The variables a, b, and c represent polynomials where a = x + 1, b = x2 + 2x − 1, and c = 2x. what is ab c in simplest form?a. x3 + 3x − 1b. x3 + 4x − 1c. x3 + 3x2 3x − 1d. x3 + 2x2 − x 1

The correct answer is: Yes, relation Q is a function,because there is exactly one y-value for every x-value.

To determine whether the given relation Q is a function, we need to check if each x-value is associated with a unique y-value. If there is any x-value that corresponds to multiple y-values, then the relation is not a function.

Let's examine the ordered pairs in relation Q: (3, -2), (-3, 1), (-2, -2), (1, -3).

We can see that each x-value in Q is associated with a unique y-value:

For x = 3, the y-value is -2.

For x = -3, the y-value is 1.

For x = -2, the y-value is -2.

For x = 1, the y-value is -3.

Since each x-value is paired with a unique y-value in relation Q, we can conclude that Q is a function.

In a function, every input (x-value) maps to a single output (y-value). If there were any repeated x-values with different y-values in the relation, it would indicate a violation of this rule and Q would not be a function. However, in this case, all the x-values have distinct y-values, satisfying the criteria for a function.

It's worth noting that we can also visualize this relation on a coordinate plane and check if there are any vertical lines that intersect the graph at more than one point. If there are no such lines, it confirms that the relation is a function.

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Answer:

1/4

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

The remaining balance on a $155,000 mortgage with a 7.75% interest rate and a 30-year term after 91/4 years (or 22.75 years) is approximately $87,343.

This is calculated by first determining the monthly payment, which is $947.05. Then, the number of remaining payments is calculated, which is 269. Finally, the remaining balance is calculated by multiplying the monthly payment by the number of remaining payments and subtracting it from the original loan amount.

Input the loan amount ($155,000), the interest rate (7.75%), and the loan term (30 years) into a mortgage calculator.

Determine the monthly payment.

Calculate the number of remaining payments (360 - 91/4 years).

Calculate the remaining balance by multiplying the monthly payment by the number of remaining payments and subtracting it from the original loan amount.

The remaining balance after 91/4 years can also be calculated using the following formula:

Remaining balance = (Original loan amount) - (Monthly payment × Number of remaining payments)

In this case, the remaining balance after 91/4 years is:

Remaining balance = ($155,000) - ($947.05 × 269) = $87,343

Therefore, the remaining balance on a $155,000 mortgage with a 7.75% interest rate and a 30-year term after 91/4 years (or 22.75 years) is approximately $87,343.

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The complete question is:

Compute The Balance, At 91/4 Years, On A $155,000,7.75%, 30-Year Mortgage.

The figure shown is a rectangular prism with a pyramid on top. To find the volume of this figure, we need to first find the volume of the rectangular prism and then add the volume of the pyramid.

The volume of the rectangular prism is calculated as length times width times height. From the diagram, we can see that the length of the prism is 7 cm, the width is 4 cm, and the height is 5 cm. Therefore, the volume of the rectangular prism is 7 x 4 x 5 = 140 cubic centimeters.

To find the volume of the pyramid, we need to first find the area of the base, which is a rectangle with dimensions 7 cm and 4 cm. The area of the base is therefore 7 x 4 = 28 square centimeters. To find the height of the pyramid, we can use the Pythagorean theorem since we know the other two sides are 5 cm and 4 cm. Solving for the height, we get sqrt(5^2 - 4^2) = 3 cm.

Now, we can find the volume of the pyramid by using the formula (1/3) x base area x height. Plugging in our values, we get (1/3) x 28 x 3 = 28 cubic centimeters.

Finally, we add the volume of the rectangular prism and the pyramid to get the total volume of the figure: 140 + 28 = 168 cubic centimeters. Therefore, the answer is 168 cm3.

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The equation of the parabola is h²-16h+8k+32=0 when parabola can be drawn with a focus of (8,10) and a directrix of y=6.

