The vertical asymptote of a given function is x = -2 and x = -3.
What is the vertical asymptote of a function?
A vertical line that directs the function's graph but is not actually a part of it is called a vertical asymptote. It appears at the x-value that is outside the domain of the function, therefore the graph can never cross it.
To find the vertical asymptotes, set the denominator equal to zero and solve for x.
For the given function,
[tex]F(x) = \frac{1}{7(x+2)(x+3)}[/tex]
To find the vertical asymptote, equate the denominator to zero.
7(x + 2)(x + 3) = 0
(x + 2)(x + 3) = 0
x + 2 = 0 (or) x + 3 = 0
x = -2 (or) x = -3
Hence, The vertical asymptote of the given function is x = -2 and x = -3.
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find the 73rd term of the following arithmetic sequence 18,22,26,30
The arithmetic sequence has the 73rd term of 306
How to find the 73rd term for the arithmetic sequence?The sequence is given as:
18,22,26,30,....
The above sequence has the following parameters
First term, a = 18Common difference, d = 4 i.e. 22 - 18 = 4Number of terms , n = 73This means that the sequence is an arithmetic sequence
The nth term of an arithmetic sequence is calculated as
f(n) = a + (n - 1) * d
Substitute the known values in the above equation
So, we have the following equation
f(73) = 18 + (73 - 1) * 4
Evaluate
f(73) = 306
Hence, the 73rd term for the arithmetic sequence is 306
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The kitchen is a square and has an area of 169 square feet.whatis the length of one side of Tito’s kitchen?
The length of one sides of the square Tito's Kitchen is 13 feet.
How to find the length of a square?A square is a quadrilateral with 4 sides equal to each other. The opposite sides of a square is parallel to each other.
The sum of angles in a square is 360 degrees. Each angle is 90 degrees.
The kitchen is a square and has an area of 169 square feet.
The length of one side of the kitchen can be calculated as follows:
area of the square kitchen = l²
where
l = side lengthTherefore,
area of the square kitchen = 169 ft²
169 = l²
square both sides of the equation
√169 = √l²
l = 13 ft
Therefore,
length of the square kitchen = 13 feet.
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What is the expected change in the dividend of a 6% preferred stock if the required rate of return drops instantly from 8% to 6%?
The expected change in the dividend of a 6% preferred stock is $75.
Given that, the required rate of return drops instantly from 8% to 6%.
What is the return?A return, also known as a financial return, in its simplest terms, is the money made or lost on an investment over some period of time.
The value of preferred stock = $100
Annual dividend = 100 × 6% = $6
Price of preferred stock when required return is 8% = Annual dividend / Required rate of return
= 6/8%
= 6 ×100/8
= $75
Therefore, the expected change in the dividend of a 6% preferred stock is $75.
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How do I solve the following equation?
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{1}{3}}x+7\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so we're really looking for the equation of a line whose slope is -1/3 and that it passes through (-2 , 5.5)
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{5.5})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5.5}=\stackrel{m}{- \cfrac{1}{3}}(x-\stackrel{x_1}{(-2)}) \implies y -5.5= -\cfrac{1}{3} (x +2)[/tex]
[tex]y-5.5=-\cfrac{1}{3}x-\cfrac{2}{3}\implies y=-\cfrac{1}{3}x-\cfrac{2}{3}+5.5\implies y=-\cfrac{1}{3}x-\cfrac{2}{3}+\cfrac{55}{10} \\\\\\ y=-\cfrac{1}{3}x-\cfrac{2}{3}+\cfrac{11}{2}\implies {\Large \begin{array}{llll} y=-\cfrac{1}{3}x+\cfrac{29}{6} \end{array}}[/tex]
2.) lee has seven 5-dollar bills and le quarters
in his pocket. How much money would he have
left in his pocket if he buyes a leather jacket
worth $35.20.
Amount of money left in Lee pocket after he buys a $35.20 leather jacket from the given amount is equal to $1.3.
