what is the term to term rule of the sequence in 5, 10, 20, 40, 80

Answer:

Step-by-step explanation:

in your calculator, type in 18.25/6.

\(\bf Step-by-step~explanation:\)

To solve for x, we have to isolate the variable.

\(\bf Our~formula: x+2-9=36x\)

\(\bf Step~1:\)

Let's subtract x from both sides to cancel x from the left.

\(\bf x(-x)+2-9=36x(-x)\\2-9=35x\)

\(\bf Step~2:\)

Them simplify 2-9, which is equal to -7.

\(\bf -7=35x\)

\(\bf Step~3:\)

Divide both sides by 35 to isolate x.

\(\bf \frac{-7}{35} =-\frac{1}{5}\)

\(\bf \frac{35x}{35}=x\)

\(\large\boxed {\bf Our~final~answer: x=-\frac{1}{5}}\)

Answer:

x= -1/5

Step-by-step explanation:

minus x from both sides

2-9=35x

-7=35x

divide both sides by 35

x=-1/5

Angles are equal as it's parallelogram

Answer:

x = 3

Step-by-step explanation:

Assuming the given shape is a rhombus.

Properties of a rhombus

As there is a reflection of symmetry over the diagonals, the diagonals bisect the vertices, i.e. the diagonal divides the vertices into 2 equal angles.  Therefore, the angles either side of the diagonal at each vertex are equal.

Therefore:

\(\implies 6x^2-15=5x^2-2x\)

Rearrange to create a quadratic (equal to zero):

\(\implies 6x^2-15-5x^2+2x=0\)

\(\implies x^2+2x-15=0\)

Solve the quadratic to find the value of x:

\(\implies x^2+2x-15=0\)

\(\implies x^2+5x-3x-15=0\)

\(\implies x(x+5)-3(x+5)=0\)

\(\implies (x-3)(x+5)=0\)

Therefore:

\((x-3)=0 \implies x=3\)

\((x+5)=0 \implies x=-5\)

Substitute the found values of x into one of the expressions:

\(x=3 \implies 6(3)^2-15=39\)

\(x=-5 \implies 6(-5)^2-15=135\)

Therefore, the options for the angles are 39° or 135°.

From inspection of the diagram, the angles are clearly acute (less than 90°), therefore the only appropriate value of x is 3.

Answer:

t>-2

Step-by-step explanation:

-6t < 12

Move the -6 over to 12 and divide

And change the sign after u divide

The solution of inequality is,

⇒ t > - 2

We have to given that,

An inequality to solve,

⇒ - 6t < 12

Now, We can simplify the inequality as,

⇒ - 6t < 12

Divide both side by 6;

⇒ - t < 2

⇒ t > - 2

Therefore, The solution of inequality is,

⇒ t > - 2

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Answer:

Prime Factors of 72: 2, 3

Step-by-step explanation:

Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72

Answer:

1. NP

2. P

3. P

4. NP

Step-by-step explanation:

if this helped, Mark as brainliest, thank you

Answer:

Not polynomial for the first one.

second is polynomial.

third is polynomial.

and fourth is not polynomial.

Step-by-step explanation:

oh wait- yeah the other person is right too LOL

Answer:

Correct answer is C

Step-by-step explanation:

The Function is linear but is not a direct variation function

The function is linear but is not a direct variation function.

The correct option is C.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of a line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

As per the information provided:

The points are collinear (i.e. they lie on a straight line), which means that the function is linear. We can find the equation of the line using the two-point form:

(y - 18)/(x - 10) = (30 - 18)/(18 - 10)

Simplifying this equation gives:

y - 18 = 3/2(x - 10)

y - 18 = 1.5x - 15

y = 1.5x + 3

So the function is linear, but not a direct variation function, and has a slope of 1.5.

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The complete question:

A coordinate plane with 3 points is plotted at (10, 18), (14, 24), and (18, 30).

Which statement describes the function through the points?

The function is a direct variation function with a constant variation of 1.5.

The function is a direct variation function with a constant variation of 1.8.

The function is linear but is not a direct variation function.

The function is not a linear function.

Answer:

the answer is 32 lawns in 12 hours!

Step-by-step explanation:

3 hours = 8 lawns

6 hours = 16 lawns

9 hours = 24 lawns

12 hours = 32 lawns

Hope thus helped

Answer:

32

Step-by-step explanation:

Step 1:

8 : 3 = x : 12      Ratio

Step 2:

3x = 96    Multiply

Step 3:

96 ÷ 3      Divide

Answer:

32 lawns

Hope This Helps :)

When b is 3, the value of the expression \(2b^3 + 5\) is 59.

