The given rational expression simplifies to (n^2 - 6)/(n^2 - 2). However, n cannot be equal to ±√2 and ±√5. These are the values that would make the denominator of the original or simplified expression equal to 0.
Explanation:To simplify the given rational expression we must first factor both the numerator and the denominator. The expression is n^4 - 11n^2 + 30/ n^4 - 7n^2 + 10. We recognize this is a quadratic in terms of n^2. Hence, the numerator factors into (n^2 - 6)(n^2 - 5), and the denominator factors into (n^2 - 5)(n^2 - 2).
The simplified version of the expression is (n^2 - 6)/(n^2 - 2) but we need to take into account the restrictions for n which are that n cannot be equal to ±√2 and ±√5. These are the values that would make the denominator of the original or simplified expression equal to 0, thus undefined.
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The rational expression [tex](n^4 - 11n^2 + 30)/(n^4 - 7n^2 + 10)[/tex] simplifies to [tex](n^2 - 6)/(n^2 - 2)[/tex], with restrictions on n being ±√5 and ±√2 since these values would cause the original denominator to be zero.
To simplify the rational expression [tex]n^4 - 11n^2 + 30[/tex] divided by [tex]n^4 - 7n^2 + 10[/tex], we start by factoring both the numerator and the denominator.
Factor the numerator:
→ [tex]n^4 - 11n^2 + 30 = (n^2 - 5)(n^2 - 6)[/tex]
Factor the denominator:
→ [tex]n^4 - 7n^2 + 10 = (n^2 - 5)(n^2 - 2)[/tex]
After factoring, we can eliminate common terms.
The term ([tex]n^2 - 5[/tex]) is present in both the numerator and the denominator and can be cancelled out.
The simplified expression is [tex](n^2 - 6)/(n^2 - 2)[/tex].
We also need to state restrictions on the variable n. These restrictions come from the values that make any denominator zero, which are not allowed.
For the initial fraction, the restrictions are the values of n that make [tex]n^2 - 5[/tex] or [tex]n^2 - 2[/tex] equal to 0. Thus, n cannot be ±√5 or ±√2.
Sandy is driving cross country. She has covered 200 miles from the east coast towards the west coast. She has driven this distance in 2 days.
If Sandy continues to drive at this rate, which equation represents the total number of miles , m, she would cover in d more days?
A
m=2d
B
m=100d+200
C
m=300d
D
m=200d+100
Item 6 Find the amount of time. I=$30, P=$500, r=3% The amount of time is years.
Solve for x X^2+10+12=36
X=-12 or x=2
X
morgan cut exactly 35 strips of wood from a larger piece of wood.Each strip of wood was 2.45 centimeters long.How long was the larger piece of wood?
The larger piece of wood was 85.75 centimeters long based on multiplying the number of strips by the length of each strip.
To find out how long the original piece of wood was, we need to multiply the number of strips by the length of each strip.
Given:
Number of strips: 35
Length of each strip: 2.45 centimeters
Step-by-Step Solution:
Multiply the number of strips by the length of each strip to get the total length: 35 strips * 2.45 cm = 85.75 cmTherefore, the larger piece of wood was 85.75 centimeters long.
this picture shows a magnified view of a tick on a penny. about how long is the tick
you have 3 bolts that are 3/8, 5/16 and 5/8 long. Which is the shortest?
This is a 5th grade Math Problem. Please help.
What is the volume of a cylinder with a radius of 5cm and height of 10cm? Use 3.14 for pi.
3 2/3 + 7 1/5 simplify if possible
The first Earth Day was observed on April 22, 1970. Since then, the week of April 22 has been Earth Week, a time for showing support for environmental causes. Fans Cafe is offering a reduced refill rate for soft drinks during Earth Week for anyone purchasing a Fans mug. The mug costs $2.95 filled with 16 ounces of soft drink. The refill price is $0.50. A 16-ounce drink in a disposable cup costs $0.85. What is the approximate break-even point for buying the mug and refills in comparison to buying soft drinks in disposable cups? a. (5, 7.8) c. (4, 6.7) b. (8, 0.5) d. (7, 5.95)
Let x specify the number of 16 ounce serving
If you buy the mug you acquire the first serving including the mug.
So the price of x is:
295 + 50(x - 1)
the x - 1 here shows that the first serving with the mug.
And then count the whole thing in cents.
The fee of throwaway cups is 85x
So breakeven is computed by:
295 + 50(x - 1) = 85x
295 + 50x - 50 = 85x
245 = 35x
x = 245/35 = 7
Checking this will give us:
mug 2.95 + 50*6 = 5.95
disposable
8.5*7 = 5.95
So the answer is D.
