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The linear equation in the list of equations is y = [tex]\frac{1}{2}x + 3[/tex]

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.

A linear equation must have the highest power of the independent variable as 1.

option A and C, the independent variable x has degree 2

option D the x variable there stands for absolute values.

So only B is a linear equation since variable x has degree 1

In conclusion, the linear equation is y = [tex]\frac{1}{2}x + 3[/tex]

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Answer: b=14

Step-by-step explanation:

we can use three steps

isolate the variable, use inverse operation and do everything on both sides of the equation to keep the equation in balance

if we had 5 back on both sides of the equation:

b-5=9

b= 14

B-5=9

b=9+5

b=14

To get variable b by itself , you add 5 to both sides of the equation.

A. The signal of each coefficient is given by:

B. The coefficient closest to zero is of B.

C. The coefficient with the least value is of C.

The transformations are vertical stretch/compression of the absolute function.

Then the signal is defined as follows:

The coefficient closest to zero is for the biggest vertical compression, which is of B, for which the graph stretches horizontally and compresses vertically.

The least value is for the biggest reflected stretching, which is in item c, in which the curve has a larger vertical stretch than in item d.

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A square and a rectangle have the same perimeter, then the area of the square and the rectangle are the same.

An object's area is how much space it takes up in two dimensions. It is the measurement of the amount of unit squares which completely encompass the surface of a compact figure. The squared unit, which is frequently expressed as inches, square feet, etc., is the accepted unit of area.

Let x be the side of the square,

The length of the rectangle, l = 2x - 4,

The width of the rectangle, w = x - 6,

So, we have: (2x - 4) × (x -6) = x²,

x = 2 (4 + √10)

= 14.32455 cm, it is the side of the square

14.32455 × 2 -4

=24.6491cm, it is the length of the rectangle.

14.32455 - 6

=8.32455cm, it is the width of the rectangle.

24.6481 × 8.32455 = 14.32455²

= 205.19 cm²

Thus, it means that the areas of square and rectangles are similar.

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Answer:

Step-by-step explanation:

The graph of the given inequalities is given below and point (0, −2) is the solution set of the given inequalities.

In thegiven question we have to graph the given system of inequalities and also check that (4, −1) is the solution set of the given system or not.

The given system of inequalities are

2x+8y≥ −16..................(1)

2x−4y< 8..................(2)

taking common 2 from the equation 1, now the system of inequality is

x+4y≥ −8..................(3)
Now graphing the inequalities.

The graph of the given inequalities is given below;

From the given grap we can see that the point (0, −2) is the point in which both given inequalities are meeting. That means (0, −2) is the solution set of the given inequalities

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g(x) is a translation of 4 units to the right, so the correct option is a: k = -4.

We know that:

g(x) = f(x + k)

This means that g(x) is a horizontal translation of f(x) of k units.

if k > 0 the translation is to the left.

if k < 0  the translation is to the right.

We know that f(x) passes through (0, 0) and (2, 2)

so f(0) = 0

And g(x) passes through (4, 0) and (-2, 2)

This means that:

g(4) = f(0)

f(4 + k) = f(0)

4 + k  = 0

k = 0 - 4 = -4

The value of k is -4, so the correct option is a.

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The area of the sector in terms of π is 35.6π inches squared.

The area of the sector is approximately  111.6 inches square

The area of sector of a circle is the amount of space enclosed within the boundary of the sector.

Therefore,

area of a sector = ∅ / 360 × πr²

where

Therefore,

∅ = 200 degrees

r = 8 inches

area of the sector = 200 / 360 × 8²π

area of the sector = 200 / 360 × 64π

area of the sector =12800π/  360

area of a sector = 35.6π inches squared

Let's find the area of the sector with π = 3.14

area of a sector = 35.6 × 3.14 = 111.6 inches square

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first multiple of 5 is 5

15 th multiple is 75

now lets use arithmetic progression

common difference d is 5

first term a=5

formula:

sum=n/2[first term + last term]

n=15

sum=15/2[75+5]

=15 x 40

=600

check it

5+10+15+20+25+30+35+40+45+50+55+60+65+70+75=600

the equation straight line y = -1/5 x + 4. of the line drawn in the picture is attached below.