To evaluate the expression\(2b^3 + 5\) when b is 3, we substitute the value of b into the expression and perform the necessary calculations.

Given that b = 3, we substitute this value into the expression:

\(2(3)^3 + 5\)

First, we evaluate the exponent, which is 3 raised to the power of 3:

2(27) + 5

Next, we perform the multiplication:

54 + 5

Finally, we add the two terms:

59

Therefore, when b is 3, the value of the expression \(2b^3 + 5\) is 59.

In summary, by substituting b = 3 into the expression \(2b^3 + 5\), we find that the value of the expression is 59.

It's important to note that the provided equation has multiple possible solutions for x, but when b is specifically given as 3, the value of x is approximately 3.78.

It's important to note that in this equation, we substituted the value of b and solved for x, resulting in a specific value for x. However, if we wanted to solve for b given a specific value of x, we would follow the same steps but rearrange the equation accordingly.

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Answer:

the secound one

Step-by-step explanation:

hope it helped:3

(a) To find the flux of the vector field F→(x, y, z) = ⟨x, y, 5z⟩ through the closed boundary S of the solid W bounded by the paraboloid z = x² + y² and the plane z = 16, we can apply the divergence theorem.

AS

The divergence theorem states that the flux of F→ through S is equal to the triple integral of the divergence of F→ over the volume V enclosed by S.

First, we need to calculate the divergence of F→. Taking the divergence, we have div(F→) = ∂/∂x(x) + ∂/∂y(y) + ∂/∂z(5z) = 1 + 1 + 5 = 7.

Next, we evaluate the triple integral of the divergence over the volume V. The limits of integration for V are determined by the region bounded by the paraboloid and the plane, which can be expressed as 0 ≤ z ≤ x² + y² and 0 ≤ z ≤ 16. The integral becomes ∭V div(F→) dV = ∭V 7 dV.

To evaluate this triple integral, we need to express it in appropriate coordinates, such as cylindrical or spherical coordinates, depending on the symmetry of the problem. Then we can determine the limits of integration and perform the integration to compute the flux value.

(b) To find the flux of F→ out of the bottom of S (the truncated paraboloid) and the top of S (the disk), we need to consider the orientation of the surface and apply the divergence theorem separately for each surface.

For the bottom surface (truncated paraboloid), the outward orientation is in the negative z-direction. The flux through this surface is given by the negative of the integral ∭V div(F→) dV over the volume V enclosed by the bottom surface.

For the top surface (disk), the outward orientation is in the positive z-direction. The flux through this surface is equal to the integral ∭V div(F→) dV over the volume V enclosed by the top surface.

In both cases, we can use the same divergence value calculated earlier, div(F→) = 7, and integrate over the appropriate limits of integration based on the geometry of the surfaces.

In summary, to find the flux of F→ through the closed boundary S, we apply the divergence theorem by calculating the divergence of F→ and evaluating the triple integral over the volume enclosed by S. To find the flux out of the bottom and top surfaces separately, we consider the orientations and integrate over the appropriate volumes.

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Answer:

$9.00

Step-by-step explanation:

1.75 x 2 = 3.5+5.5= 9

Answer:

-16

Step-by-step explanation:

\(28-(\sqrt{44} )^2\\28 - (44)\\-16\)

When you square a square root, the number inside is the answer.

To translate an entire triangle, find the coordinates of each of the triangle's vertices, add the horizontal translation then plot the three translated points.

Whenever an object is moved from one location to the next without changing its size, shape, or orientation, a translation takes place. If we know which way and how far the figure to be moved, we can draw the translation in the coordinate plane.

Use P′(x+a,y+b) to translate the point P(x,y), a unit to the right, and b unit up. Use P′(x−a,y−b) to translate the point P(x,y), a unit to the left and b unit to the lower.

There are some steps of translating the triangle:

Step 1: Find the coordinates of each of the triangle's vertices in step one.

Step 2: Add the horizontal translation value to each vertex's x-coordinate and the vertical translation value to each point's y-coordinate to translate each point. If the horizontal translation is to the left or the vertical translation is downward for these translations, add a negative number.

Step 3: Plot the three translated points and draw the triangle by drawing a straight line between each pair of points.

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The value of x in the given equation will be 2/5

From the data,

We have to determine the value of x.

The given equation is: 18x-16=-12x-4

For determining the value of x, we will first shift the like terms on one side of the equation.