The break-even point occurs after nine soft drink purchases(8,0.5). Hence, the correct option is b.
First, let's consider the cost of the mug with a soft drink:
Mug + Soft drink = $2.95
Next, the cost of each refill:
Refill = $0.50
Then, the cost of a soft drink in a disposable cup:
Disposable cup soft drink = $0.85
To find the break-even point, let's set up the equation. Let x be the number of refills (including the initial drink from the mug):
Cost of mug with initial drink + (Cost per refill × number of refills) = Cost of disposable cup × number of drinks
2.95 + 0.50x = 0.85x
Now we solve for x:
2.95 = 0.85x - 0.50x
2.95 = 0.35x
x = 2.95 / 0.35
x = 8.43
Since we cannot have a fraction of a refill, we will round up to the nearest whole number. Therefore, the break-even point is after 9 refills (including the initial drink from the mug).
The approximate break-even point is after purchasing nine 16-ounce drinks. Therefore, the correct answer is (8, 0.5).
the model below represents the equation 2x + 3 = 11. What is the first step in finding the value of x?
Answer:
B
Step-by-step explanation:
picture:)
Which tax bracket a person Falls into is determined by his or her ?
A. Salary
B. Taxable income
C. AGI
D.Gross income
Answer:
B. Taxable income
Step-by-step explanation:
Taxable income is the amount of money that a person earns in a period of time that can be taxated by the government, you could earn money that is not taxated, for example life insurances from deceased family members is not taxable, also upto a certain amount of money as a gift is not taxable. So the tax bracket a person falls into depends solely on the taxable income that they make in a year.
Final answer:
B: Taxable income
A person's tax bracket is determined by their taxable income, which is their adjusted gross income minus any deductions and exemptions.
Explanation:
The tax bracket into which a person falls is determined by his or her taxable income.
Taxable income is the amount of income that is subject to the official tax rates for each bracket.
This figure is the result of subtracting deductions and exemptions from your adjusted gross income (AGI). It's important to note that taxable income and AGI are not the same, as the latter is your income from various sources minus specific adjustments but before deductions and exemptions.
To calculate taxable income, the equation used is: taxable income = adjusted gross income - (deductions + exemptions).
Income Tax Brackets are the thresholds of income that are taxed at varying rates. As an individual’s taxable income increases, not only does the amount of tax paid increase, but typically so does the percentage of tax on additional income, as the tax rates in higher brackets are usually higher.
A deck of cards has three yellow cards and five green cards. One green card is drawn from the deck and not replaced. One more card is random drawn. Find the probability that the second card is yellow.
3/8
3/7
15/56
The probability that the second card is yellow after one green card is drawn and not replaced from a deck of 8 (3 yellow, 5 green) cards is 3/7. The correct answer is option b) 3/7.
To find the probability that the second card is yellow after drawing one green card (and not replacing it), we can follow these steps:
Determine the total number of cards in the deck after the first green card is drawn. Initially, we have 3 yellow + 5 green = 8 cards. After drawing one green card, there are 7 cards left (2 yellow and 5 green).Since one green card is drawn and not replaced, the number of green cards that remain in the deck is now 4, and the total number of cards left in the deck is 7.Calculate the probability of drawing a yellow card from the remaining 7 cards. There are still 3 yellow cards, so the probability is 3 yellow cards divided by the 7 total remaining cards.Thus, the probability that the second card is yellow is 3/7, which is corresponding to (b).
The pyramid shown has a square base that is 18 inches on each side. The slant height is 16 inches. What is the surface area of the pyramid?
Answer:
txt
Step-by-step explanation:
Yul and Sarah's art class started at 11:25 A.M.The class lasted 30 minutes. Yulieft when the class was done. Sarah stayed an extra 5 minutes to talk with the teacher and then left. Write the time that each student left.Explain how you found each time.
Yul left the class at 11:55 A.M. after it ended, having added 30 minutes to the start time. Sarah stayed for an extra 5 minutes, which implies she departed at 12:00 P.M.
Yul and Sarah's art class started at 11:25 A.M. and it lasted 30 minutes. To find out when Yul left, we simply add 30 minutes to the starting time. Starting at 11:25 A.M., after 30 minutes, it will be 11:55 A.M. That's when Yul left the class.
Sarah stayed an additional 5 minutes after the class to talk with the teacher. So, we add those 5 minutes to the time Yul left, which was 11:55 A.M. If we add 5 minutes to 11:55 A.M., it becomes 12:00 P.M. Therefore, Sarah left the class at noon.
calculate the distance nathan rides his bike if he rides 9/12 mile each day for 3 days
Final answer:
Nathan rides a total distance of 2 1/4 miles when he rides 9/12 of a mile each day for 3 days. To calculate this, multiply the daily distance by the number of days and simplify the result.