What is equation straight line?

There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.

Given two line-side coordinates, use the slope formula to determine the slope of the line. The slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1).

The given equation y = -1/5 x + 4.

Here m = -1/5

and c= 4

So the plot on the graph will be as fallow.

Hence the equation of the line drawn in the picture attached below

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As per the concept of transformation, there is a single rigid motion that would map triangle WXY to triangle W"X"Y"' is reflection.

Single rigid motion:

Basically, the single rigid motions are also called congruence transformations. Translations, reflections, rotations, and glide reflections are rigid motions.

Given,

Here we have the graph.

And we need to find is there a single rigid motion that would map triangle WXY to triangle W"X"Y"'.

While we looking into the graph, we have identified that, the image of the triangle is moved from one position to another position.

Here we need to identify the Single rigid motion that would map triangle WXY to triangle W"X"Y"',

For that, we have to carefully looking on the image,

So, we have identified that the triangle X"Y"Z" is the mirror reflection of the triangle XYZ.

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Answer:

okay i'll keep this in mind

Step-by-step explanation:

The median of the wages is class 2,001-3,000 and the modal of the wages is 2,001-3,000

The table of values is given as

Wage                  Number of Employees

1,001-2,000           5

2,001-3,000           9

3,001-4,000          4

4,000-5,000         2

The total frequency is

Total = 5 + 9 + 4 + 2

Evaluate

Total = 20

So, the median position is

Median = (20 + 1)/2 th

Evaluate

Median = 11.5 th

This position is located at class 2,001-3,000

So, the median is wages 2,001-3,000

The table of values is given as

Wage                  Number of Employees

1,001-2,000           5

2,001-3,000           9

3,001-4,000          4

4,000-5,000         2

The mode is the highest frequency of the class

The highest frequency above is 9

So, the modal is wages 2,001-3,000

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8.00 - 3.50 = 4.50

4.50 / .75 = 6

Nataly can travel 6 miles

The correct options for she walk all together are;

⇒ 12 + 1/4 x 12

⇒ 12 ( 1 + 1/4 )

⇒ 12 x 5/4

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Susan jogged 12 miles.

And, Then she walked 1/4 that distance.

Now,

Since, Susan jogged 12 miles.

And, Then she walked 1/4 that distance.

Hence, Total distance = 12 + 12 x 1/4

                                  = 12 + 3

                                  = 15

Thus, The total distance she walk all together will be 15 miles.

Therefore, The correct options for she walk all together are;

⇒ 12 + 1/4 x 12

⇒ 12 ( 1 + 1/4 )

⇒ 12 x 5/4

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The perimeter of triangle ABC = 60 + 20√3  cm

What is perimeter?

The complete length of a shape's edge serves as its perimeter in geometric terms. Adding the lengths of all the sides and edges that surround a form yields its perimeter. It is calculated using linear length units such centimeters, meters, inches, and feet.

In triangle ADB,

sin (30°) = AD/AB

1/2 = ( 10 √3 ) /AB

AB  = 20√3

In triangle ABC,

cos (30°) = AB/BC

√3 /2 =  20√3 / BC

BC = 40

tan (30°) = AC/AB

1/√3 =  AC/ 20√3

AC = 20

Perimeter of triangle ABC =  AB +BC  + AC

                                           = 20√3  +  40  + 20

                                           = 60 + 20√3

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Answer:

1.728 m^3

Step-by-step explanation:

120 cm = 1.20 m

V = 1.20^ 3 = 1.728 m^3

Answer:

[tex]\huge\boxed{\sf Volume = 1.728 \ m\³}[/tex]

Step-by-step explanation:

Length = l = 120 cm = 1.2 m

We know that,

Volume = 1.2³

Volume = 1.728 m³

[tex]\rule[225]{225}{2}[/tex]

The equation of the line is x is -6

A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).

