Simplify the expression 7x^2y^2 − 3xy − 8xy + 4x^2y^2



1. 11x^2y^2 + 11xy

2. 11x^4y^4 − 11x^2y^2

3. x2y2

4. 11x^2y^2 − 11xy

1) 3/7

2) 9/21

3) 150/350

Volume is the quantum of space an object occupies. Saddie uses 8 pints of lemon- lime juice rather of orange juice.

This is simply because there are 4 cups of juice in 1 liter. volume is a measure of space possessed by matter.

It is frequently quantified using SI deduced units or colorful US Customary or Imperial units. The description of length refers to volume.

A liter is a measure of commodity liquid, like milk or makeup. A gallon is four liters.

Question:

Sadie is making punch. how numerous further quarts of bomb lime juice will she use than orange juice?

constituents for punch-

8qts Lemon Lime Juice. 4 scoops of vanilla ice cream and 8 mugs of orange juice

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The linear equation that shows the interest earned from each investment is (d): "4a + 6b + 5c = 950"

Investment refers to the act of allocating money or other resources to an asset or venture with the expectation of generating a profit or some other form of return over a period of time.  The primary goal of investing is to use the available resources to generate a return that is greater than the initial investment, thus growing wealth over time.

A linear equation is an algebraic equation in which the highest power of the variable is one. In other words, a linear equation is a polynomial of degree one. It represents a straight line when plotted on a graph. The general form of a linear equation with one variable, x, is:

ax + b = 0

In the given question,

Let's assume that Mr. Silverstone invested a dollars in the first annuity with an interest rate of 2%, b dollars in the second annuity with an interest rate of 4%, and c dollars in the bond with an interest rate of 5%. The interest earned from each investment can be calculated as follows:

Interest earned from the first annuity = 0.02a

Interest earned from the second annuity = 0.04b

Interest earned from the bond = 0.05c

The total interest earned from all three investments together is given as $950. Therefore, we can write the equation:

0.02a + 0.04b + 0.05c = 950

This is the same as option (c) given in the question: "0.04a + 0.06b + 0.05c = 950". However, option (c) has some errors in the coefficients, as the interest rates for the annuities were given as 2% and 4%, not 4% and 6%.

Therefore, the linear equation that shows the interest earned from each investment if the total was $950 is:

0.02a + 0.04b + 0.05c = 950

This can also be simplified as:

2a + 4b + 5c = 95000 (by multiplying both sides by 100 to remove the decimals)

So, the correct option is (d): "4a + 6b + 5c = 950".

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The ratio of fiction books to nonfiction books in the library is 5:3.

What are Ratios?

A ratio is a comparison of two or more quantities that have the same units or are of the same kind. It is expressed as a fraction, using a colon or as a quotient of the two quantities.

Let the number of fiction books in the library be 5x and the total number of books be 8x (since the ratio of fiction books to total books is 5:8).

Then, the number of nonfiction books in the library is 8x - 5x = 3x.

Therefore, the ratio of fiction books to nonfiction books in the library is 5x : 3x, which simplifies to:

5x/3x = 5/3

So, the ratio of fiction books to nonfiction books in the library is 5:3.

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B. Lela walked f miles yesterday, and miles fewer today.

What is expression?

One or more variables or numbers are combined with one additional action to form an expression.

The situation that could be described by the expression f + 1/2 is:

B. Lela walked f miles yesterday, and miles fewer today.

The expression f + 1/2 represents the total distance that Lela walked over two days, where "f" represents the distance she walked yesterday, and "1/2" represents the distance she walked today.

Option B describes the situation where Lela walked "f" miles yesterday and "1/2" times fewer miles today (or, equivalently, "1/2" times the distance she walked yesterday).

Therefore, the expression f + 1/2 is a valid way to describe this situation.

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The answer response are:

   A duck with wings: Likely

   Duck number 7: Unlikely

   A duck with a number greater than 3: Certain

   Duck number 15: Impossible

   A duck with a number greater than 10: Unlikely

   A duck with a number: Certain

   Duck number 4: Unlikely

   A duck with sunglasses: Impossible

   A duck with a hat: Unlikely

Lastly,  An even-numbered duck: Likely

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See transcribed text below



Date:

Period:

What is the probability you will choose each duck described below? Write the answer as a fraction in lowest terms and place it in the appropriate box (certain, likely, unlikely, impossible).