Given that,

A parabola can be drawn with a focus of (8,10) and a directrix of y=6.

We have to find the equation of the parabola in any form.

We know that,

The distance of any point P is (h,k) on a parabola form a focus is equal to its perpendicular distance from the directrix.

So,

√((h-8)²+(k-2)²) = | (k-6)/√0²+1² |

Squaring on both sides

(h-8)²+(k-2)² = (k-6)²

From th formula (a-b)² = a²-2ab+b²

We get,

h²-16h+64+k²-4k+4 = k²-12k+36

h²-16h+64+k²-4k+4 - k²+12k-36 =0

h²-16h+64-4k+4+12k-36=0

h²-16h+8k+32=0

Therefore, The equation of the parabola is h²-16h+8k+32=0 when parabola can be drawn with a focus of (8,10) and a directrix of y=6.

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Recursive algorithm for minimum number of bills needed to make an amount, given n and k denominations:Calculate the minimum number of bills by considering each denomination and recursively reducing the remaining amount

Here's a description and analysis of a recursive algorithm that computes the minimum number of bills needed to make an amount n using a system of k denominations:

Algorithm: MinimumBills(n, denominations)

If n is zero, return 0 (no bills needed).

If n is negative, return infinity (impossible to make the amount).

If n is a value that has already been computed and stored, return the stored value.

Set minBills to infinity.

For each denomination d in the k denominations:

a. If n is greater than or equal to d, recursively call MinimumBills(n - d, denominations) and store the result in numBills.

b. If numBills is less than minBills, update minBills to numBills.

Store minBills for the value of n.

Return minBills.

Analysis:

The recursive algorithm computes the minimum number of bills needed to make the amount n using the given denominations. The algorithm explores all possible combinations of denominations to find the optimal solution.

Time Complexity: The time complexity of the algorithm depends on the values of n and k denominations. Since the algorithm explores all possible combinations, the worst-case time complexity is exponential, \(O(k^n)\).

However, if the denominations are limited and n is relatively small, the algorithm can run in polynomial time.

Space Complexity: The space complexity of the algorithm is determined by the recursion depth, which is equal to n. Therefore, the space complexity is \(O(n).\)

Note: To optimize the algorithm and avoid redundant calculations, you can use memoization by storing the results for previously computed values of n in a lookup table. This can significantly reduce the number of recursive calls and improve the overall performance.

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Answer:

14x-35

Step-by-step explanation:

Use distributive property so,

you multiply 2x and -5 by 7

2x*7=14x

-5*7=-35

Answer:

B

Step-by-step explanation:

because it just is

Answer: 4x^2+16x-2

Step-by-step explanation:

You need to use BEDMAS order. (Brackets, exponents, division & multiplication left to right, addition & subtraction left to right)

Since there is nothing else you can do to the brackets, leave it for now.

There is also nothing you can do to the exponents, since you can't square a variable you don't know the value of.

Now, we do division & multiplication (there is no division in this case)

2x(3x + 4)−2x^2+8x-2 (start with the underlined section, using distributive property)

6x^2+8x−2x^2+8x-2

Now, since this is not an equation (no equal sign) but an expression, we just need to combine like terms.

6x^2+8x−2x^2+8x-2 (start with the x^2 terms. 6-2=4, so we end up with 4x^2)

4x^2+8x+8x-2 (now move on to the x terms. 8+8=16, so we end up with 16x)

4x^2+16x-2

And we're done! No more like terms to combine!

Answer: 0.36

Step-by-step explanation:

A=L*W

Since all sides of a square is the same you just do 3/5(3/5) which is 0.36 or 9/25

Answer:

see explanation

Step-by-step explanation:

∠ 1 + ∠ 2 = 90, that is

x + x - 8 = 90

2x - 8 = 90 ( add 8 to both sides )

2x = 98 ( divide both sides by 2 )

x = 49

The volume of a square based pyramid is 927.7 cubic centimeter.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Given that, a square base pyramid with the side length of the base is 16.6 and the height of the pyramid is 10.1 m.

