Designing a Garden

In this activity, you will apply mathematics to problems arising in everyday life and communicate

mathematical ideas using multiple representations.

Part

Melissa is planning a rectangular vegetable garden with a square patch for tomatoes. She wants the length of

the garden to exceed three times the length of the tomato patch by 2 feet. She also wants the garden's width

to exceed the width of the tomato patch by 5 feet.

Let x represent the length, in feet, of the square tomato patch.

Question 1

? Question

Write expressions to represent the length and width of Melissa's vegetable garden in terms of x.

Enter the correct answer in the box. Y= ?+?

1. You can solve a system of equations using graphs when there are no decimals or fractions in the equations. This can allow you to almost precisely plot a graph, and determine the values of the variables.

2. You can use the substitution method when one (or both) of the equations is already solved for one of the variables.

3. Elimination is best used when the equations are written in the form Ax + B = C, and also when the coefficients are values not equal to 1.

Answer:

x=-9

Step-by-step explanation:

M(slope)=y2-y1/x2-x1

m=-5-5/-9+9

m= -10/0

This means the slope is undefined. Whenever the slope is undefined, the line is vertical and is passing through the x-axis and parallel to the y-axis. Take the given coordinate (-9,5) and all you do is put x= -9. That's the equation of the line.

Answer:

x=2

Step-by-step explanation:

Combine like terms, add 8 to both sides of the equation, simplify, divide both sides by the same term, simplify

Answer:

x = 2

Step-by-step explanation:

1. Combine like terms

15x - 8 - 3x = 16

1 2  −  8  =  1 6

2. Add  8  to both sides of the equation

1 2  −  8  =  1 6

      +8   +8

3. Simplify

12x = 24

12x/12 = 24/12

x = 2

Answer:

Its a

Step-by-step explanation:

since its moving 2 units to the right its only moving in the x direction so you just add 2 to each value of x  

Answer:

They are increasing at the same rate.

Given the word problem, we can deduce the following information:

1. The diameter of the circle is 3 meters.

2. The side length of the square is 3 meters.

To determine the difference in area between a circle and a square, we note first the formulas of a circle with a diameter d and the area of a square with side length d:

where:

d=diameter

where:

d=side length

The figures are shown below:

Based on this, the difference of areas would be:

Next, we plug in d=3:

Therefore, the difference in areas is:

Step-by-step explanation:

the sequence is arithmetic due to the common difference that is equal

d=11-15=7-11=-4

 a(n) = a1 +(n-1)d

a1=15

Then :

a(n) = 15+(n-1)-4

hope this helps

Answer: I think the answer is arithmetic sequence and the common ration is equal to 1/3.

Step-by-step explanation:

The primary purpose of the passage is to show how the author discovered Black women’s history when she was in graduate school.

What was Black women’s history?

People of color play played numerous significant parts in U.S. history since the times of the American Revolution. A large number of these ladies are key figures in the battle for social liberties, however they have likewise made significant commitments to human expression, science, and common society. People of color play played numerous significant parts in U.S. history since the times of the American Revolution. A considerable lot of these ladies are key figures in the battle for social liberties, however they have likewise made significant commitments to human expression, science, and common society. Even with orientation and racial predisposition, African American ladies have broken obstructions, rocked the boat, and battled for equivalent privileges for all. The achievements of dark female verifiable figures in governmental issues, science, artistic expression, and more keep on affecting society.

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The price that maximizes revenue is p = 120.

The price that maximizes revenue, we need to find the value of price (p) that corresponds to the maximum value of revenue (R). Revenue is calculated by multiplying the quantity (q) sold by the price (p), so we can express revenue as R = p × q.

Given the demand function q = -5p + 1200, we can substitute this expression for q into the revenue equation:

R = p × q

R = p × (-5p + 1200)

To find the price that maximizes revenue, we can take the derivative of the revenue function with respect to price (p), set it equal to zero, and solve for p.

dR/dp = -10p + 1200 = 0

Solving this equation for p:

-10p + 1200 = 0

-10p = -1200

p = -1200 / -10

p = 120

Therefore, the price that maximizes revenue is p = 120.

