Both planes will reach the city at the same time again at 11 PM.
How to deal with periodic events?Considering periodic events, they will repeat on the same day for the least common factor of the periods of each event.
The periods for this problem are given as follows:
5 hours.3 hours.As 5 and 3 are prime numbers, the least common factor is given as follows:
5 x 3 = 15.
15 hours after 8 AM is of 11 PM.
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Factorise completely.
1.1) 2x + 4y - 6z
1.2) 10p6q²-4p³q2 + 2p*q*
1.3) (m+n)²-5p(m + n)
1.4) 4(7c-d)+a(d-7c)
The completely factorized forms are:
1.1) 2x + 4y - 6z (no further factorization)
[tex]1.2) 2pq(5p^5q - 2p^2 + 1)[/tex]
1.3) (m + n)(m + n - 5p)
1.4) 7c(4 - a) + d(-4 + a)
We have,
Let's factorize each expression completely:
1.1)
2x + 4y - 6z
There are no common factors among the terms, so we can't factorize it further.
1.2)
[tex]10p^6q^2 - 4p^3q^2 + 2pq[/tex]
The common factor among the terms is 2pq, so we can factor it out:
[tex]2pq (5p^5q - 2p^2 + 1)[/tex]
1.3)
(m + n)² - 5p(m + n)
Using the distributive property, we can expand the squared term:
(m + n)(m + n) - 5p(m + n)
Now we can factor out the common factor (m + n):
(m + n)(m + n - 5p)
1.4)
4(7c - d) + a(d - 7c)
Using the distributive property, we can expand the terms:
28c - 4d + ad - 7ac
Rearranging the terms:
(28c - 7ac) + (-4d + ad)
Factoring out common factors:
7c(4 - a) + d(-4 + a)
Thus,
The completely factorized forms are:
1.1) 2x + 4y - 6z (no further factorization)
[tex]1.2) 2pq(5p^5q - 2p^2 + 1)[/tex]
1.3) (m + n)(m + n - 5p)
1.4) 7c(4 - a) + d(-4 + a)
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(iv) MP= Rs. 26600, Discount-10%
The discounted price of the item would be Rs. 23,940.
To calculate the discounted price of an item, you can use the following formula:
Discounted Price = Original Price - (Original Price * Discount Percentage)
Given that the original price (MP) is Rs. 26,600 and the discount is 10%, we can calculate the discounted price as follows:
Discounted Price = Rs. 26,600 - (Rs. 26,600 x 0.10)
Discounted Price = Rs. 26,600 - Rs. 2,660
Discounted Price = Rs. 23,940
Therefore, with a 10% discount, the discounted price of the item would be Rs. 23,940.
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which statement is true of this function
The correct statement is:
C. The function has a y-intercept at (0, -2).
Let's analyze each statement:
A. As the value of x increases, the value of f(x) moves toward a constant.
This statement is false.
The function f(x) = (1/5)ˣ - 2 is an exponential function with a base of 1/5. As x increases, the exponential term (1/5)ˣ becomes smaller and approaches zero, causing f(x) to approach -2.
However, it does not approach a constant value.
B. The domain of the function is (-2, ∞).
This statement is false.
The function f(x) = (1/5)ˣ - 2 is defined for all real numbers.
There are no restrictions on the domain, so the correct statement is that the domain is (-∞, ∞).
C. The function has a y-intercept at (0, -2).
This statement is true.
To find the y-intercept, we set x = 0 in the function and solve for f(x):
f(0) = (1/5)⁰ - 2
= 1 - 2
= -1
Therefore, the y-intercept of the function is (0, -2).
D. The function is increasing.
This statement is true.
An exponential function with a positive base, such as (1/5)ˣ, is always decreasing.
However, when we subtract 2 from the exponential term, it shifts the graph vertically downward by 2 units.
This transformation makes the function f(x) = (1/5)ˣ - 2 increasing.
So, the correct statement is:
C. The function has a y-intercept at (0, -2).
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The graph shows a function of the form () = ab
.
