For the function [tex]\frac{10}{x + 5}[/tex] , we can say
The domain of f(x) is (–∞, –5) U (–5, ∞).
The y-intercept is (0, 2).
There is a vertical asymptote at x = –5.
The end behavior is x → –∞, f(x) → 0 and x → ∞, f(x) → 0.
What is a function?A mathematical relationship from a set of inputs to a set of outputs is called a function.
What is domain of a function?The domain of a function is the set of all possible inputs for the function.
What is range of a function?The range of a function is the set of outputs the function achieves when it is applied to its whole set of outputs
What is asymptote?An asymptote is a straight line that can be horizontal, vertical or oblique that goes closer and closer to a curve which is the graphic of a given function.
What is intercept?An intercept of any function is a point where the graph of the function crosses, or intercepts, the x-axis or y-axis.To find the x-intercept we need to do y = 0To find the y-intercept, we need to do x = 0How to know the domain of function?The given function is [tex]\frac{10}{x + 5}[/tex]
Now, if x = -5 then the function becomes undefined.
∴ The domain of the function is all real numbers except -5
So, The domain of f(x) is (–∞, –5) U (–5, ∞).
So, option a is correct.
How to know the range of the function?Clearly, the range of the function includes all real numbers
So, option B is wrong
How to find the x-intercept?To find the x-intercept , we will have to solve f(x) = 0, which is not at all possible for this function.
So, option C is wrong
How to find the y-intercept?To find the y-intercept, we need to do x = 0So, putting x = 0 in the function we get f(x) = 2
So, the y- intercept is (0, 2).
So, option D is correct.
How to find vertical asymptote ?To find the vertical asymptote, we need to make the denominator = 0∴ x+ 5 = 0
∴ x = -5
So, there is a vertical asymptote at x = –5.
Hence option E is correct.
How to find the end behavior?We can see,
As x tends to -∞, x + 5 will also tend to -∞We know that a number divided by ∞ or -∞ becomes 0So, as x tends to -∞, f(x) will tend to 0
So, Option F is correct.
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Answer:
ADEF
Step-by-step explanation:
ADEF
In June 2012, Twitter was reporting 400 million tweets per day. Each tweet can consist of up to 140 characters (letter, numbers, etc.). Create a comparison to help understand the amount of tweets in a year by imagining each character was a drop of water and comparing to filling something up
What is the least common multiple of these two denominators 3/6 2/12
Answer:
1 1/2 = 36/24
3/8 = 9/24
5/6 = 20/24
3 = 72/24
Step-by-step explanation:
if this answers it or it is just 12
The least common multiple of these two denominators 6 and 12 is 2.
To find the least common multiple (LCM) of the denominators 6 and 12, follow these steps:
Step 1: Prime factorize each denominator.
6 = 2 × 3
12 = 2 × 2 × 3
Step 2: Identify the highest power of each prime factor.
In this case, the highest power of 2² is 2 and the highest power of 3 is 3.
Step 3: Multiply the highest powers of all prime factors.
[tex]2^2 * 3^1 = 4 * 3 = 12[/tex]
Therefore, the LCM of the denominators 6 and 12 is 2.
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Point S is on line segment RT. Given ST = 2x – 10, RS = 2x - 5, and
RT = 3x + 1, determine the numerical length of RT.
Answer: 49
Step-by-step explanation:
The numerical length of RT is 49 units if point S is on the line segment RT. Given ST = 2x – 10, RS = 2x - 5, and RT = 3x + 1.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
Point S is on line segment RT.
ST = 2x – 10,
RS = 2x - 5, and
RT = 3x + 1,
RT = RS + ST
3x + 1 = 2x - 5 + 2x - 10
The above equation is representing a linear equation in one variable.
After simplifying:
3x + 1 = 4x - 15
4x - 3x = 15 + 1
x = 16
RT = 3x + 1
Plug x = -14
RT = 3(16) + 1
RT = 48 + 1
RT = 49
The numerical value of RT = 49
Thus, the numerical length of RT is 49 units if point S is on line segment RT. Given ST = 2x – 10, RS = 2x - 5, and RT = 3x + 1.
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plz help i need to rase my grade
The average of anything is calculated by adding up all the terms in the data set and dividing by the amount of terms in the data set.
In this problem,
The average = $1000
the amount of terms = 3
x = the amount earned Sunday
($1073 + $1108 + x) / 3 = $1000
First, multiply both sides by 3
$1073 + $1108 + x = $3000
Add together like terms
$2181 + x = $3000
Subtract $2181 from both sides.
x = $819
The restaurant needs to earn $819 on Sunday to have an average of $1000
* 1. Name a point on line n. 2. Name a segment on line m. 3. Name a ray with endpoint C. 4. Name three collinear points.