As given in the question,
Conversion of quarter into dollars is :
1 quarter = 0.25 dollars
Amount of money with Lee in his pocket is equal to :
= ( 7 × 5) dollars + ( 6 × 0.25) dollars
= (35 +1.5) dollars
=$ 36.5
Cost of leather jacket buy by Lee = $35.20
Amount of money left in lee's pockets after purchasing jacket
= $( 36.5 - 35.20)
= $ 1.3
Therefore, amount of money left in Lee pocket after he buys a $35.20 leather jacket from the given amount is equal to $1.3.
The complete question is :
Lee has seven 5-dollar bills and 6 quarters in his pocket. How much money would he have left in his pocket if he buys a leather jacket
worth $35.20?
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y=2/3x-18 rate of change
The rate of change of the equation, y = 2/3x - 18, is: 2/3.
How to Determine the Rate of Change of a Linear Equation?The rate of change of a linear equation that is expressed in slope-intercept form as y = mx + b is represented by the value of m in the equation. It is also referred to as the slope of the equation.
For example, if we are given the equation, y = 4x + 5, the value of m is 4. This implies that the rate of change, which is the slope, is equal to 4.
In the same vein, we are given the equation, y = 2/3x - 18.
The value of m, which is the slope or rate of change in the equation y = 2/3x - 18 is equal to 2/3.
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What miles per gallon did the car get after 280 miles using 8 gallons of gas?
Answer: 35 miles
Step-by-step explanation:
First we divide 280 by 8 to get the answer per gallon. 280 / 8 = 35, therefore each gallon equals 35 miles.
A house was valued at $321,000. Over several years, the value decreased by 9%, giving the house a new value.
Answer:
The new value is $292,110
Step-by-step explanation:
321,000 - (1 - 0.09) = 292,110
A math class has a total of 33 students. The number of males is 15 more than the number of females. How many males and how many females are in the class?
Who wants brainliest? First come first serve
Desmond is training for a bike race and is attempting to improve his average speed. With his old trainer, Desmond averaged a pace of 24 MPH. With his new trainer, he rode at an average speed of 30 MPH. By what percent did his average speed increase? %
The percent that Desmond average speed increase is 25%.
How to calculate the percentage?From the information, with his old trainer, Desmond averaged a pace of 24 MPH and with his new trainer, he rode at an average speed of 30 MPH.
It should be noted that the percentage increase in speed will be:
= Change in speed / Initial speed × 100
= (30 - 24) / 24 × 100
= 6/24 × 100
= 25%
The percentage is 25%.
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Write an exponential function represented by the graph
y= ?
Answer:
y = 8 [tex](\frac{1}{2}) ^{x}[/tex]
Step-by-step explanation:
an exponential function can be expressed in the form
y = a [tex]b^{x}[/tex]
to find a and b use points that lie on the graph
using (0, 8 ) , then
8 = a[tex]b^{0}[/tex] [ [tex]b^{0}[/tex] = 1 ] , then a = 8
y = 8[tex]b^{x}[/tex]
using (1, 4 ) , then
4 = 8[tex]b^{1}[/tex] = 8b ( divide both sides by 8 )
[tex]\frac{4}{8}[/tex] = b , that is b = [tex]\frac{1}{2}[/tex]
y = 8 [tex](\frac{1}{2}) ^{x}[/tex] is the exponential function
Hey can someone please help me out? Thank you so much!
Answer:
Step-by-step explanation:
area=10×5+[(15-5)+7]/2×(10-6)
=50+(17)/2×4
=50+34
=?
Describe the features of the function that can be easily seen when a quadratic function is given
in the form: y= A(x−A )( x− B) and how they can be identified from the equation.
The features of the functions when a quadratic function is given in the form: y = a (x − p) (x − q)
y = value in the y coordinates
a = constant in the equation
p and q = zeros or roots
x = value in the x coordinates
How to identify features in the equationWhen quadratic equation is written of the form y = a (x − p) (x − q), it is called the factored form of quadratic equation
The other form is ax^2 + bx + c and called standard form of quadratic equation
a in both cases are same and it helps to da if the curve opens upward or downward
when a is positive the curve opens upward but when it is negative the curve opens downward
Expanding the factored form of quadratic equation brings the equation to the standard form
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I don’t know it and I need help. question is in picture
Quincy has a jewelry business in which he designs and sells bracelets. His daily profit, Q(x), can be modeled by the function Q(x) = 8.25x − 24.75, where x is the number of bracelets he sells. What is the value of Q(3), and what is its interpretation?
