Factor the following expression. Simplify your answer.
3s(s - 1)^1/3 + 2(s - 1)^4/3

The coordinate of the midpoint of the line segment with endpoints -2 and 12 is 5.

To find the coordinate of the midpoint of a line segment,

we can use the formula:

Midpoint = (Endpoint1 + Endpoint2) / 2

In this case, the endpoints of the line segment are -2 and 12. Let's substitute these values into the formula to find the midpoint:

Midpoint = (-2 + 12) / 2

             = 10 / 2

               = 5

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The coordinate of the midpoint of the line segment p b, with endpoints at -2 and 12 on the number line, is 5.

To find the coordinate of the midpoint, we need to calculate the average of the coordinates of the endpoints. The midpoint is the point that divides the line segment into two equal parts. In this case, the coordinates of the endpoints are -2 and 12. To find the midpoint, we add the coordinates of the endpoints and divide the sum by 2.

Sum of the coordinates: -2 + 12 = 10

Dividing the sum by 2: 10 ÷ 2 = 5

Therefore, the coordinate of the midpoint of the line segment p b is 5.

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Answer:

The correct answer is Option C: \(2x-3(-3x-4)=-21\)

Step-by-step explanation:

The given equations are:

\(y + 3x =-4\ \ \ Eqn\ 1\\2x-3y =-21\ \ \ Eqn\ 2\)

The equations have to be solved using substitution method. In substitution method we find the value of a variable from one equation and put it in the other equation.

To find the value, we usually choose the equation in which a variable without any coefficient is available.

From equation 1

\(y +3x = -4\\y = -3x-4\\\)

This value of y will be put in equation 2

\(2x-3(-3x-4)=-21\)

It is the C option in choices

Hence,

The correct answer is Option C: \(2x-3(-3x-4)=-21\)

Answer:

Hey, where did you get this question? Do you have answer key of this worksheets all things I need it to.

Step-by-step explanation:

Answer:

(6,8)

I know because I did it coool

Answer:

7

Explain:

7 x 1 = 7

7 x 2 = 14

7 x 3 = 21

7 x 4 = 28

7 x 5 = 35

7 x 6 = 42

7 x 7 = 49

So it's 7!

Answer:

I would say -F=0.4

Step-by-step explanation:

if F=-0.4 and -F is the opposite of F then the opposite of -0.4 is 0.4

Answer:

4

Step-by-step explanation:

The part of the function that is (2x - 1)² has a minimum value of 0. The reason is that any real number you for x will give you a positive, negative, or zero value for 2x - 1. When you square it, you must get a non-negative answer.

Then you add 4, and you get a value that is greater than or equal 4.

Answer:

75.39822

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

Respuesta:

C: 10xy^4 + 3x^3y^2 - 6x^2y

¡¡Espero te sirva!!

Answer:

Perimeter = 4.5√3 + 4.5

Area = 3.375√3

Step-by-step explanation:

Well you can first see that triangle ABC is a 30°60°90° triangle.

Since angle A is 60 and it is bisected, you will have a small 30°60°90° triangle and a 120°30°30° triangle.

You can say that DA is congruent to BD by Base Angle Theorem.

DA = 3

By using the ratios of the sides of the 30°60°90° you get that CD is 1.5 and CA is 1.5√3

CD = 1.5

CA = 1.5√3

BC = 4.5

Area = (4.5 * 1.5√3) / 3 = 6.75√3 / 2

Area = 3.375√3

By using the 30°60°90° ratio again, you get that BA = 3√3

Perimeter = 1.5√3 + 3√3 + 4.5

Perimeter = 4.5√3 + 4.5

I'm not 100% sure that the answer is right so check it.

The equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is y = (5/2) * x^2y + 1. This equation represents a curve where the y-coordinate is a function of the x-coordinate, satisfying the conditions.

