Which of the following is an equivalent expression of 15x2 +12x + 8?

27x3 + 8
15x2(12x + 8)
12x + 15x2 + 8
8(15x2 + 12x)

By using power properties, the expression y⁸ · y³ · x⁰ · x⁻² is equivalent to the expressions 1 / (x² · y⁵) and x⁻² · y⁻⁵. (Correct choices: C, D)

In this question we have a power function with two variables and which has to be simplified by using power properties. The detailed procedure is shown below:

By using power properties, the expression y⁸ · y³ · x⁰ · x⁻² is equivalent to the expressions 1 / (x² · y⁵) and x⁻² · y⁻⁵. (Correct choices: C, D)

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as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.

\(\stackrel{f(x)}{y}~~ = ~~2x^2+4x\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~2y^2+4y} \\\\\\ x=2(y^2+2y)\implies \cfrac{x}{2}=y^2+2y\impliedby \begin{array}{llll} \textit{now let's complete the square}\\ \textit{to make it a perfect square trinomial}\\ \textit{by using our good friend, Mr "0"} \end{array} \\\\\\ \cfrac{x}{2}=y^2+2y(+1^2-1^2)\implies \cfrac{x}{2}=y^2+2y+1-1\implies \cfrac{x}{2}=(y^2+2y+1)-1\)

\(\cfrac{x}{2}+1=(y^2+2y+1^2)\implies \cfrac{x}{2}+1=(y+1)^2\implies \sqrt{\cfrac{x}{2}+1}=y+1 \\\\\\ \sqrt{\cfrac{x+2}{2}}=y+1\implies \sqrt{\cfrac{x+2}{2}}-1=y~~ = ~~f^{-1}(x)\)

(i) The maximum domain of definition D of the function f(x, y) = ln(x - y²) is all real numbers for x greater than y². (ii) Using the error barrier theorem, the smallest possible value of c > 0 such that |f(2e, 0) - f(2, 0)| ≤ c is determined. (iii) The second-degree Taylor polynomial of f at the development point (e, 0) is calculated.

(i) The maximum domain of definition D of the function f(x, y) = ln(x - y²) is determined by the restriction that the argument of the natural logarithm, (x - y²), must be greater than zero. This implies that x > y².

(ii) Using the error barrier theorem, we consider the expression |f(2e, 0) - f(2, 0)| and seek the smallest value of c > 0 such that this expression is satisfied. By substituting the given values into the function and simplifying, we can determine the value of c.

(iii) To calculate the second-degree Taylor polynomial of f at the development point (e, 0), we need to find the first and second partial derivatives of f with respect to x and y, evaluate them at the development point, and use the Taylor polynomial formula. By expanding the function into a Taylor polynomial, we can approximate the function's behavior near the development point.

These steps will provide the necessary information regarding the maximum domain of definition of the function, the smallest possible value of c satisfying the error barrier condition, and the second-degree Taylor polynomial of f at the given development point.

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The f′(a) when a = −6 is -7. This means that the slope of the tangent line of the graph of f(x) at x = -6 is -7.

To compute f′(a) algebraically for the given value of a, we use the following differentiation rule which is known as the Power Rule.

This states that:If f(x) = xn, where n is any real number, then f′(x) = nxⁿ⁻¹This is valid for any value of x.

Therefore, we can differentiate f(x) = −7x + 5 with respect to x using the power rule as follows:

f(x) = −7x + 5

⇒ f′(x) = d/dx (−7x + 5)

⇒ f′(x) = d/dx (−7x) + d/dx(5)

⇒ f′(x) = −7(d/dx(x)) + 0

⇒ f′(x) = −7⋅1 = −7

Hence, the derivative of f(x) with respect to x is -7.Now, we evaluate f′(a) when a = −6 as follows:f′(x) = −7 evaluated at x = −6⇒ f′(−6) = −7

Therefore, f′(a) when a = −6 is -7. This means that the slope of the tangent line of the graph of f(x) at x = -6 is -7.

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Answer:

D

Step-by-step explanation:

I believe the answer is D because if you follow the rules of SOHCAHTOA. To find the tangent you need opposite over adjacent. Opposite for this example would be 12, adjacent would be 35. So the fraction would 12/35. I hope that helps!!!

Given that triangle GHI and JKL are similar, the measure of side JK to the nearest tenth is 43.7

Similar triangles are triangles that have the same shape and are proportional, but their sizes may vary.

Given that;

Since the triangle are similar;

IH/GH = LK/JK

Plug in the given values and solve for side JK.

13/9.8 = 58/JK

Cross multiply

13 × JK = 58 × 9.8

13 × JK = 568.4

JK = 568.4 / 13

JK = 43.7

Given that triangle GHI and JKL are similar, the measure of side JK to the nearest tenth is 43.7.

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1. The portion in the distribution corresponding to a z-score of -1.20 is option B. Below the mean by a distance equal to 1.20 standard deviations. This is because the z-score measures the number of standard deviations that a given data point is from the mean of the data set.

A z-score of -1.20 means that the data point is 1.20 standard deviations below the mean. 2. The z-score corresponding to a score that is above the mean by 2 standard deviations is option C. 2. This is because the z-score measures the number of standard deviations that a given data point is from the mean of the data set. A score that is 2 standard deviations above the mean corresponds to a z-score of 2.3.

If a student's exam score in Chemistry was the same as the mean score for the entire Chemistry class of 35 students, their z-score would be option D. z = 0.00. This is because the z-score measures the number of standard deviations that a given data point is from the mean of the data set. If the student's score is the same as the mean, their z-score would be zero.4. For a population with M = 75 and

s = 5, the z-score corresponding to

x = 65 is option A.

z = -2.00. This is because the z-score measures the number of standard deviations that a given data point is from the mean of the data set.

Therefore, the z-score can be calculated as follows: z = (x - M) / s

= (65 - 75) / 5

= -2.005. True. A z-score indicates how an individual performed on a test relative to the other people who took the same test.6. The student's score was above the mean of the 3000 students. This is because a z-score of +0.80 means that the student's score was 0.80 standard deviations above the mean of the data set. Therefore, the student performed better than the average student in the class. Option D is the correct answer.

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The average speed in miles per hour during her drive that morning is 43.5 miles per hour   .

In the question ,

it is given that ,

the distance between home to freeway entrance is = 0.6 miles

the distance between freeway entrance to freeway exit is = 15.4 miles

the distance between freeway exit to workplace is = 1.4 miles

So , the distance from home to work place = 0.6 + 15.4 + 1.4 = 17.4 miles

we know that 24 minutes = 24/60 = 0.4 hours ,

the average speed = total  distance / total time

= 17.4/0.4

= 43.5 miles per hour

Therefore , the average speed is 43.5 miles per hour .

The given question is incomplete , the complete question is

One morning, Ms. Simon drove directly from her home to her workplace in 24 minutes. what was her average speed, in miles per hour, during her drive that morning ?

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The probability that the three friends are seated next to each other is 1/420

The total number of ways to seat the 7 people is 7! To find the number of ways to seat the three friends next to each other, we need to consider the number of ways to seat the other 4 people around them. So the number of favorable outcomes is 4!

The probability that the three friends are next to each other is then given by the ratio of the number of favorable outcomes to the total number of outcomes: (4!)/(7!) = 4!/5040 = 1/420.

So the probability that the three friends are seated next to each other is 1/420.

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When computing the given expressions for f(x) = 3x - 1, we find that f(3 + 1) = 15, f(3) + f(1) = 8, f(3-1) = 5, f(3) = 8, f(1) = 2, and f(3-1) = 5.

To find f(3 + 1), we substitute the value of 3 + 1 into the expression for f(x): f(3 + 1) = 3(3 + 1) - 1 = 12 - 1 = 11.

Next, to calculate f(3) + f(1), we substitute the values of 3 and 1 into the expression for f(x) separately and add them together: f(3) + f(1) = (3 * 3 - 1) + (3 * 1 - 1) = 8.

For f(3-1), we substitute the value of 3 - 1 into the expression for f(x): f(3-1) = 3(3-1) - 1 = 5.

Since f(3) and f(1) are both defined as 3x - 1, they have the same value: f(3) = f(1) = 8.

Finally, to compute f(3) f(1), we multiply the values of f(3) and f(1) together: f(3) f(1) = (3 * 3 - 1)(3 * 1 - 1) = 5.

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I can't tell necessarily what the question is but I'd it is 24= 8÷3y then y is 1/9

if the question is 24=8/3(y) then the answer is y=9

Answer:

24 = \(\frac{8}{3}\) y

\(\frac{8}{3}\) = 2.6 repeating

24 ÷ 2.6 repeating = 9

Step-by-step explanation:

Answer:

the gravity is 100

Step-by-step explanation:

machel liconl said it in 1st ammenmens

Answer: -1/28 gallon

Step-by-step explanation:

divide both numbers by 4 since its 1/4 a minute (-5/7 ÷ 4 and 4/7 ÷ 4) then add them, (-5/28 + 4/28= -1/28)

Answer: -1/28 gallon

Step-by-step explanation:

The product of three consecutive positive integers is always divisible by 6.

We can prove this statement using mathematical induction. The statement we want to prove is that the product of three consecutive positive integers is divisible by 6. To do this, we will use the induction hypothesis:

Let P(n) be the statement: The product of three consecutive positive integers starting with n is divisible by 6.

We will prove that P(n) is true for all natural numbers n.

Base Case: Let n = 1. Then the product of the three consecutive positive integers (1, 2, 3) is 6, which is divisible by 6. Therefore, P(1) is true.

Inductive Step: Assume that P(k) is true, where k is any natural number. We will now prove that P(k + 1) is also true.

The three consecutive positive integers starting with k + 1 are k + 1, k + 2, and k + 3. We can then rewrite the product of these three consecutive positive integers as follows:

(k + 1)(k + 2)(k + 3) = k3 + 3k2 + 6k + 6.

Since we assumed that P(k) is true, we know that k3 + 3k2 + 6k is divisible by 6. Therefore, the entire expression k3 + 3k2 + 6k + 6 is also divisible by 6. Since 6 is also added to this expression, we know that the product of three consecutive positive integers starting with k + 1 is divisible by 6. Therefore, P(k + 1) is true.

Since we have proven the base case and the inductive step, we have proven the statement for all natural numbers n. Therefore, the product of three consecutive positive integers is always divisible by 6.

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Using it's concept, there is a 0.726 = 72.6% probability that all 4 cards have distinct characters (letters or numbers).

A probability is given by the number of desired outcomes divided by the number of total outcomes.

A standard deck is given by 4 suits of 13 cards, each with either a number from 1 to 10 or one letter from A, Q or K, hence:

Hence the probability is given by:

p = 48/51 x 45/50 x 42/49 = 0.726.

0.726 = 72.6% probability that all 4 cards have distinct characters (letters or numbers).

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Answer:

n=5

Step-by-step explanation:

(1/3)^2 divided by (1/3)^7 = 243

3^5=243

Answer:

n = 5

Step-by-step explanation:

\(\frac{(\frac{1}{3})^{2} }{(\frac{1}{3})^{7} } =(\frac{1}{3} )^{2-7} =(\frac{1}{3})^{-5}\)

\((\frac{1}{3} )^{-5} =\frac{1}{(\frac{1}{3})^{5} } =\frac{1}{\frac{1}{3^{5} } } =3^{5}\)

\(3^{5} =3^{n}\)

\(n=5\)

Hope this helps

The quotient of the polynomial 10x⁶ + 20x⁴ - 15x² by 5x² will be (2x⁴ + 4x² - 3).

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.

The polynomials are given below.

10x⁶ + 20x⁴ - 15x² and 5x²

The factor of the polynomial 10x⁶ + 20x⁴ - 15x² will be given as,

10x⁶ + 20x⁴ - 15x² = (5x²) · (2x⁴ + 4x² - 3)

The quotient of the polynomial 10x⁶ + 20x⁴ - 15x² by 5x² will be given as,

⇒ (10x⁶ + 20x⁴ - 15x²) ÷ (5x²)

⇒ [(5x²) · (2x⁴ + 4x² - 3)] ÷ (5x²)

⇒ (2x⁴ + 4x² - 3)

The quotient of the polynomial 10x⁶ + 20x⁴ - 15x² by 5x² will be (2x⁴ + 4x² - 3).

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Answer:

yes pls continue we need full questions

Step-by-step explanation:

the answer is in the above image

please give me brainliest

(a) To find the values of z for which the matrix does not have an inverse, we can set up the determinant of the matrix and solve for z when the determinant is equal to zero.

The given matrix is:

|x3  x|

|9   1|

The determinant of a 2x2 matrix can be found using the formula ad - bc. Applying this formula to the given matrix, we have:

Det = (x3)(1) - (9)(x) = x3 - 9x

For the matrix to have an inverse, the determinant must be non-zero. Therefore, we solve the equation x3 - 9x = 0:

x(x2 - 9) = 0

This equation has two solutions: x = 0 and x2 - 9 = 0. Solving x2 - 9 = 0, we find x = ±3.

So, the values of x for which the matrix has no inverse are x = 0 and x = ±3.

(b) (i) To find the size of the acute angle between the vectors (3,0) and (5,5), we can use the dot product formula:

u · v = |u| |v| cos θ

where u and v are the given vectors, |u| and |v| are their magnitudes, and θ is the angle between them.

Calculating the dot product:

(3,0) · (5,5) = 3(5) + 0(5) = 15

The magnitudes of the vectors are:

|u| = sqrt(3^2 + 0^2) = 3

|v| = sqrt(5^2 + 5^2) = 5 sqrt(2)

Substituting these values into the dot product formula:

15 = 3(5 sqrt(2)) cos θ

Simplifying:

cos θ = 15 / (3(5 sqrt(2))) = 1 / (sqrt(2))

To find the acute angle θ, we take the inverse cosine of 1 / (sqrt(2)):

θ = arccos(1 / (sqrt(2)))

(ii) If the vector (-k, 3) is orthogonal to (5,5), it means their dot product is zero:

(-k, 3) · (5,5) = (-k)(5) + 3(5) = -5k + 15 = 0

Solving for k:

-5k = -15

k = 3

So, the value of k is 3.

(c) Let J be the linear transformation from R2 to R2 that reflects points in the horizontal axis and then scales them by a factor of 2. The matrix of J can be found by multiplying the reflection matrix and the scaling matrix.

The reflection matrix in the horizontal axis is:

|1  0|

|0 -1|

The scaling matrix by a factor of 2 is:

|2  0|

|0  2|

Multiplying these two matrices:

J = |1  0| * |2  0| = |2  0|

   |0 -1|   |0  2|   |0 -2|

So, the matrix of J is:

|2  0|

|0 -2|

Therefore, y = 2 and z = -2.

(d) The volume of a parallelepiped can be found by taking the dot product of two adjacent sides and then taking the absolute value of the result.

The adjacent sides of the parallelepiped P are (0,3,0)

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Hey there! I'm happy to help!

Let's write this equation out.

2/3+1/3x=2x

We want to get all of the variables on the left side and all the numbers on the right side so we can see what number x is equal to. First, Let's subtract 2/x from both sides.

2/3+1/3x-2x=0

We subtract 2/3 from both sides.

1/3x-2x=-2/3

We combine our x values.

-5/3x=-2/3

We divide both sides by -5/3.

x=-5

Have a wonderful day and keep on learning! :D

1. Three examples of situations where consistency is important:

Healthcare: when treating patients, healthcare providers must follow consistent procedures and protocols to ensure that every patient receives the same level of care.

Financial transaction: when making financial transactions, it is important to follow regular security rules to prevent fraud.

Support rules: Adherence to consistent rules and regulations in sports is essential to ensure fair play and the safety of all participants.

2. The number 0 is important in mathematical systems because it represents the absence of a number and serves as a placeholder. Without zero, our mathematical system would be affected in many ways. For example, writing the number 100 would be difficult without the zero. Without the invention of zero, progress in mathematics would have been delayed.

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a) The first neglected term in the series is \((1/16)(0.4)^7 = 3.3\times 10^-7\), which is smaller than the desired error of\(5 \times 10^-6\).

b) The first neglected term in the series is\((1/384)(0.5)^8 = 1.7\times10^-5,\)which is smaller than the desired error of 0.001.

a) To approximate the integral ∫\(0.4√(1+x^2)dx\) with an error of less than \(5x10^-6\), we can use a Taylor series expansion centered at x=0 to approximate the integrand:

√(\(1+x^2) = 1 + (1/2)x^2 - (1/8)x^4 + (1/16)x^6 -\) ...

Integrating this series term by term from 0 to 0.4, we get an approximation for the integral with error given by the first neglected term:

\(I = 0.4 + (1/2)(0.4)^3 - (1/8)(0.4)^5 = 0.389362\)

b) To approximate the integral ∫\(0.5x^3e^-x^2dx\) with an error of less than 0.001, we can use a Maclaurin series expansion for \(e^-x^2\):

\(e^-x^2 = 1 - x^2 + (1/2)x^4 - (1/6)x^6 + ...\)

Multiplying this series by \(x^3\) and integrating term by term from 0 to 0.5, we get an approximation for the integral with error given by the first neglected term:

\(I = (1/2) - (1/4)(0.5)^2 + (1/8)(0.5)^4 - (1/30)(0.5)^6 = 0.11796\)

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Answer:

2 000 000 \(cm^{2}\)

Step-by-step explanation:

100 \(km^{2}\) = 1 000 000 000 000 \(cm^{2}\)

the scale of 1:500000 means that 1 cm in the map represents 500000 cm in reality

So on the map this pond's area would be

\(\frac{1 000 000 000 000}{500000}\) = 2 000 000 \(cm^{2}\)

Answer:

8 units

Step-by-step explanation:

Answer: 9x I’m pretty sure

Step-by-step explanation:

Answer:

you have more outfits than your friend

Step-by-step explanation:

you:

5*13=65outfits

friend:

4*9=36outfits