9+36} =\sqrt{45}= 3\sqrt{5}[/tex]
3)
Given complex numbers -3 +4i and -6-i
The points are ( -3 ,4 ) and (-6 ,-1)
[tex]\sqrt{(-1-4 )^{2} +(-6-4)^2 } = \sqrt{25+100} =\sqrt{125}= 5\sqrt{5}[/tex]
4)
Given complex numbers are -2+3i and 2-2i
The points are ( -2 ,3) and (2 , -2)
[tex]\sqrt{(-2-3 )^{2} +(2+4)^2 } = \sqrt{25+36} =\sqrt{41}[/tex]
5)
Given complex numbers are 3 and 5+i
The points are( 3,0) and (5,1)
[tex]\sqrt{(1-0 )^{2} +(5-3)^2 } = \sqrt{1+4} =\sqrt{5}[/tex]
6)
Given complex numbers are -4+5i and 2-i
The points are ( -4 ,5) and ( 2,-1)
[tex]\sqrt{(-1-5 )^{2} +(2-(-4))^2 } = \sqrt{36+36} =\sqrt{72}= 6\sqrt{2}[/tex]
9.6x10^85/3x10^63 in scientific notation
Answers
Answer:
3.27*10^22
Step-by-step explanation:
Given the expression 9.6x10^85/3x10^63, we are to write it on scientific notation as shown:
9.6x10^85/3x10^63
= (9.8/3) * (10^85/10^63)
= (9.8/3) * 10^{85-63}
= (9.8/3) *10^22
= 3.27 *10^22
Hence the expression in scientific notation is 3.27*10^22
Write the decimal equivalent for 6 1/9
Answers
Answer: 6.11
Step-by-step explanation:
Step 1: Multiply the whole number by the denominator:
6 × 9 = 54
Step 2: Add the product you got in Step 1 to the numerator:
54 + 1 = 55
Step 3: Divide the sum from Step 2 by the denominator:
55 ÷ 9 = 6.111111
That's it folks! The answer to 6 1/9 in decimal form is displayed below:
6 1/9 ≈ 6.11
Answer b.
Hope this answer helps you
Answer: b 6 1/9 = 6.11
Step-by-step explanation: what I did first was figure out the decimal version of 1.9 which equaled to 0.11111 etc. then due to it having a zero in front of it, you just place the in that spot making the answer 6.1111111 :)
hope this helped!
What is the standard deviation of the data set {2,1,1,2,2,3}?
Answers
Answer:
0.687
Step-by-step explanation:
step 1: find mean of 6 data values (should be 11/6)
step 2: find the difference of the mean and each of the six data values
step 3: square each of those six differences
step 4: find the mean of the squared values (should be 102/216)
step 5: take the square root of 102/216
Answer:
0.6
Step-by-step explanation:
i just took the test
A movie is being shown on television. The movie is scheduled for a 150 minute time lot and will include some commercial breaks. The number of commercial breaks can be determined by the equation 6x + 114 = 150, where x represents the number of commercial breaks.
A. Identify the meaning of the coefficient and the constant in the context of this situation.
B. Solve to find the number of commercial breaks.
C. Graph the solution.
Answers
Answer:
x=6
Step-by-step explanation:
5tgghjkli
The list shows numbers in order from least to greatest. -34, -2 .-1.5.0.2.3, 10,25 Which is an integer that can be integer on the blank line in the list? 0 -2.5 -2 1 0 -1
Answers
Answer:-2
Step-by-step explanation: I think
Answer: -2
Step by step explaination:
which pair of lines are perpendicular
Answers
Answer:
you're right!! its C
Step-by-step explanation:
For lines to be perpendicular, the multiplied slopes of the line need to be -1, so
y=1/3x-1
y=-3x-4
(1/3)*(-3)=-1
therefore, they are perpendicular
a(x) = 5x – 2
a(m – 3) = ?
Answers
Answer:
a(m - 3)=5m - 17
Step-by-step explanation:
Hope this helps
Cheesy Chicken and Rice has 430 kcals per serving. How many grams of protein are in one serving of the meal if 31% of the kcals come from protein?