So, for solving the value of x we will shift the terms containing x and the constant on both sides of the equation.

So, shifting -12x from the right-hand side of the equation to the left-hand side of the equation,

We will get it as:

18x+12x = -4+16

30x=12

Now for solving the value of x we will shift x from the left side of the equation to the right side of the equation.

So, the value of x will be = 12/30 = 2/5

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The correct question may be:

What is the value of x

18x-16=-12x-4

Enter your answer in the box.

Answer:

y=-3x+2

Step-by-step explanation:

Answer:

18.445

Step-by-step explanation:

Multiply

Answer:

\(10x - \frac{1}{x} = 3 \\ 10x = 3 + \frac{1}{x} \\ 10x = \frac{3x + 1}{x} \\ 10x \times x = 3x + 1 \\ 10 {x}^{2} = 3x + 1 \\ 10 {x}^{2} - 3x - 1 = 0 \\ 10 {x}^{2} - 5x + 2x - 1 = 0 \\ 5x(2x - 1) + 1(2x - 1) = 0 \\ (5x + 1)(2x - 1) = 0 \\ \\ 5x + 1 = 0 \\ 5x = - 1 \\ x = \frac{ - 1}{5} \\ \\ 2x - 1 = 0 \\ 2x = 1 \\ x = \frac{1}{2} \)

hope this helps you.

Have a nice day!

The dog's running speed of 5 km/hr can be converted to approximately 3.125 mi/hr by multiplying it by the conversion factor of 1 mi/1.6 km. Rounding to the nearest thousandth, the dog can run at about 3.125 mi/hr.

To convert the dog's running speed from kilometers per hour (km/hr) to miles per hour (mi/hr), we need to use the conversion factor of 1.6 km = 1 mi.First, we can convert the dog's speed from km/hr to mi/hr by multiplying it by the conversion factor: 5 km/hr * (1 mi/1.6 km) = 3.125 mi/hr.

However, we need to round the answer to the nearest thousandth (three decimal places). Since the digit after the thousandth place is 5, we round up the thousandth place to obtain the final answer.

Therefore, the dog can run at approximately 3.125 mi/hr.

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Answer:

d. 15√5

Step-by-step explanation:

Perimeter = 3√5 × 5 sides

= 15√5

Answer: B - 15√5

Step-by-step explanation:

As said in the question, the perimeter is the total length of all sides of a figure. The question also says that all sides are the same length, and the length of one side is 3√5 yards.

In that case, all 5 sides have length 3√5 yards, so the perimeter would be this value added 5 times, or this value multiplied by 5:

\(P=3\sqrt{5}+3\sqrt{5}+3\sqrt{5}+3\sqrt{5}+3\sqrt{5}=5*3\sqrt{5}\)

\(P=15\sqrt{5}\)

Hence, the perimeter of the chicken coop is 15√5 yards.

The value of x will be 34°

Given that

(x+12)°+100°+x° are forming linear pair

Linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°. Such angles are also known as supplementary angles.

As mentioned, adjacent angles are angles that are next to each other. If you are sitting next to someone in class or on the bus, you could say that you are adjacent to them. More specifically, adjacent angles share a vertex and have a common side.

(x+12)°+100°+x°= 180°

⇒ x+ 12+ 100+x = 180°

⇒ 2x+112 = 180°

⇒ 2x = 180- 112

⇒ 2x = 68

⇒ x= 68/2

⇒ x= 34

For verification we will put value of x

(34+12)°+100°+34°

⇒ 46°+100°+34°

⇒146°+34°

⇒ 180°

So here we can see that by putting value of x we are getting the sum of 180°

Therefore value of x is 34

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The optimal solution a* corresponds to the eigenvector corresponding to the maximum eigenvalue This implies that the matrix (W - λD) must have a nontrivial , determinant must be zero \(\[\det(W - λD) = 0\]\)

To solve the problem of maximizing the Rayleigh quotient using the method of Lagrange multipliers, we can start by formulating the constrained maximization problem. We want to maximize the Rayleigh quotient, which is given by:

\(\[\frac{{a^T Wa}}{{a^T Ba}}\]\)

subject to the constraint:

\(\[a^T W a = 1\]\)

To introduce the constraint, we can use a Lagrange multiplier λ and consider the Lagrangian function:

\(\[L(a, λ) = \frac{{a^T Wa}}{{a^T Ba}} - λ(a^T W a - 1)\]\)

To find the optimal solution, we take the partial derivatives of L with respect to a and λ, and set them equal to zero:

