If f(x) = 3x − 1 and g(x) = x + 2, find (ƒ– g)(x) ​

Answers

Answer 1

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:2x - 3 [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: (f - g)(x)[/tex]

[tex]\qquad \tt \rightarrow \: f(x) - g(x)[/tex]

Simple procedure :

[tex]\qquad \tt \rightarrow \: 3x - 1 - (x + 2)[/tex]

[tex]\qquad \tt \rightarrow \: 3x - 1 - x - 2[/tex]

[tex]\qquad \tt \rightarrow \: 3x - x - 1 - 2[/tex]

[tex]\qquad \tt \rightarrow \: 2x - 3[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞


Related Questions

Suntract (7x-3x)-(5x-6).

Answers

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: final \:\:value = -x + 6 \degree[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: (7x - 3x) - (5x - 6)[/tex]

[tex]\qquad \tt \rightarrow \: (4x) - 5x - ( - 6)[/tex]

[tex]\qquad \tt \rightarrow \: 4x - 5x + 6[/tex]

[tex]\qquad \tt \rightarrow \: - x + 6[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:6-x

Step-by-step explanation:

The solution is in the image

What must be added to -31 to get 12

Answers

Answer:

43

Step-by-step explanation:

31+12=43

Therefore adding 43 to -31 should give the answer 12.

Hii!

____________________________________________________________

Answer:

43

Step-by-step explanation:

We can find an answer to this question by setting up an equation.

-31+x=12

x is the unknown amount we should add to -31 to obtain 12.

Now, to solve it for the variable, x, we need to add 31 to both sides.

Upon doing this we obtain.

x=43

∴, 43 should be added to -31 to get 12

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Hope that this helped! Best wishes.

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Describe the graph of a quadratic function below given in table form

Answers

1526273784483883 the form of the h=

What is the surface area of prism below?

Answers

Answer:

Aprism =  483.246 yd2

Step-by-step explanation:

The surface area is the sum of the 2 circles areas and the rectangle area.

Ac1 = PI*r2

Ac1 = (3.14)*(11.4/2)2

Ac1 = 102.0186 yd2

Ac1 = Ac2 then

Ac2 = 102.0186 yd2

Now the perimeter of the circle is one the sides of the rectangle:

Pc = 2PI*r

Pc = 2*3.14*(11.4/2)

Pc = 35.796 yd

Now the area of the rectangle is:

Ar = 7.8yd*35.796yd

Ar = 279.2088 yd2

Then, the surface area of prism is:

Aprism = Ac1 + Ac2 + ArAprism = 102.0186yd2 + 102.0186yd2 + 279.2088yd2Aprism =  483.246 yd2

What are the rational roots of ? x = 1, x = -1 x = 1, x = 0 x = 1, x = 2 This polynomial has no rational roots.

Answers

The sneer is x= 1.5 big bro

The table displays the scores of students on a recent exam. Find the mean of the
scores to the nearest 10th.
Score Number of Students
70
7
75
5
80
4
85
1
90
6

Answers

Answer:

78.7

Step-by-step explanation:

To find the mean, we can do the sum of all scores divided by the total amount of scores.

We see that there are 7 scores of 70, and 70*7=490.

We see that there are 5 scores of 75, and 75*5=375.

We see that there are 4 scores of 80, and 80*4=320.

We see that there is 1 score of 85, and 85*1=85.

We see that there are 6 scores of 90, and 90*6=540.

Now we can do [tex]\frac{490+375+320+85+540}{7+5+4+1+6} =\frac{1810}{23} =78.7[/tex]

PLEASE GIVE STEP BY STEP EXPLANATION !!

The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x): A graph with two linear functions; f of x passes through 0, negative 1 and 5, 14, and g of x passes through negative 6, negative 1 and negative 1, 14. Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points) Part B: Solve for k in each type of transformation. (4 points) Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)

Answers

The two types of transformations that can be used to transform f(x) to g(x).  g (x) = f(x) + 16 and g (x) = f(x + 8)

ABC has vertices at A (12, 8), B (4, 8)

What is the equation about?

f(x)= 0, -1 ,5,14

g(x)= -6, -1, -1, 14

g(x)=f(x)+k

-6= 0+k

k= -6

A) g (x) = f(x) + 16 and

g(x) = f(x + 8)

