Answer:
Option 1 - There is no extraneous solution i.e. 0.
Step-by-step explanation:
Given : Expression [tex]\frac{9}{n^2+1}=\frac{n+3}{4}[/tex]
To find : How many extraneous solutions does the equation have ?
Solution :
First we solve to expression to determine the extraneous solution,
[tex]\frac{9}{n^2+1}=\frac{n+3}{4}[/tex]
Cross multiply,
[tex]9\times 4=(n+3)(n^2+1)[/tex]
[tex]36=n^3+n+3n^2+3[/tex]
[tex]n^3+3n^2+n-33=0[/tex]
An extraneous solution is defined as a solution, such as that to an equation, that emerges from the process of solving the problem but is not a valid solution to the problem.
The equation form is a cubic function so it has 3 solutions.
Therefore, There is no extraneous solution.
Classify each pair of labeled angles as complementary, supplementary, or neither. Drag and drop the choices into the boxes to correctly complete the table. Each pair of angles may belong to more than one category. complementary supplementary neither Two angles, on the left a fifty three degree angle and on the right a one hundred twenty seven degree angleTwo angles, on the top a thirty four degree angle and on the bottom a fifty six degree angleTwo lines intersect with an angle on the top left labeled sixty seven degrees and on the bottom right sixty seven degrees
Answer:
Step-by-step explanation:
Since it is given that when two lines intersect, the angle on the top left is 53° and 127°, thus they both form supplementary angles as the sum of both angles that is 53+127=180°.
Also, from the given information, the angle on the top is 34° and on the bottom is 56°, they both form a complementary angle pair, a sthe sum of both the two angles is 90° as 56+34=90°.
Also, the angle on the top left is =67° and the angle on the bottom right =67°, they both form vertical pair angles as both the angles are vertically opposite to each other.
If s = 1 over 2 unit and A = 12s2, what is the value of A, in square units? ____ square unit(s). (Input whole number only.)
the answer is three square units
Keller boat travels 24mph. find the rate of the river if she can travel 6 mi upstream. in the same amount of time she can go 10 mi downstream.
Carly bought a new house for $125,000. The value of the house appreciates approximately 3.5% each year. What will be the value of the house after 10 years
Simplify the sum 4/m+9+5/m^2-81
A. 9/(m-9)(m+9)
B. 4m+41/(m-9)(m+9)
C.9/m2+m-72
D.4m-31/(m-9)(m+9)
Earth's diameter at the equator is 7,926 miles. Find the distance around Earth at it's equator to the nearest tenth.
inverse of f(x)=5x+4
The president of the math club is conducting a survey to see where the twelfth-grade class wants to go on their field trip. Instead of asking the whole class, she surveys only the twelfth-grade members of the math club. She records their choices and plans to present the results to the school principal. What type of sampling did she use?
The answer is convenience sampling.
Step-by-step explanation:
As per the given scenario, the president of the math club is conducting a survey to see where the twelfth-grade class wants to go on their field trip and she surveys only the twelfth-grade members of the math club.
This is convenience sampling as here the samples are the closest people available. Convenience sampling is a method where the samples are taken who are close to hand.
Here also the math club president is asking the math club students only. This is why it is convenience sampling.
Ben has b dollars. Cam has 7 fewer dollars than Ben. How many dollars does Cam have? Write your answer as an expression.
Answer:
Cam has [tex]b-7[/tex] dollars.
Step-by-step explanation:
Here b represents the number of dollars Ben has,
Given,
Cam has 7 fewer dollars than Ben,
So, the number of dollars cam has = The number of Ben's dollar - 7
[tex]=b-7[/tex]
Hence, the expression that represents cam's dollar is,
[tex]' b-7 '[/tex]
The length of a side of a rectangle is 2 units less than a number, and the width is 4 units more than the length. Which of the following expressions represents the area of the rectangle, in square units?
the product of nine and x is greater than six more than the product of three and x...?
You buy a house for $130,000. It appreciate 1.6% per year. identify the initial amount, growth rate and growth factor for the situation above. Then great an equation that will model it.
What would happen to a monthly payment if the interest rate increased
If the interest rate increases it is expected the monthly payment also increases.
What is the interest rate?This is usually a low percentage of money paid to the bank or a similar institution for borrowing money. The interest rate is established when the loan is approved and it is proportional to the amount of money that needs to be paid.
What would happen if the interest rate increased?As both the payment and the interest rate are directly related if the interest rate increases, the amount of money to be paid would also increase.
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Find the radius and the circumference to the nearest hundredth when d ≈ 3.8 in. Use 3.14 for π.
The radius is approximately 1.9 in and the circumference is approximately 11.94 in, both rounded to the nearest hundredth.
We have,
If we let d be the diameter of a circle, then the radius of the circle, r, is half of the diameter.
Therefore, we can find the radius of the circle by dividing the diameter by 2:
r = d/2
In this problem,
d ≈ 3.8 in, so we have:
r = 3.8/2 = 1.9 in
To find the circumference of the circle, we can use the formula:
C = 2πr
where π is approximately equal to 3.14 and r is the radius we just found. Substituting in the values, we get:
C = 2 x 3.14 x 1.9 ≈ 11.94 in
Therefore,
The radius is approximately 1.9 in and the circumference is approximately 11.94 in, both rounded to the nearest hundredth.
