Find the average rate of change of g(x) = 2x² + on the interval [-1,2]

The explicit rule for the nth term of the geometric sequence: 3, 18, 108, 648, 3,888, … is aₙ = 3( 6ⁿ⁻¹ )

The geometric sequence is expressed as aₙ = a₁ × rⁿ⁻¹

Given the set of numbers in the question;

3, 18, 108, 648, 3,888, …

The first term a₁ = 3

Next, we determine the common ratio r.

Divide a term by the previous term gives the common ratio.

Common ratio r = 18/3

Common ratio r = 6

Now, plug in the values of first and common ratio into the above formula to determine the nth term.

aₙ = a₁ × rⁿ⁻¹

aₙ = 3 × 6ⁿ⁻¹

aₙ = 3( 6ⁿ⁻¹ )

Therefore, the nth term of the sequence is aₙ = 3( 6ⁿ⁻¹ ).

Option D) aₙ = 3( 6ⁿ⁻¹ ) is the correct answer.

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Answer: x<3

Step-by-step explanation:

Bring the 11 to the other side of the equation, and subtract.

5x<15.

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{11 + 5x < 26}[/tex]

[tex]\mathsf{5x + 11 < 26}[/tex]

[tex]\large\textbf{Subtract 11 to both sides:}[/tex]

[tex]\mathsf{5x + 11 - 11 < 26 - 11}[/tex]

[tex]\large\textbf{Simplify it}[/tex]

[tex]\mathsf{5x < 26 - 11}[/tex]

[tex]\mathsf{5x < 15}[/tex]

[tex]\large\textbf{Divide 5 to both sides}[/tex]

[tex]\mathsf{\dfrac{5x}{5} < \dfrac{15}{5}}[/tex]

[tex]\large\textbf{Simplify it}[/tex]

[tex]\mathsf{x < \dfrac{15}{5}}[/tex]

[tex]\mathsf{x < 3}[/tex]
[tex]\large\textbf{You have an \boxed{\rm{\bf o p e n e d}} circle shaded to the left}[/tex]

[tex]\huge\boxed{\mathsf{x < 3}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The point (1, 1/2) lie on the equation  y(x² + 1) = 1.

An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence.

Pair in Order = (x, y)

x is the abscissa, the distance measure of a point from the primary axis x

y is the ordinate, the distance measure of a point from the secondary axis y

Given, A function y(x² + 1) = 1.

y = 1/(x² + 1).

When x = 1, y = 1/2.

When x = - 1, y = 1/2.

So, The points that lie on the equation y(x² + 1) = 1 is (1, 1/2).

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Answer:

A. 12 cm, 5 cm, 17 cm

Step-by-step explanation:

For any three given lengths to be the sides of a triangle, they must satisfy the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides must be greater than the length of the third side.

Let's check each of the options:

A. 12 cm, 5 cm, 17 cm: 5 + 12 = 17, which is greater than 17, so this is a valid triangle.

B. 10 cm, 15 cm, 24 cm: 10 + 15 = 25, which is greater than 24, so this is a valid triangle.

C. 9 cm, 22 cm, 11 cm: 9 + 11 = 20, which is not greater than 22, so this is not a valid triangle.

D. 21 cm, 7 cm, 6 cm: 7 + 6 = 13, which is not greater than 21, so this is not a valid triangle.

Therefore, the three lengths that could be the sides of a triangle are A (12 cm, 5 cm, 17 cm) and B (10 cm, 15 cm, 24 cm).

The value -2 is the rate of change of the linear equation.

A general linear equation is:

y = a*x + b

Where a is the rate of change and b is the y-intercept.

The rate of change tells us how the variable y changes when the variable x changes.

In this case we have:

y=-2x+10

So the "-2" is the rate of change, it tells us that each time that x increases 1 unit, the value of y decreases by 2 units.

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Answer:

u ≥ 2

Step-by-step explanation:

2u-5>7 :

Add 5 to both sides:

2u = 7 + 5

2u > 12

Divide by 2:

u > 6

-3u ≤ -6

Multiply both sides by -1, inequality reverses
-3u(-1) ≥ -6(-1)

3u ≥ 6

Divide by 3:

u ≥ 2

Since  u > 6  is a subset of u ≥ 2, the interval for both inequalities is

u ≥ 2

Therefore , the solution of the given problem of trigonometry comes out to be the five functions value are written above Cosθ = 3/5.