B) g(x)=f(x)+k

-1= -1+ k

k= -1+1=0

g(x)=f(x)+k

-1= 5+k

k= -1-5=-6

g(x)=f(x)+k

14= 14+k

k= 0

k= -6,0,-6,0

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radical 5* radical 2

Answers

Answer:

[tex] \sqrt{10} [/tex]

Step-by-step explanation:

Rule: [tex] \sqrt{a} \times \sqrt{b} = \sqrt{ab} [/tex]

[tex] \sqrt{5} \times \sqrt{2} = \sqrt{5 \times 2} = \sqrt{10} [/tex]

The probability that the number of students who will take the mathematics exam is 40 out of 50. What is the expressed as a percentage

Answers

Answer:

I think it's 80%

Step-by-step explanation:

Method 1: (40/50)*100 = 80%

Method 2: [tex]\frac{40*2}{50*2} = \frac{80}{100}[/tex] = 80%

The table shows the height of water in a pool as it is being filled. A table showing Height of Water in a Pool with two columns and six rows. The first column, Time in minutes, has the entries, 2, 4, 6, 8, 10. The second column, Height in inches, has the entries, 8, 12, 16, 20, 24. The slope of the line through the points is 2. Which statement describes how the slope relates to the height of the water in the pool? The height of the water increases 2 inches per minute. The height of the water decreases 2 inches per minute. The height of the water was 2 inches before any water was added. The height of the water will be 2 inches when the pool is filled. help me

Answers

Answer:

The height of the water increases 2 inches per minute.

Step-by-step explanation:

the slope is always the ratio of

y coordinate change / x coordinate change

in our case, x is the time (minutes), and y is the water height (inches).

we see, the longer the pool get filled, the higher the water gets. logical, right ?

by checking the data points we see :

with every 2 minutes passing the water height increases by 4 inches.

so, the slope is +4/+2 = 2/1 = 2

and that ratio tells us now the increase of the water height with every fraction or multiple of the measured 2-minute interval.

every 2 minutes 4 inches more.

so, e.g. every 3×2 = 6 minutes we get 3×4 = 12 inches more.

and - every 1/2 × 2 = 1 minute more we get 1/2 × 4 = 2 inches more.

What is the solution to the following equation?
3( x - 4 ) - 5 = x - 3
A. x = 8
B. x = 3
C. x = 12
D. x = 7

Answers

Answer:

x = 7

Step-by-step explanation:

3(x - 4) - 5 = x - 3

3x - 12 - 5 = x - 3

2x = -3 + 12 + 5

2x = 14

x = 7

The answer is D, x=7 !

A condominium is taxed based on its $78,584 value. The tax rate is $3.49 for every $100 of value. If the tax is paid before March 1, 4%
of the normal tax is given as a discount. How much tax is paid if the condominium owner takes advantage of the discount?

Answers

The tax paid by the condominium owner  is $2,632.88.

What is the tax paid?

Tax is a compulsory levy that is paid to the government. The type of tax that is paid by the condominium owner is known as property tax.

Tax paid = (78,584 / 100) x $3.49 x (1 - 0.04) = $2,632.88.

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If anyone can help me to solve this.​

Answers

Answer:

1)  x + 96 = 90°

2)  x + 89 = 80°

Step-by-step explanation:

Consecutive Interior Angles Theorem

When a transversal line intersects two parallel lines, it forms two pairs of consecutive angles on either side of the transversal line.  Each pair of consecutive interior angles are supplementary (sum to 180°).

Question 1

To find the measure of the angle circled on the diagram, find the value of x by using the Consecutive Interior Angle Theorem:

⇒ (x + 96)° + (x + 96)° = 180°

⇒ x + 96 + x + 96 = 180

⇒ 2x + 192 = 180

⇒ 2x + 192 - 192 = 180 - 192

⇒ 2x = -12

⇒ 2x ÷ 2 = -12 ÷ 2

⇒ x = -6

Substitute the found value of x into the expression to find the measure of the angle circled on the diagram:

⇒ x + 96 = -6 + 96 = 90°

x + 96 = 90°

Question 2

To find the measure of the angle circled on the diagram, find the value of x by using the Consecutive Interior Angle Theorem:

⇒ (x + 109)° + (x + 89)° = 180°

⇒ x + 109 + x + 89 = 180

⇒ 2x + 198 = 180

⇒ 2x + 198 - 198 = 180 - 198

⇒ 2x = -18

⇒ 2x ÷ 2 = -18 ÷ 2

⇒ x = -9

Substitute the found value of x into the expression to find the measure of the angle circled on the diagram:

⇒ x + 89 = -9 + 89

x + 89 = 80°

Answer:

[tex]\boxed {1) 90^{o}}\\\boxed {2) 80^{o}}[/tex]

Step-by-step explanation:

Part 1 :

x + 96 + x + 96 = 180 (angle pairs of a line)2x + 192 = 1802x = -12x = -6

∠ = -6 + 96∠ = 90°

Part 2 :

x + 109 + x + 89 = 180 (same reason)2x + 198 = 1802x = -18x = -9

∠ = -9 + 89∠ = 80°

On a coordinate plane, a parabola opens down with solid circles along the parabola at (negative 3, negative 5), (negative 2, 0), (negative 1, 3), (0, 4), (1, 3), (2, 0), (3, negative 5). Which statement is true regarding the intervals where the function is increasing and decreasing? The function is increasing from (–∞, 0). The function is increasing from (0, ∞). The function is decreasing from (–∞, 0). The function is decreasing from (–∞, ∞).

Answers

The true statement regarding the intervals where the function is increasing and decreasing is option A: The function is increasing from (–∞, 0).

What is a function?

A function is defined as a relation between the set of inputs having exactly one output each.

On a coordinate plane, a parabola opens down with solid circles along the parabola at (-3, -5), (-2, 0), (-1, 3), (0, 4), (1, 3), (2, 0), (3, -5).

The domain is all real numbers.

The range is all real numbers.

If for an interval I, when x decreases meanwhile staying in interval I, the function's output increases (or can stay same), then we say that the function is increasing in the interval.

The true statement regarding the intervals where the function is increasing and decreasing is option A: The function is increasing from (–∞, 0).

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Answer:

A

Step-by-step explanation:

The students in Mr. McIntyre’s class and the students in Mrs. Ramos’s class were asked how many pets they each have. The dot plots below show the results.

Mr. McIntyre’s Class
A dot plot titled Mister McIntyre's Class. A number line going from 0 to 5 is labeled Number of Pets. There are 5 dots above 0, 5 above 1, 4 above 2, 1 above 3, and 0 above 4 and 5.

Mrs. Ramos’s Class
A dot plot titled Misses Ramos's Class. A number line going from 0 to 5 is labeled Number of Pets. There is 1 dot above 0, 2 above 1, 2 above 2, 4 above 3, 3 above 4, 3 above 5.

Which statement correctly compares the means of the data in the dot plots?

Answers

The correct statement compares the means of the data in the dot plots is option C; the mode is greater for Mrs. Ramos’s class.

What are the median and mode of the data?

Median represents the middle value of the given data when arranged in a particular order.

Mode is that number that appears most frequently in the given set of data.

Given;

The Number of pets in Mr. McIntyre’s class ;

0,0,0,0,0,1, 1, 1, 1, 1, 4, 4, 4, 4, 1,

Median = 1

Mode = 0 and 1

The Number of pets in Mrs. Ramos’s Class;

0, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 3, 3, 3

Median = 3

Mode = 4 and 5

Hence, C; The mode is greater for Mrs. Ramos’s class.

The remaining part of the question is

"Which statement correctly compares the measures of center of the data in the dot plots?

The median is greater for Mr. McIntyre’s class.

The median is the same for both classes.

The mode is greater for Mrs. Ramos’s class.

The mode is the same for both classes."

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If ( 3 y − 9 ) 2 + 7 = 43 , then what is(are) the values of y?