Use the drop-down menus to complete the statements about the function, and then write an equation that represents this function.
Answer:
When [tex]x=0[/tex], the value of f(x) is 1.
Each time x increases by 1, f(x) is multiplied by 4.
Equation of function: [tex]f(x)=1\cdot 4^x[/tex]
Step-by-step explanation:
The detailed explanation is attached below.
Fabrizio cut a square paper vertically to make two rectangle pieces. Each rectangle had a perimeter of 57 inches. How long is each side of the original square paper?
The length of each side of the original square paper is √812.25 = 28.5 inches.
Let us assume that the length and breadth of the square paper are 'a' and 'b' respectively. Now, Fabrizio cuts the paper vertically to make two rectangular pieces.
Since the paper is cut vertically, it can be assumed that the breadth of the square is equal to the height of the rectangle.
Therefore, the perimeter of one rectangle can be calculated by the formula P = 2l + 2wwhere l = length and w = widthNow, P = 57 inches.
Therefore, 2l + 2w = 572(l + w) = 57l + 57w = 28.5(2l + 2w)Since the paper is cut into two rectangles, the length of the square paper is divided equally into the two pieces.
Therefore, the length of the side of the original square paper can be calculated as follows:Length of one rectangle = l = 28.5Width of one rectangle = w = 57 - 28.5 = 28.5
Therefore, the breadth of the original square paper = width of one rectangle = 28.5 inches.
The area of the square can be calculated as length * breadthTherefore, the area of the square paper is given by a * b = 28.5 * 28.5 = 812.25 square inches.
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Linear equations graph
Step-by-step explanation:
PLot two pioints....connect the points
Use the y -intercept given y = -1 when x = 0 Plot that
when y = 0 x = 1/2 plot that
draw line through these points :
Answer:
Step-by-step explanation:
enter the number that belongs in the green box
The value of the unknown side to the nearest hundredth is 6.78
What is cosine rule?Cosine rule states that; if a, b,c are the sides of a triangle and A,B,C are the opposite angles of the sides, then
c² = a² + b² -2ab CosC
Cosine rule is used when all the sides or two of the sides are given. The angle opposite to side c is angle C.
c² = 4² + 10² - 2(4)(10)cos 29
c² = 16 +100 - 80cos29
c² = 116 -69.97
c² = 46.03
c = √ 46.03
c = 6.78 ( nearest hundredth).
Therefore the value of c is 6.78
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need help please. any body
The given limit is 0.
To solve the given limit, we can recognize the sum as a Riemann sum and convert it into an integral.
The given sum can be rewritten as:
[tex]\lim_{n \to \infty} \sum_{i=1}^{n} \frac{3}{n} \sqrt{1+\frac{3i}{n}}[/tex]
Let's rewrite it in terms of integration:
[tex]\lim_{n \to \infty} \frac{3}{n} \sum_{i=1}^{n} \sqrt{1+\frac{3i}{n}}[/tex]
Since we are taking the limit as n approaches infinity, we can approximate the sum as an integral.
The integral that corresponds to the given sum is:
[tex]\lim_{n \to \infty} \frac{3}{n} \sum_{i=1}^{n} \sqrt{1+\frac{3i}{n}} \approx \lim_{n \to \infty} \frac{3}{n} \int_{0}^{1} \sqrt{1+3x} ,dx[/tex]
To solve this integral, we can use a change of variables.
Let u = 1 + 3x, then du = 3dx.
The integral becomes:
[tex]\lim_{n \to \infty} \frac{3}{n} \int_{0}^{1} \sqrt{1+3x} ,dx = \lim_{n \to \infty} \frac{1}{n} \int_{1}^{4} \sqrt{u} ,du[/tex]
Integrating [tex]\sqrt{u}[/tex], we get,
[tex]\lim_{n \to \infty} \frac{1}{n} \int_{1}^{4} \sqrt{u} ,du = \lim_{n \to \infty} \frac{1}{n} \left[\frac{2}{3} u^{3/2}\right]_{1}^{4}[/tex]
Substituting the limits, we have:
[tex]\lim_{n \to \infty} \frac{1}{n} \left[\frac{2}{3} (4)^{3/2} - \frac{2}{3} (1)^{3/2}\right][/tex]
Simplifying further:
[tex]\lim_{n \to \infty} \frac{1}{n} \left[\frac{2}{3} (8 - 2)\right] = \lim_{n \to \infty} \frac{1}{n} \left[\frac{12}{3}\right] = \lim_{n \to \infty} \frac{4}{n} = 0[/tex]
Therefore, the given limit is 0.