33

1. A duck with wings

2. duck number 7

3. a duck with a number greater than 3

4. duck number 15

5. a duck with a number greater than 10

6. a duck with a number

7. duck number 4

8. a duck with sunglasses

9. a duck with a hat

10. an even-numbered duck

The ducks are numbered From one through twelve!

Kibb

Certain

Likely

Even

Unlikely Impossible

ว

The simplified functions of f(g(x)) and g(f(x)) are: f(g(x))=x3 and g(f(x))=x3−6x2+12x−6

To find the function f(g(x)), we need to substitute g(x) into f(x). This means we will replace the x in f(x) with the expression for g(x):

f(g(x))=f(x3+2)=(x3+2)−2

Simplifying this expression gives us:

f(g(x))=x3

Similarly, to find the function g(f(x)), we need to substitute f(x) into g(x):

g(f(x))=g(x−2)=(x−2)3+2

Simplifying this expression gives us:

g(f(x))=x3−6x2+12x−6

Therefore, the functions f(g(x)) and g(f(x)) are:

f(g(x))=x3

g(f(x))=x3−6x2+12x−6

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Note that the correct theorem or definition that justifies the given statement for the diagram is the definition of Right angle postulate.

The postulate indicates that if two lines intersect and make the two adjacent angles equal to each other, then each of the equal angle is a right angle. Also, the two lines that intersect this way is said to be perpendicular to each other.

Since the ∠MRS ≅ ∠MRO, we can state that the correct theorem or definition that justifies the given statement for the diagram is the definition of Right angle postulate.

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Answer:

nothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanks

The domain and range for the given functions are: a) Domain: (-∞, -2) ∪ (2, ∞), Range: (0, ∞) b) Domain: (-∞, ∞), Range: [9/2, ∞) c) Domain: (-∞, 2) ∪ (2, ∞), Range: (-∞, 0) ∪ (0, ∞)

The domain of a function is the set of all possible values of x that can be input into the function. The range of a function is the set of all possible values of y that can be output from the function.

a) y = 1/√(x^2 - 4)
The domain of this function is all values of x that make the denominator nonzero and the square root positive. Therefore, x^2 - 4 > 0, which means (x - 2)(x + 2) > 0. The solution to this inequality is x < -2 or x > 2. So the domain is (-∞, -2) ∪ (2, ∞).

The range of this function is all positive values of y, since the square root in the denominator is always positive. So the range is (0, ∞).

b) y = (2x^2) - 2x + 5
The domain of this function is all real numbers, since there are no restrictions on the values of x. So the domain is (-∞, ∞).

The range of this function is all values of y greater than or equal to the vertex of the parabola. The vertex of this parabola is (-b/2a, f(-b/2a)), which is (1/2, 9/2). So the range is [9/2, ∞).

c) y = 1/(1 - 1/(x - 1))
The domain of this function is all values of x that make the denominator nonzero. Therefore, 1 - 1/(x - 1) ≠ 0, which means x ≠ 2. So the domain is (-∞, 2) ∪ (2, ∞).

The range of this function is all values of y except 0, since the denominator can never be zero. So the range is (-∞, 0) ∪ (0, ∞).

In conclusion, the domain and range for the given functions are:
a) Domain: (-∞, -2) ∪ (2, ∞), Range: (0, ∞)
b) Domain: (-∞, ∞), Range: [9/2, ∞)
c) Domain: (-∞, 2) ∪ (2, ∞), Range: (-∞, 0) ∪ (0, ∞)

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Since speckled chickens have both b and w feathers, they must inherit one allele for w feathers and one allele for b feathers. Therefore, to produce the greatest percentage of speckled chickens, the breeder should cross a w chicken with a b chicken.

The Punnett square for this cross would be:

    | F         F

A | A F   A F

A | A F   A F

This shows that all offspring (100%) will be heterozygous for both white and b feathers (genotype: AFAF), which is the genotype for speckled feathers. Therefore, the percentage of speckled offspring that will result from this cross is 100%.

