(4x² – 11x³ – 13x² +96x
+52) ÷ (4x + 9)

Answer:

P = 17

Step-by-step explanation:

let's separate this into x and y components

x component: 3x

as x increases, so does the x component. e.g. 0 * 3 = 0, 4 * 3 = 12. therefore, we want x as high as possible

y component: y

as y increases, so does the y component. this is because the y component is literally just y.

therefore, given these two, to maximize P, we want x and y to be as high as possible

in 0 ≤ x ≤ 4, the maximum of x is 4

in -1 ≤ y ≤ 5, the maximum of y is 5

plug these in to get

3(4) + 5 = 17 as our answer

Answer:

17

Step-by-step explanation:

Answer:

$60.42

Step-by-step explanation:

0.06 x $57 = $3.42

$57 + $3.42 = $60.42

Hope this helped! :)

We can show that x² + 5x = 3 given the dimensions of the rectangle that has an area of 9 cm² as explained below.

To find the area of a rectangle, use the formula given below:

Area of a rectangle = (length)(width).

Given the parameters:

To show that x² + 5x = 3, plug in the values into the formula for the area of a rectangle:

(x + 3)(x + 2) = 9

Apply the distributive property of equality

x(x + 2) + 3(x + 2) = 9

x² + 2x + 3x + 6 = 9

Combine like terms:

x² + 5x + 6 = 9

Add -6 to both sides of the equation

x² + 5x + 6 - 6 = 9 - 6 [subtraction property of equality]

x² + 5x = 3

Thus, if the area of the rectangle with the given dimensions is 9 cm², then we can show that, x² + 5x = 3 as explained above.

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Answer:

\(sss\)

Step-by-step explanation:

Because

AB = ED ( Side)

BC = EF ( Side )

AC = DF ( Side )

So,

ABC Triangle is congruent to EDF triangle ( SSS)

Please...Can I have the brainliest?

Answer:

the answer is B which is y= -2/3x + 29/3

Step-by-step explanation:

Given that \(\(T(n)\) = \(10n^2-3n\)\) if (\(\(n=1\)\)), you have to prove it by induction. So, we have proved it by induction that  \($$\(T(n)=10n^2-3n\)$$\)  if ( n= 1). The given statement is true for all positive integers n

Let's do it below: The base case (n=1) is given as follows: \(T(1)\) =\(10\cdot 1^2-3\cdot 1\\&\)=\(7\end{aligned}$$\). This implies that \(\(T(1)\)\) holds true for the base case.

Now, let's assume that \(\(T(k)=10k^2-3k\)\) holds true for some arbitrary \(\(k\geq 1\).\)

Thus, for n=k+1, T(k+1) = \(10(k+1)^2-3(k+1)\\&\) = \(10(k^2+2k+1)-3k-3\\&\)=\(10k^2+20k+7k+7\\&\) = \(10k^2-3k+20k+7k+7\\&\) = \(T(k)+23k+7\\&\) = \((10k^2-3k)+23k+7\\&\) =  \(10(k+1)^2-3(k+1)\).

Therefore, we have proved that the statement holds true for n=k+1 as well. Hence, we have proved it by induction that  \($$\(T(n)=10n^2-3n\)$$\)  if (n=1). Therefore, the given statement is true for all positive integers n.

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The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x  ≥ -6

From the question, we have the following parameters that can be used in our computation:

\(f(x) = \sqrt{\frac{1}{3}x + 2\)

Set the radicand greater than or equal to 0

So, we have

1/3x + 2 ≥ 0

Next, we have

1/3x  ≥ -2

So, we have

x  ≥ -6

Hence, the domain of the function is (d) x  ≥ -6

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a) the dimension of its column space is also 2. b) the rank of A is 2. c) the nullity of matrix A is 1. d) the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

(a) The dimension of the row space of a matrix is equal to the dimension of its column space. So, if the dimension of the row space of matrix A is 2, then the dimension of its column space is also 2.

(b) The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. Since the dimension of the row space of matrix A is 2, the rank of A is also 2.

