Using it's concept, it is found that the vertical asymptote of the function [tex]f(x) = \frac{3}{x+5}[/tex] is of x = -5.
What are the vertical asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.
In this problem, the function is fraction given by:
[tex]f(x) = \frac{3}{x + 5}[/tex]
At the denominator, we have that:
x + 5 = 0 -> x = -5
Hence the vertical asymptote of the function [tex]f(x) = \frac{3}{x+5}[/tex] is of x = -5.
More can be learned about asymptotes at https://brainly.com/question/16948935
#SPJ1
Answer: A) x= -5
Took the test and got 100% :)
Suppose that $b$ is a positive integer greater than or equal to $2.$ When $197$ is converted to base $b$, the resulting representation has $4$ digits. What is the number of possible values for $b$
Suppose that b is a positive integer greater than or equal to 2. When 197 is converted to base b, the resulting representation has 4 digits. What is the number of possible values for b?
The possible values of b are 4 and 5
How to determine the possible numbers of b?The conditions are given as:
b is at least 2When 197 in base b has 4 digits.So, we start by converting 197 to base 2 and above.
This is done as follows:
197 to base 2
2 | 197
98 R 1
49 R 0
24 R 1
12 R 0
6 R 0
3 R 0
1 R 1
0 R 1
So, we have:
197 = 11000101 in base 2
11000101 has more than 4 digits.
This means that b cannot be 2
Using the above method of conversion, we have:
197 = 21022 in base 3197 = 3011 in base 4197 = 1242 in base 5197 = 525 in base 6197 = 401 in base 7See that as the base increases, the number of digits decreases.
The numbers in base 4 and 5 have 4 digits.
Hence, the possible values of b are 4 and 5
Read more about base conversions at:
https://brainly.com/question/17946394
#SPJ4
Help and please show work!
Factor sin^8Θ + 2sin^4Θcos^4Θ + cos^8Θ
hi
Step-by-step explanation:
I
don't
know
see you in next question
The graph of a quadratic function passes through the points (0,-4) and (-2,0). what is a zero of the function
Answer:
-2
Step-by-step explanation:
the zero of the function is -2 because it's the root of the equation when y= 0
A bicyclist pedals 40 miles in 3 hours. Write the bicyclist's speed as a rate (but not a unit rate yet). Then use the dropdown menus to report the bicyclist's rate. Numerator (top of the fraction): [ Select ] [ Select ] Denominator (bottom of the fraction): [ Select ] [ Select ]
The bicyclist's speed as a rate is 40/3 miles per hour
How to determine the bicyclist's speed as a rate?The given parameters are:
Distance = 40 milesTime = 3 hoursThe rate is calculated as:
Rate = Distance/Time
Substitute known values
Rate = 40 miles/3 hours
Rewrite as:
Rate = 40/3 miles per hour
Hence, the bicyclist's speed as a rate is 40/3 miles per hour
Read more about speed and rate at:
https://brainly.com/question/19493296
#SPJ1
Find the midpoint of A and B where A has coordinates (2, 3)
and B has coordinates (8, 9).
Step-by-step explanation:
Solution,Given,Coordinates of A and B are (2,3) and(8,9) respectively. Let A(2,3)= (x1,y1) and B(8,9)=(x2,y2)Midpoint of AB(m)=?Now,using midpoint formulam= {(x1+x2)/2 ,(y1+y2)/2}or m= {(2+8)/2,(3+9)/2}.°. m=(5,6)Answer:Mxy= [(Xa+Xb/2);(Ya+Yb/2)]
=(2+8/2);(3+9/2)
Midpoint= (5, 6)
Step-by-step explanation:
What is the slope of the line that passes through the points (-6, 8) and (-9, 7)? Write your answer in simplest form.
Answer:
m=1/3
equation y=1/3x+10
Step-by-step explanation:
Find the rise and run.
1. -6--9=run=3
2. 8-7=rise=1
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to find the slope of the line that passes through (-6, 8) and (-9, 7).
[tex]\triangle~\fbox{\bf{KEY:}}[/tex] (formula for Slope)
[tex]\longmapsto\bf{\cfrac{y2-y1}{x2-x1}}[/tex]
y2 & y1 = the y-coordinates of the two points
x2 & x1 = the x-coordinates of the two points
[tex]\ddot\bigstar[/tex] Remember this...