Putting the alleles for the hen and rooster in the blank boxes outside the Punnett square would look like this:

    | F        F

A | A F   A F

A | A F   A F

Hen Rooster

The number of child tickets were sold that day are 73.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We are given that;

Cost of child admission= $5.30

Cost of adult admission= $8.70

Now,

Let's assume that "c" represents the number of child tickets sold, and "a" represents the number of adult tickets sold. We can create two equations based on the given information:

c + a = 163 (equation 1: the total number of tickets sold)

5.30c + 8.70a = 1169.90 (equation 2: the total sales)

We can use equation 1 to solve for "a" in terms of "c":

a = 163 - c

Substituting this expression for "a" into equation 2, we get:

5.30c + 8.70(163 - c) = 1169.90

Simplifying and solving for "c", we get:

5.30c + 1418.10 - 8.70c = 1169.90

-3.4c = -248.20

c = 73

Therefore, by algebra the answer will be 73.

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With nearly 68% of genuine votes going to Venkaiah Naidu and 32% going to Gopalkrishna Gandhi, the opposition candidate, who earned 244 votes, the difference between the two candidates was bigger at 272 than Mr. Gandhi's total.

According to the given information, M Venkaiah Naidu received 516 votes out of the valid votes cast in the vice-presidential election. The total number of valid votes cast was not explicitly mentioned in the statement, but we can calculate it by adding up the votes received by the two candidates. M Venkaiah Naidu received 516 votes, while his opponent Gopalkrishna Gandhi received 244 votes. Therefore, the total number of valid votes cast was 760 (516 + 244).

To calculate the percentage of valid votes that M Venkaiah Naidu received, we need to divide his number of votes by the total number of valid votes cast and then multiply by 100. Therefore, M Venkaiah Naidu received approximately 68% of the valid votes (516/760 x 100).

It's important to note that this calculation only considers the valid votes cast and not any abstentions or spoiled ballots. Additionally, this percentage reflects the support received by M Venkaiah Naidu among the MPs who voted and does not necessarily reflect the opinions of the broader public or electorate.

Complete question:

According to BJP sources, around two dozen MPs from opposing parties disobeyed their leaders and supported M Venkaiah Naidu for vice president of the NDA. Against the estimated 495 votes of pledged support, Mr. Naidu received 516 votes.

With nearly 68% of genuine votes going to Venkaiah Naidu and 32% going to the opposition's Gopalkrishna Gandhi, who earned 244 votes, the difference between the two candidates was bigger at 272 than Mr. Gandhi's total.

What is the % of the votes did MRS Naido receive to write the answers to the east wholw%

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Answer:

1.3 × .85 = 1.105

10.5% greater than original

Answer:

we have to check the chemical property of the daisy perfume

Answer:its 80 i did the same problem

Step-by-step explanation:

In the diagram, the length of minor arc AB is approximately 3.9 inches

From the question, we are to calculate the length of the minor arc AB

To calculate the length of an arc, we can use the formula:

Arc Length = (Central Angle / 360) x (2πr)

Where:

Central Angle is the angle formed by the two radii at the center of the circle

r is the radius of the circle

From the given information,

Central angle = 56°

r = 4 in

Substituting the given values, we get:

Arc Length = (56° / 360) x (2π x 4 in)

Arc Length = 3.9095 in

Arc Length ≈ 3.9 in

Hence, the length of minor arc AB is approximately 3.9 inches

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The quadratic equation f(x) = 3 · x² + 36 · x + 33 shows the quickest choice to determine the y-intercept. The y-intercept is equal to (0, 33).

In this problem we must look up for the quickest way to determine the y-intercept of a quadratic equation, this can be done by evaluating at x = 0 when the expression is of the form, that is, standard form:

f(x) = a · x² + b · x + c

Where a, b, c are real coefficients.

The standard form f(x) = 3 · x² + 36 · x + 33 may help us to determine the y-intercept quickly. The y-intercept is equal to (0, 33).

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Answer:

<RHF = 68°

Step-by-step explanation:

<RHG and <FHY are vertical opposite angle which mean they equal to each other.

