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zysi [14]
2 years ago
10

Please help solve questions

Mathematics
2 answers:
Ipatiy [6.2K]2 years ago
5 0

Answer:

<u>Given inequality</u>

\sf 2x + 3y < 6

<u>Rearrange to make y the subject</u>

\sf \implies 2x + 3y < 6

Subtract 2x from both sides:

\sf \implies 3y < -2x + 6

Divide both sides by 3:

\sf \implies y < -\dfrac23x + 2

<u>When graphing inequalities</u>

If the inequality sign is < or > then the line of the graph should be dashed.

If the inequality sign is ≤ or ≥ then the line of the graph should be solid.

If y < (less than) then the shading is below the line.

If y > (more than) then the shading is above the line.

Therefore, as the inequality is y < the line should be dashed and the shading should be below the dashed line.

To plot the line, substitute x = 0 and x = 3 into the equation:

\sf  \implies -\dfrac23(0) + 2=2

\sf  \implies -\dfrac23(3) + 2=0

Therefore, plot points (0, 2) and (3, 0).  Draw a dashed straight line through the points.  Shade below the dashed line.

Alekssandra [29.7K]2 years ago
4 0

Take some points

  • 2x+3y<6
  • 3y<-2x+6
  • y<-2/3x+2

As here < sign present line will be dashed and shading should be done below the line

So

  • (1,1)
  • (1,0)
  • (2,0)
  • (-1,2)

Graph attached

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Given f(x) = log(x+1), x &gt;-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

x

+

−

Step 2 Find . ( ) 3 f

g

⎛ ⎞ ⎜ ⎟ ⎝ ⎠

Since = , then 1

1

x

x

+

− ( ) f x

g

⎛ ⎞ ⎜ ⎟ ⎝ ⎠

=

3 1

3 1

+

− ( ) 3 f

g

⎛ ⎞ ⎜ ⎟ ⎝ ⎠

=

4

2

= 2

Step-by-step explanation:

did this Help?

3 0
3 years ago
Is this statement always, sometimes, or never true.
cestrela7 [59]

Answer:

Never true

Step-by-step explanation:

Linear angles are adjacent angles whose sum is 180

3 0
3 years ago
Evaluate the expression for x = -2, y = 3, z = -4. -4x + 5y + 6z *
babunello [35]

Answer:

-1

Step-by-step explanation:

Plug in given values

-4x + 5y + 6z

-4(-2) + 5(3) + 6(-4)

8 + 15 -24

23-24

-1

6 0
3 years ago
Read 2 more answers
The ratio of sweaters to dresses that Jennifer has is 8:5. If
melomori [17]

Answer:

Ratio of sweaters to dresses = 8 : 5

Sum of ratios = 13

Let number of sweater + dresses = x

number \ of \ sweaters = \frac{8}{13} *x\\\\24 = \frac{8}{13}*x\\\\x = \frac{24*13}{8} = 3*13 = 39

number \ of \ dresses = 39 - 24 = 15

8 0
3 years ago
F(x) = 12 + x<br> X<br> f(x)<br> -3<br> -1<br> 0<br> 4<br> 6
katen-ka-za [31]

9514 1404 393

Answer:

  (-3, 9), (-1, 11), (0, 12), (4, 16), (6, 18)

Step-by-step explanation:

The function definition tells you that adding 12 to the x-value will give you the value of f(x).

  -3 +12 = 9, for example

The (x, f(x)) values for the table are shown above.

7 0
3 years ago
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