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3 years ago

Write an inequality for each statement.

Mathematics

1 answer:

Pie3 years ago

3 0

Answer:

1. $l \leq 45$ ( in this inequality, the time can be less than or equal to 45, but no more than 45)

2. $m > 60$ (Mario's height is more than 60.)

3. $f > 8000$ (More than 8000 fans attended.)

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A rancher wants to fence in an area of 1000000 square feet in a rectangular field and then divide it in half with a fence down t

frosja888 [35]

The shortest length of the fence used by the rancher in a rectangular field of 1000000 square feet is 4899 ft.

<h3>What is the area of a rectangle?</h3>

The area of a rectangle is a region enclosed in four corners where two opposite sides are equal. The area of the rectangle is mathematically expressed as:

Area of a rectangle = length(x) × breath(y)

1000000 sq.ft = (x) × (y) ---- (1)

However, to determine the fencing, we have:

Length of fencing = 2x + 2y

since the rectangle has four sides and opposite sides are equal

Suppose we use the x-direction to estimate the region where the fencing is located, we have:

Length of fencing = 2x + 2y + x

Length of fencing = 3x + 2y ---- (2)

From equation (1), make (y) the subject of the formula and replace the value of y with equation (2)

The Length of fencing is:

$\mathbf{L = 3x - 2( \dfrac{1000000}{x})}$

$\mathbf{\dfrac{dL}{dx} = 3 - \dfrac{2000000}{x^2} = 0}$

$\mathbf{ x^2= \dfrac{2000000}{3} }$

$\mathbf{ x= \dfrac{1000\sqrt{2}}{\sqrt{3}} }$

$\mathbf{x = \dfrac{1000 \sqrt{6}}{3}}$

Now, if we replace the value with equation (1), then y will be:

$\mathbf{y = \dfrac{1000000}{\dfrac{1000 \sqrt{6}}{3}} }\\ \\ \\ \\ \mathbf{y = \dfrac{3000 }{\sqrt{6}}}$

$\mathbf{x =500\sqrt{6}}$

Now, the shortest length of the fencing can be computed by using the equation (2):

L = 3x + 2y

$\mathbf{L = 3( \dfrac{1000 \sqrt{6}}{3}) + 2(500 \sqrt{6})}$

$\mathbf{L =1000 \sqrt{6} + 1000 \sqrt{6}}$

$\mathbf{L =2000 \sqrt{6} }$

$\mathbf{L \simeq 4899 \ ft}$

Learn more about the area of a rectangle here:

brainly.com/question/25292087

6 0

2 years ago

Using words, explain all steps of dimensional analysis when converting 6.7 hectometers to meters.

9966 [12]

<h2>6.7 hectometers is equal to "670 meters".</h2>

Step-by-step explanation:

We have,

6.7 hectometers

To convert 6.7 hectometers to meters.

We know that,

1 hectometer = 100 meters

⇒ 1 hm = 100 m

∴ 6.7 hectometers

= 6.7 × 100 meters

= 670 meters

∴ 6.7 hectometers (hm) = 670 meters (m)

Thus, 6.7 hectometers is equal to "670 meters".

3 0

3 years ago

Line segment AB is drawn in the coordinate plane. Carlos graphed the set of points that are the same distance from both point A

Illusion [34]

Answer:

Carlos graphed the perpendicular bisector of AB.

Step-by-step explanation:

Given a line segment AB drawn in a coordinate plane. The set of points that are the same distance from points A and B divides the line segment AB into two equal parts.

This line is referred to as the perpendicular bisector of AB.

Therefore, Carlos graphed the perpendicular bisector of AB.

6 0

3 years ago

For the inverse variation equation xy = k, what is the constant of variation, k, when x = 7 and y = 3?

sleet_krkn [62]

Answer:

k = 21

Step-by-step explanation:

$xy = k\\\\Plugging\: x = 7\: and\: y = 3,\: we\; find:\\7\times 3 = k\\21 = k\\\huge\red{\boxed{k = 21}}\\$

6 0

3 years ago

Which statement can you use to conclude that the relationship must be non-proportional? A. The graph of the relationship is line

bezimeni [28]

Answer:

The Anwer is B because since its not starting at 0,0 its a non porptinatal

Step-by-step explanation:

5 0

3 years ago