Answer: p(t) = 100×1.0153^(12t)
1.53% per month
In general, the function will be written ...
p(t) = (initial value)×(growth factor)^t
where t is in units comparable to those applicable to the growth factor. The growth factor is found from ...
growth factor = 1 + growth rate
Here, the growth rate is given as 20% per year, so the growth factor per year is ...
1 +20% = 1.20
The initial value is given as 100, so we can write the exponential function as ...
p(t) = 100×1.20^t
__
The time period units for t are supposed to be years, but we want to find the growth rate for a month. We can do that by recognizing there are 12 months in a year. In the above equation, we can use (1/12)(12t) in place of t, then figure the growth factor (and growth rate) per month.
p(t) = 100×(1.20^(1/12))^( 12t)
p(t) = 100×1.0153^(12t) . . . . population exponential function
This shows the monthly growth factor is 1.0153, so the monthly rate of change (growth rate) is ...
1.0153 -1 = 0.0153 = 1.53% . . . . monthly rate of change
Step-by-step explanation:
For a segment of a radio show, a disc jockey can play 5 records. If there are 7 records to select from, in how many ways can the program for this segment be arranged?
There are 2520 possible ways to arrange the programs
How to determine the ways the program can be arranged?From the question, we have
Total number of jockey records, n = 7
Total number of disc jockey records to select, r = 5
To determine the ways the program can be arranged, we make use of permutation
The number of ways of selection could be drawn is calculated using the following permutation formula
Total = ⁿPᵣ
Where
n = 7 and r = 5
Substitute the known values in the above equation
So, we have the following representation
Total = ⁷P₅
Apply the permutation formula
ⁿPᵣ = n!/(n - r)!
So, we have
Total = 7!/2!
Evaluate
Total = 2520
Hence, the number of ways is 2520
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A Tyrannosaurus rex weighed about 1.4 tons more than one tenth the weight of a Patagotitan mayorum. About how much did the Tyrannosaurus rex weigh?
Tyrannosaurus rex weighs about 0.14 times the weight of Patagotitan mayorum
How to determine by how much Tyrannosaurus rex weigh
In solving the proportion of the weights we use multiplication of fractions
Multiplication is a mathematical operator to handle such operation
A Tyrannosaurus rex weighed about 1.4 tons more than one tenth the weight of a Patagotitan mayorum
This is is written mathematically as
Tyrannosaurus rex weight, x = 1.4 * 1/10 * Patagotitan mayorum weight, y
x = 1.4 * 1/10 * y
x = 0.14 *y
x = 0.14y
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Part of the pride of being an American comes from the fact that most people that want jobs have jobs. However, this is not always the case. Sometimes, as happened in 2008, the economy slows down, and jobs become harder to find or keep. Businesses make less money and so can keep fewer people employed. Those people who lost their jobs then have less money to spend. Because they have less money to spend, other businesses make less money, and then they, too, have to cut workers. In the United States, these cycles always end and the economy recovers, but it can take a while. People have to get creative about making money if they lose their jobs. Sometimes, they can use the skills they used at their old jobs to make money independently. For example, people don’t buy many car stereos when the economy is bad. So, car stereo stores have to layoff some of their stereo installers. If an installer has a place to work, that person can install stereos without a store. Often, this person will charge less than the store where he or she used to work. Also, the installer will get to keep all of the money he or she charged. At the store where the installer used to work, the store would have made most of the money. During hard times, it is important to be open-minded. There are always ways to make money outside of a formal job, if a person is willing to do things he or she wouldn’t normally do. A computer programmer, for example, might not be able to find work as a computer programmer. However, if the programmer is good with his or her hands, he or she may be able to find work in construction. Lawns never stop growing, and many aspects of life do not stop just because the economy has slowed down. A person who lost a job at a supermarket may be able to mow lawns for money, or do many other things. Most importantly, a person who loses a job must not give up. One’s attitude is very important in determining if he or she will be successful. A hopeful person is more likely to find a new job. Also, a hopeful person will
The sentence which supports the idea that people can use the skills they used at their old jobs to make money independently is "If an installer has a place to work, that person can install stereos without a store."