(c) The nullity of a matrix is defined as the dimension of the null space, which is the set of all solutions to the homogeneous equation Ax = 0. In this case, the matrix A is a 3 x 3 matrix, so the nullity can be calculated using the formula:

nullity = number of columns - rank

nullity = 3 - 2 = 1

Therefore, the nullity of matrix A is 1.

(d) The dimension of the solution space of the homogeneous system Ax = 0 is equal to the nullity of the matrix A. In this case, we have already determined that the nullity of matrix A is 1. Therefore, the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

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Let's assume the amount invested at the higher interest rate (16%) is x dollars.

The amount invested at the lower interest rate (6%) would then be ($80,000 - x) dollars, as the total investment is $80,000.

The interest earned from the investment at 16% is calculated as (x * 16%) = 0.16x dollars.

The interest earned from the investment at 6% is calculated as (($80,000 - x) * 6%) = 0.06(80,000 - x) dollars.

According to the given information, the retiree receives a total interest of $8,900 per year. So we can set up the equation:

0.16x + 0.06(80,000 - x) = 8,900

Now, let's solve the equation to find the value of x:

0.16x + 0.06(80,000 - x) = 8,900

0.16x + 4,800 - 0.06x = 8,900

0.1x + 4,800 = 8,900

0.1x = 8,900 - 4,800

0.1x = 4,100

x = 4,100 / 0.1

x = 41,000

Therefore, $41,000 is being invested at the higher interest rate (16%).

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Limits function lim p(x) can be calculated if p is a polynomial function by:

To calculate the limits of a polynomial function, p(x), first identify the degree of the polynomial. Then, use the formula Lim p(x) = aₙ xⁿ + aₙ₋₁ xⁿ⁻¹ + ... + a₀, where an is the leading coefficient. For example, if the polynomial is of degree 3, then the formula would be:

Lim p(x) = a₃ x³ + a₂ x² + a₁ x + a₀.

Next, we need to subtitute the variable x with the defined limits. For example, if the defined limit of the function is 2, then the limit function would be:

Lim p(2) =  a₃ (2)³ + a₂ (2)² + a₁ (2) + a₀

Then, we just need to simplify our finding:

Lim p(2) =  8a₃ + 4a₂ + 2a₁ + a₀

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Answer:

-13

Explanation:

I did the math lol

The function f : Z x Z → Z x Z defined by \(f(m,n) = (5m+4n, 4m+3n)\) is bijective, with its inverse given by \(f^{-1}(m,n) = (-3m + 4n, 4m - 5n)\). This means that for every pair of integers (m,n), the function f maps them uniquely to another pair of integers, and the inverse function \(f^{-1}\) maps the resulting pair back to the original pair.

The inverse of the function f(m,n) = (5m+4n, 4m+3n) is \(f^{-1}(m,n) = (-3m + 4n, 4m - 5n)\).

To show that the function f is bijective, we need to prove both injectivity (one-to-one) and surjectivity (onto).

Injectivity:

Assume f(m1, n1) = f(m2, n2), where (m1, n1) and (m2, n2) are distinct elements of Z x Z.

Then, (5m1 + 4n1, 4m1 + 3n1) = (5m2 + 4n2, 4m2 + 3n2).

This implies 5m1 + 4n1 = 5m2 + 4n2 and 4m1 + 3n1 = 4m2 + 3n2.

By solving these equations, we find m1 = m2 and n1 = n2, proving injectivity.

Surjectivity:

Let (a, b) be any element of Z x Z. We need to find (m, n) such that f(m, n) = (a, b).

By solving the equations 5m + 4n = a and 4m + 3n = b, we find m = -3a + 4b and n = 4a - 5b.

Thus, f(-3a + 4b, 4a - 5b) = (5(-3a + 4b) + 4(4a - 5b), 4(-3a + 4b) + 3(4a - 5b)) = (a, b), proving surjectivity.

Since the function f is both injective and surjective, it is bijective. The inverse function \(f^{-1}(m, n) = (-3m + 4n, 4m - 5n)\) is obtained by interchanging the roles of m and n in the original function f.

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Answer:

6

Step-by-step explanation:

Answer:

Asking four boys and four girls from each first period class which type of cake they prefer.