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The probability that all 6 flips result in heads is 1/64

The given coin is flipped 6 times. The number of heads and tails could vary from 0 to 6.Let H be the number of heads and T be the number of tails. Then the possible values of H and T are, H=0 and T=6 H=1 and T=5 H=2 and T=4 H=3 and T=3 H=4 and T=2 H=5 and T=1 H=6 and T=0

For the given question, it is given that more heads are flipped than tails.So the possible values of H are 4, 5 and 6.So the total number of possible outcomes with more heads than tails is the sum of the possible outcomes with 4, 5 and 6 heads which is, 1+6+15 = 22 (from the combinations formula)Now, the probability that all 6 flips result in heads, given more heads are flipped than tails is,

P(all 6 are heads) = P(H > T) × P(all 6 are heads | H > T)P(H > T) = 22/64

P(all 6 are heads | H > T) = 1/21 (there is only one possibility where all 6 flips are heads)

P(all 6 are heads) = P(H > T) × P(all 6 are heads | H > T) = (22/64) × (1/21) = 1/64

Therefore, the probability that all 6 flips result in heads, given more heads are flipped than tails is 1/64.

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The demand function for good X is Qx = m - 3Px + 2Py, where Qx is the quantity demanded of X, m is income, Px is the price of X, and Py is the price of a related good Y. The equation shows that the demand for X is inversely related to its price and directly related to the price of Y. Income, price of X, and price of Y collectively affect the overall demand for X.


The demand function for good X is given by Qx = m - 3Px + 2Py, where Qx represents the quantity demanded of good X, m is the income, Px is the price of good X, and Py is the price of a related good Y. In this equation, the income and prices are assumed to be positive.

To determine the demand for good X, we can analyze the equation. The coefficient -3 in front of Px indicates that the demand for good X is inversely related to its price. As the price of X increases, the quantity demanded of X decreases, assuming other factors remain constant. On the other hand, the coefficient 2 in front of Py indicates that the demand for good X is directly related to the price of the related good Y. If the price of Y increases, the quantity demanded of X also increases, assuming other factors remain constant.

Furthermore, the term (m - 3Px + 2Py) represents the overall effect of income, price of X, and price of Y on the quantity demanded of X. If income (m) increases, the quantity demanded of X increases. If the price of X (Px) increases, the quantity demanded of X decreases. If the price of Y (Py) increases, the quantity demanded of X increases.

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(x+1) & (x-5) are the factors of given equation.

The given Equation is,

x3- \(3x^{3}\) - 9

Here, If we substitute x =5, in the given equation, then we find

     (5)3 - 3(5)3 - 9*5 -5 = 0

x-5 is factor of given equation to find another factor dividing given equation by x-5

    we will get =(x2+2x+1) after dividing the equation by x - 5

Hence x3- \(3x^{3}\) - 9 =(x2+2x+1) (x-5)

                            =(x+2)2 (x-5)

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The expressions below best represent within the context of the word problem is x + (x - 24) = 68, Sarah's age is 46 years. Mother's age is 46 - 24 = 22. Therefore, Sarah is 46 years old, and her mother is 22 years older than her, making her mother 68 years old.

In the given word problem, we are given two pieces of information about Sarah and her mother's ages. Firstly, we know that Sarah is 24 years younger than her mother. Secondly, we know that the sum of their ages is 68. To find out Sarah's age, we need to represent it using an expression. Let's say Sarah's age is 'x'. Therefore, the expression that best represents Sarah's age is 'x'.

Now, we also need to represent Sarah's mother's age using an expression. As we know that Sarah's mother is 24 years older than her, we can subtract 24 from Sarah's age to get her mother's age. So, the expression that best represents Sarah's mother's age is 'x - 24'.

To find Sarah's age, we can use the sum of their ages, which is 68. We know that Sarah's age is 'x', and her mother's age is 'x - 24'. Therefore, we can write an equation:

x + (x - 24) = 68

Solving this equation, we get:

2x - 24 = 68

2x = 92

x = 46

Hence, Sarah is 46 years old.

In the given word problem, we are asked to find the age of Sarah, knowing that she is 24 years younger than her mother and the sum of their ages is 68. We can use the expressions x and x - 24 to represent Sarah's and her mother's ages, respectively.

Let x represent Sarah's age. Since Sarah is 24 years younger than her mother, we can represent her mother's age as x - 24. According to the problem, the sum of their ages is 68. We can now set up an equation using this information:

x (Sarah's age) + (x - 24) (Mother's age) = 68

Solve the equation to find the value of x, which represents Sarah's age:

x + x - 24 = 68
2x - 24 = 68

Now, add 24 to both sides of the equation:

2x = 92

Next, divide both sides by 2:

x = 46

So, Sarah's age is 46 years. To find her mother's age, we can substitute the value of x in the expression x - 24:

Mother's age = 46 - 24 = 22

Therefore, Sarah is 46 years old, and her mother is 22 years older than her, making her mother 68 years old.

