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3 years ago

Use absolute value notation to represent the following: all numbers x whose distance from 6 is no more than 7.5 units

Mathematics

1 answer:

In-s [12.5K]3 years ago

5 0

Answer:

$|x-6| \leq 7.5$

Step-by-step explanation:

We have to use absolute value notation to express the given statement.

Absolute value function:

It is a function that contains absolute value symbol.

$|x| = x, ~x > 0\\~~~~=-x, ~x < 0$

$|a-b|$ is used to express the distance between two points a and b on a number line.

We want to write a absolute value function for all numbers x whose distance from 6 is no more than 7.5 units.

Thus, we can write:

$|x-6| \leq 7.5$

This can be interpreted as the absolute value of difference between x and 6(both in positive sense and negative sense) is less than equal to 7.5 that is not more than 7.5 units.

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Rozlyn invested $2000 in an account that pays 4.25% annual simple interest. She will not make any additional deposits or withdra

PilotLPTM [1.2K]

Answer:

$850

Step-by-step explanation:

Interest = Principal x Rate x Time

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2 years ago

A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing $20/ft and on the other three s

makvit [3.9K]

Answer:

The dimensions of the garden that minimize the cost is 9.018 feet(length) and 13.528 feet(width)

Step-by-step explanation:

Let the length of garden be x

Let the breadth of garden be y

Area of Rectangular garden = $Length \times Breadth = xy$

We are given that the area of the garden is 122 square feet

So, $xy=122$ ---A

A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing $20/ft

So, cost of brick along length x = 20 x

On the other three sides by a metal fence costing $10/ft.

So, Other three side s = x+2y

So, cost of brick along the other three sides= 10(x+2y)

So, Total cost = 20x+10(x+2y)=20x+10x+20y=30x+20y

Total cost = 30x+20y

Substitute the value of y from A

Total cost = $30x+20(\frac{122}{x})$

Total cost = $\frac{2440}{x}+30x$

Now take the derivative to minimize the cost

$f(x)=\frac{2440}{x}+30x$

$f'(x)=-\frac{2440}{x^2}+30$

Equate it equal to 0

$0=-\frac{2440}{x^2}+30$

$\frac{2440}{x^2}=30$

$\sqrt{\frac{2440}{30}}=x$

$9.018 =x$

Now check whether it is minimum or not

take second derivative

$f'(x)=-\frac{2440}{x^2}+30$

$f''(x)=-(-2)\frac{2440}{x^3}$

Substitute the value of x

$f''(x)=-(-2)\frac{2440}{(9.018)^3}$

$f''(x)=6.6540$

Since it is positive ,So the x is minimum

Now find y

Substitute the value of x in A

$(9.018)y=122$

$y=\frac{122}{9.018}$

$y=13.528$

Hence the dimensions of the garden that minimize the cost is 9.018 feet(length) and 13.528 feet(width)

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2 years ago

The scale on a map is 1cm=20miles.if two airports are 4cm apart on the map, what's the distance between the airports?

Stels [109]

80 miles because if 1=20 then 2=40 3=60 4=80

8 0

2 years ago

Please help me with this. If you show your work I will give brainliest if there are 2 answers

AfilCa [17]

<h3>Answer: 22.5</h3>

Work Shown:

450 calories = 20 ounces

450/20 calories = 20/20 ounces ..... divide both sides by 20

22.5 calories = 1 ounce

This smoothie has 22.5 calories per ounce.

6 0

3 years ago

I WILL GIVE BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

NemiM [27]

Answer:

$- (x - 1) {}^{2} + 5$

Step-by-step explanation:

F(x) is a transformation from h(x).

So our starting equation is

$- (x - 1) {}^{2} - 1$

F(x) is also facing the same direction h(x) is so we dont have to reflect nothing across the x or y axis.

There isn't a vertical or horizontal stretch, compressions.

There isn't a horizontal shift as the x values stay in the same place.

There is a vertical shift. We can simply move h(x) up 6 units to get to f(x).

So our equation looks like.

$- (x - 1) {}^{2} + 5$

8 0

2 years ago