<RHG = <FHY

(6m+88) = (7m+84)

88 - 84 = 7m - 6m

4 = m

Plug m=4 into the <RHG to solve for the measurement.

<RHG = 6m+88

<RHG = 6*4+88

<RHG = 24+88

<RHG = 112°

<RHG and <RHF are supplementary angle which mean they both linear adding up to 180°

<RHF + <RHG = 180°

<RHF + 112° = 180°

<RHF = 68°

The formula for the exponential function that passes through the given points is (a) 3(2ˣ) and (b) g(x) = (2(3)^(1/2))((1/3)^(x/6)).

To find the formula for an exponential function that passes through two points, we can use the formula:
f(x) = abˣ
where a and b are constants. We can use the two points to create a system of equations and solve for the constants.

For part a:
3/4 = ab⁻²
12 = ab²

Dividing the second equation by the first equation gives us:
16 = b⁴

Taking the fourth root of both sides gives us:
b = 2

Plugging this value back into the first equation gives us:
3/4 = a2⁻²
3/4 = a(1/4)
a = 3

So the formula for the exponential function is:
f(x) = 3(2ˣ)

For part b:
6 = ab⁻³
2 = ab³

Dividing the second equation by the first equation gives us:
1/3 = b⁶

Taking the sixth root of both sides gives us:
b = (1/3)^(1/6)

Plugging this value back into the first equation gives us:
6 = a(1/3)^(-1/2)
6 = a(3)^(1/2)
a = 6 / (3)^(1/2)
a = 2(3)^(1/2)

So the formula for the exponential function is:
g(x) = (2(3)^(1/2))((1/3)^(x/6))

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Expanding the left-hand side, we have:

(px + 4) (9x + 3) = 9px^2 + 3(4p + 9)x + 12

Comparing this to the right-hand side, we see that we must have:

9p = 18 (to get the x^2 term on the right)

4p + 9 = r (to get the x term on the right)

The first equation gives us p = 2, and substituting into the second equation gives us:

4(2) + 9 = r

r = 17

So one possible value of r is 17. To find the other, we use the fact that p + q = 9. Substituting p = 2, we have:

2 + q = 9

q = 7

Now we can use the same equation as before to find the other value of r:

4(2) + 9 = r

r = 17

So the two possible values of r are 17 and 17.

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The number of minutes that could have passed if the pool now has less than 74 gallons of water left is greater than 9 minutes.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

The amount of water remaining in the pool after x minutes is given by:

110 - 4x

We want to find the number of minutes, x, such that the pool now has less than 74 gallons of water left.

110 - 4x < 74

To solve for x, we can first subtract 110 from both sides of the inequality:

-4x < 74 - 110

Simplifying, we get:

-4x < -36

Divide both sides of the inequality by -4,

x > 9

Therefore, the number of minutes that could have passed if the pool now has less than 74 gallons of water left is greater than 9 minutes.

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Answer:

277 milliliters

Step-by-step explanation:

945-668= 277

The total number of months he made deposits and multiply that by the monthly deposit amount.

Chase started an IRA at the age of 26 and deposited $400 each month until he retired at the age of 65. To determine the amount of money Chase deposited over the length of the investment, we need to calculate the total number of months he made deposits and multiply that by the monthly deposit amount.

Number of months = (Retirement age - Starting age) * 12
Number of months = (65 - 26) * 12
Number of months = 468

Total deposits = Number of months * Monthly deposit amount
Total deposits = 468 * 400
Total deposits = $187,200

To determine how much Chase made in interest upon retirement, we need to subtract the total deposits from the retirement savings.

Interest = Retirement savings - Total deposits
Interest = $838,879.58 - $187,200
Interest = $651,679.58

Therefore, Chase deposited a total of $187,200 over the length of the investment and made $651,679.58 in interest upon retirement.

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Ms. Twinkle walks a total of 6.6 miles around the park.

What is perimeter ?

Perimeter is the total distance around the outside of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape.

To find how far Ms. Twinkle walks, we need to find the perimeter of the rectangle-shaped park, which is the sum of the lengths of all its sides.