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We have been given the domain-range pairs of the function g.

We have a pair of domain-range pair as (5, 2)

Therefore,

Next, we find

Lastly, we find:

Answer:

y=-2x-13

Step-by-step explanation:

y=mx+b

3=-2(-8)+b

3=16+b

3-16=b

-13=b

Answer:I think you can say like the most bought music in class B is alternative and the lowest one is classical and so on

Step-by-step explanation:

Answer:

The last option 8x + 4 = 196

Step-by-step explanation:

8x + 4 = 196

8x = 192

x=192/8

x=24

The strategy that can help solve this word problem is : If x represents the number of pencils per box, solve the equation 8x + 4 = 196.

A strategy is an approach that leads someone to the nearest of the solution of a problem.

Soni has 196 pencils.

Let, one box can accommodate x number of pencils.

Therefore 8 boxes can accommodate 8x number of pencils.

But she has 4 more pencils.

Hence, the required equation is 8x+4=196.

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Polynomial are expression that have a leading degree of 3. The other polynomial function will be 3yz^2 – 3z^2 – 4y^4 - y + 3

Polynomial are expression that have a leading degree of 3. Given the following expression

Sum = –yz^2 – 3z^2 – 4y^4.

One of the polynomial = y – 4yz^2 – 3

Required

The other polynomial

Let the unknown polynomial be "a" such that:

a =  –yz^2 – 3z^2 – 4y^4 - (y – 4yz^2 – 3)

Expand

a =  –yz^2 – 3z^2 – 4y^4 - y + 4yz^2 + 3

a = 3yz^2 – 3z^2 – 4y^4 - y + 3

Hence the other polynomial function will be 3yz^2 – 3z^2 – 4y^4 - y + 3

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Answer: D. or 3yz^2-3z^2-5y+7

Step-by-step explanation: got it right on edge

Jamal's wealth will be affected positively and negatively depending on the investment probability

If Jamal makes a small investment and the stakes are small, the small amount can affect his wealth in a positive or negative direction. The magnitude of the impact depends on the investment's probability of success and the investment's potential return.

If the probability of success is high and the potential return is positive, the impact on Jamal's net worth could be greater. On the other hand, a low probability of success and a negative potential return may have less impact on Jamal's fortunes.

Ultimately, the impact of a small investment on Jamal's wealth will depend on the specific details of the investment and the associated risks and potential rewards.

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Summary:

(i) To find the value of α such that the vectors v1, v2, and v3 are linearly dependent, we can set up a system of equations and solve for α.(ii) The Basis Theorem states that any set of linearly independent

(i) To check if v1, v2, and v3 are linearly dependent, we can set up the following equation:

c1v1 + c2v2 + c3v3 = 0,

where c1, c2, and c3 are constants. Substituting the given values of v1, v2, and v3, we have:

c1(3,7,7) + c2(1,4,4) + c3(α,1,1) = 0.

Simplifying this equation, we get the following system of equations:

3c1 + c2 + αc3 = 0,

7c1 + 4c2 + c3 = 0,

7c1 + 4c2 + c3 = 0.

We can solve this system of equations to find the value of α that satisfies the condition.

(ii) The Basis Theorem states that any set of linearly independent vectors that span a vector space can be used as a basis for that vector space. By applying the Basis Theorem to the vectors v1, v2, and v3, we can check if they form a basis for ℝ3. If they do, we can find the coordinates of a given vector, such as (2,3,5), in terms of the basis using Gaussian Elimination.

To apply Gaussian Elimination, we set up the augmented matrix [v1 | v2 | v3 | b], where b is the given vector (2,3,5). Then we perform row operations to obtain the row-echelon form of the augmented matrix. The resulting matrix will allow us to determine the coordinates of b in terms of the basis vectors.

By performing the Gaussian Elimination process, we can find the coordinates of (2,3,5) in terms of the basis vectors.

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There is no value of α that makes the vectors linearly dependent, and the basis for ℝ³ using the vectors [377, 148, 11α] is {v₁, v₂, v₃}, with the coordinates of [2, 3, 5] in terms of the basis found through Gaussian Elimination.