We know that, the volume of square based pyramid =a²h/3.

Here, volume = 16.6²×10.1/3

= 275.56×10.1/3

= 927.7 cubic centimeter

Therefore, the volume of a pyramid is 927.7 cubic centimeter.

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"Your question is incomplete, probably the complete question/missing part is:"

Find the volume of a pyramid with a square base, where the side length of the base is 16.6 and the height of the pyramid is 10.1 m. Round your answer to the nearest tenth of a cubic meter.

The digit 3 in the number 17039 represents the value of 3 in the tens place. The place value system is a way to understand the value of each digit in a number. In this case, each digit in the number 17039 has a specific place value, starting from the rightmost digit, which is the ones place, then the tens place, followed by the hundreds place and so on. In the number 17039, the digit 3 is located in the tens place which represent 3 x 10 = 30. To understand the value of any digit in a number, you can multiply the digit by its corresponding place value.

Answer:

The digit 3 in the number 17039 represents the value of 3 in the tens place

Step-by-step explanation:

To calculate the cash balance at the end of the period, we need to consider the cash inflows and outflows.

Starting cash balance: $4,520

Cash inflows: $1,654 (receivables collected)

Cash outflows: $1,961 (payments to suppliers) + $500 (cash expenses)

Total cash inflows: $1,654

Total cash outflows: $1,961 + $500 = $2,461

To calculate the cash balance at the end of the period, we subtract the total cash outflows from the starting cash balance and add the total cash inflows:

Cash balance at the end of the period = Starting cash balance + Total cash inflows - Total cash outflows

Cash balance at the end of the period = $4,520 + $1,654 - $2,461

Cash balance at the end of the period = $4,520 - $807

Cash balance at the end of the period = $3,713

Therefore, the cash balance at the end of the period is $3,713.

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In order to calculate the percentage relation you proceed as follow:

(35.46/ 49.25)*100 = 72

Then, the percentage is 72%.

It is only necessary to calculte the quotient between the lower number and the higher one, and the result of the quotient is multiplied bu 100.

The integral of 2x / (5(5 - 4x²)¹/²) with respect to x simplifies to (1/5) * arcsin(2x/5) + C, where C is the constant of integration.

To solve the integral, we can start by simplifying the denominator. Notice that we have (5 - 4x²)¹/², which can be written as √(5 - 4x²).

Now, let's proceed with the integration step by step:

Multiply the numerator and denominator by √(5 - 4x²) to rationalize the denominator:

∫(2x / (5(5 - 4x²)¹/²)) dx = ∫(2x√(5 - 4x²) / (5(5 - 4x²))) dx

Separate the terms and simplify the integral:

∫(2x√(5 - 4x²) / (5(5 - 4x²))) dx = (2/5) ∫(x / √(5 - 4x²)) dx

Perform a substitution by letting u = 5 - 4x²:

Differentiate u with respect to x: du/dx = -8x

Rearrange to solve for dx: dx = -(1/8x) du

Substituting the values, the integral becomes:

(2/5) ∫(x / √u) (-1/8x) du

= -(1/40) ∫(1 / √u) du

Integrate the expression:

-(1/40) ∫(1 / √u) du = -(1/40) * 2√u + C

= -(1/20)√(5 - 4x²) + C

Simplify the expression:

-(1/20)√(5 - 4x²) + C = (1/20)√(4x² - 5) + C

Therefore, the final result is (1/20)√(4x² - 5) + C, where C is the constant of integration.

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Welk is most likely to be classified as a luxury good. A luxury good is a good for which demand increases more than proportionally with income.

This means that as people's incomes increase, they are more likely to spend a larger proportion of their income on luxury goods.

The income elasticity of demand for a good is a measure of how responsive demand is to changes in income. A positive income elasticity of demand indicates that demand increases as income increases, while a negative income elasticity of demand indicates that demand decreases as income increases.

