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docker41 [41]
3 years ago
6

What is the domain and range for the following function and it’s inverse ? Help needed !!!

Mathematics
1 answer:
Pie3 years ago
5 0

ANSWER

f(x)

Domain:(-∞,∞)

Range:(-∞,∞)

{f}^{ - 1} (x)

Domain:(-∞,∞)

Range:(-∞,∞)

The given function is

f(x) =  \frac{3x - 1}{2}

This is a polynomial function.

All polynomial functions are defined everywhere.

The domain is all real numbers.

Or

(-∞,∞).

The range is also all real numbers.

(-∞,∞).

The domain of the inverse function equals the range of the function.

(-∞,∞).

The range of the inverse function equals the domain of the function.

(-∞,∞).

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The triangles are similar
hoa [83]

Answer:

Part 1) x=16\ units

Part 2) x=23\ units

Part 3) AE=20\ units

Part 4) x= 6.25\ units

Part 5) x=26.67\ in

Step-by-step explanation:

Part 1) we know that

If two triangles are similar

then

the ratio of their corresponding sides are equal

so

In this problem

\frac{12}{3}=\frac{x}{4}\\\\3x=12*4\\ \\x=48/3\\ \\x=16\ units

Part 2) we know that

If two triangles are similar

then

the ratio of their corresponding sides are equal

so

In this problem

\frac{36}{12}=\frac{39}{(x-10)}\\\\3(x-10)=39\\ \\x=(39/3)+10\\ \\x=23\ units

Part 3) we know that

If two triangles are similar

then

the ratio of their corresponding sides are equal

so

In this problem

\frac{AB}{CD}=\frac{AE}{ED}

substitute the values

\frac{10}{4}=\frac{2x+10}{x+3}

2.5(x+3)=2x+10

2.5x+7.5=2x+10

2.5x-2x=10-7.5

0.5x=2.5

x=5\ units

AE=2x+10=2*5+10=20\ units

Part 4) we know that

If two triangles are similar

then

the ratio of their corresponding sides are equal

so

In this problem

\frac{4}{5}=\frac{5}{x}\\ \\4x=5*5\\ \\ x=25/4\\ \\ x= 6.25\ units

Part 5) we know that

If two triangles are similar

then

the ratio of their corresponding sides are equal

so

In this problem

\frac{30}{x}=\frac{45}{40}\\ \\45x=30*40\\ \\x=1,200/45\\ \\ x=26.67\ in



3 0
3 years ago
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Thomas went on a hike. He climbed 34 of a mile in 23 of an hour. What was his hiking speed in miles per hour?
SCORPION-xisa [38]

Answer:

Step-by-step explanation:

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What is the difference between Compound Interest and simple interest???
oksian1 [2.3K]

Answer:

Simple interest is calculated using initial principle while compound interest is calculated considering the interest also .

Step-by-step explanation:

Interest is the cost of borrowing money, where the borrower pays a fee to the lender for using his money. The interest, typically expressed as a percentage, can either be compounded or simple .

Simple interest is based on the principal amount , while compound interest is based on the principal amount and the interest that adds onto it in every period and the final principle is used for calculating the interest.

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4 0
4 years ago
The diagonal of a suitcase measures 30 inches and the height is 18 inches. What is the width of the suitcase to the
Anna007 [38]

Answer:

Step-by-step explanation:

By the Pythagorean Theorem we know

h^2=x^2+y^2 (where h is the hypotenuse and x and y are sides of a right triangle)

w^2+18^2=30^2

w^2=30^2-18^2

w^2=900-324

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3 0
3 years ago
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In order to play in chess tournaments at the Marshall Club, Malik pays a fee to become a member. In addition, he pays a set rate
Keith_Richards [23]

Answer:

p = 22.50 + 15t

Step-by-step explanation:

For Malik :

Membership fee = m

Rate per tournament = t

After 4 tournaments :

m + 4t = 85 - - - (1)

After 7 tournaments :

m + 7t = 130 - - - (2)

Subtract 2 from 1

4t - 7t = 85 - 130

-3t = - 45

t = 45 / 3

t = 15

Put, t = 15 in (1)

m + 4(15) = 85

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m = 85 - 60

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Massai pays 10% less membership fee than Malik

Hence, Massai's membership fee:

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