Explain your reasoning and include the equation you used to set up and solve this.

Please help!

The slope is undefined for figure 2.

In general, when the x-values or x-coordinates is the same for both points, the slope is undefined.

For example, let us try to get the slope for a line passing through the points  (1, 3) and (1, 9)

Let x₁ = 1 , y₁ = 9 and x₂ = 1 and y₂ = 3

Slope, m = (y₂ − y₁)/((x₂ − x₁)

m = (3 − 9)/(1 − 1)

m = -6/0, which is undefined.

The work required to lift the barbell to a height of 2 m is 1,700 J.

To calculate the work required to lift the barbell to a height of 2 m, we need to consider the gravitational potential energy. The work done is equal to the change in potential energy.

The initial potential energy of the barbell is equal to its weight multiplied by the initial height, which is 1,700 N * 1 m = 1,700 J.

The final potential energy of the barbell is equal to its weight multiplied by the final height, which is 1,700 N * 2 m = 3,400 J.

Therefore, the work required to lift the barbell to a height of 2 m is 3,400 J - 1,700 J = 1,700 J.

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Answer:

26.25 ft.

Step-by-step explanation:

The general form of a parabola is [tex]y = a(x - h)^2 + k[/tex], where the vertex of the parabola is (h,k).

Given that

[tex]y = a(x - h)^2 + k[/tex]

A. The quadratic equation

The lowest point (which stands for the vertex) is given as:

[tex](h,k) = (90,6)[/tex]

So, we have:

[tex]y = a(x - 90)^2 + 6[/tex]

From the question, we understand that:

At a horizontal distance of 30ft, the cable is at 15ft. This means:

[tex](x,y) = (30,15)[/tex]

Substitute these values in: [tex]y = a(x - 90)^2 + 6[/tex]

So, we have:

[tex]15 = a(30 - 90)^2 + 6[/tex]

[tex]15 = a(- 60)^2 + 6[/tex]

[tex]15 = a \times 3600 + 6[/tex]

Collect like terms

[tex]3600a = 15 - 6[/tex]

[tex]3600a = 9[/tex]

Make a, the subject

[tex]a = \frac{9}{3600}[/tex]

[tex]a = 0.0025[/tex]

Substitute [tex]a = 0.0025[/tex] in [tex]y = a(x - 90)^2 + 6[/tex].

[tex]y = 0.0025(x - 90)^2 + 6[/tex]

B. The horizontal distance at a height of 26.25ft.

This means that, y = 26.25

So, we have:

[tex]26.25 = 0.0025(x - 90)^2 + 6[/tex]

Collect like terms

[tex]-6 + 26.25 = 0.0025(x - 90)^2[/tex]

[tex]20.25= 0.0025(x - 90)^2[/tex]

Divide both sides by 0.0025

[tex]8100 = (x - 90)^2[/tex]

Take square roots of both sides

[tex]\±90 = x - 90[/tex]

Solve for x

[tex]x = 90 \± 90[/tex]

To the left of the cable, the horizontal distance is:

[tex]x_1 = 90 - 90[/tex]

[tex]x_1 = 0[/tex]

To the right of the cable, the vertical distance is:

[tex]x_2 = 90 + 90[/tex]

[tex]x_2 = 180[/tex]

So, the coordinates of the left and right support at a height of 26.25 is:

(0,26.25) and (180, 26.25)

The distance (d) between them is calculated using:

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 -y_1)^2}[/tex]

[tex]d = \sqrt{(180- 0)^2 + (26.25-26.25)^2}[/tex]

[tex]d = \sqrt{180^2 + 0^2}[/tex]

[tex]d = \sqrt{180^2}[/tex]

[tex]d = 180[/tex]

The distance between them is 180ft

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The given equation is

   [tex]\rightarrow 9r+16=\frac{\pi}{5}[/tex]

The value of π is 3.14 or [tex]\frac{22}{7}[/tex] that is a fixed Value.

   [tex]\rightarrow 9r +16=\frac{3.14}{5}\\\\9r+16=0.628\\\\9r=0.628-16\\\\9r=-15.372\\\\r=\frac{-15.372}{9}\\\\r=-1.708[/tex]

So, the given equation is Literal ,because variable value is Known.

