Answers
==================================================
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
How much simple interest does $5,000 earn in 4 years at an interest rate of 5%. Round to
the nearest cent.
Answers
Answer:
1000
Step-by-step explanation:
This my homework and I'm bad at math if you can take the time please help me out f(x)= (x-5)to the power of 2 +12
I need the vertex
Axis of symmetry
Domain
Range
Answers
Answer:
Vertex: (5,12)
Axis of Symmetry: x=5
Domain: (-infinity, +infinity)
Range: [12, +infinity)
Step-by-step explanation:
The lines A and B are parallel. Identify a pair of corresponding angles?
Answers
Answer:
2 and 5............................
Answer:
Yes. 2 & 5 / 4 & 8 / 1 & 6 / 3 & 7 (Choose one yourself)
Step-by-step explanation:
Corresponding angles are angles that have one angle outside a pair of parallel lines and one angle within it and they are equal to each other.
I really need help with -8 - 4(5m + 9)
Answers
Patricia added 1 1/4 of salsa to a pot of her homemade chili. With the salsa the pot held 2 1/2 quarts of chili how many cups of salsa are in on quart of chili
A 1/2
B 2
C 5/8
D 1 & 1/4
Answers
40:10 = 12 :
Equivalent ratio
Answers
Solution:
Since
40 : 10 = 12 : X
Then we know
10/40 = X/12
Multiplying both sides by 12 cancels on the right
12 × (10/40) = (X/12) × 12
12 × (10/40) = X
Then solving for X
X = 12 × (10/40)
X = 3
Therefore
40 : 10 = 12 : 3
Lourdes recorded in this table the change in her dog's weight, in ounces, each month. Which statement can be suppor by the data in the table? Change in Dog's Weight January February March April May +6 +4 -2 +1 -5
A) Lourdes dog gained weight in more months than it lost weight because there are more positive numbers than ne numbers.
B) Lourdes' dog lost weight in more months that it gained weight because the digit 5 is the greatest digit and it is a ne number.
C) Lourdes dog gained weight every month because it is getting older.
D) Lourdes dog lost weight every month because the change in May is a negative number.
Answers
Answer:
A). Lourdes dog gained weight in more months than it lost weight because there are more positive numbers then negative numbers
Express the percent as a decimal 6.4%
Answers
Answer:
0.064
Step-by-step explanation:
Hope this helps!
Convert 5700 milligrams into pounds. Round your answer to the nearest hundredth.
Answers
The value of the 5,700 milligrams in pounds is approximately 0.01 lb
What is a unit of measurement?A unit of measurement is a specified magnitude of a quantity that is accepted and adopted by convention or backed by law, and used as a measurement standard.
In other to successfully convert a quantity in one unit to another unit, both units (initial and destination unit) should refer to the same characteristics of the object being measured.
Once both units are confirmed to refer to the same quantity, conversion factors are used to multiply the quantity in the first unit in order to express it in the other unit.
The given parameters are;
The quantity to be converted to pounds = 5,700 milligrams
The factor of conversion is 1,000 mg ≈ [tex]2.205 \times 10^{-6}[/tex] lb
Therefore;
[tex]5,700\: mg = 5,700 \times 2.205 \times 10^(-3) ≈ 0.0126[/tex]
Therefore, to the nearest hundredth, we have;
5,700 mg ≈ 0.01 lb
Learn more about unit conversion in mathematics here:
https://brainly.com/question/141163
#SPJ1
Please help me answer this :)
I will give braisnlt
Answers
Answer:
y = -1/2x + 4
Step-by-step explanation:
I got -1/2x because for every 2 spaces, the line goes down 1 (rise/run)
I got +4 because 4 is where x = 0, or the y intercept
Express 236% as a mixed number in simplest form
Answers
Answer:
2[tex]\frac{9}{25}[/tex]
Step-by-step explanation:
Evaluate 5x - 9y if x = 8 and y=-3
Plz help like soon
Answers
Find 83 1/3 % of 384
Answers
Answer:
319.872
Step-by-step explanation:
319.872 / 384 = 83 1/3 / 100
Final Answer: [tex]320[/tex]
Steps/Reasons/Explanation:
Question: Find [tex]83\frac{1}{3}[/tex]% of [tex]384[/tex].
Step 1: Convert mixed fraction into improper fraction.
[tex]\frac{250}{3}[/tex]
Step 2: Multiply [tex]\frac{250}{3 * 100}[/tex] with [tex]384[/tex].
[tex]\frac{96000}{300}[/tex]
Step 3: Simplify
[tex]320[/tex]
~I hope I helped you :)~
The clothing store marked down all their shirts by 30%. If a shirt originally cost $24, what is the sale price of the shirt?