The income elasticity of demand for Welk is 4.667, which is much higher than the income elasticities of demand for Kang (-3) and Lafgar (1.667). This indicates that demand for Welk is much more responsive to changes in income than demand for Kang or Lafgar.

Therefore, Welk is most likely to be classified as a luxury good.

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Answer:

probability of rolling a number greater than 3 is 1/2

Step-by-step explanation:

all numbers on a standard number cube: 1, 2, 3, 4, 5, 6

number greater than 3:  4, 5, 6

three out of six, of one-half, are greater than three

The graph of the sequence may pass toward the vertical line test.

Functions are defined as a fundamental part of the calculus in mathematics. These are the special types of relations. A function is visualized as a rule, which gives a unique output for every input x.

Given the information that, he gives two away on day 1, four away on day 2, and eight away on day 3. He continues this pattern for 10 days.

Let x be the number of days and f(x) be the number of cards.

So, the pattern is

f(x)=2, when x=1

f(x)=4, when x=2

f(x)=8, when x=3

Then, the function will be f(x)=2ˣ

The equation of the graph is passing through a vertical line.

The vertical line test is a graphical method that determines whether a curve in the plane represents the graph of a function by visually examining the number of intersections of the curve with vertical lines.

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Answer:

3/2 pages per hour

Step-by-step explanation:

1 : 2/3

= 3/2 : 1

Answer:

128 in^2

Step-by-step explanation:

L * W

16 * 8 = 128 in^2

Answer:

\(15x+8=6x+2\\9x+8=2\\9x=-6\\x=-6/9 or -2/3\\Hope this helps plz hit the crown :D\)

Answer: x = -2/3

Step-by-step explanation:

1. Isolate the x on one side of the equation by subtracting 6x from each side

9x + 8 =2

2. Subtract 8 from each side to get the x on one side of the equation and the whole numbers on the other side.

9x = -6

3. Divide each side by 9 to find the value of x

x = -2/3

Answer:

x = 4

Step-by-step explanation:

2(x/4 + 8) = 18

First: Distribute 2 into "x/4 + 8".

2x/4 + 16 = 18

2x/4 = 18 - 16

1x/2 = 2

x/2 • 2 = 2 • 2

x = 4

P.S "•" means to multiply.

Hope This Helps! •v•

Answer:

\(\boxed{\boxed{\sf x=4}}\)

Step-by-step explanation:

\(\blacksquare \:\:\sf 2\left(\cfrac{x}{4}+8\right)=18\)

Divide both sides by 2:

\(\mapsto \sf \cfrac{2\left(\cfrac{x}{4}+8\right)}{2}=\cfrac{18}{2}\)

\(\mapsto \sf \cfrac{x}{4}+8=9\)

Subtract 8 from both sides:

\(\mapsto \sf \cfrac{x}{4}+8-8=9-8\)

\(\mapsto \sf \cfrac{x}{4}=1\)

Multiply both sides by 4:

\(\mapsto \sf \cfrac{4x}{4}=1\times \:4\)

\(\mapsto \sf x=4\)

To maximize the amount of peaches produced by the orchard, the peach orchard owner should plant a certain number of trees per acre. The per-tree yield is given by the equation Y = 1200 - 15x, where Y represents the yield per tree and x represents the number of trees planted per acre.

To find the number of trees per acre that maximizes the crop yield, we need to determine the value of x that corresponds to the vertex of the equation. The vertex of a downward-opening parabola, represented by the given equation, occurs at the x-coordinate given by x = -b / (2a).

In this case, the coefficient of x is -15 and the constant term is 0, so b = 0 and a = -15. Substituting these values into the formula, we get x = -0 / (2 * -15) = 0.

While the mathematical calculation suggests that planting zero trees per acre would maximize the yield, this result is not practical. Therefore, the closest feasible value greater than zero would be 1 tree per acre.

For 1 tree per acre, substituting x = 1 into the equation, we find that each tree would produce a yield of Y = 1200 - 15 * 1 = 1185 peaches. Consequently, the resulting total yield would be 1185 peaches per acre.