[tex]\fbox{y2\;and\;y1\;are\;y-coordinates\;of\;the\;two\;points,\;and\;x2\;and\;x1\;are\;x-coordinates}}[/tex]
So we substitute the values and obtain:
[tex]\bf{\cfrac{7-8}{-9-(-6)}[/tex]
Simplifying:
[tex]\bf{\cfrac{-1}{-9+6}}[/tex]
Simplifying more:
[tex]\bf{\cfrac{-1}{-3}}[/tex]
Divide the top and bottom by -1:
[tex]\bf{\cfrac{1}{3}}[/tex]
There's the slope.
Hope it helps you out! :D
Ask in comments if any queries arise.
~Just a smiley person helping fellow students
What is the slope of the line containing (-2,5) and (4, -4)?
O A. -2
O B.
3
2
O c. 2
O D.
3
2
Answer:
-3/2
Step-by-step explanation:
See attached image
Answer:
[tex]m=\frac{-3}{2}[/tex]
Step-by-step explanation:
m = slope
[tex]m=\frac{-4-5}{4--2}[/tex]
[tex]m=\frac{-9}{6}[/tex]
[tex]m=\frac{-3}{2}[/tex]
Carmen used a random number generator to simulate a survey of how many children live in the households in her town. There are 1,346 unique addresses in her town with numbers ranging from zero to five children. The results of 50 randomly generated households are shown below.
Children in 50 Households
Number of Children
Number of Households
0
5
1
11
2
13
3
10
4
9
5
2
Using a proportion, what can you infer about the number of households in her town that have more than three children?
About 242 households have more than three children.
About 269 households have more than three children.
About 296 households have more than three children.
About 565 households have more than three children.
About 296 households have more than three children. Then the correct option is C.
How to find that a given condition can be modeled by binomial distribution?Suppose we have random variable X pertaining to a binomial distribution with parameters n and p, then it is written as
The expected value will be
E(X) = np
Carmen used a random number generator to simulate a survey of how many children live in the households in her town.
There are 1,346 unique addresses in her town with numbers ranging from zero to five children.
The results of 50 randomly generated households are shown below.
Children in 50 Households
Number of Children Number of Households
0 5
1 11
2 13
3 10
4 9
5 2
Then the value of p and n will be
p = 11/50
n = 1346
Then the expected value will be
E(x) = (11/50) x 1346
E(x) = 296.12 ≈ 296
Then the correct option is C.
Learn more about binomial distribution here:
https://brainly.com/question/13609688
#SPJ1
Find the equation of the line shown.
y
X
0 1 2 3 4 5 6 7 8 9 10
10
987654321
Answer:
y = 2x
Step-by-step explanation:
The graph is of a straight line through the origin. Its slope can be determined from the grid points it passes through. That slope will be the constant of proportionality for the proportion represented.
__
When the graph is a line through the origin, it is a representation of a proportion that can have the equation ...
y = kx
where k is the constant of proportionality, also the slope of the line.
The value of k will be the y-value when x=1. Reading from the graph, we find the line goes through point (1, 2), so y = 2 when x = 1. That means k = 2 and the equation of the line is ...
y = 2x
31 32 33 34
Which polynomial function could be represented by the graph below?
16
14
42
10
8-6
6 8 X
O f(x) = x³ + x² - 6x
O f(x)=x²-x² - 6x
4
1:00:00+
bocchette
ANLAT
K
C
The polynomial function that could be represented by the graph is f(x) = x³ + x² - 6x
How to determine the polynomial?The attached graph represents the missing part of the question
From the attached graph, the x-intercepts of the graph are:
x1 = -3
x2 = 0
x3 = 2
The equation of the graph is then calculated as:
f(x) = (x - x1)(x - x2)(x - x3)
This gives
f(x) = (x + 3)(x - 0)(x - 2)
Expand
f(x) = x(x² + 3x - 2x - 6)
Evaluate
f(x) = x(x² + x - 6)
Expand
f(x) = x³ + x² - 6x
Hence, the polynomial function that could be represented by the graph is f(x) = x³ + x² - 6x
Read more about polynomials at:
https://brainly.com/question/4142886
#SPJ1
9. A box contains 50 discs which are numbered 1 to 50. If one disc is drawn at random from the box. Find the probability that it bears: a 2 digit no. (ii) a perfect square no. (iii) a no. divisible by 5
The probability that it bears a 2 digit no. is 41/50; a perfect square no is; 3/25; a no. divisible by 5 is; 0.2
How to find the probability?