Explanation:
To calculate the distance Nathan rides his bike if he rides 9/12 of a mile each day for 3 days, you need to multiply the distance he rides in a day by the number of days he rides.
Distance per day: 9/12 mileNumber of days: 3 daysSo, the total distance Nathan rides is:
9/12 mile/day × 3 days = 27/12 miles
To simplify the fraction:
Divide the numerator (27) and the denominator (12) by their greatest common divisor, which is 3.This gives us 9/4 miles.Convert 9/4 to a mixed number: 9 ÷ 4 = 2 with a remainder of 1, so it's 2 1/4 miles.Therefore, Nathan rides a total distance of 2 1/4 miles over the three days.
A woman borrows $6,000 at 9% compounded monthly, which is to be amortized over 3 years in equal monthly payments. for tax purposes, she needs to know the amount of interest paid during each year of the loan. find the interest paid during the first year, the second year, and the third year of the loan. [hint: find the unpaid balance after 12 payments and after 24 payments.
Find a rational number that is between 9.5 and 9.7
9.5000032 i think i'm not sure
A 8920 note is signed for 160 days at a rate of 6.5% find the proceeds
write the computation in words for an expression that uses all four operations (addition, subtraction, multiplication, and division). Then write the expression for the words
Expression that has all the four basic mathematical operators can be written as [tex](\dfrac{a+b}{2}) \times [c-(a+b)][/tex].
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
Let's take three numbers, a, b, and c.
Now, the expression in the word can be written as, The product of the addition of the first two numbers (a and b), divided by 2 and the sum subtracted from c.
If we try to write the above statement as an expression then we can write it as,
[tex](\dfrac{a+b}{2}) \times [c-(a+b)][/tex]
Hence, An expression that has all the four basic mathematical operators can be written as [tex](\dfrac{a+b}{2}) \times [c-(a+b)][/tex].
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Final answer:
The computation described involves multiplying six by three, adding eight, subtracting two, and then dividing the result by four. This results in the expression ((6 * 3) + 8 - 2) / 4, incorporating all four basic mathematical operations.
Explanation:
Writing the computation in words for an expression that uses all four operations - addition, subtraction, multiplication, and division - helps in understanding the application of these operations in a complex expression. Here's an example:
First, multiply six by three, then add eight to the product. From this sum, subtract two. Finally, divide the result by four. This sequence of operations involves all four basic mathematical operations.
The corresponding expression for the described computation is: ((6 * 3) + 8 - 2) / 4.
Breaking down the expression:
Multiplication: 6 * 3Addition: + 8Subtraction: - 2Division: / 4Write the equation in standard form for the circle passing through ( - 1,3) centered at the origin.
Final answer:
The standard form equation of a circle centered at the origin and passing through (-1,3) is x² + y² = 10, where √10 is the radius of the circle calculated using the distance formula.
Explanation:
To write the equation of a circle in standard form that is centered at the origin and passes through the point (-1,3), you first need to calculate the radius using the distance formula. The distance formula is √((x2-x1)² + (y2-y1)²), where (x1, y1) is a point on the circle and (x2, y2) is the center of the circle. Since the circle is centered at the origin, (0,0), we can compute the radius as follows:
Radius = √((-1 - 0)² + (3 - 0)²) = √(1 + 9) = √10
The standard form of the equation for a circle centered at (h, k) with a radius r is:
(x - h)² + (y - k)² = r²
Since our circle is centered at the origin, h = 0 and k = 0, and the radius r = √10, the equation becomes:
x² + y² = 10
What is the volume of a sphere with a radius of 5 cm
Use 3.14 for pie
The standard form of the equation of a circle is (x−5)2+(y−6)2=1.
What is the general form of the equation?
x2+y2−10x−12y+60=0
x2+y2−10x−12y−62=0
x2+y2+10x+12y+62=0
x2+y2+10x+12y+60=0
Answer:
(A)[tex]x^2+y^2-10x-12y+60=0[/tex]
Step-by-step explanation:
The standard form of the equation of a circle is given as:
[tex](x-5)^2+(y-6)^2=1[/tex]
Simplifying the above given equation, we get
[tex]x^2+25-10x+y^2+36-12y=1[/tex]
[tex]x^2+y^2-10x-12y+36+25=1[/tex]
[tex]x^2+y^2-10x-12y+61=1[/tex]
[tex]x^2+y^2-10x-12y+60=0[/tex]
which is the required general form of the equation.