Answers
Answer:
$16.80
Step-by-step explanation:
Since the shirts are marked down by 30%, you need to multiply the cost of the shirt by the percentage.
$24 × 0.3 = $7.20
Next, subtract the discount from the original price to find the discounted price.
$24 - $7.20 = $16.80
We want to find the zeros of this polynomial:
p(x) = (2x2 – 9x + 7)(x - 2)
Answers
Answer:
Step-by-step explanation: Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2".
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
p*(x)-((2*x^2-9*x+7)*(x-2))=0
STEP
1
:
Equation at the end of step 1
px - (((2x2 - 9x) + 7) • (x - 2)) = 0
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring 2x2-9x+7
The first term is, 2x2 its coefficient is 2 .
The middle term is, -9x its coefficient is -9 .
The last term, "the constant", is +7
Step-1 : Multiply the coefficient of the first term by the constant 2 • 7 = 14
Step-2 : Find two factors of 14 whose sum equals the coefficient of the middle term, which is -9 .
-14 + -1 = -15
-7 + -2 = -9 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and -2
2x2 - 7x - 2x - 7
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (2x-7)
Add up the last 2 terms, pulling out common factors :
1 • (2x-7)
Step-5 : Add up the four terms of step 4 :
(x-1) • (2x-7)
Which is the desired factorization
Equation at the end of step
2
:
px - (2x - 7) • (x - 1) • (x - 2) = 0
STEP
3
:
Equation at the end of step 3
px - 2x3 + 13x2 - 25x + 14 = 0
STEP
4
:
Solving a Single Variable Equation:
4.1 Solve px-2x3+13x2-25x+14 = 0
In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.
We shall not handle this type of equations at this time.
Supplement : Solving Quadratic Equation Directly
Solving 2x2-9x+7 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula
Parabola, Finding the Vertex:
5.1 Find the Vertex of y = 2x2-9x+7
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 2 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 2.2500
Plugging into the parabola formula 2.2500 for x we can calculate the y -coordinate :
y = 2.0 * 2.25 * 2.25 - 9.0 * 2.25 + 7.0
or y = -3.125
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = 2x2-9x+7
Axis of Symmetry (dashed) {x}={ 2.25}
Vertex at {x,y} = { 2.25,-3.12}
x -Intercepts (Roots) :
Root 1 at {x,y} = { 1.00, 0.00}
Root 2 at {x,y} = { 3.50, 0.00}
3 Solving 2x2-9x+7 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 2
B = -9
C = 7
Accordingly, B2 - 4AC =
81 - 56 =
25
Applying the quadratic formula :
9 ± √ 25
x = —————
4
Can √ 25 be simplified ?
Yes! The prime factorization of 25 is
5•5
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).
√ 25 = √ 5•5 =
± 5 • √ 1 =
± 5
So now we are looking at:
x = ( 9 ± 5) / 4
Two real solutions:
x =(9+√25)/4=(9+5)/4= 3.500
or:
x =(9-√25)/4=(9-5)/4= 1.000
The area of a square shaped park measures 16900 square feet. How many feet of fencing would be needed to enclose that park?
Answers
Answer:
520 feet
Step-by-step explanation:
The area=16900
Area formula=b^2
b^2=16900
square root of 16900=130
130*4=520
A utility company estimates that a power line repair job will take a total of 24 person-hours. If 3 workers are assigned to the job, how long will it take them to complete the job according to this estimate?
Answers
Answer:
8hrs
Step-by-step explanation:
[tex] \frac{24}{3} \\ \\ [/tex]
Based on the information given, the number of hours that will be used will be 8 hours.
From the information given, the company estimates that a power line repair job will take a total of 24 person-hours and 3 workers are assigned to the job.
Therefore, the number of hours that will be used will be:
= 24 hours / 3
= 8 hours
Learn more about division on:
https://brainly.com/question/4320580
he;ppppppppppppppppppppppppppppppppppppppppppppppppppppp
Answers
Answer:
y = 64
Step-by-step explanation:
The angles are supplementary, that is sum to 180° , thus
2(x + 6) + y = 180 ← substitute x = 52
2(52 + 6) + y = 180
2(58) + y = 180
116 + y = 180 ( subtract 116 from both sides )
y = 64
what is the slope, m, and the y-intercept of the line that is graphed below?
Answers
Answer:
m= 1; (0, 3)
Step-by-step explanation:
jus bc
The life span of a domestic cat is normally distributed with a mean of 15.7 years and a standard deviation of 1.6 years. a. Find the probability that a cat will live to be older than 14 years. b. Find the probability that a cat will live between 14 and 18 years. c. If a cat lives to be over 18 years, would that be unusual? Why or why not? d. How old would a cat have to be to be older than 90% of other cats?