Step-by-step explanation:

cant really explain it just knew it off the top of my head.

gcd(40, 64) = 8, gcd(110, 68) = 2, and gcd(2021, 2023) = 1.
lcm(40, 64) = 320, lcm(35, 42) = 210, and lcm(2^2022 - 1, 2^2022 + 1) = 2^2022 - 1.
The value of 5152535455 modulo 7 is 4, and the value of 20192020202120222023 modulo 8 is 7.

To find the greatest common divisor (gcd) of two numbers, we determine the largest number that divides both of them without leaving a remainder. Thus, gcd(40, 64) = 8, gcd(110, 68) = 2, and gcd(2021, 2023) = 1.The least common multiple (lcm) of two numbers is the smallest number that is divisible by both of them. lcm(40, 64) = 320 because it is the smallest number that is divisible by both 40 and 64. Similarly, lcm(35, 42) = 210. The lcm of two consecutive odd numbers is their product. Hence, lcm(2^2022 - 1, 2^2022 + 1) = 2^2022 - 1.
To find the value of an expression modulo a number, we calculate the remainder when the expression is divided by that number. For the expression 5152535455, we can simplify the calculation by considering the congruence modulo 7. We can observe that each factor is congruent to 2 modulo 7, so their product is congruent to 2^5 ≡ 32 ≡ 4 modulo 7. Similarly, for the expression 20192020202120222023, each factor is congruent to 3 modulo 8. Multiplying them gives 3^5 ≡ 243 ≡ 7 modulo 8.
Therefore, the value of 5152535455 modulo 7 is 4, and the value of 20192020202120222023 modulo 8 is 7.

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Answer:

96 ft is the perimeter of the figure.

Step-by-step explanation:

9 + 9 + 9 + 9 + 9 + 9 + 12 + 30 = 96

Have a nice day!

Answer:

105

Step-by-step explanation:

9+9+9+9+9+9+30+21 = 105

HAVE A GREAT DAY SHAWTYYY

Answer:

16.3 N

Step-by-step explanation:

subtract if the forces are opposite

The slope of the ramp is 1/3 and the ramp should rest approximately 8.57 feet from the van to maintain a slope of 1.4 inches per foot or less.

a) To determine the slope of the ramp, we can use the formula:

Slope = Vertical rise / Horizontal run

In this case, the vertical rise is the height of the van door, which is given as 16 inches. The horizontal run is the distance from the bottom of the ramp to the van, which is 4 feet or 48 inches.

Slope = 16 inches / 48 inches = 1/3

Therefore, the slope of the ramp is 1/3.

b) If the ramp cannot have a slope of more than 1.4 inches per foot, we can set up a proportion to find the appropriate distance from the van for the ramp to rest.

Let x be the distance from the van that the ramp should rest (in feet).

According to the given condition, the maximum slope allowed is 1.4 inches per foot. This can be written as:

1.4 inches / 12 inches = x feet / x

Simplifying the proportion:

1.4 / 12 = x / x

1.4x = 12

x = 12 / 1.4

x ≈ 8.57 feet

Therefore, the ramp should rest approximately 8.57 feet from the van to maintain a slope of 1.4 inches per foot or less.

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Answer:

y = 33.94 mm

x = 19.80 mm

Step-by-step explanation:

Because AC = CB, then ∠ABC = 45°

cos ∠ABC = 24/y

cos 45° = 0.7071 = 24/y

y = 33.94 mm

EF/BC = x/y

14/24 = x/33.94

24x = 475.16

x = 19.80 mm

Answer:Its D

Step-by-step explanation:

Answer:

no because 2/3 is 0.6666666667

We would expect to land on red about 45 times in the additional 700 spins.

Probability is a number that indicates the likelihood of an event occurring. Probability is defined as the ratio of favourable outcomes to all outcomes.

Probability = Number of favourable outcomes / Number of samples

There are a total of 2 + 2 + 9 + 7 + 11 = 31 spins recorded in the given results. The proportion of spins that landed on red is:

frequency of red spins / total number of spins = 2 / 31

To estimate the expected number of red spins out of the additional 700 spins, we can use the proportion of red spins in the recorded results and assume that the same proportion will hold for the additional spins. That is:

expected frequency of red spins in 700 additional spins = (2 / 31) x 700

Using a calculator simplifies to:

expected frequency of red spins in 700 additional spins ≈ 45

Rounding to the nearest whole number, we would expect to land on red about 45 times in the additional 700 spins.

