Four more than a number is half the number

You want to purchase a house for $185,000. To avoid certain costs, you want to make a down payment of 20%. What is

aleksley [76]

Answer:

37,000

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

Which expression is equivalent to 6t⁻⁷x 3 t⁵

aleksandrvk [35]

6t^-7 * 3t^5 = 1/6t^7 * 3t^5

6 0

2 years ago

Given f(x) = log(x+1), x >-1 and g(x) = x^2 + 2x, XER find (f•g)(1)

worty [1.4K]

Answer:

Like terms, functions may be combined by addition, subtraction, multiplication or division.

Example 1. Given f ( x ) = 2x + 1 and g ( x ) = x2

+ 2x – 1 find ( f + g ) ( x ) and

( f + g ) ( 2 )

Solution

Step 1. Find ( f + g ) ( x )

Since ( f + g ) ( x ) = f ( x ) + g ( x ) then;

( f + g ) ( x ) = ( 2x + 1 ) + (x2

+ 2x – 1 )

= 2x + 1 + x2

+ 2x – 1

= x

2

+ 4x

Step 2. Find ( f + g ) ( 2 )

To find the solution for ( f + g ) ( 2 ), evaluate the solution above for 2.

Since ( f + g ) ( x ) = x2

+ 4x then;

( f + g ) ( 2 ) = 22

+ 4(2)

= 4 + 8

= 12

Example 2. Given f ( x ) = 2x – 5 and g ( x ) = 1 – x find ( f – g ) ( x ) and ( f – g ) ( 2 ).

Solution

Step 1. Find ( f – g ) ( x ).

( f – g ) ( x ) = f ( x ) – g ( x )

= ( 2x – 5 ) – ( 1 – x )

= 2x – 5 – 1 + x

= 3x – 6

Step 2. Find ( f – g ) ( 2 ).

( f – g ) ( x ) = 3x – 6

( f – g ) ( 2 ) = 3 (2) – 6

= 6 – 6

= 0

Example 3. Given f ( x ) = x2

+ 1 and g ( x ) = x – 4 , find ( f g ) ( x ) and ( f g ) ( 3 ).

Solution

Step 1. Solve for ( f g ) ( x ).

Since ( f g ) ( x ) = f ( x ) * g ( x ) , then

= (x2

+ 1 ) ( x – 4 )

= x

3

– 4 x2

+ x – 4 .

Step 2. Find ( f g ) ( 3 ).

Since ( f g ) ( x ) = x3

– 4 x2

+ x – 4, then

( f g ) ( 3 ) = (3)3

– 4 (3)2

+ (3) – 4

= 27 – 36 + 3 – 4

= -10

Example 4. Given f ( x ) = x + 1 and g ( x ) = x – 1 , find ( x ) and ( 3 ). f

g

⎛ ⎞ ⎜

⎝ ⎠

f

g

⎛ ⎞ ⎜

⎝ ⎠ ⎟ ⎟

Solution

Step 1. Solve for ( x ). f

g

⎛

⎜

⎝ ⎠

⎞

⎟

Since ( x ) = , then ( )

( )

f x

g x

f

g

⎛

⎜

⎝ ⎠

⎞

⎟

= ; x ≠ 1 1

1

x

+

−

Step 2 Find . ( ) 3 f

g

⎛ ⎞ ⎜ ⎟ ⎝ ⎠

Since = , then 1

1

x

+

− ( ) f x

g

⎛ ⎞ ⎜ ⎟ ⎝ ⎠

=

3 1

+

− ( ) 3 f

g

⎛ ⎞ ⎜ ⎟ ⎝ ⎠

=

4

2

= 2

Step-by-step explanation:

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3 0

2 years ago

The following histogram presents the amounts of silver (in parts per million) found in a sample of rocks. One rectangle from the

gladu [14]

Answer:

The height of the missing rectangle is 0.15

Explanation:

The image attached has the mentioned histogram.

Such histogram presents the relative frequencies for the clases [0,1], [1,2],[2,3], [4,5], and [5,6] Silver in ppm.

Only the rectangle for the class [3,4] is missing.

The height of each rectangle is the relative frequency of the corresponding class.

The relative frequencies must add 1, because each relative frequency is calculated dividing the absolute class frequency by the total number in the sample; hence, the sum of all the relative frequencies is equal to the total absolute class frequencies divided by the same number, yielding 1.

In consequence, you can sum all the known relative frequencies and subtract from 1 to get the missing relative frequency, which is the height of the missing rectangle.

1. Sum of the known relative frequencies:

0.2 + 0.3 + 0.15 + 0.1 + 0.1 = 0.85

2. Missing frequency:

1 - 0.85 = 0.15

3. Conclusion:

The height of the missing rectangle is 0.15

4 0

2 years ago

The dimensions of the swimming pool and the gym are proportional.

Paladinen [302]

<h3>The dimensions of the gym floor could be 150 feet by 120 feet</h3><h3>The dimensions of the gym floor could be 225 feet by 180 feet</h3>

Solution:

Given that,

The dimensions of the swimming pool and the gym are proportional

The pool is 75 feet long by 60 feet wide

To find: set of possible dimensions for the gym

To determine the possible dimensions for the gym, you would use the same number to multiply both 75 and 60

One set of dimensions are:

75 x 2 = 150

60 x 2 = 120

The dimensions of the gym floor could be 150 feet by 120 feet

Other set of dimensions:

75 x 3 = 225

60 x 3 = 180

The dimensions of the gym floor could be 225 feet by 180 feet

4 0

3 years ago