Answers
Notice that:
[tex]1^2-1=0.[/tex]Therefore:
[tex]f(x)=\frac{x-1}{x^2-1}[/tex]is undefined at x=1.
Now, recall that the natural logarithm is defined over the positive numbers, therefore:
[tex]x^2-1>0[/tex]Then:
[tex]x>1\text{ or }x<-1.[/tex]Therefore the function
[tex]f(x)=ln(x^2-1)[/tex]is not well defined over the interval (0,2).
Finally, notice that:
[tex]p(x)=x^2+1,[/tex]has no real zeros, therefore the function:
[tex]f(x)=\frac{x+1}{x^2+1}[/tex]is well defined over all real numbers, also is continuous over all real numbers, particularly over the interval (0,2).
Answer: First option.
II only.
Related Questions
which is he mode of this data set? 55, 78, 43, 39, 78, 61, 75, 75, 43, 78
Answers
Step by Step explanation: The mode is a number that repeats itself more than once. 78 repeats three times. 43 repeats twice. 75 repeats itself twice. 78 shows up the most amount of times so the answer is 78.
The height (in inches) of a plant after 't' days is (1/2t + 6). After how many days is the plant 21 inches tall? *
Answers
Height = 1/2t + 6
To find after how many days the plant is 21 inches tall, replace height by 21:
21 = 1/2t + 6
Solve for t (days)
21-6 = 1/2t
15 = 1/2t
Multiply both sides of the equation by 2:
15(2) = 1/2t (2)
30 =t
After 30 days
PLEASE HELP IT FOR FINALS 15. Complete the paragraph proof below by selecting the missing justification. Given: CB bisects ZABD and ZACD. Prove: AABC ADCB А B n C D Gred that CB bisects ZABD and ZACD then by definition of angle bisector LABCLDBC and LACBEZDCB. Next, BC & CB by the Therefore by ASA, AABC ADCB Answer choices -Reflexive Property of CongruenceDefinition of Congruent Segments CPCTCTransitive Property of Congruence
Answers
Solution
For this case we can see that the correct solution would be;
Given that CB bisects angle bisector theorem
Therefore by ASA. Triangle ABC = Triangle DCB
A line has a slope of -8 and passes through the point (0,5)
Answers
A line has a slope of -8 and passes through the point (0,5)
Find out the equation of the line in slope-intercept form
y=mx+b
where
m is the slope
b is the y-coordinate of the y-intercept
in this problem
m=-8
b=5
therefore
y=-8x+5 -----> equation of the line in slope-intercept formHELP PLEASEEEEEEEEEEE!! ILL MARK BRAINLIEST
Answers
Find the slope, y-intercept and equation of the line for the points (0,3) (2,-1) show work please
Answers
we are asked to determine the slope of the line that passes through the points (0, 3) and (2, -1). To do that we need to use the formula for the slope of a line:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where:
[tex]\begin{gathered} (x_1,y_1)=(0,3) \\ (x_2,y_2)=(2,-1) \end{gathered}[/tex]Replacing in the formula:
[tex]m=\frac{-1-3}{2-0}[/tex]Solving the operations:
[tex]m=-\frac{4}{2}=-2[/tex]therefore, the slope is -2.
To determine the y-intercept we can use the point (0,3), since this means that when x = 0, y = 3. Since the y-intercept is the value of "y" when x = 0, this means that the y-intercept is 3.
To determine the equation of the line we need to use the general form of a line equation:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" the y-intercept. Replacing the value of the slope and "b"
[tex]y=-2x+3[/tex]Factor the polynomial completely.
x3 + 6x + x2 + 6
Group of answer choices
(x2 + 1)(x + 6)
(6x + 1)(x + 1)
(x2 + 6)(x + 1)
Answers
Answer:
(x² + 6)(x + 1)
Step-by-step explanation:
x³ + 6x + x² + 6
x³ + x² + 6x + 6
(x³ + x²) + (6x + 6)
x²(x + 1) + 6(x + 1)
(x² + 6)(x + 1)
I hope this helps!