We are given;
Number of Discs in box = 50
Type of discs in box = Numbered 1 to 50
i) Number of 2 digit numbers = 41
Thus;
P(2 digit numbers) = 41/50
ii) Perfect square numbers are; 4, 9, 16, 25, 36 and 49. Thus;
P(perfect square number) = 6/50 = 3/25
iii) Numbers divisible by 5 are; 5, 10, 15, 20, 25, 30, 35, 40, 45, 50.
Thus;
P(numbers divisible by 5) = 10/50 = 0.2
Read more about Probability at; https://brainly.com/question/24756209
#SPJ1
5/8 of a number is 200. What is 7/10 of the number ?
Answer:
224Step-by-step explanation:
Let x be the unknown number.
(5÷8)x = 200
Then
x = (8×200) ÷ 5
= 1600 ÷ 5
=320
……………………………
(7/10)x = (7/10)×320
= (7×320) ÷ 10
= 224
Answer:
= 224
Step-by-step explanation:
Hi there!, here is how we solve the problem;
To begin, the question wants us to determine
[tex] \frac{7}{10} [/tex]
of the number x (unknown).
[tex] \frac{5}{8} = 200 \\ \frac{8}{8} = x \\ ( \frac{ \frac{8}{8} \times 200 }{ \frac{5}{8} } ) \\ = \frac{8}{8} \times 200 \times \frac{8}{5} \\ = 320 \\ x = 320[/tex]
We have found our x = 320
Lets now determine
[tex] \frac{7}{10} [/tex]
Which is given by;
[tex]( \frac{7}{10} \times 320 \\ = 224[/tex]
[tex] \frac{7}{10} [/tex]
of the number is therefore 224.
= 224 <<<<<< Ans
I hope this helps.
Have a nice studies.
Express in simplest radical form.
5x√192x³+√3x5
please help!!
[tex]-5x\sqrt{192x^3} + \sqrt{3x^5}\\\\=-5x\left(192x^3 \right)^{\tfrac 12} + \left(3x^5 \right)^{\tfrac 12}\\\\=-5\cdot (192)^{\tfrac 12} \cdot x \cdot x^{\tfrac 32} + 3^{\tfrac 12} \cdot x^{\tfrac 52}\\\\=-5\left( 64 \cdot 3 \right)^{\tfrac 12} \cdot x^{1+\tfrac 32} + 3^{\tfrac 12} \cdot x^{\tfrac 52}\\\\=-5\cdot 8\cdot 3^{\tfrac 12} \cdot x^{\tfrac 15} + 3^{\tfrac 12} \cdot x^{\tfrac 52}\\\\=-40\cdot 3^{\tfrac 12} \cdot x^{\tfrac 52}+3^{\tfrac 12} \cdot x^{\tfrac 52}\\\\[/tex]
[tex]=-39\cdot 3^{\tfrac 12} \cdot x^{\tfrac 52}\\\\=-39\sqrt 3 \sqrt{x^5}[/tex]
PLEASE HELP ME!!!!!!!!!!!!!!!
Answer:
hypotenuse(h)^2 = 3^2 + 7^2
h^2 = 9 + 49
h = √58
h = 7.6
En 2018 la empresa SAC-OLC fabrico 24000 ollas, si cada dia se fabricaron 80 ollas ¿cuantos dias no se trabajaron en la empresa?
Usando proporciones, hay que no se trabajaron en 65 dias durante el año de 2018 en la empresa SAC-OLC.
¿Qué es una proporción?Una proporción es una fracción de la cantidad total, e los problemas pueden ser resolvidos con una regla de três.
En este problema, hay que se fabricaran 24000 ollas en el año de 2018, con una taja de 80 ollas al dia. Así, el número de dias trabajados es dado por:
n = 24000/80 = 300.