Answer:
1. D
2. AE (with a line above the 2 letters)
3. AC (with an arrowpointing to the right above the 2 letters)
4. B, A, and C
HELP !! Find the x with the details in this picture^^
Answer:
x = 3.9
Step-by-step explanation:
So the whole angle PQS = 111 degrees
it gave you part of it so subtract that off . 111 - 72 = 39 degrees
10 times what equals about 39 degrees.
39/ 10 = 3.9
Think of a number. Double the number. Substract 6 from the result and divide the answer by 2. The quotien will be 20. What is the number?
Answer:
23 is your answer hope this helps
Answer:
The number is 23
Step-by-step explanation:
23*2=46
46-6=40
40/2=20
The answer is 23
Hope that helps!
What does this say? Please Help me!
Answer:
That is a child mom with triplets.
Step-by-step explanation:
In a population of elderly war veterans, the probability that a veteran will have been exposed to agent orange (a militarized herbicide) and develop cancer is 0.35. The probability is 0.75 that a veteran exposed to agent orange will develop cancer. The average age of the veterans is 67 years old. What is the probability that a random veteran will have been exposed to agent orange
Answer:
Probability that a random veteran will have been exposed to agent orange is 0.4667
Step-by-step explanation:
P(exposed to agent cancer and develop cancer) = 0.35
P(develop cancer given he is already exposed to agent orange) = 0.75
P(is exposed to agent cancer) = ?
P(A given B) = P(A and B)/P(B),
P(develop cancer | exposed to agent orange) = P(develop cancer and exposed to agent orange)/P(exposed to agent orange)
0.75 = 0.35/P(exposed to agent orange)
P(exposed to agent orange) = 0.35/0.75
P(exposed to agent orange) = 0.4667
You have a band concert coming up. You need to make sure that everyone in the audience has a seat. 70 people bought tickets. You set 6 rows of 11 chairs. Is that enough chairs? Why or why not? Show Work!
no this is not enough chairs!
if you have 6 rows of 11 chairs it would look like this
xxxxxx
xxxxxx
xxxxxx
xxxxxx
xxxxxx
(each x is a chair)
this would mean to figure out the amount of chairs you set down you would do 6 x 11 which is 66. so you would need 4 more chairs to fit all 70 people.
what is an equivalent expression to 6(x-5)?
Answer:
6x-30
Step-by-step explanation:
you use distribution
Answer: 6x -30
Step-by-step explanation: Distribute the 6 to x and -5 to get 6x -30.
1. Name the indicated geometric figures for the figure shown. Be sure to use correct notation.
A Name a point. _________
B Name a ray through Y. _________
C Name a line through Z. _________
D Name a plane. _________
Answer:
Step-by-step explanation:
A). There are three points given on the plane R.
Point X, point Y and Point Z.
B). A ray from the point Y → [tex]\overrightarrow{XY}[/tex]
A ray starting from point X and passing through Y to infinity.
C). Name of a line → [tex]\overleftrightarrow{YZ}[/tex]
Aline passes through two points with both the ends directing towards infinity.
D). Name of a plane → Plane R or Plane XYZ
A plane is defined by three points lying on the same surface.
Identify the intersection of line l line m
Porsches mom told her to choose 3 crayons out of a box
Find the slope intercept form of the equation of the line through the points(2,-4) parallel to the line 8x+2y+2=0
Answer:
y = -4x + 4
Step-by-step explanation:
8x+2y+2=0
turn that into slope intercept form:
y = -4x - 1
a parallel line has the same slope, but different y-intercept
y = -4x + b
put (2,-4) into the equation
-4 = -4(2) + b
you get b=4
final product:
y = -4x + 4
Round $537.307 to the nearest cent
Answer:
$531.31
round to the nearest cent is round to 2 decimal places
Answer:
537.31 hope this helps you out
10 decreased by twice a is 23
THERE YOU GO I HAVE TO TYPE WORDS
Crude oil imports to one country from another for 2009–2013 could be approximated by the following model where t is time in years since the start of 2000. I(t) = −33t2 + 800t − 3,000 thousand barrels per day (9 ≤ t ≤ 13) According to the model, approximately when were oil imports to the country greatest?
Answer:
Import in 2012 was the greatest
Step-by-step explanation:
Given
l(t) = -33t² + 800t - 3000
9 ≤ t ≤ 13
Required
Determine the year with highest import.
To do this we simply substitute the values of t from 9 to 13 in the given function.
