Use the graph below to answer the following question:
What is the average rate of change from x = –4 to x = 1?
A. -3
B. -1
C. 0
D. 1

Points A, F, and G are three collinear points on line l.

[tex]\boxed{ \ The \ Answer \ is \ B \ }[/tex]

Let us consider the definition of collinear.  

Collinear  

Collinear points represent points that lie on a straight line. Any two points are always collinear because we can constantly connect them with a straight line. A collinear relationship can occur from three points or more, but they don’t have to be.  

Noncollinear  

Noncollinear points represent the points that do not lie in a similar straight line.  

Given that lines k, l, and m with points A, B, C, D, F, and G. The logical conclusions that can be taken correctly based on the attached picture are as follows:  

Hence, the specific answer to this key question is undoubted, i.e., points A, F, and G.  

Note:

All points can, also, be said to be coplanar. This is because the three lines intersect with each other and lie on a planar surface.

Coplanar  

Coplanar points represent a group of points that lie on the same plane, i.e. a planar surface that extends without end in all directions. Any two or three points are always coplanar, but four or more points might or might not be coplanar.  

Keywords: what are, three collinear points A, F, and G, noncollinear, located, similar straight line, definition, represents, relationship, coplanar

Answer: B

Step-by-step explanation:

Answer:

±1, ±2, ±3, ±4, ±6 and ±12

Step-by-step explanation:

The potential roots are obtained as following:

potential roots = factors of the constant term / factors of leading coefficient

The constant term is -12, its factors are ±1, ±2, ±3, ±4, ±6 and ±12

The leading coefficient is 1, its factors are  ±1

Therefore the potential roots are ±1, ±2, ±3, ±4, ±6 and ±12

The length of each side of the given square would be 5 cm if square has an area of 25cm².

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

A square is defined as a polygon that has four sides and is a closed, two-dimensional (2D) object. A square has equal and parallel sides on all four sides.

The area of a square is equal to the squared of sides or the multiplication of two sides.

We have been given a square has an area of 25 cm²

The length of one side = √( the area of a square)

The length of one side = √(25)

The length of one side = 5 cm

Therefore, the length of each side of the given square would be 5 cm.

Learn more about the area of the square here:

brainly.com/question/1561162

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Answer:

cos(Z) = 12/13

Step-by-step explanation:

Given that the triangles ABC and XYZ are similar (their corresponding angles are congruent and the corresponding sides are in proportion), then cos(Z) is equal to cos(C).

From the picture attached:

cos(C) = adjacent/hypotenuse

cos(C) = 12/13

Final answer:

Without additional information about triangle XYZ or its similarity ratio to triangle ABC, it is impossible to provide the exact value of cos(Z).

Explanation:

The question involves finding the value of cos(Z) in a triangle similar to triangle ABC. When triangles are similar, their corresponding angles are equal. However, without additional information such as side lengths or other angle values, it's not possible to calculate the exact value of cos(Z). But in general for any triangle, the value of cosine for any angle can be found using the cosine formula or by using the ratio of the adjacent side to the hypotenuse in a right triangle. For non-right triangles, one could utilize the Law of Cosines to determine the cosine of the included angle.

Answer: [tex]40^{\circ}[/tex]

Step-by-step explanation:

Given: A regular nonagon with 9 sides.

For a regular nonagon, it maps onto itself 9 times during a rotation of 360°.

Mow, the angle at Lusia can rotate the regular nonagon through to map it onto itself=[tex]\frac{360}{\text{number of sides of regular polygon}}=\frac{360}{9}=40^{\circ}[/tex]

A shape that maps onto itself after rotation, has a rotation symmetry

The angles of rotation that would map the nonagon onto itself are:

[tex]\mathbf{40, 80, 120\ and\ 160}[/tex]

A regular nonagon has nine equal sides i.e.

[tex]\mathbf{n = 9}[/tex]

The angle at the center of the nonagon is:

[tex]\mathbf{\theta = 360}[/tex]

So, the angle of rotation symmetry is:

[tex]\mathbf{\alpha = \frac{\theta}{n}}[/tex]

This gives:

[tex]\mathbf{\alpha = \frac{360}{9}}[/tex]

[tex]\mathbf{\alpha = 40}[/tex]

This means that, the nonagon would map onto itself, when rotated at 40 degrees.

Other angles of rotation symmetry must be a multiple of 40

i.e.

[tex]\mathbf{\alpha = 40, 80, 120, 160, 200, 240, 280......}[/tex]

Using the above list of angles, the angles of rotation that would map the nonagon onto itself are:

[tex]\mathbf{40, 80, 120\ and\ 160}[/tex]

Read more about rotational symmetry at:

https://brainly.com/question/1597409

Answer:  The given number is NOT rational.

Step-by-step explanation:  We are given to check whether the number 0.12112111211112 . . . a rational number or not.

We know that

if the digits after the decimal in a number are either repeating or terminating, then the number is rational.

The given number is

[tex]x=0.12112111211112 . . .[/tex]

We can see that the digits after the decimal are neither repeating nor terminating.

Therefore, the given number is NOT rational.

Answer:

120

Step-by-step explanation:

y = arctan(8/10)

y = 38.65

y = 39

Answer:

Option (b) is correct.

The measure of angle y is 39°

Step-by-step explanation:

Given : A right angled triangle with some measurements.

We have to find the value of y.

Consider the given triangle,

Using trigonometric ratios,

We know tangent is the ratio of perpendicular to its base.

Mathematically written as

[tex]\tan\theta=\frac{Perpendicular}{base}[/tex]

So, for given triangle, [tex]\theta=y[/tex]

and for y, perpendicular is 8 and base is 10

Substitue, we have,

[tex]\tan y=\frac{8}{10}[/tex]

Simplify, we have,

[tex]\tan y=\frac{4}{5}[/tex]

Taking inverse of tan both side, we have,

[tex]\tan^{-1}(\tan y)=\tan^{-1}(\frac{4}{5})[/tex]

[tex]y=\tan^{-1}(\frac{8}{10})[/tex]

Simplify , we have,

[tex]y=38.65^{\circ}[/tex]

Thus, the measure of angle y is 39°

Answer:

Lizabeth remembers the poverty of her childhood hometown but also the marigolds in Miss Lottie's yard.

Explanation:

The short story "Marigolds" by Eugenia Collier is a story of a little girl's childhood experience. In the story, Lizabeth talks of how her community is impoverished, "—the brown, crumbly dust of late summer—arid, sterile dust that gets  into the eyes and makes them water, gets into the throat and between the  toes of bare brown feet". But despite the background image of poverty all around her, she could also remember "a brilliant splash of sunny  yellow against the dust—Miss Lottie’s marigolds". Through her remembering of the marigolds amidst the poverty of her childhood hometown, Lizabeth develops the theme of beauty appreciated even in the worse circumstances.

Final answer:

Kevin is 7 years old. The problem is solved by setting up an equation 19 = 2K + 5, subtracting 5 from both sides to get 14 = 2K, and then dividing by 2 to find Kevin's age.

Explanation:

The question asks us to find Kevin's age given that James's age is five more than two times Kevin's age and that James is 19 years old. To solve this, we'll set up an equation based on the information provided.

Let K represent Kevin's age. According to the problem, we have:
James's age = 2 × Kevin's age + 5
Since James's age is 19, we can write:
19 = 2K + 5

To solve for K, we first subtract 5 from both sides of the equation:
14 = 2K
Then, we divide both sides by 2 to isolate K:
K = 7

Therefore, Kevin is 7 years old.

Answer: $64000

Step-by-step explanation:

The exponential equation for growth in function with growth factor 'b'in time 't' is given by :-

[tex]y=Ab^x[/tex] , where A is the initial value.

Given : The initial value : [tex]A=\$2000 [/tex]

Growth rate = [tex]b=2\text{ every 9 years} [/tex]

Time periods in 45 years :[tex]t=\dfrac{45}{9}=5[/tex]

Then , the exponential equation for growth for t=5 is given by :-

[tex]y=2000(2)^{5}=64000[/tex]

Hence, the money you would have after 45 years = $64000

the correct interpretation of the inequality –2 > –8 is On a number line, −2 is located to the right of –8.