In geometry, how do defined terms and undefined terms relate to each other

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

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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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:

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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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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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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Denise should plan to spend around 4.2 hours walking back after running. This is calculated using the concept of time = distance / speed and sum of the times, with the total time, running speed and walking speed given as 6 hours, 7 mph, and 3 mph, respectively.

To answer the question 'How long should Denise plan to spend walking back?' we can start by finding the time she spends running. We know that Denise has 6 hours to spend training for an upcoming race. We also know that she runs at a speed of 7mph and walks back at a speed of 3mph.

The total time spent running and walking is 6 hours. To find the running time, we should know that time = distance / speed. However, we don't have the distance. But since the distance ran is equal to the distance walked back, we can use the concept of time = distance / speed and sum of times to solve it.

We can denote the distance by D, thus the time spent running is D/7 and the time walking back is D/3. Adding these times should equal 6 hours.

Putting this into an equation: D/7 + D/3 = 6.

We solve this equation to find D, and find the time spent walking back by substituting D back into D/3. Which gives us about 4.2 hours. So, Denise should plan to spend about 4.2 hours walking back after her run.

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Answer: 7/100

Step-by-step explanation:

Count with yo Hands fool

Answer:

[tex]\huge\boxed{\boxed{\tt{65\::)}}}[/tex]

Step-by-step explanation:

Hello.

First, add 10+3.

The sum is 13.

Now, multiply that by 5.

13×5=65

And we're done!

I hope it helps & have an outstanding day! :)

~ST2710 :)

Answer:

There are 1000 millimeters in a meter.

Starting from lower scale that is, centimeter, decimeter and then meter

1 cm = 10 mm

1 dm = 10 cm

And 1 meter = 10 dm

So, when you go up to mm from meter, we will do [tex]10^{3}[/tex] to get the relation between meter and mm.

Hence, 1 meter = [tex]10\times10\times10=1000[/tex] millimeters.

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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To find g(x+1) for the function g(x)=x^2, you substitute x+1 into the function to get (x+1)^2, which expands to x^2 + 2x + 1.

The function given is g(x) = x^2. To find g(x + 1), you just need to substitute x + 1 into the function where x is. So, g(x + 1) = (x + 1)^2. If we expand this, it becomes x^2 + 2x + 1.

Therefore, the expression that is equal to g(x + 1) is x^2 + 2x + 1.

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