To determine an equation of the curve that satisfies the conditions, we can integrate the slope function with respect to x to obtain the equation of the curve. Let's proceed with the calculations:

We have:

Point: (0, 1)

Slope: 5xy

We can start by integrating the slope function to find the equation of the curve:

∫(dy/dx) dx = ∫(5xy) dx

Integrating both sides:

∫dy = ∫(5xy) dx

Integrating with respect to y on the left side gives us:

y = ∫(5xy) dx

To solve this integral, we treat y as a constant and integrate with respect to x:

y = 5∫(xy) dx

Using the power rule of integration, where the integral of x^n dx is (1/(n+1)) * x^(n+1), we integrate x with respect to x and get:

y = 5 * (1/2) * x^2y + C

Applying the initial condition (0, 1), we substitute x = 0 and y = 1 into the equation to find the value of the constant C:

1 = 5 * (1/2) * (0)^2 * 1 + C

1 = C

Therefore, the equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is:

y = 5 * (1/2) * x^2y + 1

Simplifying further, we have:

y = (5/2) * x^2y + 1

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Answer:

above sea level

Step-by-step explanation:

Answer: r=2.69. Calculate the radius of circle:Round the number: r=2.69Answer: r=2.69

Answer:

The difference between the area of the original triangle and the area of the new triangle is 5(3x + 7)(5x - 1)/2

Step-by-step explanation:

We know that the area of a triangle A = 1/2bh where b = base and h = height.

Let A be the area of triangle 1 with base (3x + 7) and height (5x - 1).

So its area A = (3x + 7)(5x - 1)/2.

Now for the second triangle, the base is tripled, so its base is 3(3x + 7) and its height is doubled, so its height is 2(5x - 1)

So its area is A' = 3(3x + 7) × 2(5x - 1)/2 = 3(3x + 7)(5x - 1)

So the difference between the area of the original triangle and the new triangle is

A' - A = 3(3x + 7)(5x - 1) - (3x + 7)(5x - 1)/2

= (3x + 7)(5x - 1)(3 - 1/2)

= 5(3x + 7)(5x - 1)/2

So the difference between the area of the original triangle and the area of the new triangle is 5(3x + 7)(5x - 1)/2

The value of determinant of the matrix det (AB) is 15.

Given matrices A and B are 3 by 3 matrices with

det (A) = 3 and

det (b) = 5.

We need to find the value of det (AB).

Writing the given matrices into the augmented matrix form gives [A | I] and [B | I] respectively.

By multiplying A and B, we get AB. Similarly, by multiplying I and I, we get I. We can then write AB into an augmented matrix form as [AB | I].

Therefore, we can solve the augmented matrix [AB | I] by row reducing [A | I] and [B | I] simultaneously using elementary row operations as shown below.


The determinant of AB can be calculated as det(AB) = det(A) × det(B)

= 3 × 5

= 15.

Conclusion: The value of det (AB) is 15.

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We need to find the value of determinant det(AB), using the formula: det(AB) = det(A)det(B)

=> det(AB) = 3 × 5

=> det(AB) = 15.

Hence, the value of det(AB) is 15.

The given matrices are A and B. Here, we need to determine the value of det(AB). To calculate the determinant of the product of two matrices, we can follow this rule:

det(AB) = det(A)det(B).

Given that: det(A) = 3

det(B) = 5

Now, let C = AB be the matrix product. Then,

det(C) = det(AB).

To evaluate det(C), we have to compute C first. We can use the following method to solve the augmented matrix by elementary row operations.

Given matrices A and B are: Matrix A and B:

[A|B] = [3 0 0|1 0 1] [0 3 0|0 1 1] [0 0 3|1 1 0][A|B]

= [3 0 0|1 0 1] [0 3 0|0 1 1] [0 0 3|1 1 0].

We can see that the coefficient matrix is an identity matrix. So, we can directly evaluate the determinant of A to be 3.

det(A) = 3.

Therefore, det(AB) = det(A)det(B)

= 3 × 5

= 15.

Conclusion: Therefore, the value of det(AB) is 15.

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Answer:

(6, -3) aka x = 6 and y = -3

Step-by-step explanation:

since you are given y = -2x + 9, you should start by substituting the expression -2x + 9 for y in the equation 2x + 3y = 3.

here's your equation after plugging in the expression that's equal to y:

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

distribute 3 to -2x

2x + 3(-2x + 9) = 3 ⇒ 3 · -2x = -6x

...and to 9.

2x + 3(-2x + 9) = 3 ⇒ 3 · 9 = 27

now you're left with 2x - 6x + 27 = 3.

combine like terms.

2x - 6x + 27 = 3 ⇒ -4x + 27 = 3

subtract 27 from both sides of the equation. since +27 and -27 cancel each other out, you're left with subtracting 27 from 3, which gives you -24.

now your equation is -4x = -24.

divide both sides of the equation by -4.

-24/-4 = 6

...therefore x = 6.

since you have your x value now, you can plug that into the equation for y in order to solve for y.

y = -2x + 9 ⇒ y = -2(6) + 9

multiply -2 and 6.

y = -2(6) + 9 ⇒ y = -12 + 9

add -12 and 9.

y = -12 + 9 ⇒ y = -3

...and now you've solved for y, which is -3.

therefore, your solution is (6, -3), aka x = 6 and y = -3.

hope this helps! have a nice day <3

Answer:

4.32 francs

Step-by-step explanation:

45p × £/(100p) × 9.6 francs / £ = 4.32 francs

Using diagonal method |A| = (2)(3)(-6) + (2)(3)(3) + (-4)(3)(2) - (-6)(3)(2) - (3)(2)(-4) - (3)(-4)(2) |A| = -36 + 18 - 24 + 36 + 24 - 24 = 6

Therefore, |A| = 6. |

Given A = 2  -4  3  2  3  -6 To find: |A| using the diagonal methodWe have a 2×2 matrix, which gives us: |A| = (2)(3) - (2)(-4) = 6 + 8 = 14Now, let's do the diagonal method for 3×3 matrix:

Step 1: Draw two diagonal lines:

Step 2: Write matrix elements on both sides of the lines:

Step 3: Multiply the elements on the left diagonal, then multiply the elements on the right diagonal, and then find the difference of these two: |A| = (2)(3)(-6) + (2)(3)(3) + (-4)(3)(2) - (-6)(3)(2) - (3)(2)(-4) - (3)(-4)(2) |A| = -36 + 18 - 24 + 36 + 24 - 24 = 6Therefore, |A| = 6.

To find the determinant of a 2×2 matrix, we use the formula: |A| = ad - bcLet A be the given matrix, so a = 2, b = -4, c = 3, and d = 2. Thus,|A| = (2)(2) - (-4)(3) = 4 + 12 = 16

To find the determinant of a 3×3 matrix, we use the diagonal method. This method involves making a diagonal with three boxes at each end, like so: In this case, we let A be the given 3×3 matrix. We fill in the boxes as shown below: Then, we evaluate the diagonal products and add them up with the appropriate signs.

For example, the leftmost diagonal product is 2×3×(-6) = -36.

The second product on the left is 3×2×(-4) = -24. The third product on the left is (-4)×3×2 = -24.

Therefore, the left diagonal sum is -36 - 24 - 24 = -84. The right diagonal sum is 2×3×(-6) + 3×(-4)×2 + (-6)×2×(-4) = -36 - 24 + 48 = -12.

Finally, we subtract the right diagonal sum from the left diagonal sum to get |A| = -84 - (-12) = -72.

Thus, we found the determinant of the given matrix using the diagonal method. The determinant of a 2×2 matrix is found using the formula |A| = ad - bc, where a, b, c, and d are the elements of the matrix. For a 3×3 matrix, we use the diagonal method.

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Answer:

6,520

Step-by-step explanation:

Because that is the answer when you multiply them together.

Answer:

6,520

Hope this helps!

Answer:

  1.  S(1) = 1; S(n) = S(n-1) +n^2

  2. see attached

  3. neither

Step-by-step explanation:

1. The first step shows 1 square, so the first part of the recursive definition is ...

  S(1) = 1

Each successive step has n^2 squares added to the number in the previous step. So, that part of the recursive definition is ...

  S(n) = S(n-1) +n^2

__

2. See the attachment for a graph.

__

3. The recursive relation for an arithmetic function is of the form ...

  S(n) = S(n-1) +k . . . . . for k = some constant

The recursive relation for a geometric function is of the form ...

  S(n) = k·S(n-1) . . . . . . for k = some constant

The above recursive relation is not in either of these forms, so it is neither geometric nor arithmetic.