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2. In a complete paragraph, pick a scenario where concepts from this course would be used - it could be in you
or working in a business, etc.
Choose at least 2-3 concepts to include, explain your scenario, how these concepts apply, and provide a wa
Use the following format:
Topic Sentence: 1 concise sentence describing a scenario where concepts from this course could be used.
Supporting Detail: 1-2 sentences explaining how 1 concept from the class can be applied to the scenario.
Worked Example: Show a worked example for the concept described above.
Supporting Detail: 1-2 sentences explaining how 1 concept from the class can be applied to the scenario.
Worked Example: Show a worked example for the concept described above.
Conclusion: 1-2 sentences describing how applying the concepts in this course to a real-life situation helps
Write your response using your own words and do not use any other sources outside of this course
Topic Sentence: In a business setting, concepts from this course can be applied when optimizing customer service operations and improving customer satisfaction.
The Supporting DetailsSupporting Detail: One concept from the course that can be applied is the use of queuing theory to manage customer wait times and reduce service bottlenecks. By analyzing arrival rates, service rates, and queue lengths, businesses can optimize staffing levels and allocate resources efficiently.
Worked Example: One practical application of queuing theory is in call centers. With the aid of this theory, the center can analyze the number of customer service reps required in different periods of the day. The objective is to keep waiting times at their lowest and deliver timely service to customers.
Supporting Detail: Another concept that can be applied is the concept of customer lifetime value (CLV). By understanding CLV, businesses can identify their most valuable customers, prioritize their needs, and tailor personalized marketing strategies to enhance customer retention.
Worked Example: An e-commerce business may use information on customer buying patterns, typical order amounts, and the rate of customer loss to determine the overall lifetime value of a customer. By utilizing this data, the organization has the opportunity to execute tailored loyalty initiatives and customized suggestions, ultimately enhancing customer contentment and optimizing overall revenue for the long haul.
Conclusion:
The application of course concepts in a business environment can result in better customer service, shorter wait times, higher customer approval, and increased customer allegiance, thereby fueling the expansion and profitability of a business.
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Could someone explain how to solve this?
Answer:
Step-by-step explanation:
The points with coordinates (4,8), (2,10), and (5,7) all lie on the line 2x+2y=24
Since all three points satisfy the equation 2x + 2y = 24 when their coordinates are substituted, we can conclude that the points (4,8), (2,10), and (5,7) indeed lie on the line represented by the equation 2x + 2y = 24.
To determine if the points (4,8), (2,10), and (5,7) lie on the line 2x + 2y = 24, we can substitute the x and y values of each point into the equation and check if the equation holds true.
For the point (4,8):
2(4) + 2(8) = 8 + 16 = 24, which satisfies the equation.
For the point (2,10):
2(2) + 2(10) = 4 + 20 = 24, which also satisfies the equation.
For the point (5,7):
2(5) + 2(7) = 10 + 14 = 24, which satisfies the equation as well.
Since all three points satisfy the equation 2x + 2y = 24 when their coordinates are substituted, we can conclude that the points (4,8), (2,10), and (5,7) indeed lie on the line represented by the equation 2x + 2y = 24.
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7. How a change in fixed costs affects the profit-maximizing quantity
Manuel owns and operates a hot dog stand in downtown New York City. In order to operate his hot dog stand, regardless of the number of hot dogs sold, Manuel must purchase a permit from the local government in New York City. Manuel's initial profit hill is plotted in green (triangle symbols) on the following graph.
Suppose the price Manuel must pay for a permit decreases by $10 per day.
On the following graph, use the purple diamond symbols to plot Manuel's new profit hill, for 0, 10, 20, 30, 40, 50, 60, and 70 hot dogs, after the decrease in the price of a permit (with all other factors remaining constant).
you can tell that Manuel initially faces a fixed cost of $ per day.
Initially, Manuel's profit-maximizing level of output is hot dogs per day. After the price of a permit falls, Manuel's profit-maximizing level of output is hot dogs per day.
Fixed costs are expenses that do not change with the level of output or production. Examples of fixed costs in Manuel's case might include the permit cost, rent for the hot dog stand, or insurance premiums.
In order to answer your question accurately, I would need the specific values for Manuel's profit and cost functions. The information you provided is incomplete, as you mentioned Manuel's initial profit hill is plotted in green on a graph, but the graph itself is not available for reference.
To determine how a change in fixed costs affects the profit-maximizing quantity, we typically analyze the cost and revenue functions. Without these functions or the corresponding data, it is not possible to provide an exact numerical answer.
However, I can explain the general concept. Fixed costs are expenses that do not change with the level of output or production. Examples of fixed costs in Manuel's case might include the permit cost, rent for the hot dog stand, or insurance premiums.
When fixed costs decrease, it reduces the overall cost of production for each level of output. This means that Manuel can achieve higher profits or reduce losses for any given level of sales. Consequently, the profit-maximizing quantity may change as a result.
If we assume that the decrease in the price of the permit is the only change in fixed costs and all other factors remain constant, the new profit hill can be expected to shift upward. This is because the reduction in fixed costs increases the potential for higher profits at each level of output.
Without more specific information about Manuel's profit and cost functions, it is not possible to determine the exact profit-maximizing levels before and after the decrease in the price of the permit.
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Darren says that more students hands are 4 2/4 inches longer than 4 and 5 1/4 inches combined. is he right?Explain you're answer
In a case whereby Darren says that more students hands are 4 2/4 inches longer than 4 and 5 1/4 inches combined, he is wrong
What is the justification?
[tex]4\frac{2}{4}[/tex] that was given in the question can be seen as mixed fraction, we can expressed this as improper fraction so that it will be easier to handle.
[tex]4\frac{2}{4} = \frac{16+4}{2}[/tex]
=[tex]\frac{18}{4}[/tex]
Then [tex]4 + 5\frac{1}{4} = \frac{16}{4} +\frac{20+1}{4} \\\\=\frac{37}{4}[/tex]
Then after expressing the given fractions as improper fraction we can now compare them so that e will know may be Darren is right or wrong, then here we can see that [tex]\frac{18}{4}[/tex] is less than [tex]\frac{37}{4}[/tex] Hence, Darren is wrong.
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7
Drag the tiles to the boxes to form correct pairs.
Find the probability for the given situations, and then match the situations with the number of times each event is predicted to occur.
Josie rolls a six-sided die 18 times.
What is the estimated number of
times she rolls a two?
3
Slips of paper are numbered 1
through 10. If one slip is drawn and
replaced 40 times, how many times
should the slip with number 10
appear?
5
A spinner consists of 10 equal-
sized spaces: 2 red, 3 black, and 5
white. If the spinner is spun 30
times, how many times should it
land on a red space?
6
A card is picked from a standard
deck of playing cards 65 times and
replaced each time. About how
many times would the card drawn
be an ace?
4
ASAP Pls
Answer:
Pin copied text snippets to stop them expiring after 1 hourText you copy will automatically show hereSlide clips to delete them
Step-by-step explanation:
:/
Find the mystery number from the following clues
It is a 2-digit number
It is a factor of 48
It is a multiple of 6
The sum of the digits is 3
Based on the given clues, the mystery number is 12.
Let's analyze the clues given to find the mystery number:
It is a 2-digit number: This means the number is greater than or equal to 10 and less than 100.
It is a factor of 48: The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
It is a multiple of 6: The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, and so on.
The sum of the digits is 3: From the clues, we know that the mystery number is a 2-digit number, so let's consider the possible numbers where the sum of the digits is 3:
12 (1 + 2 = 3)
21 (2 + 1 = 3)
Now let's check which of these numbers satisfy the first three clues:
12: This number is a factor of 48 (48 ÷ 12 = 4) and it is a multiple of 6 (12 ÷ 6 = 2). The sum of the digits is 3. Therefore, 12 satisfies all the clues.
21: This number is not a factor of 48 (48 ÷ 21 ≈ 2.29), so it doesn't satisfy the second clue.
Based on the given clues, the mystery number is 12.
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What is the temperature in °C? Hint: (°F -32) ÷ 1.8 °C or °F= 1.8 °C
+32
Converting the temperature from Celsius to Fahrenheit:
Subtract the given temperature by 32 and divide it by 1.8°C.
°C = (F - 32) / 1.8°C, or use the equation °F= 1.8 °C+32
(°F-32) / 1.8°C
a) The given temperature is 60°F
substitute the given values in the above equation:
(60 - 32) / 1.8
28 / 1.8
= 15.5555 approx 16°C
60°F = 16°C
b) The given temperature is 10°F
°C = (F - 32) / 1.8°C
substitute the given values in the above equation:
(10 -32) / 1.8
-22 / 1.8
-12.222 approx -12°C
10°F = -12°C
correct question:
What is the temperature in °C, if the temperature is
a) 60F
b) 10F
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Part A
Study the two functions shown, A(t) and 12∙J(t). Based on the graph and the data, what kinds of functions are they? Choose among linear, quadratic, and exponential. Describe the features of each function that gave you clues.
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Part B
The equation A = Pert describes a bank loan that compounds continuously. The variables in the equation are described in the table:
Variable Definition
A This is the principal and interest on the loan. Principal is the amount of money borrowed. Interest is a graduated fee paid to the bank for the privilege of borrowing its money.
P This is the principal, or the amount of money borrowed. Don’t confuse P in the compounding interest equation with P in the profit equation. One is principal, the other is profit.
e This is Euler’s number, e ≈ 2.7, used in exponential functions that are continuously compounding.
r This is the interest rate expressed as a percentage.
t This is the time allotted, in years, to repay the loan. It’s also called the life of the loan.
For the sake of this activity, assume that you will collect profit from sales for a number of months and then use a portion of that profit to pay off the entire loan in one lump-sum payment once the loan terminates. Based on this assumption, what does the intersection of the 12∙J(t) curve and the A(t) curve represent? Explain using your own words.
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Part C
Take some time to gradually increase P in increments of $100,000 while keeping r and J(t) constant. What happens to the relationship between the two curves? What does this mean with respect to the bank loan? Why is this a dangerous situation with respect to the financial health of your business? Why would banks put safeguards in place to prevent this from occurring?
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Part A:
A(t) is a linear function, and 12∙J(t) is an exponential function. The straight line nature of A(t) indicates linear growth, while the curve of 12∙J(t) suggests exponential growth.
Part B:
The intersection of the 12∙J(t) curve and the A(t) curve represents the point where the accumulated profit from sales is sufficient to pay off the entire loan in one lump-sum payment.
Part C:
As P increases while keeping r and J(t) constant, the relationship between the two curves shifts, indicating a higher profit requirement to cover the increased loan amount. This is dangerous for business financial health and banks have safeguards to prevent excessive debt and defaults.
Part A:
From the given information, we have two functions: A(t) and 12∙J(t). Let's analyze their features to determine their types.
A(t) is a linear function:
A linear function is characterized by a constant rate of change and forms a straight line on a graph.
In the given graph, A(t) is represented by a straight line, indicating a linear relationship between the variables.
This suggests that A(t) is a linear function.
12∙J(t) is an exponential function:
An exponential function is characterized by a constant ratio or base and shows exponential growth or decay.
In the given graph, 12∙J(t) is represented by a curve that exhibits exponential growth.
The increasing rate of change as time progresses indicates an exponential relationship.
Therefore, 12∙J(t) is an exponential function.
Part B:
The intersection of the 12∙J(t) curve and the A(t) curve represents the point at which the profit generated from sales is sufficient to pay off the entire loan in one lump-sum payment. In other words, it represents the point in time when the accumulated profit matches the amount of the loan.
At this intersection point, the profit generated from sales has reached a level where it can fully cover the principal and interest owed on the loan. This indicates that the business has generated enough funds to repay the loan in its entirety.
Part C:
As the principal (P) is increased while keeping the interest rate (r) and 12∙J(t) constant, the relationship between the two curves changes. Specifically, the intersection point between the curves shifts to the right on the graph.
This change in the relationship between the curves signifies that the business needs a higher level of profit to cover the increased loan amount. It suggests that the business has taken on a larger loan, which requires a higher profit to repay.
This situation is considered dangerous for the financial health of the business because it increases the risk of not generating sufficient profit to repay the loan. If the business fails to generate enough profit to cover the loan payments, it may lead to financial instability and potential default on the loan.
To mitigate such risks, banks put safeguards in place to prevent businesses from taking on excessive debt. These safeguards include conducting thorough evaluations of the business's financial health, setting limits on loan amounts based on the business's income and creditworthiness, and assessing the repayment capacity of the borrower. These measures aim to minimize the risk of defaults and protect both the borrower and the lender.
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Given the polynomial 9x2y6 − 25x4y8, rewrite as a product of polynomials.
(9xy3 − 25x2y4)(xy3 + x2y4)
(9xy3 − 25x2y4)(xy3 − x2y4)
(3xy3 − 5x2y4)(3xy3 + 5x2y4)
(3xy3 − 5x2y4)(3xy3 − 5x2y4)
Answer:
Option 3
(3xy³ + 5x²y⁴) (3xy³ - 5x²y⁴)
Step-by-step explanation:
Factorize polynomials:
Use exponent law:
[tex]\boxed{\bf a^{m*n}=(a^m)^n} \ & \\\\\boxed{\bf a^m * b^m = (a*b)^m}[/tex]
9x²y⁶ = 3²* x² * y³*² = 3² * x² * (y³)² = (3xy³)²
25x⁴y⁸ = 5² * x²*² * y⁴*² = 5² * (x²)² * (y⁴)² = (5x²y⁴)²
Now use the identity: a² - b² = (a +b) (a -b)
Here, a = 3xy³ & b = 5x²y⁴
9x²y⁶ - 25x⁴y⁸ = 3²x²(y³)² - 5²(x²)² (y⁴)²
= (3xy³)² - (5x²y⁴)²
= (3xy³ + 5x²y⁴) (3xy³ - 5x²y⁴)
if f(x)=x+2/x^2-9 and g(x)=11/x^2+3x
A. find f(x)+g(x)
B. list all of the excluded values
C. classify each type of discontinuty
To receive credit, this must be done by Algebraic methods, not graphing
The types of discontinuities are: removable discontinuity at x = -3 and vertical asymptotes at x = 0 and x = 3.
A. To find f(x) + g(x), we add the two functions together:
f(x) + g(x) = (x + 2)/(x^2 - 9) + 11/(x^2 + 3x)
To add these fractions, we need a common denominator. The common denominator in this case is (x^2 - 9)(x^2 + 3x). So, we rewrite the fractions with the common denominator:
f(x) + g(x) = [(x + 2)(x^2 + 3x) + 11(x^2 - 9)] / [(x^2 - 9)(x^2 + 3x)]
Simplifying the numerator:
f(x) + g(x) = (x^3 + 3x^2 + 2x^2 + 6x + 11x^2 - 99) / [(x^2 - 9)(x^2 + 3x)]
Combining like terms:
f(x) + g(x) = (x^3 + 16x^2 + 6x - 99) / [(x^2 - 9)(x^2 + 3x)]
B. To find the excluded values, we look for values of x that would make the denominators zero, as division by zero is undefined. In this case, the excluded values occur when:
(x^2 - 9) = 0 --> x = -3, 3
(x^2 + 3x) = 0 --> x = 0, -3
So, the excluded values are x = -3, 0, and 3.
C. To classify each type of discontinuity, we examine the excluded values and the behavior of the function around these points.
At x = -3, we have a removable discontinuity or hole since the denominator approaches zero but the numerator doesn't. The function can be simplified and defined at this point.
At x = 0 and x = 3, we have vertical asymptotes. The function approaches positive or negative infinity as x approaches these points, indicating a vertical asymptote.
Therefore, the types of discontinuities are: removable discontinuity at x = -3 and vertical asymptotes at x = 0 and x = 3.
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you take a loan out to finance $175,000 on a house. if the rate is 3% and compounds continuously, how much will the loan cost after 30 years?
Answer:approximately $396,849.46 after 30 years with continuous compounding.
Step-by-step explanation:
To calculate the cost of the loan after 30 years with continuous compounding, we can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = the total amount after interest
P = the principal amount (loan amount)
e = Euler's number, approximately 2.71828
r = interest rate per period
t = time in years
Given:
Principal amount (loan amount), P = $175,000
Interest rate, r = 3% = 0.03 (as a decimal)
Time, t = 30 years
Using the formula, we can calculate the total amount (A):
A = $175,000 * e^(0.03 * 30)
Now, let's calculate the cost of the loan after 30 years:
A = $175,000 * 2.71828^(0.03 * 30)
Using a calculator or software, we find:
A ≈ $396,849.46
Therefore, the loan will cost approximately $396,849.46 after 30 years with continuous compounding.
Help please with this question
Answer:
84
Step-by-step explanation:
a² + b² = c²
4² + b² = 10²
16 + b² = 100
b² = 100 - 16
b² = √84
Answer:
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Step-by-step explanation:
Using Pythagorean theorem
hyp² = adj² + opp²
10² = 4² +b²
100-16 = b²
84= b²
√84 = b²
.°. b = 9.17
or b = √84
Solve for x: 2(4-x)-3(x+3)=-11
Answer:
x=2
Step-by-step explanation:
I don’t really have an explanation, it was all mental math
Answer:
[tex]\sf x=2[/tex]Step-by-step explanation:
[tex]\sf 2(4-x)-3(x+3)=-11[/tex]
Expand:-
[tex]\sf 2\left(4-x\right)-3\left(x+3\right)[/tex][tex]\sf 8-2x-3\left(x+3\right)[/tex][tex]\sf 8-2x-3x-9[/tex][tex]\sf -5x-1[/tex][tex]\sf -5x-1=-11[/tex]Now, add 1 to both sides:-
[tex]\sf -5x-1+1=-11+1[/tex][tex]\sf -5x=-10[/tex]Divide both sides by -5:-
[tex]\sf \cfrac{-5x}{-5}=\cfrac{-10}{-5}[/tex][tex]\sf x=2[/tex]Therefore, the value of x is 2!
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How many roots do the functions have in common f(x)=x^2+x-6
To find the common roots between two functions, we need to find the roots (or solutions) of each function individually and then identify the shared solutions.
For the function f(x) = x^2 + x - 6, we can find the roots by setting the function equal to zero and solving for x:
x^2 + x - 6 = 0
To factorize this quadratic equation, we need to find two numbers that multiply to -6 and add up to 1 (the coefficient of x). The numbers that satisfy these conditions are 3 and -2:
(x + 3)(x - 2) = 0
Setting each factor equal to zero:
x + 3 = 0 or x - 2 = 0
Solving for x in each equation:
x = -3 or x = 2
Therefore, the function f(x) = x^2 + x - 6 has two roots: x = -3 and x = 2.
To find the common roots between this function and another function, we would need to know the second function. If you provide the second function, I can help determine if there are any shared roots.
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The diagrams show a polygon and the image of the polygon after a transformation.
Use the diagrams to determine which statements are true. Select all statements that are true.