Number of trees per acre: 1 tree per acre

Total yield: 1185 peaches per acre

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Answer:

Step-by-step explanation:

Given roots:

Polynomial with same roots will have factors of:

So correct choices are:

The solution to the given differential equation is:

\(\[y(x)\ =\ a_0 + a_1x + \frac{1}{4}a_1x^4 + \sum_{n=2}^{\infty} \frac{2a_{n-2}}{(n-2)(n-1)}x^{n+3}\]\)

To solve the given differential equation

\(x^3y'''\ -\ 6y\ =\ 0,\)

we can use the method of power series. Let's assume a power series solution of the form

\(y(x)\ =\ \sum_{n=0}^{\infty} a_nx^n.\)

Differentiating y(x) with respect to x gives:

\(\[y'(x)\ =\ \sum_{n=0}^{\infty} n a_n x^{n-1}\ =\ \sum_{n=0}^{\infty} (n+1) a_{n+1} x^n\]\)

Differentiating again gives:

\(\[y''(x)\ =\ \sum_{n=0}^{\infty} (n+1)na_{n+1}x^{n-1}\ =\ \sum_{n=0}^{\infty} (n+2)(n+1)a_{n+2}x^n\]\)

Differentiating one more time gives:

\(\[y'''(x)\ =\ \sum_{n=0}^{\infty} (n+2)(n+1)na_{n+2}x^{n-1}\ =\ \sum_{n=0}^{\infty} (n+3)(n+2)(n+1)a_{n+3}x^n\]\)

Substituting these expressions into the differential equation, we have:

\(\[x^3 \sum_{n=0}^{\infty} (n+3)(n+2)(n+1)a_{n+3}x^n - 6 \sum_{n=0}^{\infty} a_n x^n\ =\ 0\]\)

Rearranging the terms and combining like powers of x, we get:

\(\[\sum_{n=0}^{\infty} (n+3)(n+2)(n+1)a_{n+3}x^{n+3} - 6 \sum_{n=0}^{\infty} a_n x^n\ =\ 0\]\)

Now, let's equate the coefficients of like powers of x to zero:

For n=0:

\(\[(3)(2)(1)a_3 - 6a_0 = 0 \implies 6a_3 - 6a_0 = 0 \implies a_3 = a_0\]\)

For n=1:

\(\[(4)(3)(2)a_4 - 6a_1 = 0 \implies 24a_4 - 6a_1 = 0 \implies a_4 = \frac{1}{4}a_1\]\)

\(For \: n\geq 2:

\[(n+3)(n+2)(n+1)a_{n+3} - 6a_n = 0 \implies a_{n+3} = \frac{6a_n}{(n+3)(n+2)(n+1)}\]

\)

Now we can write the solution as:

\(\[y(x)\ =\ a_0 + a_1x + \frac{1}{4}a_1x^4 + \sum_{n=2}^{\infty} \frac{6a_{n-2}}{n(n-1)(n-2)}x^{n+3}\]

\)

Simplifying the series, we get:

\(\[y(x)\ =\ a_0 + a_1x + \frac{1}{4}a_

1x^4 + \sum_{n=2}^{\infty} \frac{2a_{n-2}}{(n-2)(n-1)}x^{n+3}\]

\)

Therefore, the solution to the given differential equation is:

\(\[y(x)\ =\ a_0 + a_1x + \frac{1}{4}a_1x^4 + \sum_{n=2}^{\infty} \frac{2a_{n-2}}{(n-2)(n-1)}x^{n+3}\]\)

where a₀ and a₁ are arbitrary constants to be determined based on the initial conditions or boundary conditions given in the problem.

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Answer:

-2

a^2+5a+6

Step-by-step explanation:

this is the answer

Answer:

ok so i dont care lol

Step-by-step explanation:

Answer:

The first one (1/6 divided by 1/2)

Step-by-step explanation:

Since Alice is splitting 1/6 of the box of cereal into 1/2, you need to divide.