Q(3) = 0; If Quincy sells 3 bracelets, he will earn $0.
Q(3) = 0; If Quincy sells 0 bracelets, he will earn $3.
Q(3) = 3.36; If Quincy sells 3 bracelets, he will earn $3.36.
Q(3) = 3.36; If Quincy sells 3.36 bracelets, he will earn $3.
The correct interpretation is Q(3) = 0; If Quincy sells 3 bracelets, he will earn $0.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Q(x) = 8.25x − 24.75, where x is the number of bracelets he sells.
So, for x= 3 them Q(3)
Q(3)= 8.25 (3) - 24.75
Q(3) = 24.75 - 24.75
Q(3) = 0
Hence, Q(3) = 0; If Quincy sells 3 bracelets, he will earn $0.
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The probability that a vehicle entering the Lu-
ray Caverns has Canadian license plates is 0.12; the
probability that it is a camper is 0.28; and the proba-
bility that it is a camper with Canadian license plates
is 0.09. What is the probability that
The conditional probability that a camper entering the Luray Caverns has Canadian license Plates is given by:
0.3214 = 32.14%.
What is Conditional Probability?Conditional probability is the probability of one event happening, considering the outcome of a previous event. The formula is given by the rule presented as follows:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
The probabilities that compose the formula are listed as follows:
P(B|A) is the probability of the event B happening, given that the event A has already happened.[tex]P(A \cap B)[/tex] is the probability of both the events, A and B, happening.P(A) is the probability of the event A happening.The events in this problem are given as follows:
Event A: Camper.Event B: Canadian license plates.The probabilities are given as follows:
P(A) = 0.28, P(A and B) = 0.09.
Hence the conditional probability is obtained as follows:
P(B|A) = P(A and B)/P(A) = 0.09/0.28 = 0.3214 = 32.14%.
Missing InformationThe probability asked is that a camper entering the Luray Caverns has Canadian license Plates.
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You are on a safari and pass by some hippos and birds (the kind
that hang out on top of the hippos). You see a total of 42 animals ane
114 legs. how many of each animal were there?
Answer:
15 hippos27 birdsStep-by-step explanation:
You have a total of 114 legs among hippos and birds, of which there are a total of 42. You want the number of each kind of animal.
SetupLet h represent the number of hippos. Then 42-h is the number of birds, and the total number of legs is ...
4h +2(42 -h) = 114
SolutionSimplifying the equation gives ...
2h +84 = 114
2h = 30 . . . . . . subtract 84
h = 15 . . . . . . . . number of hippos
42 -h = 27 . . . . number of birds
There were 15 hippos and 27 birds.
Multiply the difference of 10 and 8 by 4 expression
The Mathematical Expression formed is 4(10-8)
What is a Mathematical Expression?
In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations.
Solution:
The mathematical expression formed frrom the statement;
Multiply the difference of 10 and 8 by 4
is as follows,
4(10-8)
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14 11/12 + 3 1/6 need help
Answer:
18.0833333333
Step-by-step explanation:
online calculator
a notebook manufacturer expectations fixed monthly costs of $46and variables costs of $1.50 per notebook produced.The notebooks are then sold for $3.50.
Answer: 13
Step-by-step explanation:
calculate the length of a scarf with sections if each section is 1/2 foot long
Answer:
depends on how many sections there are
Step-by-step explanation:
if there were 2 then it would be one foot 4 sections equal 2 and so on. the ratio for this 2:1 meaning there has to be 2 sections for there to be one foot.