The length of the park is 2 miles and the width is 1 3/10 miles. We can write the width as a mixed number of 1 + 3/10 = 13/10 miles.

Therefore, the perimeter of the park is:

Perimeter = 2(length + width)

Perimeter = 2(2 + 13/10)

Perimeter = 2(20/10 + 13/10)

Perimeter = 2(33/10)

Perimeter = 66/10

Perimeter = 6.6 miles

Therefore, Ms. Twinkle walks a total of 6.6 miles around the park.

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Answer:

I think question #1 is C

Question #2 is C

and Question #3 is A

the bigger number x= 61 and the smaller number y = 11. The system of equations are x + y= 72 and x - y = 50

The sum of two numbers is 72 can be expressed as a linear equation: x + y = 72. The difference of the two numbers is 50 can be expressed as a linear equation: x - y = 50. We can set up a system of equations to determine the values of x and y:

First equation: x + y = 72

Second equation: x - y = 50

To solve the system of equations, we can use the elimination method. We can add the two equations together to eliminate the y variable:

x + y = 72

x - y = 50

--------------

2x = 122

Next, we can solve for x by dividing both sides of the equation by 2:

2x/2 = 122/2

x = 61

Now that we know the value of x, we can plug it back into one of the equations to find the value of y:

61 + y = 72

y = 72 - 61

y = 11

So the solution to the system of equations is x = 61 and y = 11.

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Answer:

Step-by-step explanation:

The formula to calculate the doubling time for continuously compounded interest is:

t = ln(2) / (r * ln(1 + (r/n)))

where t is the time in years, r is the annual interest rate as a decimal, and n is the number of times the interest is compounded per year (which is infinity for continuous compounding).

For Logan's investment, we have:

r = 0.05

n = infinity

t1 = ln(2) / (0.05 * ln(1 + (0.05/infinity)))

t1 ≈ 13.86 years

For Qasim's investment, we have:

r = 0.06

n = 1

t2 = ln(2) / (0.06 * ln(1 + (0.06/1)))

t2 ≈ 11.55 years

To find the difference in the time it takes for their investments to double, we can subtract t2 from t1:

t1 - t2 ≈ 13.86 - 11.55 ≈ 2.31

So it would take Logan's money approximately 2.31 years longer to double than Qasim's money, to the nearest hundredth of a year.

Answer:

system of equation:

(x,y)

(3,-50)

Step-by-step explanation:

equation solving

Abstract Algebra

By additive inverse property, \( 0_{R} x=0_{R} \) for all \( x \in R \) is hence proved. And by distributive property, \( -(a b)=(-a) b \) is proved.

Question 1: We know that the additive identity of a ring is 0. So, 0+0=0. Now, for any element x in R, we have 0x=(0+0)x=0x+0x. By the additive inverse property, we can subtract 0x from both sides to get 0=0x. So, 0x=0 for all x in R.

Question 2: We know that the additive inverse of an element a in a ring R is -a, such that a+(-a)=0. Now, for any elements a and b in R, we have ab+(-ab)=0. By the distributive property, we can rewrite this as ab+((-a)b)=0. So, -(ab)=(-a)b for all a and b in R.

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Mengxi invested $4,200 in the term deposit paying 5% /year and $5,800 in Canada Savings Bonds paying 3.5% /year. The total interest earned is $413.

Let's assume that Mengxi invests x dollars in the term deposit paying 5% /year, and the remaining (10000 - x) dollars in Canada Savings Bonds paying 3.5% /year.

At the end of the year, Mengxi earns a total of $413 in simple interest. The interest earned from the investment in the term deposit is calculated as 0.05x, while the interest earned from the investment in Canada Savings Bonds is 0.035(10000 - x).

Thus, we can write the following equation to represent the total interest earned:

0.05x + 0.035(10000 - x) = 413

Simplifying the equation, we get:

0.015x + 350 = 413

0.015x = 63

x = 4200

Therefore, Mengxi invested $4,200 in the term deposit paying 5% /year, and $5,800 (10000 - 4200) in Canada Savings Bonds paying 3.5% /year.

To check the answer, we can calculate the interest earned from each investment and add them up:

0.05(4200) + 0.035(5800) = 210 + 203 = 413

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