Answers

Answer:

y = 5 and y = 1

Step-by-step explanation:

[tex]\textsc {Subtract 7 from each side :}[/tex]

⇒ (3y - 2)² + 7 - 7 = 43 - 7

⇒ (3y - 2)² = 36

[tex]\textsc {take the square root on each side :}[/tex]

⇒ √(3y - 9)² = √36

⇒ 3y - 9 = ±6

[tex]\textsc {When equal to +6, add 9 on each side :}[/tex]

⇒ 3y - 9 + 9 = 6 + 9

⇒ 3y = 15

[tex]\textsc {Divide by 3 on each side :}[/tex]

⇒ 3y/3 = 15/3

y = 5

[tex]\textsc {When equal to -6, add 9 on each side :}[/tex]

⇒ 3y - 9 + 9 = -6 + 9

⇒ 3y = 3

[tex]\textsc {Divide by 3 on each side :}[/tex]

⇒ 3y/3 = 3/3

y = 1

The graphs below have the same shapes. What is the equation for the red graph?

Answers

The equation of the red graphed function is: g(x) = 1 - x².

How to Find the Equation of a Graphed Function?

Given the graph shown in the attachment below, the graphed function heads downwards, and the x - axis is intercepted at ( 1, 0 ) and (-1,0).

Thus, the x-intercepts, which is the zeros of the function, are: 1 and -1.

So, g(x) = (x + 1)(x -1)

Expand:

g(x) = 1 - x²

The equation of the red graph is: g(x) = 1 - x².

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Thalia, a quiz show contestant, answered 20 questions. She was awarded 2 points for every correct answer that she gave, but she was penalized 1 point for every incorrect answer. In the end, Thalia had a total of 28 points. In order to determine the number of correct and incorrect answers that she gave, a viewer at home used the system of linear equations x + y = 20 and 2 x + y = 28, with x being the number of correct answers and y being the number of incorrect answers. The viewer solved the system by using the linear combination method as shown.

x + y = 20. + StartFraction Negative 2 x minus y = negative 28 over Negative x = negative 8 EndFraction. StartFraction negative x Over negative 1 EndFraction = StartFraction negative 8 Over negative 1 EndFraction. X = 8.
8 + y = 20. 8 + y minus 8 = 20 minus 8. y = 12.

The viewer calculated that the contestant answered 8 questions correctly and 12 questions incorrectly. What went wrong?
The viewer mistakenly determined that one of the equations in the system should be x + y = 20.Instead modifications should have been made before applying the equation.
The viewer mistakenly determined that one of the equations in the system should be 2 x + y = 28. Instead modifications should have been made before applying the equation.
The viewer multiplied the equation 2 x + y = 28 by –1 incorrectly.
The viewer added the equations x + y = 20 and Negative 2 x minus y = negative 28 incorrectly.

Answers

The viewer mistakenly determined that one of the equations in the system should be 2 x + y = 28. Instead modifications should have been made before applying the equation.

What is an Equation ?

An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.

Total Questions = 20

Total Points = 28

Correct Answers = +2 points

Incorrect Answers = -1 point

The viewer represents the correct answers with x and the incorrect ones with y.

x+y = 20

for every correct answers 2 points;

and for every incorrect answers, -1 point

This can be written as

2x-y = 28

The viewer's mistake is that; instead of subtracting total incorrect points from the correct points, the viewer added them together;

now

2x-y = 28

x+y = 20

On adding the equations

]3x = 48

x = 16

y = 4

This means that the contestant answered 16 questions correctly and 4 questions incorrectly

The viewer mistakenly determined that one of the equations in the system should be 2 x + y = 28.

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Find the value of the function f(x) = x2 + 9x + 10, for x = -1.

Answers

Answer:

this is pretty easy we just replace the x with -1 so

(-1)^2+(-1)9+10

-1*-1=1

-1*9=-9

1+-9=-8

-8+10=2

f(-1)=2

Hope This Helps!!!

1) When the polynomial P(x) is divided by x+5, the remainder is 3. Which of the following is definitely true?
a) P(3) = 5
b) P(-5) = 3
c) P(5) = 3
d) P(-3) = 5

2) P is a degree 3 polynomial with real coefficients and three zeros. Two of the zeros are 5 and 3+4i. What is the other zero?
a) 4-3i
b) 4+3i
c) -5
d) 3-4i

Answers

1) The definitely true for the statement is b) P(-5) = 3.

2) The three roots are 5, 3 + 4i, and 3 - 4i. Option D is correct.

What is the remainder theorem for polynomials?

If there is a polynomial p(x), and a constant number 'a', then

[tex]\dfrac{p(x)}{(x-a)} = g(x) + p(a)[/tex]

where g(x) is a factor of p(x)

Given;

1) When the polynomial P(x) is divided by x+5, the remainder is 3.