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Answer: B (18.5b-21.2)

The required expression −18.5b − 21.2 is equivalent to the given expression which is the correct answer that would be option (A).

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

We have been given the expression below as

5(−2.3b − 4.1) − (7b + 0.7)

Open the parentheses and apply the distributive property of multiplication,

⇒ −2.3b × 5 − 4.1 × 5 − 7b - 0.7

⇒ -11.5 - 20.5 − 7b - 0.7

Rearrange the likewise terms and apply the arithmetic operation,

⇒ −18.5b − 21.2

Hence, the required expression −18.5b − 21.2 is equivalent to the given expression.

Thus, the correct answer would be an option (A).

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☽------------❀-------------☾

Hi there!

~

Answer:

Divide both sides by 3.

\(3x=9\)

\(\frac{3x}{3} = \frac{9}{3}\)

\(x = 3\)

❀Hope this helped you!❀

☽------------❀-------------☾

Answer:

f(x)=19

Step-by-step explanation:

2(3)²+1

2(9)+1

19

The value of function at x = 3 is,

⇒ f (3) = 19

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The function is,

⇒ f (x) = 2x² + 1

Now, Substitute x = 3 in above function,

⇒ f (x) = 2x² + 1

⇒ f (3) = 2 × 3² + 1

⇒ f (3) = 19

Thus, The value of function at x = 3 is,

⇒ f (3) = 19

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a) The relevant population is the heavy soft-drink users in the given case, and the appropriate sampling design that should be used is  stratified random sampling. The list of all heavy soft-drink users is the sampling frame.

b) Cluster sampling refers to a sampling design where population is divided into naturally occurring groups and a random sample of clusters is chosen.

The advantages are efficient, easy to perform, and used when the population is widely dispersed. The disadvantages are sampling errors, have lower level of precision, and have the standard error of the estimate.

a) The relevant population for the public relations research department to investigate the initial reactions of heavy soft-drink users to a new all-natural soft drink is heavy soft-drink users. The appropriate sampling design that can be used to investigate the issues is stratified random sampling.

Stratified random sampling is a technique of sampling in which the entire population is divided into subgroups (or strata) based on a particular characteristic that the population shares. Then, simple random sampling is done from each stratum. Stratified random sampling is appropriate because it ensures that every member of the population has an equal chance of being selected.

Moreover, it ensures that every subgroup of the population is adequately represented, and reliable estimates can be made concerning the entire population. The list of all heavy soft-drink users can be the sampling frame.

b) Cluster sampling is a type of sampling design in which the population is divided into naturally occurring groups or clusters, and a random sample of clusters is chosen. The elements within each chosen cluster are then sampled.

The advantages of cluster sampling are:

The disadvantages of cluster sampling are:

A situation where cluster sampling would be appropriate is in investigating the effects of a new medication on various groups of people. In this case, the population can be divided into different clinics, and a random sample of clinics can be selected. Then, all patients who meet the inclusion criteria from the selected clinics can be recruited for the study. This way, the study will be less expensive, and it will ensure that the sample is representative of the entire population.

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If the margin of error is 4.6, the interval estimate would be the point estimate plus or minus 4.6.

In statistical estimation, the margin of error represents the maximum amount by which the point estimate may deviate from the true population parameter. It provides a measure of the precision or uncertainty associated with the estimate. When constructing a confidence interval, the margin of error is used to determine the range within which the true parameter is likely to fall.

To obtain the interval estimate, we add and subtract the margin of error from the point estimate. Let's denote the point estimate as x bar. Therefore, the interval estimate can be expressed as X bar ± 4.6, where ± denotes the range above and below the point estimate.

In summary, if the margin of error in an interval estimate of μ is 4.6, the interval estimate is given by the point estimate plus or minus 4.6. This range captures the likely range of values for the true population parameter μ.

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