Answers
Answer: 133,300
Step-by-step explanation:
Given that:
Number of kcals per serving = 430
Percentage of protein in the kcal = 31%
To obtain the number or amount of protein in one serving :
31% of 430
= 0.31 * 430
= 133.3 kcal
I kcal = 1000 gram calories
Hence,
133.3 kcal = (1000 * 133.3) = 133,300 gram calories
D
E
F
Using the Pythagorean Theorem, which of the following is true?
Answers
Answer:
D
Step-by-step explanation:
A classroom has an area of 3x^2 -4x-7. If the length of the classroom is ( 3x-7), what is the width of the classroom?
Answers
Answer: X+1
Step-by-step explanation:
Using only the values given in the table for the function, f(x)=x^3-3x-2,
what is the interval of x-values over which the function is decreasing ?
Answers
What is 6% on a 250$ bike
Answers
answer is 15$
250×6:100= 15
Answer:
the answer is 15 dollars
15 lb 7 oz - 6 lb 8 oz
Answers
Answer: 8.5lbs 7 oz
Step-by-step explanation:
8oz=.5lbs
15lbs 7oz-6.5lbs=
8.5lbs 7 oz
Identify the graph that displays the speed of a car accelerating onto a highway until it reaches the speed limit, and then continuing on the highway at the speed limit.
Answers
Answer: D
Step-by-step explanation:
Graph D shows the car increasing speed over time, then, the flat line shows the car remains at a constant speed. In order for the scenario to apply, there needs to be a line parallel to the x-axis which shows a speed remaining the same over a given amount of time. D is the only graph which has this feature, thus this graph displays the scenario.
PLEASE HELP WILL MARK BEST!
Tristan and Devin are brother and sister. Their parents put a total of $200 a month into a
college account. Tristan just graduated from high school, and Devin has two years of high school left.
Suppose Tristan and Devin each graduate college 4 years after they graduate high school, and their
parents will continue to put $200 into the college account monthly until both children have graduated
from college. If there is $10,000 in the account right now, how much money should each child get per
year in order to get an equal share?
Answers
Answer:
I think the answer is 5,000 .
What is x?
A. 0.75
B. 1.25
C. 1.67
D. 1.33
Answers
Answer:
D. 1.33
Step-by-step explanation:
[tex] \because \: x = tan (\theta) \\ \\ tan (\theta) = \frac{4}{3} \\ \\ tan (\theta) = 1.33 \\ \\ \implies \: x = 1.33[/tex]
an even even Function has a graph symmetric about _____, thus ______.
A. x-axis
B. y-axis
C. origin
A. f(x)= f(-x)
B. f(x)= -f(-x)
Answers
Answer:
B. y-axis
A. f(x) = f(-x)
mcgregor is growing alfalfa on 180 acres,which is 30% of his farmland. mcgregor has how many acres of farmland?
Answers
Answer:
600 acres
Step-by-step explanation:
Hope this helps!
The number of acres of land Mcgregor has 600 acres.
Given that, Mcgregor is growing alfalfa on 180 acres, which is 30% of his farmland.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Let the total number of acres be x.
So, 30% of x=180
⇒ 30/100 × x=180
⇒ 0.3x=180
⇒ x=180/0.3
⇒ x=600
Hence, the number of acres of land Mcgregor has 600 acres.
To learn more about the percentage visit:
brainly.com/question/24159063.
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The diameter of a circle is 8 cm. What is the area of the circle? Use 3.14 for pi
Answers
Answer:
50.27
Step-by-step explanation:
In order to get a good workout on your treadmill, you figure you have to run 528 feet in one minute. What are the possible numbers of miles you have to run in 20 minutes to exceed this rate? (Hint: 1 mile = 5280 feet)
PLEASE PROVIDE AN EXPLANATION, thank you!
Answers
Answer:
2 miles.
Step-by-step explanation: Because 528 times 20 is 10560 then divide by 5280 equaling 2 miles.
There are 36 students in Mr. Barrett's math class. If 25% of the students are boys, how many students are girls?
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Answer:
27 of the students are girls
What is 4 2/5 times 2 2/3
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HELP ASAP PLEASE!!! senora need 300 grams of a spice mix to put in her pasta dish. The store sells the spice mix by the ounce. there are approximately 28.35 grams in 1 ounce how many ounces of spice mix does senora need, rounded to the nearest hundredth?
Answers
Answer: 3,969
Step-by-step explanation:
multiply 140x28.35