Relationships between cubic splines and trigonometry When the professions of mathematicians were united, it is thought that the field was founded during the third millennium BC. Precise mathematical methods can be used to solve a wide range of geometric issues or to determine the outcomes of calculations that use them. The study of the six fundamental trigonometric operations is known as trigonometry.

Here,

Given :

There are in 3 quadrant :

=> Sinθ = -4/5

=> Cosθ = √1 - Sin²θ

=>  Cosθ  = √1 - 16/25

=> Cosθ = 3/5

=>Tan θ = -4/5 / 3/5

=> Tan θ  = -4/3

=>Cot θ = -3/4

and

Cosec θ = -5/4

Sec  θ = 5/3

Therefore , the solution of the given problem of trigonometry comes out to be the five functions value are written above Cosθ = 3/5.

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Step-by-step explanation:

Cross multiply to solve for "a":

6 * a = 8 * 8

Simplify the right side:

6 * a = 64

Divide both sides by 6 to isolate "a":

a = 64 / 6

Simplify:

a = 10.67

Answer:Hypothesis: A polygon has four equal sides and four right angles.

Conclusion: The polygon is a square.

Converse: If the angles are congruent, then the measure of 4] equals the measure of K.

Inverse: If the measure of 4] does not equal the measure of K, then the angles are not congruent.

Contrapositive: If the angles are not congruent, then the measure of 4] does not equal the measure of K.

Original statement: If a number is even, then it is divisible by two.

Inverse: If a number is not divisible by two, then it is not even.

Biconditional statement: This month is November if and only if next month is December.

Biconditional statement: A triangle is a right triangle if and only if it contains a right angle.

Converse: If a triangle contains a right angle, then it is a right triangle.

The converse is not necessarily a true statement as a triangle can contain a right angle and still not be a right triangle (i.e. it may not meet the requirements of all sides being of equal length).

Step-by-step explanation:

Hypothesis: A polygon has four equal sides and four right angles.

Conclusion: The polygon is a square.

Converse: If the angles are congruent, then the measure of 4] equals the measure of K.

Inverse: If the measure of 4] does not equal the measure of K, then the angles are not congruent.

Contrapositive: If the angles are not congruent, then the measure of 4] does not equal the measure of K.

Original statement: If a number is even, then it is divisible by two.

Inverse: If a number is not divisible by two, then it is not even.

Biconditional statement: This month is November if and only if next month is December.

Biconditional statement: A triangle is a right triangle if and only if it contains a right angle.

Converse: If a triangle contains a right angle, then it is a right triangle.

The converse is not necessarily a true statement as a triangle can contain a right angle and still not be a right triangle (i.e. it may not meet the requirements of all sides being of equal length).

The similarity statement is competed as follows

The proportion is completed as below

This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions

Examining the figure shows that pair of equivalent sides are

KL / KJ and ML / KL

LJ / MJ and KJ / LJ

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The error in River's analysis is that it is known if LM and MJ are perpendicular to KL and KJ.

What is error analysis?

Error analysis is a technique used to track out errors in learner language, ascertain whether they are systematic, and (if possible) provide an explanation for why they occurred.

It is given that -

Line segment KM is the bisector of ∠LKJ.

Also, line segment LM = MJ.

According to the angle bisector theorem if a line is a bisector of an angle then the corresponding sides of the angle should be perpendicular to the third side which is getting bisected.

Although it is given that  LM = MJ, but it is not known that if LM and MJ are   perpendicular to the sides of ∠LKJ.

Therefore, River cannot conclude that KM is the bisector of ∠LKJ.

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Answer:

Below

Step-by-step explanation:

Area is base ( which is 6 m) times the height ( which is 8m)

6 x 8 = 48 m^2

Answer:

4/161

Step-by-step explanation:

2×2
____
23×7

=4
161

=4
161

Step-by-step explanation:

well, you have it further up :

P(A) = 17x = 17 × 1/32 = 17/32 = 0.53125

Answer: x = 14; y = 74; Isosceles and Acute

Step-by-step explanation: 3(x+7) = 3x + 21

Isosceles triangles have congruent base angles making 63 = 3x +21

Solve for x.

All angles of a triangle add up to 180 making y = 180 - 63 - 63.