Answers
Answer
a. 0.856
b. 0.78071
c. It is not unusual
d. 13.65 years old
Step-by-step explanation:
The life span of a domestic cat is normally distributed with a mean of 15.7 years and a standard deviation of 1.6 years.
We solve this question using z score formula:
z = (x-μ)/σ, where
x is the raw score
μ is the population mean
σ is the population standard deviation.
a. Find the probability that a cat will live to be older than 14 years.
For x > 14 years
z = 14 - 15.7/1.6
z = -1.0625
Probability value from Z-Table:
P(x<14) = 0.144
P(x>14) = 1 - P(x<14) = 0.856
b. Find the probability that a cat will live between 14 and 18 years.
For x = 14 years
z = 14 - 15.7/1.6
z = -1.0625
Probability value from Z-Table:
P(x = 14) = 0.144
For x = 18 years
z = 18 - 15.7/1.6
z= 1.4375
Probability value from Z-Table:
P(x = 18) = 0.92471
The probability that a cat will live between 14 and 18 years is calculated as:
P(x = 18) - P(x = 14)
0.92471 - 0.144
= 0.78071
c. If a cat lives to be over 18 years, would that be unusual? Why or why not?
For x > 18 years
z = 18 - 15.7/1.6
z= 1.4375
Probability value from Z-Table:
P(x<18) = 0.92471
P(x>18) = 1 - P(x<18) = 0.075288
Converting this to percentage:
0.075288 × 100 = 7.5288%
Hence, 7.5288% of the cats live to be over 18 years. Hence, it is not unusual.
d. How old would a cat have to be to be older than 90% of other cats?
From the question above, 10% of the cats would be older than 90% of other cats.
Hence, we find the z score of the 10th percentile
= -1.282
Hence,
-1.282 = x - 15.7/1.6
Cross Multiply
-1.282 × 1.6 = x - 15.7
- 2.0512 = x - 15.7
x = 15.7 -2.0512
x = 13.6488 years old
Approximately = 13.65 years old
If A = (2, 4, 6, 8, 10) and B = {4, 8, 10), then which of the following statements is false?
Answers
Answer:
A⊂B is the false
Step-by-step explanation:
because there are elements in A not exist in B
Answer:
A is the subset of B
is the false statement.
can you guys help me pls this is my final :(
Answers
Answer:
look up on math..way:)
Step-by-step explanation:
Solve for x:abx²-(a⁴+b⁴)x+a³b³=0
Answers
Step-by-step explanation:
abx² - (a⁴ + b⁴)x + (a³b³) = 0
(ax - b³)(bx - a³) = 0
Therefore x = b³/a or x = a³/b.
Slope and y intercept of y=2.7x+8
Answers
Answer:
slope: 2.7
y-intercept: (0,8)
Step-by-step explanation:
In the form y = mx + b, m is the slope and b is the y-intercept.
y-intercept : (0,8)
Choose a true statement
g(x) is not a function because f(x) is not a
function.
g(x) is not a function because f(x) is not one-
to-one.
gx) is a function because f(x) is one-to-one.
g(x) is a function because f(x) is not one-to-
O
one.
Answers
I think it is the first one
Answer:
Keep it simple: part one. D, part two. C
Step-by-step explanation:
write an equation of the line y=5x+8 that passes through the point (4,-3)
Answers
How can this expression be written another way?
Apply the distributive property and the greatest common factor to write an equivalent expression.
Enter your answer by filling in the boxes.
105 + 35m = __ (__)
Answers
Answer:
(105 x 30) + (105 x 5) + m
Step-by-step explanation:
Answer:
(105 x 30) + (105 x 5) + m
Step-by-step explanation:
Hope this helped have an amazing day!
A gas tank holds exactly 13 gallons. If the tank is 2/3 empty, how many gallons remain in the tank? (Round your answer to the nearest tenth)
Group of answer choices-
4.3
5.5
6.5
8.7
Answers
A math club receives a 120 discount on calculators. If each
calculator costs S15 before the discount, how much will the
club spend on 60 calculators after the discount?
Answers
Answer:
$780
Step-by-step explanation:
15x60 = 900 900 - 120 = $780
The price of admission to the Everglades Historical Museum is $11 more for non-members than for members of the museum’s Friends of the Museum program.
If a group of 3 members and 4 non-members pays a total of $79 to visit the Museum, what is the cost, in dollars, of the ticket for one non-member?
Select one:
A. $9.00
B. $11.00
C. $15.00
D. $16.00
Answers
Answer:
d. $16.
Step-by-step explanation:
3 members (m) + 4 nonmembers (n) = $79
nonmembers = $11 more or n=m+11 so...
3m + 4(m+11)=79 [replace "n" with "m+11"]
3m + 4m + 44=79
7m + 44 = 79
7m=35 and reduced m=5 so members pay $5 and nonmembers pay 5+11=$16