When t = 9
l(t) = -33t² + 800t - 3000
l(9) = -33 * 9² + 800 * 9 - 3000
l(9) = -33 * 81 + 800 * 9 - 3000
l(9) = -2673 + 7200 -3000
l(9) = 1527
When t = 10
l(10) = -33 * 10² + 800 * 10 - 3000
l(10) = -33 * 100 + 800 * 10 - 3000
l(10) = -3300 + 8000 - 3000
l(10) = 1700
When t = 11
l(11) = -33 * 11² + 800 * 11 - 3000
l(11) = -33 * 121 + 800 * 11 - 3000
l(11) = -3993 + 8800 - 3000
l(11) = 1807
When t = 12
l(12) = -33 * 12² + 800 * 12 - 3000
l(12) = -33 * 144 + 800 * 12 - 3000
l(12) = -4752 + 9600 - 3000
l(12) = 1848
When t = 13
l(13) = -33 * 13² + 800 * 13 - 3000
l(13) = -33 * 169 + 800 * 13 - 3000
l(13) = -5577 + 10400 - 3000
l(13) = 1823
Comparing the values of l(t) for the range of t = 9 to 13,
The highest value of l(t) is:
l(12) = 1848
Hence, the year with the highest import is 2012
The oil imports to the country are greatest during the year 2012
Given the model where t is time in years since the start of 2000 expressed as I(t) = −33t² + 800t − 3,000
The oil imports more oil during the year 2012, is t = 12
I(12) = −33(12)² + 800(12) − 3,000
I(12) = -33(144) + 9600 - 3000
I(12) = -4752 + 6600
I(12) = 1848
Hence the oil imports to the country are greatest during the year 2012
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Savannah's balance in her checking account was –$638.57. She deposited two checks, each in the amount of $298.40. What is Savannah’s new checking account balance after the deposits?
Ms. D bought 18 bagels for $1.35 each and 2 containers of cream cheese for $3.45 each. Write and evaluate ONE expression to find the total cost of the food.
Answer:
(18+2)x($1.35+$3.45)= $96
Could I please have BRAINLIEST.
Chin researched the body weight, in pounds, of professional football players. He created a table of different sample means from his data. Sample Sample Mean (pounds) 1 240 2 236 3 245 4 243 5 238 6 242 Which statements are true? Select three choices. The variation in the sample means makes it possible to make predictions about the population mean. The actual population mean is greater than 236. The actual population mean is less than 245. The actual population mean is greater than 245. The population mean is the average of the sample means.
Answer:
The variation in the sample means makes it possible to make predictions about the population mean. The actual population mean is greater than 236. The actual population mean is less than 245.Step-by-step explanation:
Sample data
1 2 3 4 5 6240 236 245 243 238 242Mean = sum of sample data/sample frequency
(240+236+245+243+238+242)/6 = 240.67Answer choices:
The variation in the sample means makes it possible to make predictions about the population mean.
Correct.The actual population mean is greater than 236.
Correct. 240.67 > 236The actual population mean is less than 245.
Correct. 240.67 < 245The actual population mean is greater than 245
Incorrect.The population mean is the average of the sample means.
Incorrect.Answer:
It is numbers 1, 2, and 3!
Step-by-step explanation:
Suppose you work for a company that manufactures electronics. The development analysts estimate that 5% of their flagship product will fail within 2 years of the purchase date, with a replacement cost of $ 1200. A newly hired associate at the company proposes to charge $ 50 for a 2-year warranty. 1. Compute the expected value of this proposal. Let X be the amount profited or lost (by the company) on the warranties and P(X) is the probability. 2. Interpret the expected value in complete sentences.
The expected value of the proposal is -$10. This means that, on average, the company can expect to lose $10 per warranty sold.
Interpretation of the expected value:
The expected value of -$10 indicates that, on average, for every 2-year warranty sold, the company can expect to lose $10. This means that the proposal is not a profitable venture for the company. The replacement costs of the 5% of failed products are higher than the revenue generated by selling the warranties and cannot cover the potential losses.
To compute the expected value of the proposal, we need to calculate the amount profited or lost (X) by the company on the warranties and the probability (P(X)) of each outcome.
Now, we have,
The product doesn't fail within 2 years, and the company earns $50 from the warranty.
The product fails within 2 years, and the company incurs a replacement cost of $1200 but keeps the $50 warranty fee.
The probability of the product not failing within 2 years is 1 - 0.05 = 0.95,
and the probability of the product failing within 2 years is 0.05.
Now, we have to find the expected value (E(X)):
[tex]E(X) = P(X_1) * X_1 + P(X_2) * X_2[/tex]
Where:
[tex]P(X_1)[/tex] = Probability of the product not failing within 2 years = 0.95
[tex]X_1[/tex] = Amount profited when the product doesn't fail within 2 years = $50
[tex]P(X_2)[/tex] = Probability of the product failing within 2 years = 0.05
[tex]X_2[/tex] = Amount lost when the product fails within 2 years = -$1150 (Replacement cost of $1200 - $50 warranty fee)
E(X) = 0.95 * $50 + 0.05 * (-$1150)
E(X) = $47.50 - $57.50
E(X) = -$10
The expected value of the proposal is -$10. This means that, on average, the company can expect to lose $10 per warranty sold.