El año de 2018 tuvo 365 dias, así, el número de dias no trajados fue de:
365 - 300 = 65.
Puede-se aprender mas a cerca de proporciones es brainly.com/question/26950887
How many solutions are in 17x-8=3x+16
Melissa rolls 2 fair dice and adds the results from each.
Work out the probability of getting a total less than 12.
Answer:
It would be 35/36
Step-by-step explanation:
so if you did like 1+1, 1+2, 1+3....2+1,2+2, 2+3 yada yada
the only possible number combo that would equal twelve is 6+6 and there is 36 possible combos so your answer is 35/36
- a former algebra 2 student
A bakery sold a total of 400 cupcakes in a day, and 43% of them were vanilla flavored. how many of the cupcakes sold that day were vanilla flavored?
The number of the cupcakes sold that day that were vanilla flavored is 172.
How do we calculate a number from a percentage?The number of the cupcakes sold that day that were vanilla flavored can be calculated using the following formula:
Number of vanilla flavored cupcakes sold = Total number of cupcakes sold * Percentage that were vanilla flavored .............. (1)
Substituting the relevant values into equation (1), we have:
Number of vanilla flavored cupcakes sold = 400 * 43% = 172
Learn more about percentages here: brainly.com/question/14801224.
#SPJ1
As seen in the diagram below, Shandra is building a walkway with a width of xx feet to go around a swimming pool that measures 8 feet by 6 feet. If the total area of the pool and the walkway will be 168 square feet, how wide should the walkway be?
The total surface area of the building is the sum of the total faces an object contains. The walkway should be about 2.57feet
How to calculate the total surface area the building?The total surface area of the building is the sum of the total faces an object contains. The formula is expressed as:
TSA = 2(lw + wh + lh)
where
l is the lengthw is the widthh is the heightGiven the following parameters
TSA = 168 square feet
length = 8feet
Height = 6 feet
Required
Width of the walkway
Substitute
168 = 2(lw + wh + lh)
84 = (8(6) + 6w + 8w)
84 = 48 + 14w
14w = 84 - 48
14w = 36
w = 2.57feet
Hence the walkway should be about 2.57feet
Learn more on surface area here: https://brainly.com/question/20771646
#SPJ1
A flower bed in your yard is in the shape of a right triangle. The perpendicular sides of the bed measure 14 feet and 11 feet. Calculate the area of the flower bed.
The area of the flower bed is 77 square feet
How to determine the area?The given parameters are:
Shape = TrianglePerpendicular sides = 14 feet and 11 feetThe area of the flower bed is calculated as:
Area = 0.5 * Product of perpendicular sides
So, we have:
Area = 0.5 * 14 * 11
Evaluate
Area = 77
Hence, the area of the flower bed is 77 square feet
Read more about areas at:
https://brainly.com/question/24487155
#SPJ1
100 points plus brainliest
Answer:
45 degrees
Step-by-step explanation:
so we know there is one 90 degree angle
and the other two angles are congruent
so the math would go like this
180-90=90
90/2= 45
(the 2 represents the two angles)
Answer:
x = 22.62° (nearest hundredth)
Step-by-step explanation:
As this is a right triangle, we can use the cosine trigonometric ratio to find x.
[tex]\sf \cos(\theta)=\dfrac{A}{H}[/tex]
where:
[tex]\theta[/tex] is the angleA is the side adjacent the angleH is the hypotenuse (the side opposite the right angle)Given:
[tex]\theta=x[/tex]A = 12H = 13Substitute the given values into the formula and solve for x:
[tex]\implies \cos(x)=\dfrac{12}{13}[/tex]
[tex]\implies x=\cos^{-1}\left(\dfrac{12}{13}\right)[/tex]
[tex]\implies x=22.61986495...^{\circ}[/tex]
[tex]\implies x=22.62^{\circ}\:\: \sf(nearest\:hundredth)[/tex]
A 2-ft vertical post casts a 20-in shadow at the same time a nearby cell phone tower casts a 115-ft shadow. how tall is the cell phone tower?
the cell phone tower is _ ft
The height of the cell phone tower will be 138 feet.
What are ratio and proportion?A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A proportional is a mathematical expression in which two things are equal.
A 2-ft vertical post casts a 20-in shadow at the same time a nearby cell phone tower casts a 115-ft shadow.