The time is takes an object to move a certain distance is inversely propotional to the speed that it's travelling at.
it takes a car 12 minutes to travel the length of a road if it goes at an average speed of 60mph
a) How long would it take the car to travel down the same road if it travelled at an average speed of 30mph
Answer:
Hope the picture will help you
There are 10 applicants applying for 3 positions Hostess server and busier how many ways
The number of ways to select 3 position out of 10 applicant is 120 ways
What is combination?Combinations implies the selection of things from a given set of things. In this case, we intend to select the objects. Combination formula is illustrated as:
nCr = n! / ((n – r)! r!)
n = the number of items.
r = how many items are taken at a time.
Since there are 10 applicants applying for 3 positions. This will be:
= 10! / (10 - 3)!3!
= 10! / 7!3!
= 10 × 9 × 8 / 3 × 2
= 120
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What is the value of csc 47° to the nearest thousandth?
Answer: 1.367
Step-by-step explanation:
csc47° = 1.3673 ≈ 1.367
The value of cosec 47° is 1.367.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
cosec 47°
The value of cosec 47°.
= 1.367334
Rounding to the nearest thousandth.
= 1.367
Thus,
The value of cosec 47° is 1.367.
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Find the volume of the rectangular prism.
8 m
8 m
8 m
Answer:
Step-by-step explanation:
I believe that the volume of the rectangular prism is 512.
Explanation: V = whl = 8 · 8 · 8 = 512
V=Volume
W= Width
H= Height
L= Length
Mexico City had an estimated population of 18,066,000 people while Tokyo had an estimated population of 34,450,000 people. What was their combined population?
Answer:
Scientific notation: 5.2516 x [tex]10^{7}[/tex]
Standard notation 52,516,000
Step-by-step explanation:
Are you asking for the answer to be in scientific notation?
5.2516 x [tex]10^{7}[/tex] or 52,516,000
(1.8066 x [tex]10^{7}[/tex]) + (3.445 x [tex]10^{7}[/tex])
(1.8066 + 3.445) x [tex]10^{7}[/tex]
5.2516 x [tex]10^{7}[/tex]
The measure of an obtuse angle is A: greater than 0 and less than 90 degrees B: 90 degrees C. greater than 90 and less than 180 degrees
The measure of an obtuse angle is greater than 90° but less than 180°
What is an obtuse angle?An obtuse angle is a type of angle that is always larger than 90° but less than 180°. In other words, it lies between 90° and 180°.
An angle is the space between two intersecting lines or surfaces at or close to the point where they meet.
Angles are mostly measured in degrees. But it can also be measured in radian. Examples of obtuse angle are 91°, 100°, 150° e.t.c
Other examples of angles are acute angle, reflex angle , right angle.
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Calculate the simple interest and maturity value
The simple interest is $420 and the maturity value is $$6,720
How to find the simple interest?Using this formula to find the simple interest
Simple interest = Principal × Interest rate × Time
Where:
Principal = $6300
Interest rate =4% or 0.04
Time = 20 month = 20/12 = 1.6666666
Let plug in the formula
Simple interest = $6,300 × 0.04 × 1.6666666
Simple interest = $420
Using this formula to find the maturity value
Maturity value = Principal + Interest
Maturity value = $6,300 + $420
Maturity value = $6,720
Therefore the interest is $420.
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(b) A local store is keeping track of service times. The table below
shows the number of customers served and the time it took.
Number of customers 2-6-7
Time (in minutes) 8-24-28
_It does not always take the same amount of time to serve each customer.
_It appears to take the same amount of time to serve each customer
Histogram for the following intervals will be,
5-9 (4)
10-14 (3)
15-19 (5)
20-24 (3)
What are histograms?The data are numerical.When establishing whether the output of a process is distributed roughly regularly, you want to see how the data are dispersed.determining whether a method can satisfy the needs of the customerexamining the appearance of the product of a supplier's procedureDetermining whether the outputs of two or more processes are different and determining whether a process has changed from one time period to another.You want to let others know about the rapid and simple sharing of data.Acc to our question-
On your y-axis, you would draw a frequency that goes up to 5. Because the data is sequential, make sure the bars are touching (in order).Name the customers on your x-axis.Label the frequency y-axis.hence, histogram will show the values.
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