Find the equation of the line through the point (1,-1) with
slope 4?
Answers
Answer:
4x - y - 5 = 0
Step-by-step explanation:
Given:
Slope = m = 4
(x1,y1) = (1,-1)
Solution:
y - y1 = m (x - x1)
y - (-1) = 4 (x - 1)
y + 1 = 4x - 4
y = 4x - 4 - 1
y = 4x - 5
4x - y - 5 = 0
Please help I would appreciate it. Solve 4x^2-4x-8 needs to be factored.
Answers
Given
[tex]4x^2-4x-8[/tex]This can be written as:
[tex]4(x-2)(x+1)[/tex]
At a restaurant, the bill comes to $40. You decide to leave a 15% tip. How much did you leave for the tip?
Answers
The tip of 15% is 15% of the total value of the bill, which is $40. So, we need to take 15% of 40.
Taking 15% of 40 is the same as multiplying 15% by 40. 15% can also be written as:
[tex]15\%=\frac{15\%}{100\%}=0.15[/tex]So, we can take 15% of 40 by multiplying 0.15 by 40:
[tex]0.15\cdot40=6[/tex]So, the amount left for the tip is $6.
simplify with three algebraic terms
0.3p+0.2p+0.4p
Answers
The simplified form of the three algebraic terms 0.3p + 0.2p + 0.4p is 0.9p
The three algebraic terms are
0.3p + 0.2p + 0.4p
The algebraic expression is defined as the expression which is made up of constants and variables with the algebraic operation. The algebraic operations are addition subtraction, division and multiplication
To solve this problem first we have to group the like terms of the given expression and add the like terms of the expression
The three algebraic terms are
= 0.3p + 0.2p + 0.4p
Group the like terms
= (0.3 + 0.2 + 0.4) ×p
Add the terms together
= 0.9p
Hence, the simplified form of the three algebraic terms 0.3p + 0.2p + 0.4p is 0.9p
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A shopkeeper wants to sell a shirt originally priced at $120. Which deal will result in the greatest sale price of the shirt?A. 20% offB. $30 couponC. 15% off and then a $15 rebateD. 10% off and then a $20 rebate
Answers
Let's determine which sale is better.
20% means that the shirt will cost:
[tex]120(0.8)=96[/tex]$30 coupon means that the shirt will cost $90
15% off and $15 rebate means:
[tex]120(0.85)-15=87[/tex]10% off and $20 rebate means:
[tex]120(0.9)-20=88[/tex]Comparing the prices we conclude that the best deal is C
f(x) = -x^2 - 10x - 13 Find f(-2)
Answers
Answer: f(-2) = 3
The the below quadratic function
[tex]f(x)=-x^2\text{ - 10x - 13}[/tex]Find f(-2). To find f(-2) let x = -2
[tex]\begin{gathered} f(-2)=-(-2)^2\text{ - 10(-2) - 13} \\ f(-2)\text{ = -(4) -10(-2) - 13} \\ f(-2)\text{ = -4 + 20 - 13} \\ f(-2)\text{ = 16 - 13} \\ f(-2)\text{ = 3} \end{gathered}[/tex]Write each expression as a sum or difference or multiple of logarithms, assume the variables represents positive numbers
Answers
SOLUTION
The given expression is:
[tex]\log_6\frac{4x}{3}[/tex]This is simplified to give
[tex]\operatorname{\log}_6\frac{4x}{3}=\operatorname{\log}_64x-\operatorname{\log}_63[/tex]This further gives
[tex]\operatorname{\log}_64x-\operatorname{\log}_63=\operatorname{\log}_64+\operatorname{\log}_6x-\operatorname{\log}_63[/tex]Therefore the required answer is:
[tex]\begin{equation*} \operatorname{\log}_64+\operatorname{\log}_6x-\operatorname{\log}_63 \end{equation*}[/tex]1. Green Forest Day Camp has 43 fewer girl campers than boy campers. There are 278 boy campers. Use rounding to estimate the total number of campers. 2. Green Forest Day Camp has 43 fewer girl campers than boy campers. There are 278 boy Campers. How many actual total campers does Green Forest Day Camp have?