Then the height of the cell phone tower will be
Let x be the height of the cell phone tower.
x / 2 = 115 x 12 / 20
x = 69 x 2
x = 138 feet
More about the ratio and the proportion link is given below.
https://brainly.com/question/14335762
#SPJ1
Consider the original triangle and the scale drawing enlargement.
A triangle with a side measurement of 2 centimeters. 2 triangles have corresponding side lengths of 2 centimeters and 8 centimeters.
Figures not drawn to scale.
What is the scale factor?
Answer:
scale factor = 4
Step-by-step explanation:
the scale factor is the ratio of corresponding sides, image to original
scale factor = [tex]\frac{8}{2}[/tex] = 4
Courtney was making curtains from some fabric she had in her closet. She measured 7 3/4 yards of fabric and needed to make 4 curtains that were the same size. How much fabric does she need for each curtain? Estimate:
Answer:
About 32
Step-by-step explanation:
It says 7 3/4 and she makes 4 curtains ESTIMATE!! So you round the 7 3/4 to 8 and do 8 x 4 since she made 4 curtains. Hope this helped!
Please help me!!!! I would really appreciate it!!!
Answer:
x=-(7 [tex]\pm i\sqrt(7)[/tex])
Step-by-step explanation:
A rescue mission is being conducted using a plane to drop supplies and medical personnel. A helicopter
is also sent from the same base station to rescue wounded persons. If the plane flies 400 mph, the
helicopter flies 200 mph, and they leave at the same time, how far away is the rescue site if the
helicopter arrives 1 hour after the plane arrives?
If t represents the time that the plane flies, which of the following equations could be used to solve the
problem?
400/t = 200/(t+1)
400t = 200(t+1)
400t = 200t+1
400 miles away is the rescue site if the helicopter arrives 1 hour after the plane arrives and the expression 400t = 200(t + 1) represents the time that the plane flies option second is correct.
What is distance?Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.
We have:
A helicopter is sent from the same base station to rescue wounded persons. If the plane flies 400 mph, the helicopter flies 200 mph, and they leave at the same time.
Let's suppose the plane takes t hours
We know,
Distance = speed×time
400×t = 200(t + 1)
or
400t = 200(t + 1)
After solving we get:
t = 1 hour
Distance = 400×1 = 400 miles
Thus, 400 miles away is the rescue site if the helicopter arrives 1 hour after the plane arrives and the expression 400t = 200(t + 1) represents the time that the plane flies option second is correct.
Learn more about the distance here:
brainly.com/question/26711747
#SPJ1
Find the volume of the sphere. Round your answer to the nearest tenth.
A sphere is shown with a radius of 7 feet.
The volume is about
cubic feet.
So we all know the FORMULA for a sphere is v=4/3 x π x r^3
So, now we SUBSTITUTE ,V=4/3 x π x 7^
This leaves us with the answer of 1436.76 ft ^2 maybe?
(hope this is correct!)
what is 1/4×2/5÷1/3 as a fraction
please help
Answer:
3/10
Step-by-step explanation:
Please give brainliest!
hope this helps :)
the first step is to multiply 1/4 and 2/5
1/4 times 2/5 = 2/20
you figure this out by multiplying the numerators and denominators.
next, we solve 2/20 ÷ 1/3
we do this by taking the reciprocal of 1/3, which is 3/1, and then multiplying the fractions
2/20 times 3/1 = 6/20
6/20 = 3/10
Factor 4x² - 121 a) (2x + 11) (2x + 11) b) (2x - 11) (2x - 11) (2x + 11) (2x - 11) d) (4x + 11) (4x - 11)
Answer:
(2x-11)(2x+11)
Step-by-step explanation:
2x-11 × 2x+11 yields
4x^2 + 22x -22x +121
22x subtracts itself and final result is
4x^2 -121
1. Which is NOT a benefit of direct deposit? (1 point)
The money is available as soon as your employer makes the transfer.
You do not need to drive to the bank to make a deposit.
You can plan when you are paying bills.
You can avoid having a hold placed on when funds are available.
Answer:
d
Step-by-step explanation:
the statement "you can avoid having a hold placed on when funds are available is noat a benefit of the direct deposit