(i) To find the value of α such that vectors v₁, v₂, and v₃ are linearly dependent, we need to determine if there exist scalars a, b, and c, not all zero, such that a(v₁) + b(v₂) + c(v₃) = 0. Substituting the given values, we have a(377) + b(148) + c(11α) = 0. By solving this equation, we can find the value of α that satisfies the condition for linear dependence.

(ii) The Basis Theorem states that any set of linearly independent vectors that spans a vector space forms a basis for that vector space. Using a different value of α than the one found in (i), we can apply the Basis Theorem to determine a basis for ℝ³ using the vectors v₁, v₂, and v₃.

By performing Gaussian Elimination or row reduction on the augmented matrix [v₁ v₂ v₃], we can determine the basis vectors. The coordinates of vector [2 3 5] in terms of the basis can be found by solving the system of equations formed by equating the linear combination of the basis vectors to [2 3 5].

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(a) To find the amount in the account at the end of 1 year, we use the formula:

A = P(1 + r)^n

where A is the amount in the account at the end of the year, P is the principal (the initial amount deposited), r is the interest rate as a decimal, and n is the number of times the interest is compounded in a year. In this case, P = $4500, r = 0.06 (since the interest rate is 6%), and n = 1 (since the interest is compounded once a year). So, we have:

A = $4500(1 + 0.06)^1

= $4500(1.06)

= $4770

Therefore, the amount in the account at the end of 1 year is $4770.

(b) To find the amount in the account at the end of 2 years, we again use the formula:

A = P(1 + r)^n

However, in this case, n = 2 (since the interest is compounded twice in 2 years). So, we have:

A = $4500(1 + 0.06)^2

= $4500(1.1236)

= $5061.20

Therefore, the amount in the account at the end of 2 years is $5061.20.

Answer:

Dude dont spend 100 points! This place is scamming people

Step-by-step explanation:

The total amount required to pay off the loan at the end of 8 years would be $37,784.09.

To calculate the total amount required to pay off a loan of $16,000 with an interest rate of 14% per annum compounded half-yearly over 8 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the total amount, P is the principal (or loan amount), r is the interest rate per annum, n is the number of times the interest is compounded per year, and t is the time period in years.

In this case, P = $16,000, r = 14%, n = 2 (since the interest is compounded half-yearly), and t = 8 years.

Plugging in the values, we get:

A = $16,000(1 + 0.14/2)^(2*8)

= $37,784.09

Therefore, the total amount required to pay off the loan at the end of 8 years would be $37,784.09, including the principal amount of $16,000 and the accumulated interest.

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Answer:

2,3,4,5,6,7,8

Step-by-step explanation:

In words, the expression 2 ≤ x ≤ 8 translates to

"values of x between and inclusive of 2 and 8"

since we are being asked for integers,  the possible values that match this description are 2,3,4,5,6,7,8

Answer:

The correct answer is 3,4,5,6,7

Step-by-step explanation:

The signs < and > infer that the correct answer can it be either of these.

Because x is greater than two but less that eight, the number 3,4,5,6, and 7 are the only possible answers for x

Answer:

$917

Step-by-step explanation:

Let the money be $x

x×(1+(8.75%/12))^(12)=1000

x=916.5097877016

x=917(cor.to 3 sig.fig.)

Converting x > 4 to interval notation, we have:

Answer:

Step-by-step explanation:

(x + 4)/(x+4)(x-3)

= 1/(x-3)

solution is option 4

Answer:

There are two situations involving rational exponents or radicals that will never result in a negative real solution:

Even-indexed roots: If we take the square root, fourth root, sixth root, etc. of a non-negative real number, the result will always be non-negative. For example, the square root of 9 is 3, and the fourth root of 16 is 2, both of which are non-negative. This is because even-indexed roots always produce a non-negative result, regardless of the sign of the original number.

Exponents with even denominators: If we raise a non-negative real number to an exponent with an even denominator, the result will always be non-negative. For example, (4^2/4) is equal to 4, which is non-negative. This is because any negative base raised to an even power results in a positive number, and any positive base raised to an even power also results in a positive number. Therefore, any exponent with an even denominator will always produce a non-negative result, regardless of the sign of the original number.

Answer:

66 hours

Step-by-step explanation:

Monday through Friday is 45 hours

and Saturday and Sunday is 21 hours