Answers
Answer: 513 campers
Explanation
The total number of boys in the camp is 278
There are 43 fewer girl campers than boy
Let the total number of campers be x
Let the total number of girl campers be y
Since, there are 43 fewer girl campers than boy
Hence, the total number of girl campers is
y = Boy campers - 43
Boy campers = 278
y = 278 - 43
y = 235
Since, y is the total number of girl campers, hence, the total number of girl campers is 235
The total number of campers = number of boy campers + number of girl campers
The total number of campers = 278 + 235
The total number of campers = 513 campers
The answer is 513 camperst
Consider the expression.5n -2 =9Which statement best describes this expression?O A number less than two times five is 9.O Five times a number subtracted from two equals 9.O Five minus two times a number equals 9.Two less than five times a number is 9.
Answers
1) Looking at that expression
5n -2= 9
Since the expression is written this way, we can assume the wording is
Five times a number subtracted from two equals 9.
Because the number, n is 1 unit, then. We can read like that.
5m-2 = 12m -16
SOLVE
Answers
Answer:
m=2
Step-by-step explanation:
m=2 is the answer hope this helped
Answer:
m=2
Step-by-step explanation:
Follow this step by step solution.
Hope this was helpful.
Find a and b such that
Answers
The coefficients (a, b) = (4, 2) are the solutions to the system formed by three equations with two variables.
How to find the coefficients associated with a linear coefficient
In this problem we must determine the values of two coefficients associated with a linear combination, which is equivalent to the following system of linear equations:
a + 4 · b = 12
a - b = 2
- 3 · a + 5 · b = - 2
Since the number of equations is greater than the number of variables, there are two posibilities: (i) No solution, (ii) A solution. Now we find the solution to the system formed by the first and second equations:
a + 4 · b = 12
a - b = 2
(a, b) = (4, 2)
Now we check in the third equation:
- 3 · 4 + 5 · 2 = - 2
- 12 + 10 = - 2
- 2 = - 2 (TRUE)
The coefficients (a, b) = (4, 2) are the solutions to the system.
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help me pleasee!!
thank you
Answers
Step-by-step explanation:
so, we need to get the slope-intercept form
f(x) = y = ax + b
"a" is as always the slope, "b" is the y-intercept (the y-value when x = 0).
as we have the slope and a point, we can start with the point-slope form and transform it :
y - y1 = a(x - x1)
with (x1, y1) being a point on the line.
y - 7 = -9(x - 2) = -9x + 18
y = -9x + 25
therefore, the functional equation is
f(x) = -9x + 25
Over the last three evenings, Carmen received a total of 74 phone calls at the call center. The first evening, she received 6 fewer calls than the third evening. The second evening, she received 3 times as many calls as the third evening. How many phone calls did she receive each evening?
Answers
Let x be the amount of calls that Carmen received at the third evening.
The first evening she received 6 calls fewer than the third, so that is x-6. The second evening, she received 3 times the number of calls of the third evening. So that is 3*x. The sum of this three quantities should be 74,sinche she received 74 calls in total. So, we have the equation
[tex]x\text{ - 6 +3x+x = 74}[/tex]If we add all x values we get
[tex]5x\text{ - 6 = 74}[/tex]If we add 6 on both sides, we get
[tex]5x\text{ = 74+6 = 80}[/tex]Now, if we divide by 5 on both sides, we get
[tex]x\text{ = }\frac{80}{5}=16[/tex]So in the third evening she received 16 calls. The first evening she received 16-6 = 10 calls and the second evening she received 16*3 = 48 calls.
y = 4x - 4graph the linear equation and identify the x-intercept
Answers
The length of a rectangle is three more than twice the width. Determine the dimensions that give a total area of 27ft squareda. create an equation in terms of w to model this situationb. what are the solutions to this equation c. What are the length and width of the rectangle
Answers
ok
Area = 27ft^2
length = l
width = w
Equation
l = 2w + 3
Section A
Area
A = l*w
A = (2w + 3)* w or A = 2w^2 + 3w
27 = 2w^2 + 3w
2w^2 + 3w - 27 = 0 This is the equation
Section B
2w^2 - 6w + 9w - 27 = 0
2w(w - 3) + 9(w - 3) = 0
(w - 3)(2w + 9) = 0
w1 - 3 = 0 2w + 9 = 0
What number is a reasonable estimate for 39x241 8000 2 14000 3 800 4 1400
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01
Data:
reasonable estimate = ?