A line's steepness is indicated by its slope. Any line's slope is constant along its length. The direction of the line on the coordinate plane can also be determined by the slope. A line's graph can be used to determine slope, or the coordinates of any two points on a line can be used.

Given ,

m=(y2-y1)/(x2-x1)

Using the points given, we have:

m=(3 - 3)/(-5 - 3) = 0

These would be the vertical lines, and vertical lines have an equation with only x.

So the equation of the line is x = -6.

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Answer: f(x) = -3(x + 3)² + 8

Step-by-step explanation:

(h, k) are the coordinates to the vertex of the graph, which in this case would be (-3, 8), so the function for now would be:

[tex]f(x)=a(x+3)^2+8[/tex]

Plug in the coordinates (0, -19) to find the value of a:

[tex]-19=a(0+3)^2+8\\-19=9a+8\\9a=-19-8\\9a=-27\\a=-3[/tex]

So, the function is f(x) = -3(x + 3)² + 8.

yes its a skill related mostly to math

The common ratio of a geometric sequence will be;

⇒ r = 5 / 10

What is Geometric sequence?

An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.

Given that;

In a geometric sequence,

The third term is 100 and the eighth term is 3.125.

Now,

We know that;

The nth term of geometric sequence is,

⇒ [tex]T_{n} = a r^{n - 1}[/tex]

Hence, The third term is;

⇒ [tex]T_{3} = a r^{3 - 1} = 100[/tex]

⇒ [tex]a r^{2} = 100[/tex]   ..(i)

And, The eighth term is,

⇒ [tex]T_{8} = a r^{8 - 1} = 3.125[/tex]

⇒ [tex]a r^{7} = 3.125[/tex]   ..(ii)

Divide equation (ii) by (i), we get;

⇒ ar⁷ / ar² = 3.125/100

⇒ r⁷ / r² = 3125 / 100000

⇒ r⁷⁻² = 3125 / 100000

⇒ r⁵ = 3125 / 100000

⇒ r = 5/10

Thus, The common ratio of a geometric sequence will be;

⇒ r = 5 / 10

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Any triangle with two equal sides is said to be isosceles .An equilateral triangle has congruent sides, which means that each side is the same length.

Equilateral refers to a triangle with three equally-sized sides. An isosceles triangle is one that has two equal sides.

An equilateral triangle has congruent sides, which means that each side is the same length. Additionally, each inside angle is identical (60 degrees). The words "equi" and "lateral," which both denote sides, are combined to form the phrase "equilateral." As a result, an equilateral triangle is one with equal sides.

The characteristics of an isosceles triangle are as follows: There is agreement between two sides. The base of an isosceles triangle refers to the third side of the triangle, which is unequal to the other two sides. The two angles that are opposite the equal sides line up perfectly.

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Answer: x = 9/2

Step-by-step explanation:

Given

5(2x + 1) = 50 (divide both sides by 5)

2x + 1 = 10 (subtract 1 from both sides)

2x = 9 (divide both sides by 2)

x = 9/2

The distance between the two points in the line segment A_F is 6.3 units

Distance between two points is the length of the line segment that connects the two given points. Distance between two points in coordinate geometry can be calculated by finding the length of the line segment joining the given coordinates. Let us understand the formula to find the distance between two points in a two-dimensional and three-dimensional plane.

The distance between any two points is the length of the line segment joining the points. There is only one line passing through two points. So, the distance between two points can be calculated by finding the length of this line segment connecting the two points.

The data points are;

Distance between points A and F 6.3 units

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Answer:

  y = x³ +x² -20x

Step-by-step explanation:

You want a polynomial with roots x ∈ {0, -5, 4}.

When a polynomial has a root p, it has a factor (x -p). The three given roots mean the polynomial you want can be factored as ...

  y = (x -0)(x -(-5))(x -4) = x(x+5)(x-4)

When this product is expanded, the result is ...

  y = x³ +x² -20x . . . . polynomial with roots {0, -5, 4}

Answer:

x= 67

Step-by-step explanation:

x = 21+2×(90-x)

x= 21+180-2x

x= 201-2x

3x=201

x= 67