The correct answer option is option C
A summary about employees and American economy down timeThe essay is about American employees where people who actually needs a job gets a job. Although, this is not always the case especially when the economy slows down.
This slow down in the economy causes businesses to make less profit, thereby, making most people to lose their jobs. The purchasing power of the unemployed (people who lost their job) will reduce causing a decrease in the amount of money made by businesses. This is like a vicious cycle.
However, people who are skilled can still earn a living by doing other available jobs or those who are creative can create new jobs for themselves. For instance, an accountant can become a sales person in a supermarket if he or she lost their job.
In conclusion, a person who lost their job must be determined, hopeful and hard-working and must never give up, most importantly, they should never be idle because an idle mind is the devil's workshop.
Complete question:
Which sentence supports the idea that people can use the skills they used at their old jobs to make money independently?
Answer choices
A"So, car stereo stores have to layoff some of their stereo installers."
B"Often, this person will charge less than the store where he or she used to work."
C. "If an installer has a place to work, that person can install stereos without a store."
D. "At the store where the installer used to work, the store would have made most of the money."
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Find the slope determined by the following pair of points.
(4,5), (1,3
Answer:
2/3
Step-by-step explanation:
we use y2-y1/x2-x1 to find slope
5-3/4-1
2/3
The slope is 2/3
Hopes this helps please mark brainliest
How many 2/5 can go into 1/2?
How do I solve this problem step-by -step? 57x 2(4)+2
Answer:
=57×2of4+2
=57×8+2
=456+2
=458.
hope it will help you
hope it will help youplease mark me as brainalist
If the function f(x) is the absolute value of 3 more than the value of x. Select all the true statements. A. The x-intercept of the function is 3.
The true statement about the function is that (b) the y-intercept of the function is 3
How to determine the true statement?The mathematical statement of the representation of the function is given as
The function f(x) is the absolute value of 3 more than the value of x.
Mathematically, this can be represented as
f(x) = |x + 3|
To determine the y-intercept, we set the x value of the function to 0
This means that we calculate f(x) when x = 0
i.e. f(0)
Substitute the known values in the above equation, so, we have the following representation
f(0) = |0 + 3|
Evaluate the sum
This gives
f(0) = |3|
Remove the absolute bracket
f(0) = 3
Hence, the y-intercept is 3
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Possible question
If the function f(x) is the absolute value of 3 more than the value of x. Select all the true statements.
A. The x-intercept of the function is 3.
B. The y-intercept of the function is 3.
The compression ratio in a certain engine is 7.5 to 1. If the expanded volume of a cylinder is 45 cu in., what is the
compressed volume?
If the expanded volume of a cylinder is 45 in³ , then the compressed volume is 6 in³ .
In the question ,
it is given that ,
the compression ratio in a certain engine is 7.5 : 1 .
the expanded volume of a cylinder is = 45 in³ .
we have to find the compressed volume of the cylinder ,
let the compressed volume of the cylinder be = v .
the above situation can be represented as
7.5 : 1 = expanded volume : compressed volume
7.5/1 = 45/v
7.5 = 45/v
v = 45/7.5
v = 6 cubic inches .
Therefore , If the expanded volume of a cylinder is 45 in³ , then the compressed volume is 6 in³ .
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SOMEONE PLS HELP ME!!!!!!Match the statements with their correct reason to complete the proof.
Given: AB = BC and AD = CD
Prove: Triangle ABD Triangle CBD
Proved that Triangle ABD ≅ Triangle CBD
Consider the triangle ABD and the triangle CBD
The length of the side AB = The length of the side BC
The length of the side AD = The length of the side cd
The third side is common
According to the SSS rule congruent . If the three side of the triangle is equal to the three sides of the another triangle then the both triangles are congruent
Then three sides of the triangle ABD is equal to the three sides of the triangle CBD, Therefore the triangle ABD and triangle CBD are congruent
Hence, proved that Triangle ABD ≅ Triangle CBD
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IXL Please Help Fast!
Answer:
Step-by-step explanation:
should be both line GJ and JK as well as line HK and JK
Part 1 A new bank customer with $5,000 wants to open a money market account. The bank is offering a simple interest rate of 1.9% a. How much interest will the customer earn in 20 years? b. What will the account balance be after20 years?
The account balance after20 years will be $6900 and the simple interest for 20 years is $1900
The Principal amount = $5,000
Rate of Interest (r) = 1.9 %
Time Period (t) = 20 years
The Simple Interest is given by
[tex]S.I. = \frac{P*r*t}{100}[/tex]
Now, putting the values on the formula, we get:
[tex]S.I. = \frac{5000*1.9*20}{100} = 1900[/tex]
Hence, the interest will be $1900
Now, The Account Balance after 20 years = $ (1900 + 5000) = $6900
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please check the image
The trigonometric measures in the context of this problem are given as follows:
[tex]\sin{\left(\frac{x}{2}\right)} = \sqrt{\frac{3-\sqrt{3}}{6}}[/tex][tex]\cos{\left(\frac{x}{2}\right)} = \sqrt{\frac{3+\sqrt{3}}{6}}[/tex][tex]\tan{\left(\frac{x}{2}\right)} = \sqrt{\frac{3 - \sqrt{3}}{3 + \sqrt{3}}}[/tex]How to obtain the trigonometric measures?We are given the measure of the sine for the angle and we need to find the three measures, sine, cosine and tangent for half the angle.
To find the measure for half the angle, the cosine is needed to apply the identities, and the cosine is calculated by the following identity:
sin²(x) + cos²(x) = 1
[tex]\left(\frac{2}{3}\right)^2 + \cos^2{x} = 1[/tex]
[tex]\cos^2{x} = 1 - \frac{4}{9}[/tex]
[tex]\cos{x} = \pm \sqrt{\frac{5}{9}}[/tex]
The angle is in the first quadrant, in which the cosine is positive, hence:
[tex]\cos{x} = \sqrt{\frac{5}{9}}[/tex]
[tex]\cos{x} = \frac{\sqrt{3}}{3}[/tex]
Then, applying an identity, the sine for half the angle is given as follows:
[tex]\sin{\left(\frac{x}{2}\right)} = \sqrt{\frac{1 - \cos{x}}{2}}[/tex]
Considering the calculated value for the cosine:
[tex]\sin{\left(\frac{x}{2}\right)} = \sqrt{\frac{1 - \frac{\sqrt{3}}{3}}{2}}[/tex]
[tex]\sin{\left(\frac{x}{2}\right)} = \sqrt{\frac{3-\sqrt{3}}{6}}[/tex]
The identity for the cosine is:
[tex]\cos{\left(\frac{x}{2}\right)} = \sqrt{\frac{1 + \cos{x}}{2}}[/tex]
Hence:
[tex]\cos{\left(\frac{x}{2}\right)} = \sqrt{\frac{3+\sqrt{3}}{6}}[/tex]
The tangent is obtained by the division of the sine and the cosine. The entire division can be placed into a single square root, and the common denominators of six are simplified, hence:
[tex]\tan{\left(\frac{x}{2}\right)} = \sqrt{\frac{3 - \sqrt{3}}{3 + \sqrt{3}}}[/tex]
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Please help. Find X and Y. NEED ASAP
Answer:
x=1.25 y=1.75
Step-by-step explanation:
8/10=5/5+x
50=8(5+x)
50=40+8x
50-40=8x
10=8x
x=10/8
x=1.25
while Y=8/10=7/7+y
70=8(7+y)
70=56+8y
70-56=8y
14=8y
y=14/8
y=1.75
Find the value of x (desperately need help with this please! Due today!)
Answer:
x=48
Step-by-step explanation:
the 2 given angles if added together we know it’ll be 180 degrees
3x-12+x=180
4x-12=180
+12. +12
4x=192
x=48
Hopes this helps please mark brainliest
What is –11 + |-5|-|-15|?
-1
-11
-9
-26
-21
Answer:
-1
Step-by-step explanation:
you would do -11 + (-5) which will be -16. Then do -16 - (-15) which will get you -1.
Using information provided please answer the following
1. The bank discount on the note of $6,000, which will mature in 160 days at 3.5%, is $93.33.
2. The noteholder will receive total proceeds of $5,906.67 after the 3.5% discount.
What is a bank discount?Bank discount is the difference between the discounted and face (par) values.
For example, if the bank discounts a note, the holder receives a smaller amount than the face value they would have received had they held the note till its maturity.
The bank discount represents the finance charge for cashing the note earlier than its due date.
Amount due at maturity = $6,000
Discount rate = 3.5%
Time (period) = 160 days
Days in the year for ordinary interest = 360 days
Bank discount = $93.33 ($6,000 x 3.5% x 160/360)
The proceeds = $5,906.67 ($6,000 - $93.33)
Thus, the bank discount refers to the difference between the face value and the discounted value resulting from receiving cash from a note before maturity.
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There are three consecutive odd integers.Three times the largest is seven times the smallest. What are the integers?
The three consecutive odd intergers are 3,5 and 7
What do you mean by algebraic expression ?
An algebraic expression is the idea of using letters or alphabets to represent numbers without specifying the actual values. Algebra Basics taught us how to use letters like x, y, and z to represent unknown values. These characters are called variables here.
An algebraic expression can be a combination of variables and constants. Any multiplied value that is prefixed to a variable is a factor.
Let the three consecutive odd integers are x, x+2 and x+ 4
Here x is the smallest odd integer and x+4 is the largest odd integer
According to the question:
3(x +4) = 7x
3x + 12 = 7x
7x - 3x = 12
4x = 12
x = 12/4
x = 3
Three consecutive odd integers become:
x = 3
x + 2 = 3 +2 = 5
x + 4 = 3 + 4 = 7
Hence, the three consecutive odd intergers are 3,5 and 7
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Match the equations with the value of x that makes them true. 2(2x − 3) = 6 5x − 2x − 4 = 5 x + 2x + 3 = 9 5(x + 3) = 25 4x − (2x + 1) = 3 5x − (3x − 1) = 7
Each of the equations should be matched with the value of x that makes them true as follows:
x = 2; x + 2x + 3 = 9, 5(x + 3) = 25, and 4x − (2x + 1) = 3.
x = 3; 2(2x − 3) = 6, 5x - 2x - 4 = 5, and 5x − (3x − 1) = 7.
How to determine the true equations?In order to determine which x-values are true solutions based on the given equations, we would have to test each of the values of x by substituting them into the equations as follows;
When x = 2, we have:
2(2x − 3) = 6
4x − 6 = 6
4(2) - 6 = 6
8 - 6 = 6
2 = 6 (False).
When x = 3, we have:
2(2x − 3) = 6
4x − 6 = 6
4(3) - 6 = 6
12 - 6 = 6
6 = 6 (True).
When x = 2, we have:
5x - 2x - 4 = 5
3x - 4 = 5
3(2) - 4 = 5
6 - 4 = 5
1 = 5 (False).
When x = 3, we have:
5x - 2x - 4 = 5
3x - 4 = 5
3(3) - 4 = 5
9 - 4 = 5
5 = 5 (True).
When x = 2, we have:
x + 2x + 3 = 9
3x + 3 = 9
3(2) + 3 = 12
9 = 12 (False).
When x = 3, we have:
x + 2x + 3 = 9
3x + 3 = 9
3(3) + 3 = 12
12 = 12 (True).
5(x + 3) = 25
5x + 15 = 25
5x = 25 - 15
5x = 10
x = 2 (True).
4x − (2x + 1) = 3
4x - 2x - 1 = 3
2x = 3 + 1
2x = 4
x = 2 (True).
5x − (3x − 1) = 7
5x - 3x + 1 = 7
2x = 7 - 1
2x = 6
x = 3 (True).
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The arithmetic mean of the ages of 30 pupils is 15.3 years. One boy leaves the class and one girl is enrolled and the new average age of 30 pupils in the class becomes 15.2 years. How much older is the boy than the girl
The answer will be 3 years.
1st 30 pupils at average age of 15.3 yrs. give total age of 15.3 x 30 = 459yrs
2nd group of 30 pupils at average age of 15.2 yrs
give total age of 15.2 x 30 = 456yrs
Difference in age = 459 - 456
= 3 years.
15.75 + .5x = 16.53 - .13x
Guidance Missile System A missile guidance system has eight fail-safe components. The probability of each failing is 0.35
Assume the variable is binomial. Find the following probabilities. Round your answers to at least four decimal places.
Part: 0/4
Part 1 of 4
com Rem
(a) Exactly six will fail.
P(exactly six will fail) =
The probability of exactly six will fail = 0.0808
What is Probability?
Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability. It is crucial to grasp this branch's most fundamental concepts in order to fully comprehend it, including the formula for computing probabilities in equiprobable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc.
In the given question, we have:
We know that Probability in binomial distribution with total components ' n ', probability of success ' p ', and the number "of successes " = [tex]{ }^n c_k p^k(1-p)^{n-k}[/tex]
we know that:
[tex]{ }^n c_k=\frac{n !}{(n-k) ! k !}[/tex]
[tex]\begin{aligned}P(\text { success }) &=P(\text { a part fails })=0.35 \text {. So, } \\P(x=5) &={ }^8 C_5 \times(0.35)^5(0.65)^3 \\&=56 \times(0.005252) \times(0.274625) \\&=0.0808 \\& \text { (Round to } 4 \text {-decimals) }\end{aligned}[/tex]
Hence,
The probability of exactly six will fail = 0.0808
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How much should be deposited in an account paying 4.5% interest, compounded semiannually, in order to have a balance of $ 5,000 after 19 years and 6 months?
Enter the answer in dollars and cents, and round to the nearest cent, if needed. Do not include the dollar sign. For example, if the answer is $0.61, only the number 0.61 should be entered.
Principal ≈ $ ________
The amount that should be deposited in the account to earn a balance of $5, 000 after 19 years and 6 months is $2, 099.43
How to find the amount?First, find the periodic rate:
= 4.5% / 2 semi annual periods per year
= 2.25%
Find the number of periods:
= 19 years and 6 months = 19.5 years
= 19.5 years x 2 semi annual periods per year
= 39 periods
The amount to deposit in the account can be found by the future value formula:
Future value = Deposit x ( 1 + rate) ^ number of periods
5, 000 = Deposit x ( 1 + 2.25%)³⁹
Deposit = 5,000 / ( 1 + 2.25%)³⁹
= $2, 099.43
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please help please
show answer and question.
a crate is 24cm by 18cm by 15cm . it is to be packed with boxes that are 8cm by 6cm by 5cm . what is the largest number of boxes that can fit in the crate.
The largest number of boxes that can fit in the crate will be 27.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The dimension of the crate is 24cm by 18cm by 15cm.
And, it is to be packed with boxes that are 8cm by 6cm by 5cm.
Now,
By the given data;
Volume of the crate = 24 x 18 x 15
= 6480 cm³
And, The volume of the box = 8 x 6 x 5
= 240 cm³
Thus, The largest number of boxes that can fit in the crate = 6480 / 240
= 27
Therefore, The largest number of boxes that can fit in the crate will be 27.
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(a) Write an equation representing the fact that the product of two consecutive odd Integers is 143. Use x to represent the smaller
integer.
(b) Solve the equation from part (a) to find the two integers.
(a) The equation is
The equation representing the fact that the product of two consecutive odd Integers is 143 is x(x+2) = 143 where x represents the smaller number and the value of x is 11 or -13.
According to the question,
We have the following information:
The product of two consecutive odd Integers is 143.
Now, let's take the smaller integer to be x.
Now, next consecutive odd integer:
(x+2)
So, we have the following expression:
x(x+2) = 143
[tex]x^{2} +2x = 143\\[/tex]
[tex]x^{2} +2x -143 = 0[/tex]
[tex]x^{2}[/tex]+13x-11x-143 = 0
Taking x as the common factor from first two terms and -11 from the last two terms:
x(x+13)-11(x+13) = 0
(x-11)(x+13) = 0
x-11 = 0 and x+13 = 0
x = 11 or x = -13
Next odd integer = 13 or -11
Hence, the equation representing the fact that the product of two consecutive odd Integers is 143 is x(x+2) = 143 where x represents the smaller number and the value of x is 11 or -13.
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Solve one sixth times quantity x plus 24 end quantity equals negative 6
The value of one-sixth times quantity x plus 24 end quantity equals negative 6 is -180.
What is an expression?The expression simply refers to the mathematical statements which have at least two terms that are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
In this case, the expression given will be illustrated as:
1/6x + 24 = -6
Collect like terms
x / 6 = -6 - 24
x/6 = -30
Cross multiply
x = -30 × 6
x = -180
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A standard die is rolled. Find the probability that the number rolled is less than 3. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answer:
When a die is rolled, here it's Total possible outcome is= 6
and sample space is = 2 ( i.e. 1 & 2)
So. Probability of getting less than 3 = 26
=13
That's it.
Step-by-step explanation:
Sophie put $3330 in a savings account at a simple interest rate of 7.4% per year. Adam put $2795 in a savings account at a simple interest rate of 8.1% per year.
Who will have earned more interest after 5 years? How much more?
Adam earned $100.12 more interest than the Sophie
Consider Sophie
The principal amount = $3330
The interest rate = 7.4%
The time period = 5 years
Simple interest = PRT
Where P is the principal amount
R is the interest rate
T is the time period
Substitute the values in the equation
Simple interest = 3330× (7.4/100) × 5
= $1232.1
Consider Adam
The principal amount = $2795
The interest rate = 8.1%
The time period = 5 years
Simple interest = 2795 × (8.1/100) × 5
= $1131.98
The difference = 1232.1 - 1131.98
= $100.12
Hence, the Adam earned $100.12 more interest than the Sophie
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Square of 10^4 is ?
Five hours and 20 minutes after a raft left a dock, a patrol boat left the dock and traveled in the same direction as the raft. The boat caught up to the raft 20 km away from their starting point. What was the speed of the raft if the speed of the patrol boat was 12km/hr ?
The speed of the raft was 2.86 km/hr.
What is speed?Speed is defined as the rate of change of position of an object in any direction.
Given that, a patrol boat with speed of 12 km/hr caught a raft after travelling for 20 km and patrol boat left the dock after 5 hours and 20 minutes the raft left,
The time taken by the patrol boat to catch the raft is;
t = 20/15 = 5/3 hours
5/3 hours = 1 hour 40 minutes
Thus, it took 1 hour 40 minutes for the patrol boat to catch the raft
Thus, the raft was travelling for 5 hours 20 minutes plus 1 hour 40 minutes which 7 hours,
The speed of raft = 20/7 = 2.86 km/hr
Hence, The speed of the raft was 2.86 km/hr.
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find slope intercept form and graph (-3,0) and (-3,-7)
Answer:
x = -3
Step-by-step explanation:
Slope = Rise/Run
Slope = Difference in y/Difference in x
Slope = -7/0
Slope = undefined (can not divide by 0)
This means that this is a vertical line