Isosceles because two sides are congruent. And acute because all angles are under 90.

Answer: 3/5

The total number of slices is 10, and the number of yellow or red slices is 2 yellow slices + 4 red slices = 6 slices.

So, the probability of the dial stopping on a yellow or red slice is 6 slices / 10 total slices = 3/5.

This is the final answer, and it is already in its simplest form.

Answer: 16

Step-by-step explanation:

To get from 3 to 12, you multiply by 4

To get from 5 to 20, you multiply by 4

So you just multiply 4 by 4 to get x

Answer:

x = 16

Step-by-step explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion, that is

[tex]\frac{x}{4}[/tex] = [tex]\frac{20}{5}[/tex] = 4 ( multiply both sides by 4 to clear the fraction )

x = 16

The surface area of the sphere is 1519.8 yd².

Three-dimensional shapes or solids are the names given to 3D shapes in geometry. Three separate dimensions, such as length, width, and height, are used to describe 3D shapes. The lack of thickness or depth in 2D shapes is the only distinction between them and 3D ones.

Given a sphere

diameter = 22 yards

radius = d/2 = 22/2

radius = 11 yards

the surface area of the sphere = 4πr²

S = 4πr²

S = 4(3.14)11²

S = 1519.76 yd²

S = 1519.8 yd²

Hence option A is correct

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The equation representing the total cost is 15x + 750 and the total cost of restringing 32 lacrosse sticks would be $1230.

An equation is written in the form of variables and constants separated by the operation of multiplication and division,

An equation states that terms in different forms on both sides of the equality sign are equal.

Multiplication and division do not separate the terms of an equation.

Let, The number of lacrosse sticks be 'x' and the total cost is C(x).

Therefore, The equation representing the context is,

C(x) = 25x + 750.

The total cost of restringing 32 lacrosse sticks would be,

C(32) = 15×32 + 750.

C(32) = 480 + 750.

C(32) = 1230.

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Answer:

He sleeps about 9 hours at night.

Step-by-step explanation:

If Sean's baby brother sleeps 13 hours a day, and takes 2 two-hour naps during the day, he sleeps 2 * 2 = 4 hours during the day.

SOOO, he sleeps 13 - 4 = 9 hours at night.

Answer: no solution

Step-by-step explanation:

The statement that A triangular prism contains two parallel hexagonal faces is False

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

A triangular prism contains two parallel hexagonal faces.

As a general rule, the parallel faces in a triangular prism are triangles

This is so because a triangular prism is a 3-dimensional object with a triangular base and three rectangular sides.

The two parallel faces of a triangular prism are congruent triangles, not hexagons.

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Answer:

Expression for number of girls:

2b + 15

Equation for number of boys and girls:

b + (2b + 15) = 84

Number of boys

23

Number of girls

61

Step-by-step explanation:

b = number of boys

g = number of girls

b + g = 84

g = 2b+15

b + (2b + 15) = 84

3b + 15 = 84

3b = 69

b = 23

b + g = 84

23 + g = 84

g = 61

The sample size if the probability that the mean life is less than 1120 hours is 0.92 is given as follows:

n = 24.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 1100, \sigma = 70, s = \frac{70}{\sqrt{n}}[/tex]

The p-value of Z when X = 1120 is of 0.92, hence Z = 1.405, and the sample size is obtained as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]1.405 = \frac{1120 - 1100}{\frac{70}{\sqrt{n}}}[/tex]

[tex]20\sqrt{n} = 70 \times 1.405[/tex]

[tex]n = \left(\frac{70 \times 1.405}{20}\right)^2[/tex]

n = 24.

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Answer:

E

Step-by-step explanation:

just looking for the ration if scale factor is 2

multiply it and fimd the ans

The function that is represented by the graph is y = ∛(x + 3) + 3.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The general form of a cube root function is -

y = a∛(x - h) + k and the parent graph is y = ∛x.

So the parent function is found.

The coordinate point for the parent function is -

(-1,-1) , (0,0) and (1,1).

In the graph it can be seen that the coordinate points are -

(-4,2), (-3,3) and (-2,4)

So the graph is first moved 3 units up and then moved three units left.

So, the coordinated become - (x + (-3) , y + 3)

So, the function that represents the graph is -

y = ∛(x + 3) + 3

Therefore, the function is y = ∛(x + 3) + 3.

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