Answer: C

Hope this helps :)

Answer:

s ∈ ( − ∞ , 1 )

Step-by-step explanation:

-2(s-7)>4s+8

-2s+14>4s+8

14>6s+8

6>6s

1>s

Answer:

(-inf, 1)

Step-by-step explanation:

Answer:

(f-g)(x)=2x-3

Step-by-step explanation:

Subtract the two functions:

\((f-g)(x)=f(x)-g(x)\)

\((f-g)(x)=(3x-1)-(x+2)\)

\((f-g)(x)=3x-1-x-2\)

\((f-g)(x)=2x-3\)

Explanation :

A system of equations using tables. He notices that both tables have y-values of 11 and concludes that the solution must be y = 11. To determine if Fred's conclusion is correct, we need to follow these steps:
Step 1: Identify the two equations from the given tables. Since the tables are not provided, we'll represent them as Equation 1 and Equation 2.
Step 2: Check if the y-value of 11 is consistent in both equations. This means that when y = 11, both equations should be true.
Step 3: If both equations are true when y = 11, then Fred's conclusion is correct. The solution to the system would indeed be y = 11.
However, it's important to note that just having a y-value of 11 in both tables does not necessarily mean that the solution is y = 11. We also need to check if the corresponding x-values are the same. If the x-values differ, it implies that the two equations intersect at different points, and the solution to the system is not simply y = 11. In that case, we would need to find the correct point of intersection (x, y) to identify the true solution to the system.

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An expression that has any value other than 0 is considered true by an if statement. The answer to this statement is True.

The idea of truth values in mathematics is connected to the validity of a statement or proposition. A statement can either be true or untrue; there is no other option. When dealing with Boolean values, however, a different technique is employed in programming. In this context, any value other than 0 is deemed true.

This implies that when used in an if statement, a value that is negative, decimal, or a non-zero integer will be assessed as true. This is due to the statement's focus on the presence of a value rather than its truth or falsity.

Therefore, the statement that says that an expression that has any value other than 0 is considered true by an if statement is True.

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True. In programming, an expression that has any value other than 0 is considered true by an if statement. The value of an expression can be a number, a string, a boolean, or any other data type.

If the value is not 0, then it is considered true, and the if statement will execute the code block associated with it. If the value is 0, then it is considered false, and the if statement will skip the code block associated with it.

In an if statement, an expression with any value other than 0 is considered true. If the expression's value is 0, the if statement evaluates it as false. This means the code block associated with the true condition will execute when the expression's value is not 0, and the code block associated with the false condition will execute when the expression's value is 0.

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Since 65 + 25 = 90, 90 student tickets were sold.

According to our question-

25 student tickets are $75 each. If we deduct this from the total, we find that an equal number of adult and student tickets cost $585.

The cost of one adult ticket and one child ticket is $9.

585/9= 65.

Verifying this:

65x3=195 \s65x6=390

195+390+75= 660

Hence, Since 65 + 25 = 90, 90 student tickets were sold.

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Answer: This answer is 11 square units.

Step-by-step explanation:

Find the diagram attached

First we need to find the side length of the square with known areas.

Area of a square = L²

L is the side length of the square

For the green square

44 = L²

Lg = √44

For the purple square

Ap = Lp²

33 = Lp²

Lp = √33

Get the length (L) of the unknown square using pythagoras theorem;

Lg² = L²+Lp²

(√44)² = L²+(√33)²

44 = L²+33

L² = 44-33

L² = 11

Since Al = L²

Hence the area of the square adjacent to the third side of the triangle is 11 square units

Answer:

85 units

Step-by-step explanation:

The similar triangles in the question, with proportional sides indicates;

4. The proportion that must be true is the option G

G. 4/6 = 7/x

Similar triangles are triangles are triangles that have the same shape but may have different sizes.

The possible triangles in the question includes two triangles with specified side lengths AB = 6 inches, AC = 7 inches, DE = 4 inches, DF = x inches

The definition of similar triangles indicates that we get;

DE/AB = EF/BC

DF/AC = DE/AB

DF/AC = EF/BC

Therefore;

(x/7) = 4/6

The correct option which indicates the proportion that must be true, therefore is option G

G. 4/6 = x/7

Part of the question includes two triangles, please see attached diagram created with MS Excel

The possible proportions, from which to select the proportion that must be true are;

F (7/x) = (4/6)

G 4/6 = x/7

H 6/4 = x/7

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