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2 years ago

Graph the following three equations on your own device and answer the questions below.

1 answer:

5 0

Due to length restrictions, we kindly invite to read the explanation of this question for further details on functions.

<h3>What are the characteristics of each of the three functions?</h3>

a) In this part we must evaluate each of the three functions at the given value of x:

Case 1

f(10) = 5 · 10 + 7

f(10) = 57

Case 2

f(10) = 10² + 6

f(10) = 106

Case 3

f(10) = 2¹⁰ + 3

f(10) = 1027

b) In this part we must evaluate each of the three functions at the given value of x:

Case 1

f(100) = 5 · 100 + 7

f(100) = 507

Case 2

f(100) = 100² + 6

f(100) = 10006

Case 3

f(100) = 2¹⁰⁰ + 3

f(100) = 1.267 × 10³⁰ + 3

c) In this part we must evaluate each of the three functions at the given value of x:

Case 1

f(1000) = 5 · 1000 + 7

f(1000) = 5007

Case 2

f(1000) = 1000² + 6

f(1000) = 1000006

Case 3

f(1000) = 2¹⁰⁰⁰ + 3

f(1000) = (1.268 × 10³⁰)¹⁰ + 3

f(1000) = 10.744 × 10³⁰⁰ + 3

f(1000) = 1.074 × 10³⁰¹ + 3

e) The <em>third</em> function increases the fastest.

f) In this part we need to compare the <em>third</em> function with respect to the <em>first</em> and <em>second</em> functions:

5 · x + 7 = 2ˣ + 3

2ˣ - 5 · x = 4

The solutions of the equation are x = - 0.675 and x = 4.81. The function will exceed the other <em>first</em> function at x = 4.81.

x² + 6 = 2ˣ + 3

2ˣ - x² = 3

The solution of the equation is x = 4.588. The function will exceed the other <em>second</em> function at x = 4.588.

g) Yes, <em>exponential</em> functions with bases greater than 1 will surpass <em>polynomic</em> function at any point x such that x > 0.

h) The domain represents the set of x-values of a function and the range represents the set of y-values of a function. Then, the domain and range of each function is:

Case 1

Domain - All <em>real</em> numbers.

Range - All <em>real</em> numbers

Case 2

Domain - All <em>real</em> numbers.

Range - [6, +∞)

Case 3

Domain - All <em>real</em> numbers.

Range - (3, +∞)

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What is 3/26 in simplest form

timofeeve [1]

The fraction 3/26 is alread in the simplest form, so it isn't possible to reduce it any further.
This is a PROPER FRACTION once the absolute value of the top number or numerator (3) is smaller than the absolute value of the bottom number or denomintor (26).
The fraction 3/26 is equal to 3÷26 and can also be expressed in decimal form as 0.115385.

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3 years ago

a fishing boat accidentally spills 15 barrels of diesel oil into the ocean. each barrel contains 42 gallons. if the oil film on

bezimeni [28]

The square meters of the area the oil slick will cover is 9.6 × 10⁶ m².

<h3>What is meant by volume?</h3>

Volume is defined as the amount of three-dimensional space enclosed by a closed surface.

The liter (L) is the metric system's base volume unit, with several extended volume units also available.
There are also many metric volume units based on the a cubic length dimension, including such cubic meters or cubic centimeters. Gallons and ounces are examples of imperial volume units.

Now, as per the given question;

First, we determine the entire volume of oil in gallons by multiplying the volume per barrel even by total number of barrels:

15×42 gal = 630 gal

This volume must be converted to square meters:

V = 630 gal × (0.00379 m³/ gal

V = 2.4 m³

The thickness (height) of a oil film in meters is required:

h = 250 nm × (m/10⁻⁹nm)

h = 2.5 × 10⁻⁷m

The surface area of a oil film is calculated by dividing the oil volume by height of the oil film.

A = V/h

A = 2.4 m³/2.5 × 10⁻⁷m

A = 9.6 × 10⁶ m²

Therefore, the area of the oil slick cover is found to be 9.6 × 10⁶ m².

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1 year ago

Cathy is paid at a rate of $7 20 per hour for a basic hour-week of 70 hours. She is paid time-and-a-half for over-time during th

goldenfox [79]

i believe it’s 8 hope it’s right

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4 years ago

Read 2 more answers

Identify the figure shown and find its surface area. Explain how you found your answer.

photoshop1234 [79]

This is a triangle prism, the base is a square and the four sides are equal triangles.

To find the surface area you need to first find the areas of the triangles, then the square, in the end you have to add them together.

Since we know the area of a triangle is 1/2bh we know that one if the triangle in the figure is
9*16/2=72(in^2)
there are four of these so we multiply it by 4
4*72=288(in^2 aka squared inches)

Then we need to find the area of the square. side * side=9*9=81 (in^2)

Add them together we get the surface area.
288+81=369 (in^2)

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4 years ago

1) Fred Flint is paid $11.95 an hour with time-and-a-half pay for all hours he works over 40

allsm [11]

Fred's overtime rate and pay is $17.925 and $98.5875 respectively

<h3>Total payment</h3>

Amount paid per hour = $11.95

Amount paid overtime per hour = $11.95 × 1.5

= $17.925

Total hours worked last week = 45 1/2 hours

Overwork time = 45 1/2 hours - 40 hours

= 5 1/2 hours

Fred's overtime pay = 5 1/2 hours × $17.925

= 11/2 × 17.925

= $98.5875

Normal work rate = 40 hours × $11.95

= $478

Fred's total pay = Fred's overtime pay + Normal work rate

= $98.5875 + $478

= $576.5875

Therefore, Fred's total pay is $576.5875

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2 years ago