39x24
Step 02:
39x24 = 936
reasonable estimate = 800
The answer is:
reasonable estimate = 800
What is the distance between point R(-1, 7) and point T(-7, 7)?
O 1 unit
O 6 units
O 7 units
O 8 units
Answers
Answer: 6 units
Step-by-step explanation: first set up the distance formula
d= the square root of [(-7+1)^2+(7-7)^2}
the y values =0 so we are left with the square root of -6^2=d
and this simplifies out to d=6
Plot (−134,412) on the coordinate plane.
Answers
Consider the coordinate (-1 3/4, 4 1/2).
Therefore, the x coordinate and y coordinate are - 1 3/4 and 4 1/2 respectively.
First, we must move back and forth between -1 and -2 by one and three.
In order to acquire 4 1/2, we must first get 4 above the y-axis, followed by half between 4 and 5.
The location at which the horizontal line at 4 1/2 and the vertical line at -1 3/4 would connect would be marked with a coordinate.
Or,
x = - 1 ( 3/4 ) = - 7/4 = - 1.75 and;
y = 4 1/2 = 9/2 = 4.5
Hence, ( -1 3/4, 4 1/2 ) = ( - 1.75, 4.5 ).
The shown red point on the graph is the coordinate (-1 3/4, 4 1/2).
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PLEASE HELP DUE IN 23 and I’ll be giving 25 points to whoever helps me.Thank you
Answers
————-———————
112+2x-20=180
2x+92=180
2x=88
x=44
Answer:
X is 44 - X = 44
Step-by-step explanation:
Please help me with mine.
One triangle has a height of 15 feet and a base length of 8 feet. It is proportional to a second triangle that has a height of 375 feet. What is the length of the second triangle's base (Hint: draw a visual and set up a proportion)O A 20OB. 28OC 30O 0.70
Answers
Using the data from the question, we draw the following triangles:
The dimensions are in feet.
Now, the two triangles are proportional, so if we compute the ratio between the height and the basis of the first triangle, and then we do the same with the second, we must obtain the same number:
[tex]r=\frac{h_1}{b_1}=\frac{h_2}{b_2}[/tex]Replacing the dimensions of the triangles in the last equation, we get:
[tex]\begin{gathered} \frac{h_1}{b_1}=\frac{h_2}{b_2} \\ \frac{15}{8}=\frac{375}{b_2} \end{gathered}[/tex]From the last equation we can compute b2, the basis of the second triangle, doing that we find that:
[tex]\begin{gathered} \frac{15}{8}=\frac{375}{b_2} \\ 15\cdot b_2=375\cdot8 \\ b_2=\frac{375\cdot8}{15} \\ b_2=200 \end{gathered}[/tex]So the second triangle's base is:
[tex]b_2=200[/tex](in feet)
Answer
A. 200
what is the solution set?
Answers
Answer:
the set of all the solutions of an equation or condition.
What is -|-16| +(-8)*5²
Answers
$825 due in 3 years at 10% compounded annually.
Answers
Given: Principal, P=$825
Rate, R=10% compounded annually
Time, t=3 years.
Required: To find the amount after 3 years.
Explanation: The amount, A after t years at r% rate is given by
[tex]A=P(1+\frac{r}{100})^t[/tex]Putting the values we get
[tex]\begin{gathered} A=825(1+\frac{10}{100})^3 \\ A=1098.075\text{ \$} \end{gathered}[/tex]Final Answer: The amount after 3 years is $1098.075.