If a polynomial P(x) is divided by (x-a), then the remainder is P(a).

If the polynomial P(x) is divided by (x+5), then the remainder will be P(-5).

So, P(-5) = 3

Therefore, the definitely true for the statement is b) P(-5) = 3.

2) P is a 3 degree polynomial with real coefficients and three zeros. Two of the zeros are 5 and 3+4i.

The complex roots always exist in conjugate pairs so,

3 + 4i and 3 - 4i

Thus, the three roots are 5, 3 + 4i, and 3 - 4i. Option D is correct.

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Another day, another math problem 2

Answers

Answer:

-7

Step-by-step explanation:

you can use power rule of derivatives for that.

What is the solution to this system of equations y=3x-4 4y=12x-4 a no solution b (0,4) C Infinite solutions

Answers

Answer:

C

Step-by-step explanation:

y = 3x - 4

4y = 12x - 4

divide the bottom equation by 4

y = 3x - 4

y = 3x - 1

y = -3

3x - 1 = -3

3x = -2

x = -2/3

(-2/3, -3) is the answer. by this logic, there is a splution so can't be a, the answer is not (0, 4) so not b so it must be c

a farmer uses 1/6 of his land to plant pineapples, 5/9 to plant durians and the remaining 48.5 acres to plant vegetables. calculate the area of land used to plant pineapples and durians​

Answers

Step-by-step explanation:

x = total area of land

x - 1/6 × x - 5/9 × x = 48.5 | multiply both sides by 6

6x - x - 30/9 × x = 291

5x - 30/9 × x = 291 | multitude both sides by 9

45x - 30x = 2,619

15x = 2,619

x = 174.6 acres

pineapples were planted on 174.6 × 1/6 = 29.1 acres.

durians were planted on 174.6 × 5/9 = 97 acres.

A cab company charges a $5 boarding rate in addition to its meter which is $3
for every mile. What is the equation of the line that represents this cab
company's total charge?
Re
co

Answers

Answer:

m3+5

Step-by-step explanation:

m is miles

take the number of miles  multiply by3

take that answer add 5

The equation that represents the cab's total charge is  y = 3x + 5 , Option A is the correct answer.

What is an Equation ?

A statement that relate two expressions with an equal sign is called an Equation.

It is given that

A cab company charges a $5 boarding

Charges for every mile is $3 per mile

Let x be the mile travelled

The cab's total charge is represented by y

then y = 3x + 5

Therefore the equation that represents the cab's total charge is  y = 3x + 5 , Option A is the correct answer.

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How do i find the domain of F and write in interval notation??? I completely confused

Answers

Answer:

898

Step-by-step explanation:

898999

A bag contains 3 blue, 7 green and 1 purple counter. One counter is picked
at random. What is the probability that the counter is green or purple? Give
your answer as a fraction.

Answers

A bag contains 3 blue, 7 green and 1 purple counter. One counter is picked at random, the probability of selecting a green or purple counter is 8/11.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is usually expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to occur.

There are a total of 11 counters in the bag, 3 of which are blue, 7 are green, and 1 is purple.

The probability of selecting a green or purple counter is the sum of the probabilities of selecting a green counter and a purple counter, since the events are mutually exclusive (a counter cannot be both green and purple at the same time).

So the probability of selecting a green or purple counter is:

Probability = (Number of green counters + Number of purple counters) / Total number of counters

Probability = (7 + 1) / 11

Probability = 8/11

Therefore, the probability of selecting a green or purple counter is 8/11.

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In formula P = 2L + 2W
A. solve for L
B. solve for W
C. Find P if L=12 and W=8

Answers

Answer:

P=2l+2W

if l=12 and W=8

then,

P=2L+2W

=2.18+2.8

=36+16

=52

14)
Given a circle with a radius of 5, which equation expresses it as the ratio of the circumference of a circle to its diameter?
A)
B)
C)
D)
sin
- 7
10
216
C

Answers

Answer: 10

Step-by-step explanation: The diameter is twice the radius

17, 18, 22, 31, 47 what is the next number

Answers

Answer:

the next number is 47+ 16 =63

Please help I’m confused

Answers

Answer:

Step-by-step explanation:

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