A literal equation is an equation that has at least one letter or one unknown variable.

[tex]9r + 16= \frac \pi 5[/tex] is a literal equation because it has letter r

Given that:

[tex]9r + 16= \frac \pi 5[/tex]

By analyzing the equation, we have:

[tex]9, 16, 5 \to[/tex] number

[tex]r \to[/tex] letter

[tex]\pi \to[/tex] constant

Because r is a letter, then the equation is a literal equation

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Answer:

243 ft2

Step-by-step explanation:

9*3= 27

3*3= 9

27*9=243 ft2

The area of the rectangular flower bed is 243 square feet.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.

A rectangle is a quadrilateral having four sides and the sum of the angles is 180 in the rectangle the opposite two sides are equal and parallel and the two sides are at 90-degree angles.

Given that a flower bed has the shape of a rectangle 9 yards long and 3 yards wide.

Length = 9 yards = 9 x 3 feet = 27 feet

Width = 3 yards = 3 x 3 feet = 9 feet

The area of the rectangular flower bed will be calculated as,

Area = L x W

Area = 27 x 9

Area = 243

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Answer: 7/100

Step-by-step explanation:

Count with yo Hands fool

The length of a side of the patio, rounded to the nearest tenth of a yard, is 7.5 yards.

To find the length of a side of the patio, we need to find the square root of the area. The area of the patio is given as 56 square yards.

To find the length of a side, let's take the square root of 56. The square root of 56 is approximately 7.48.

Therefore, the length of a side of the patio, rounded to the nearest tenth of a yard, is 7.5 yards.

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Answer:

[tex]x=20[/tex]

Step-by-step explanation:

We have been a triangle has one angle measuring [tex]3x[/tex] degrees the second angle measures [tex]2x+20[/tex] degrees and the third angle measures [tex]4x-20[/tex] degrees. We are asked to find the value of x.

We know that all interior angles of a triangle add up-to 180 degrees.

[tex]3x+2x+20+4x-20=180[/tex]

Combine like terms:

[tex]3x+2x+4x-20+20=180[/tex]

[tex]9x=180[/tex]

Divide both sides by 9:

[tex]\frac{9x}{9}=\frac{180}{9}[/tex]

[tex]x=20[/tex]

Therefore, the value of x is 20 for our given triangle.

The greater number between 1/3 and 0.33 is 1/3

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

1/3 or 0.33

Express them as decimals

So, we have

1/3 = 0.333..

0.33 = 0.33

By comparison

0.333.. is greater than 0.33

This means that the greater number is 1/3

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Answer:

lets

h =# of hens in the filed and c = # of cows in

the field

hens and cows have 50 heads

h + c = 50 (1)

hens and cows have 180 legs (hen has 2

legs and cow has 4 legs)

2h+4c180 (2)

From equation (1) h + c = 50 ----> h = 50 - c

substitute h = 50 c into 2h + 4c = 180 (

-

2h+4c 180

2(50-c) + 4c = 180

1002c+ 4c = 180

2c 180-100

2c=80

C = 40

2h + 4(40) = 180

2h+160 180

2h = 20

h = 10

answer

hens = 10 and cows = 40

double check:

heads: 10 hens + 40 cows = 50 total legs:10(2) + 40(4) = 20 + 160 = 180

Answer:

f(x)=11 and f(x)=16

Step-by-step explanation:

f(x)=5(2)+1

f(x)=11

f(x)= 5(3)+1

f(x)=16

The decimal form of 'five thousands and eighty-five thousandths' is 5000.085. Therefore, your answer choice C) 5000.085 is correct.

The decimal number 5000.085 can be understood as a combination of two distinct parts: the whole number component, 5000, signifies 'five thousands,' representing a quantity in the thousands place, and the fractional part, 0.085, signifies 'eighty-five thousandths,' indicating a value less than one but greater than zero. When these two components are integrated, the number 5000.085 emerges, illustrating a precise quantity with both an integral and fractional significance. This understanding showcases the inherent nature of decimal notation, where whole numbers and fractional values harmoniously coexist, providing a comprehensive representation of numerical quantities.

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