Hence, option A is correct.
explain why the pattern for the products of 10s facts is a straight column.
You can use the fact that when staying in the same column and walking from row to row, there is addition of 10.
Why is there straight column for multiple of 10 in number counting having 10 columns?First choose a row. Since there are 10 columns per row, thus changing the row by choosing same column will give difference of 10.
Go down in rows on same column and you'll see increment of 10, and go up in rows with same column and you'll see decrement of 10.
]This is the key reason behind that straight columns of multiples of 10s.
Let the number be x
Then moving from row to row on the same column, we will get:
x, x + 10, x + 20, x + 30, ...
If x = 10, we get 10, 20, 30, 40 which are multiples of 10 since
[tex]10 + 10 = 10 \times 2\\10 + 20 = 10 \times 3\\...\\ 10 + 10y = 10 \times (y+1)[/tex]
See the given table below:
[tex]\begin{array}{cccc}\cdots&x&\cdots & 10\\\cdots & x + 10 & \cdots & 10 + 10 = 10 \times 2 = 20\\\cdots & x+ 10 + 10 = x + 20 & \cdots & 20 + 10 = 10 \times 2 + 10 = 10 \times 3 = 30\\\cdots & \cdots & \cdots & \cdots\end{array}[/tex]
The last column, therefore, has multiples of 10 since adding 10 for multiple of 10 is like multiplying 10 by one bigger number which is same as increasing multiples of 10.
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Positive linear relationships are represented by values of the correlation, r, that are _____.
Suppose you borrow 13,000 for four years at 7% toward the purchase of a car.
wade is 6 years older than Mariah in 8 years the sum of their ages will be 80 how old is Wade now
holly is making a stir fry holly measures 5/8 cup of chicken and then adds 1/9 cup more how much chicken did holly use altogether?
Holly used a total of 53/72 cup of chicken for her stir fry, by adding 5/8 cup and 1/9 cup together after converting them to have a common denominator.
Explanation:Holly is making a stir fry and needs to calculate the total amount of chicken she has used.
Initially, she measures 5/8 cup of chicken and then adds 1/9 cup of chicken.
To find the total amount of chicken used, we need to add these two fractions together.
This is a simple arithmetic operation called fraction addition.
First, we find a common denominator for the two fractions, which in this case is 72 (the least common multiple of 8 and 9).
Next, we convert each fraction to an equivalent fraction with the common denominator.
The fraction 5/8 converts to (5×72)/(8×72) = 45/72, and 1/9 converts to (1×72)/(9×72) = 8/72.
Now that the fractions share a common denominator, we can add them:
45/72 + 8/72 = 53/72
The sum of the two fractions gives us the total amount of chicken used by Holly, which is 53/72 cup.
To find out how much chicken Holly used altogether, we need to add the two fractions together. First, we find a common denominator, then convert the fractions to have that denominator. Finally, we add the numerators and keep the denominator the same. Holly used a total of 53/72 cup of chicken for her stir fry.
Explanation:To find out how much chicken Holly used altogether, we need to add the two fractions together.
First, we need to find a common denominator for these fractions. The smallest number that both 8 and 9 can divide into is 72.
Next, we need to convert both fractions to have a denominator of 72. To do this, we multiply the numerator and denominator of each fraction by the same number.
For the first fraction, we multiply both the numerator and denominator by 9, obtaining 45/72. For the second fraction, we multiply both the numerator and denominator by 8, obtaining 8/72.
Now that we have both fractions with a denominator of 72, we can add them together. 45/72 + 8/72 = 53/72.
Therefore, Holly used a total of 53/72 cup of chicken for her stir fry.
if m/\a =150 and /\ a and /\b at supplementary, what is m/\ b
Subtract -7a^2 + 3a -9 from 5a^2 - 6a -4
Answer should be polynomial in standard form
The polynomial in standard form after subtraction will be 12a² - 9a + 5.
What is polynomial?A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.
It simply implies subtracting something from an entity, group, location, etc. Subtracting from a collection or a list of ways is known as subtraction.
The polynomial is given below.
-7a² + 3a - 9 and 5a² - 6a - 4
Subtract -7a² + 3a - 9 from 5a² - 6a - 4, then we have
(5a² - 6a - 4) - (-7a² + 3a - 9)
Simplify the equation, then we have
(5a² - 6a - 4) - (-7a² + 3a - 9)
5a² - 6a - 4 + 7a² - 3a + 9
12a² - 9a + 5
The polynomial in standard form after subtraction will be 12a² - 9a + 5.
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