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A probability experiment consists of rolling a a 6 6-sided die. find the probability of the event below. rolling a number with exactly 2 not necessarily unique prime factors number with exactly 2 not necessarily unique prime factors
The probability of rolling a number with exactly two prime factors on a six-sided die is 1/3, as there are two outcomes (4 and 6) with exactly two prime factors and six possible outcomes in total.
The student is asking about the probability of an event in a probability experiment involving rolling a single six-sided die. The specific event of interest is rolling a number with exactly two, not necessarily unique, prime factors. On a standard six-sided die, the faces are labeled with the numbers 1 through 6. When considering the numbers on a die with two prime factors, we must first identify which of these numbers have exactly two prime factors. The numbers are:
4 has two prime factors: 2 and 2 (2 squared).6 has two prime factors: 2 and 3.The other numbers (1, 2, 3, and 5) have fewer than two prime factors. Since 4 and 6 are the only outcomes with exactly two prime factors, we have two favorable outcomes out of six possible outcomes on a six-sided die.
Thus, the probability of rolling a number with exactly two prime factors is:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 2 / 6 = 1 / 3
Therefore, the probability of the event is 1/3, or approximately 0.3333 (repeating).
Finley's pumpkin had a mass of 6.5 kilograms before he carved it. After carving it, the pumpkin had a mass of 3.9 k.g.
What was the percent decrease in the mass of the pumpkin?
Which of the points listed is the same distance from the x-axis as the point (7, 8.75)?
Answer:
(7,-3.25)
Step-by-step explanation:
How would the domain and range of the function y= 1/4x-6 be determined
Answer: Create a table or a graph of the function. The domain represents all input values and the range represents all output values. The domain and range contain all real numbers
Combine like terms to simplify the expression below 5y-8x-y+12x
square root of -72 written in terms of i
Greg drew a pair of parallel lines and a line segment next to each other on a chalkboard. Which of these statements best compares the pair of parallel lines and the line segment? (1 point) Parallel lines and the line segment have no dimensions of measurement. The parallel lines and the line segment always meet at a common endpoint which is called the vertex. Parallel lines and a line segment cannot lie on the same plane at the same time because they do not overlap. The parallel lines extend infinitely in both directions, and the line segment has two endpoints.
Answer: If drew drew a pair of lines and draw the segment between them, in a way that the segment is delimited by both lines, then:
If two lines are parallel, then they will never overlap each other, and if you draw a segment between them, then the segment will have two endpoints (one at each intersection with the lines)
So the correct answer is that the parallel lines extend infinitely in both directions, and the line segment has two endpoints.
Find all the points where the tangent plane to this ellipsoid is parallel to the plane y-8x-4z = 0
what is the discount on shirts if shirts cost $24 and there is a discount 25%
Step-by-step explanation:
25% × $24 = $6
Subtract the discount from the original
24 - 6 = $18.00
If the graph of the function h defined by h(x)=-3x^2+3 is translated vertically upward by 3 units , it becomes the graph of a function g. Find the expression for g(x)
A video game club has 42 members. The number of high school members is six less than twice the number of middle school members. Which expression represents the number of high school members in the club?
Answer:
2x-6
Step-by-step explanation:
when derek planted a tree it was 36 inches tall. the tree grew 1 1/4 inches per year the tree is now 44 3/4 inches tall. how many years ago did derek lant the tree?
find x intercepts of y=-3^× + 2
Lars deposited $50 into a savings account. According to the rule of 72, what interest rate will cause his money to double in approximately 29 years?
Answer:
Step-by-step explanation:
The answer is 2.5%
Clayton wants to make a cylindrical case that will fit a bass drum with a height of 14 inches and a diameter of 24 inches. With is the surface area of the case? Use 3.14 \pi[tex] \pi [/tex]
Find the sum of each row in the table. Explain why these sums make sense.
Table:
Food | Rent | Transportation
1/4 6/10 3/20
25%. 60%. 15%
0.25 0.60 0.15
Final answer:
The sums of each row in the table represent allocations of a whole expressed in different formats (fractions, percentages, and decimals), and they all add up to 1 or 100%, signifying a full allocation of resources.
Explanation:
To find the sum of each row in the provided table, we add the numbers given within that row. Since the table is arranged with fractions, percentages, and decimals that all represent proportions of a whole, the sum of each row should theoretically be equal if converted into the same format. For instance, we should expect each row to total 1 or 100% if we are discussing a full allocation of resources like a budget.
For the first row, we need to add the fractions: 1/4 + 6/10 + 3/20. To do this, we'd need a common denominator, which is 20. So we get (5/20) + (12/20) + (3/20) = 20/20, which simplifies to 1.
The second row represents percentages and they need to total 100%: 25% + 60% + 15% = 100%
Finally, the third row lists decimals which should sum up to 1: 0.25 + 0.60 + 0.15 = 1.00
All three rows make sense because they represent different ways of expressing the whole, which is split into portions allocated to Food, Rent, and Transportation.