\(\[\frac{{\partial L}}{{\partial a}} = \frac{{2W a}}{{a^T Ba}} - 2λW a = 0\]\)

\(\[\frac{{\partial L}}{{\partial λ}} = a^T W a - 1 = 0\]\)

From the first equation, we can simplify it to:

\(\[(W - λB)a = 0\]\)

Since B is a symmetric positive definite matrix, it can be decomposed as B = \(\[(QDQ^T)\]\), where Q is an orthogonal matrix of eigenvectors and D is a diagonal matrix of eigenvalues. Substituting this into the equation, we have:

\(\[(W - λQDQ^T)a = 0\]\)

\(\[Q^T(W - λD)Qa = 0\]\)

Since Q is orthogonal, we have:

\(\[(W - λD)Qa = 0\]\)

This implies that the matrix (W - λD) must have a nontrivial nullspace, which means its determinant must be zero:

\(\[\det(W - λD) = 0\]\)

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The optimal solution a* corresponds to the eigenvector of B associated with the eigenvalue λ. We find that a* is an eigenvector of the matrix B with eigenvalue λ. Hence, the matrix related to B and W is the matrix B itself.

To solve the problem of maximizing the Rayleigh quotient using the method of Lagrange multipliers, we first need to rewrite the unconstrained maximization as a constrained maximization problem. We can use the scale invariance of the Rayleigh quotient to do this.

The Rayleigh quotient is given by \(R(a) = \frac{a^T \cdot Wa}{a^T \cdot Ba}\), where a is a vector, W is a symmetric positive definite matrix, and B is also a symmetric positive definite matrix.

Let's introduce a Lagrange multiplier λ to incorporate the constraint that \(a^T \cdot Wa = 1\).

Now, our constrained maximization problem becomes:
maximize R(a) subject to the constraint \(a^T \cdot Wa - \lambda = 0\).

To solve this problem, we need to find the critical points of the Lagrangian function.

Taking the partial derivatives of \(L(a, \lambda) = R(a) - \lambda(a^T \cdot Wa - 1)\)

L(a, λ) with respect to a and λ, and setting them equal to zero, we can find the optimal solution a*.

Differentiating L(a, λ) with respect to a, we get:

\(\frac{\partial L(a, \lambda)}{\partial a} = (2Ba^* - \lambda Wa^*) = 0\).


In summary, by using the method of Lagrange multipliers, we have shown that the optimal solution a* for maximizing the Rayleigh quotient is an eigenvector of the matrix B, with the matrix B itself being the matrix related to B and W. The eigenvector a* corresponds to the eigenvalue λ.

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The ΔH values associated with the dissolution of lithium chloride that are exothermic involve the release of heat energy. When a substance dissolves in a solvent, it can either release heat (exothermic) or absorb heat (endothermic).

Here are the steps to determine if the dissolution of lithium chloride is exothermic:

1. Look for the chemical equation that represents the dissolution of lithium chloride. In this case, it would be:

LiCl(s) → Li+(aq) + Cl-(aq)

2. Examine the enthalpy change (ΔH) associated with this chemical equation. If the ΔH value is negative, it indicates an exothermic process, meaning that heat is released during the dissolution. If the ΔH value is positive, it indicates an endothermic process, meaning that heat is absorbed during the dissolution.

So, to identify the exothermic ΔH values associated with the dissolution of lithium chloride, you need to find experiments or reliable sources that provide the enthalpy change values for this reaction.

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Answer:

Step-by-step explanation:

Given the decimal value 588.55

The ones digit value is 8

The tens digits value is 80

Taking the ratio

The ones digits/the tens digits = 8/80

The ones digits/the tens digits = 1/10

The ones digits = 1/10 * the tens digits '

Hence the value of the ones digit is 1/10 of the value of the tens digit.

Option C is correct

Answer:

1 -5

don't know the answer of q2 and q3

Answer: 338.5 mm²

Step-by-step explanation:

There are 3 rectangles for the lateral surface area

LA=Ph           lateral surface area is the are around which is found Permiter*height

LA=(7.5+10.5+11)9.5=275.5

Total area = LA + 2B                    B is the area of the base 1/2 bh

A=275.5+2(1/2)(10.5)(6)

=338.5 mm²

The range of the function f include the following: [-20, ∞].

In Mathematics and Geometry, a range is the set of all real numbers that connects with the elements of a domain.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following range and domain:

Range = [-20, ∞] or -20 ≤ y ≤ ∞.

Domain = [-∞, ∞] or -1 < x < ∞.

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Answer:$109.81

Step-by-step explanation: