Consider the equations and graph below.

y = negative 3 (x minus 1). Y = negative 3 x minus 1

On a coordinate plane, 2 lines are parallel to each other.

By studying the graph of the function, it can be inferred that -

Domain = [-3, 3]

Range = ([tex]-\infty[/tex], 4]

Local maximum = 0, 4

Local minimum = -0.5

Increasing interval = [-3, -2) [tex]\cup[/tex] (-1, 2)

Decreasing interval = (-2, -1) [tex]\cup[/tex] (2, 3]

There is no constant interval.

What is graph of a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Graph of a function f(x) is the collection of all points of the form (x, f(x)).

Suppose the size of each square of the graph is 1 unit

From the graph, it can be seen that the value on the horizontal axis ranges from -3 to 3

Domain = [-3, 3]

The value on the vertical axis ranges from [tex]-\infty[/tex] to 4

Range = ([tex]-\infty[/tex], 4]

The graph has a local maximum at (2, 4) and (-2, 0)

Local maximum = 0, 4

The graph has local minimum at (-1, -0.5)

Local minimum = -0.5

Increasing interval [-3, -2) [tex]\cup[/tex] (-1, 2)

Decreasing interval = (-2, -1) [tex]\cup[/tex] (2, 3]

There is no constant interval.

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According to the given statement the answer of angle A is  [tex]\mathrm{m} \angle A=65^{\circ}[/tex].

A parallelogram with the opposing sides perpendicular is called a quadrilateral (and therefore opposite angles equal). A parallelogram among all right angles generally known as a rectangle, whereas a quadrilateral having equal angles is known as a rhombus.

[tex]\mathrm{m} \angle F G D=35^{\circ}\\\mathrm{m} \angle DFG=180^{\circ}-69^{\circ}\\\\[linear pair of angle]\\mathrm{m} \angle DFG=111^{\circ}\\\mathrm{m} \angle F DG=180^{\circ}-(35^{\circ}+111^{\circ})\\\\mathrm{m} \angle F DG=34^{\circ}[/tex]

because DC||AB, so  

[tex]\mathrm{m} \angle BDC={m} \angle ABD=Alternate angle[/tex]

[tex]so, \mathrm{m} \angle ABD=34^{\circ}[/tex]

because the sum of interior angle of a triangle = 180

[tex]so, \mathrm{m} \angle A=180^{\circ}-(81^{\circ}+34^{\circ})\\ \mathrm{m} \angle A=65^{\circ}[/tex]

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[tex]\qquad \textit{Centroid of a Triangle} \\\\ \left(\cfrac{x_1+x_2+x_3}{3}~~,\cfrac{y_1+y_2+y_3}{3}~~ \right)\quad \begin{cases} X(\stackrel{x_1}{6},\stackrel{y_1}{0})\\ Y(\stackrel{x_2}{2},\stackrel{y_2}{8})\\ Z(\stackrel{x_3}{-2},\stackrel{y_3}{-2}) \end{cases} \\\\\\ \left( \cfrac{6+2-2}{3}~~,~~\cfrac{0+8-2}{3} \right)\implies \left(\cfrac{6}{3}~~,~~ \cfrac{6}{3} \right)\implies \text{\LARGE (2~~,~~2)}[/tex]

Answer:

a) 5

b) -4/3

c) y = -4/3x - 11/3

Step-by-step explanation:

The length of the segment means the length in between two points. Use 2 dimensional distance formula.

[tex]d = \sqrt{(x_{2}-x_{1})^2 + (y_{2}-y_{1})^2 }[/tex]

Plug in your points.

x value is the first point in the set, the horizontal measure in units.

y value is the second point in the set, the vertical measure in units.

x values of 2 points: -2, -5

y values of 2 points: -1, 3

[tex]d = \sqrt{(-5--2)^2 + (3--1)^2 }[/tex]

A negative value subtracted by another negative value is the first negative value plus the inverse of the second negative value.

For example,

-5 - -6 = -5 + 6 = 1

Simplify.

[tex]d = \sqrt{(-3)^2 + (4)^2 }[/tex]

[tex]d = \sqrt{9 + 16}[/tex]

[tex]d = \sqrt{25}[/tex]

5

Square root of 25 is 5 because 5^2, which is 5 x 5 is 25.

The slope is how much the y-value changes when the x-value increases by 1.

To calculate this, plug your points into the slope formula.

[tex]Slope = \frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\frac{3--1}{-5--2}[/tex]

[tex]\frac{4}{-3}[/tex]

-4/3

I'm going to assume that the problem is asking you to write it in the form of y=mx+b, or slope-intercept form, a way of easily graphing a line. If it  is asking you to express it in another way like Standard or Point-Slope Form, comment and I'll change it.

y = mx+b

m = slope

b = y-intercept, or the y-value of when the x-value is 0 on a line

y and x stays as variables if you want to graph it and for generally answering problems.

So, if x = 0, we can plug it into what we currently know.

We know the points: (-2,-1) or (-5,3)

Plug in either set of points into the slope-intercept equation.

I'll use -2,-1 but you can use either.

-1 = (-4/3) (-2) + b

Because we're solving for when x is 0, replace -2 for 0.

-1 = 8/3 + b

Subtract 8/3 on both sides.

-1 - 8/3 = 8/3 - 8/3 + b

-1 - 8/3 = b

b = -11/3

Now, the equation is:

y = -4/3x - 11/3

This is the beauty of the forms of linear equations. You can plug in any points to solve for the full set of points. You can convert any form of the linear equation to another form.

When a population is subjected to directional selection over time, the traits that are selected for will remain stable while the traits that are selected against will disappear.

Evolution is the study of how populations change over time. Most traits have multiple genes controlling their structure, function, appearance, and other characteristics. Single genes only very infrequently control a trait.

As a result, most traits have a tendency to be continuous in nature and to have a wide range of values. One side of these values will be picked against during directional selection, while the other side will be selected in favor of. Look at the illustration of a lemur's fur color below.

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Answer:

Step-by-step explanation:

-0.17301038

Answer: 3 years

Step-by-step explanation:

Answer: x < -3

Step-by-step explanation: even tho if we solve you will get a big number number then you reduce the number to a smaller number

The y-intercepts of the functions are

The complete question is added at the end of this solution as an attachment

As a general rule, the y-intercept is the point in an equation or a function where x = 0

Using the above as a guide, we have the following:

For the function g(x), we have

g(x) = abˣ

Using the given points (1, -2) and the growth factor of 2, we have

g(x) = a(2)ˣ

This means that

a(2)¹ = -2

So, we have

2a = -2

a = -1

So, the equation is

g(x) = -1(2)ˣ

Set x = 0

g(0) = -1(2)⁰

g(0) = -1

So, the y-intercept of function g(x) = -1

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Answer:

c=-35/4

Step-by-step explanation:

For this, we would use Vieta's theorem, which states the roots of the equation added together would equal -b/a, x₁ + x₂ = -b/a

Lets create a system with this:
x₁ - x₂ = 6 (This is given from the problem)

x₁ + x₂ = -b/a  or -1/1, plugging in the values from your equation

next, we would add these systems together

x₁ + x₂ + (x₁ - x₂) = 6 + (-1)
x₁ + x₁ = 5
2x₁ = 5

x₁ = 2.5

If we plug x₁ back in, we get:

2.5 - x₂ = 6

-x₂ = 3.5

x₂ = -3.5

Now that we have the roots, we can use Vieta's theorem again to say

x₁ * x₂ = c/a

Plugging this in, we get:

2.5 * -3.5 = c/a

Lets change things to fractions to make things easier

5/2 * -7/2 = c/a

Plugging in a, we get

-35/4 = c/1

-35 = 4c

c = -35/4

Hope this helps!

The value of x in the triangle is 26.1°

A triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.

Acute triangle - all three angles are less than 90°

Right triangle - one angle is 90°

Obtuse triangle - one angle is greater than 90°

Equilateral triangle - all three sides are the same length

Isosceles triangle - two sides are the same length

Scalene triangle - all three sides are different lengths

Since the triangle is right-angled

tan x = opposite/adjacent

tan x = 26/53

tan x = 0.4905

x = arc(tan) 0.4905

x = 26.1°

In conclusion x = 26.1°

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By algebra properties we find the following relationships between each pair of algebraic expressions:

In this we must determine the equivalent algebraic expression related to given expressions, this can be done by applying algebra properties on equations from the second column until equivalent expression is found. Now we proceed to find for each case:

First equation

(7 - 2 · x) + (3 · x - 11)

(7 - 11) + (- 2 · x + 3 · x)

- 4 + (- 2 + 3) · x

- 4 + (1) · x

- 4 + (5 - 4) · x

- 4 - 4 · x + 5 · x

- 4 · (x + 1) + 5 · x → Case 4

Second equation

- 7 + 6 · x - 4 · x + 3

(6 · x - 4 · x) + (- 7 + 3)

(6 - 4) · x - 4

2 · x - 4

2 · (x - 2) → Case 1

Third equation

9 · x - 2 · (3 · x - 3)

9 · x - 6 · x + 6

3 · x + 6

(2 + 1) · x + (14 - 8)

[1 - (- 2)] · x + (14 - 8)

(x + 14) - (8 - 2 · x) → Case 2

Fourth equation

- 3 · x + 6 + 4 · x

x + 6

(5 - 4) · x + (7 - 1)

(7 + 5 · x) + (- 4 · x - 1) → Case 5

Fifth equation

- 2 · x + 9 + 5 · x  + 6

3 · x + 15

3 · (x + 5) → Case 3

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Answer:

$0.27875 or $0.28 1 cup = 2 ounces Number of cups in 1 jar = 4 ounce

Step-by-step explanation:

Since the rectangle's shorter side is half as long as its longer side, its top left vertex is (0,a).

A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y). You do the reverse to determine a point's coordinates in a coordinate system. Start at the point, then move up or down a vertical line until you reach the x-axis. Your x-coordinate is shown there. To find the y-coordinate, repeat the previous step while adhering to a horizontal line.

Here,

Let x be the length and y be the width,

y=x/2

x=2a

y=a

The top left vertex=(0,a)

The top left vertex is (0,a) as shorter side of the rectangle is half the length of the longer side.

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