The correct statements regarding the transformations are given as follows:
Parallel lines will always be parallel after a reflection.Lines that are not parallel will never be parallel after a translation.What are transformations on the graph of a function?Examples of transformations are given as follows:
A translation is defined as lateral or vertical movements.A reflection is either over one of the axis on the graph or over a line.A rotation is over a degree measure, either clockwise or counterclockwise.For a dilation, the coordinates of the vertices of the original figure are multiplied by the scale factor, which can either enlarge or reduce the figure.Parallel lines are lines that have the same slope, that is, lines that do not intercept, and the transformations do not change whether the lines are parallel or not.
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a) What fraction of an hour is 40 minutes, in its simplest b) I sleep 8 hours a night. What fraction of a day is this? c) How many hours is of a day? How many hours is 1 5 pond of her n
a) The value of fraction is,
⇒ 2 / 3
b) The value of fraction is,
⇒ 1 / 3
c) There are 24 hours in a day.
Now, We can simplify all the fraction as,
a) To find fraction of an hour is 40 minutes,
Since, 1 hour = 60 minutes
Hence,
⇒ 40 / 60
⇒ 4 / 6
⇒ 2 / 3
b) Since, 1 day = 24 hours
Hence, we get;
⇒ 8 / 24
⇒ 1 / 3
c) We know that,
⇒ 1 day = 24 hours
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Lets find the square of the no. from 1 to 10. Then observe the digits at one's place of each square no. what did you notice Write a short note.
The observation of the pattern is discussed below.
When we calculate the squares of the numbers from 1 to 10 and observe the digits at the one's place of each square, we notice a pattern:
1²=1
2²=4
3²=9
4²=16
5²=25
6²=36
7²=49
8²=64
9²=81
10²=100
If we focus on the digits at the one's place, we can see that they form a repeating pattern: 1, 4, 9, 6, 5, 6, 9, 4, 1, 0. This pattern repeats itself as we calculate the squares of higher numbers.
This observation is known as the "digit at one's place pattern" or the "units digit pattern." It occurs because the square of any number depends only on the digit at the one's place of that number. Hence, when we square numbers that have the same digit at the one's place, we get the same digit at the one's place in the result.
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Square root square for cube rootMcmfelssmmxemkwkwvgg. Guggenheim
The square root of the number 32 and the values of the perfect squares before and after 32 indicates;
5 < √(32) < 6
What are the methods for calculating the square root of a number?The square root of a number can be calculated by using the following methods; 1. Estimation, 2. Longhand method, 3. Calculator, and 4. Newton method.
The square root of 32 is; √(32) ≈ 5.66
Therefore, the value of the square root of 32 is between 5 and 6, and we get;
The square root of 32 is between the square root of 25 = 5², and the square root of 36 = 6², and the completed inequality can be expressed in the form;
5 < √(32) < 6
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find the length represented by x for each pair of similar triangles 12in x 20in 15in 40in 25in
The length x in the similar triangles is given as follows:
x = 15 cm.
What are similar triangles?Two triangles are defined as similar triangles when they share these two features listed as follows:
Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.The proportional relationship for the side lengths in this triangle is given as follows:
x/25 = 9/15 = 18/30
Hence the value of x is obtained as follows:
x/25 = 9/15
15x = 25 x 9
x = 25 x 9/15
x = 15 cm.
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Can someone answer this please
Answer: N= 12
Step-by-step explanation: if you follow PEMDAS, you take (4^3)^4 and multiply 3*4 which is 12.
Because the base of 4^12=4^n is the same you leave it alone and N is equal to 12
Answer:
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The central angle of the given circle is seen as: ∠GQH
How to identify the central angle?A central angle of a circle is defined as an angle that exists between two radii with the vertex at the center. The central angle of an arc is also defined as the central angle subtended by the arc. The measure of an arc is the measure of its central angle.
We are given the arc name as Arc GEH.
From the definition above, it is very clear that the central angle will be ∠GQH because it includes the two radii with the vertex at the center.
Thus, we conclude that the correct central angle from the given arc is stated as ∠GQH
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