Interpretation of the expected value:
The expected value of -$10 indicates that, on average, for every 2-year warranty sold, the company can expect to lose $10. This means that the proposal is not a profitable venture for the company. The replacement costs of the 5% of failed products are higher than the revenue generated by selling the warranties and cannot cover the potential losses. As a result, the company might want to reconsider the pricing of the warranty or look for other ways to reduce the potential costs associated with the product failures.
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Find the dimensions of a rectangle whose width is 8 miles less than its length and whose area is 105 square miles
Area of a rectangle = w*l
w = width
l = length
In our problem,
Area = 105mi^2
l = x
w = x - 8
Let's plug our values into the formula above.
105mi^2 = x(x - 8)
Distribute the x
105mi^2 = x^2 - 8x
Subtract 105mi^2 from both sides.
0 = x^2 - 8x - 105
Let's factor the right side.
0 = (x - 15)(x + 7)
Set both terms equal to 0
x - 15 = 0
Add 15 to both sides.
x = 15
x + 7 = 0
Subtract 7 from both sides.
x = -7
Since the length cant be a negative number, 15 is the correct answer.
Length = x = 15 mi
Width = x - 8 = 15 - 8 = 7 mi
The length of the rectangle is 15 miles while the width is 7 miles.
What is a rectangle?A rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
The perimeter of rectangle = 2( length + width).
Suppose the length is L while the width is W.
Area of rectangle = length × width.
L x W = 105
W = L - 8
By substitution,
L x (L - 8) = 105
L² - 8L - 105 = 0
L² - 15L + 7L - 105 = 0
L(L - 15) + 7(L - 15) = 0
(L + 7)(L - 15) = 0
L = -7, L = 15
Since length will not be negative thus L = 15 miles.
W = 15 - 8 = 7 miles
Hence "The length of the rectangle is 15 miles while the width is 7 miles."
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y varies directly with x Part 1
19. If y = 4 when x = -2, find x when y = 6
20. If y = 6 when x = 2, find x when y = 12
21. If y = 7 when x = 2, find x when y =3
Answer:
19. -3
20. 4
21. 6/7
Step-by-step explanation:
Since the variables are proportional, you can multiply the given x value by the new/old ratio of y-values.
19. x = 6/4(-2) = -3
20. x = (12/6)(2) = 4
21. x = (3/7)(2) = 6/7
HELPP PLEASEEEE THANK YOUUU MU FRIEND!
Answer:
co.: 14, -2, -5 var. terms: 14x,-2x,-5x con. terms: 9,8,1
Step-by-step explanation:
I need to know this I don’t understand and it is last one
Answer:
The answer is 4x
Step-by-step explanation:
Hope this helped
In comparing different job opportunities, you found that firm A will start your salary at
RM25000 per year and guarantee you a raise of RM1200 each year while firm B will start
your salary at RM28000 per year but will guarantee you a raise of RM900 each year.
(a) In what year of service the yearly salary from both firm will be the same?
(b) In what year of service the total salary from both firm will be the same?
(c) Hence, state the firm for which you should choose if you plan to work for 25 years.
Answer: the answer i think is c
what is 3/5 times 9/7
Answer:
[tex] \frac{27}{35} \\ [/tex]
Step-by-step explanation:
If you are going to multiply fractions, you just going to multiply their numerators and denominators and simplify when needed.
[tex] \frac{3}{5} \times \frac{9}{7} \\ \frac{3 \times 9}{5 \times 7} \\ \frac{27}{35} [/tex]
Translate the following algebraic expression into a written expression 3x ^ 2 + 2y + 1/2
Answer:
5
Step-by-step explanation:
A tourist information center is between a bus station and a train station. When mapped on a grid, the tourist information center is located at (1,4) and the bus is located at (-3,7) The train station is located at point
Answer: The train station is located at point (5,1).
Step-by-step explanation:
Given: On a grid, information center is located at (1,4) and the bus is located at (-3,7).
A tourist information center is between bus station and train station.
i.e. tourist information center is a mid point of line joining bus station and train station.
Midpoint between (a,b) and (c,d) is given by :-
[tex](x,y)=(\dfrac{a+c}{2},\dfrac{b+d}{2})[/tex]
Let (a,b) be the coordinates of train station , then
[tex](1,4)=(\dfrac{-3+a}{2},\dfrac{7+b}{2})\\\\\Rightarrow\ 1=\dfrac{-3+a}{2}\ \ \ , 4=\dfrac{7+b}{2}\\\\\Rightarrow\ 2=-3+a\ \ \ , 8=7+b\\\\\Rightarrow\ 2+3=a\ \ \ , 8-7=b\\\\\Rightarrow a= 5,\ \ b=1[/tex]
Hence, the train station is located at point (5,1).