1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
insens350 [35]
3 years ago
15

If f(x)=3x-1 and g(x)=x+2,find (f-g)(x)

Mathematics
1 answer:
oksian1 [2.3K]3 years ago
7 0

Answer:

\large\boxed{(f-g)(x)=2x-3}

Step-by-step explanation:

(f-g)(x)=f(x)-g(x)\\\\f(x)=3x-1,\ g(x)=x+2\\\\\text{substitute:}\\\\(f-g)(x)=(3x-1)-(x+2)\\\\=3x-1-x-2\qquad\text{combine like terms}\\\\=(3x-x)+(-1-2)\\\\=2x-3

You might be interested in
What is the equation of log x 729=3?
pishuonlain [190]

Answer:

Step-by-step explanation:

Move 729  to the left side of the equation by subtracting it from both sides.  x  3 − 729  = 0  Factor the left side of the equation.  Rewrite  729  as 9

3

.  x

3

−

9

3

=

0

. Since both terms are perfect cubes, factor using the difference of cubes formula,  a

3

−

b

3

=

(

a

−

b

)

(

a

2+ab+b2). Where a

=x and  b=9. (x−9)(x2+x⋅9+92)=0

. Simplify.  Move 9  to the left of x

.  (x−9)(x2+9x+92)=0.  Raise  9  to the power of 2

.  (x

−9

)(

x

2

+

9

x

+81

)=0

. Set x

−9  equal to  0 and solve for x.  Set the factor equal to  0. x−

9=

0. Add 9  to both sides of the equation.  x=9

. Set x2+

9

x

+

81 equal to  0  and solve for  x

.  Set the factor equal to 0

.  x2+9x+81=0.  Use the quadratic formula to find the solutions.  −b±√b2−4(ac) 2a. Substitute the values  a=1, b=9, and c=81  into the quadratic formula and solve for  x.  −9±√92−4⋅ (1⋅81

) 2⋅

1  Simplify.  Simplify the numerator. Raise 9  to the power of 2. x=−9±√81−4⋅(1⋅81) 2⋅1. Multiply  

81

by  

1

.

x

=

−

9

±

√

81

−

4

⋅

81

2

⋅

1

Multiply  

−

4

by  

81

.

x

=

−

9

±

√

81

−

324

2

⋅

1

Subtract  

324

from  

81

.

x

=

−

9

±

√

−

243

2

⋅

1

Rewrite  

−

243

as  

−

1

(

243

)

.

x

=

−

9

±

√

−

1

⋅

243

2

⋅

1

Rewrite  

√

−

1

(

243

)

as  

√

−

1

⋅

√

243

.

x

=

−

9

±

√

−

1

⋅

√

243

2

⋅

1

Rewrite  

√

−

1

as  

i

.

x

=

−

9

±

i

⋅

√

243

2

⋅

1

Rewrite  

243

as  

9

2

⋅

3

.

Tap for fewer steps...

Factor  

81

out of  

243

.

x

=

−

9

±

i

⋅

√

81

(

3

)

2

⋅

1

Rewrite  

81

as  

9

2

.

x

=

−

9

±

i

⋅

√

9

2

⋅

3

2

⋅

1

Pull terms out from under the radical.

x

=

−

9

±

i

⋅

(

9

√

3

)

2

⋅

1

Move  

9

to the left of  

i

.

x

=

−

9

±

9

i

√

3

2

⋅

1

Multiply  

2

by  

1

.

x

=

−

9

±

9

i

√

3

2

Factor  

−

1

out of  

−

9

±

9

i

√

3

.

x

=

−

1

9

±

9

i

√

3

2

Multiply  

−

1

by  

−

1

.

x

=

1

−

9

±

9

i

√

3

2

Multiply  

−

9

±

9

i

√

3

by  

1

.

x

=

−

9

±

9

i

√

3

2

The final answer is the combination of both solutions.

x

=

−

9

−

9

i

√

3

2

,

−

9

+

9

i

√

3

2

The solution is the result of  

x

−

9

=

0

and  

x

2

+

9

x

+

81

=

0

.

x

=

9

,

−

9

−

9

i

√

3

2

,

−

9

+

i

√

3

2

7 0
3 years ago
What is the solution for x in the equation? 16x − 4 + 5x = -67
Luden [163]

Answer:

x = -3

Step-by-step explanation:

16x − 4 + 5x = -67

Combine like terms

21x -4 = -67

Add 4 to each side

21x-4+4 = -67+4

21x = -63

Divide each side by 21

21x/21 = -63/21

x = -3

3 0
2 years ago
Read 2 more answers
A food processor packages orange juice in small jars. The weights of the filled jars are approximately normally distributed with
Ratling [72]

Answer:

P(X>10.983)=P(\frac{X-\mu}{\sigma}>\frac{10.983-\mu}{\sigma})=P(Z>\frac{10.983-10.5}{0.3})=P(z>1.61)

And we can find this probability using the complement rule and with excel or the normal standard table:

P(z>1.61)=1-P(z

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

X \sim N(10.5,0.3)  

Where \mu=10.5 and \sigma=0.3

We are interested on this probability

P(X>10.983)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X>10.983)=P(\frac{X-\mu}{\sigma}>\frac{10.983-\mu}{\sigma})=P(Z>\frac{10.983-10.5}{0.3})=P(z>1.61)

And we can find this probability using the complement rule and with excel or the normal standard table:

P(z>1.61)=1-P(z

8 0
3 years ago
Find the product. Simplify. 1/10 x 3/4
FrozenT [24]

Answer:

Alright just simplify the expression So the exact form is

Exact form: 3/40 Hope this helps :)

Step-by-step explanation:


6 0
3 years ago
Read 2 more answers
Select all the rates that are unit rates.
Nataly_w [17]

Answer:

\frac{2/3}{1} and \frac{3}{1}

Step-by-step explanation:

Options

\frac{1}{1/3}     \frac{2/3}{1}     \frac{2}{3}     \frac{3}{1}     \frac{1}{9}

Required

Select the unit rates

Unit rate involve two items where the first item being measured can be any positive number, but the second item must be measured in units (i.e. 1)

For clarity:

If \frac{a}{b} represents unit rate, then b = 1

Having said that:

Only \frac{2/3}{1} and \frac{3}{1} satisfy the condition of unit rates; others are not because they have a denominator other than 1

3 0
2 years ago
Other questions:
  • 1. 7 2/3 + 2 7/12
    15·1 answer
  • Deals with Area of Triangle, thankyou so very much for your help!
    7·1 answer
  • What is the exact circumference of a circle with a diameter of 15 in.? Enter your answer in the box.
    11·1 answer
  • 2/3 of the product of 3/8 and 16
    5·1 answer
  • A small passenger airplane has 9 rows of seats . The first 8 rows have 4 seats . The last row has 5 seats m. How many seats are
    6·1 answer
  • What is 20+50+20+50+20
    14·2 answers
  • A triangle has one angle measure of 55 degrees and a second angle measuring 53 degrees. What is the third missing angle measure?
    10·2 answers
  • Base: 5 ft<br> area: 5 5/6 <br> what's the height( pls hurry&lt;3)
    14·1 answer
  • For which set of values is y a function of x? x у <br> -1 6<br> 0 8<br> 1 1 10<br> 2 12 ​
    15·1 answer
  • A 15-foot ladder is placed against a vertical wall of a​ building, with the bottom of the ladder standing on level ground 9 feet
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!