Define a function f : R → R by the formula
f(x) = 2x − 8.


Prove that f is one-to-one.
Let a, b is in R, and suppose that
f(a) = f(b).
Then
2a − 8 =

Answers

Answer 1
We are given a function f(x) = 2x - 8 and a condition that f (a) = f (b). We are then asked the next terms of 2a - 8 = ______. 

Now, we have to think that the parent function is f(x) = 2x - 8 and f (a) = f (b). This means the value of the function f(a) is if a is substituted to x:

f (a) = 2a - 8, same goes for f (b):

f (b) = 2b - 8.

Since we have a condition that f(a) = f (b), then,

2a - 8 = 2b - 8. 

If we simplify further, 

2a = 2b - 8 + 8
( 2a = 2b ) / 2

the equation becomes:

a = b; this proves that f is a one-to-one function. 


 

Related Questions

PLEASE HELP!! ISSA DUMB KID!

Answers

The length spans from 1 to 9.
9-1= 8 <=== length
The height spans from 4 to 7.
7-4=3 <=== height

Area of a rectangle is equal to length times width.
8*3=24
Final answer: C

Harvey the wonder hamster can run 3 1/6 km in 1/4 hour find his average speed in kilometers pe hour

Answers

there are 4 quarters to 1 hour

3 1/6 x 4 =

19/6 * 4 = 76/6 = 12 4/6, reduces to 12 2/3 km per hour

Answer:- The average speed of Harvey the wonder hamster is[tex]12\frac{2}{3}\ km/hour[/tex].


Explanation:-

Given: Distance traveled by Harvey [tex]=3\frac{1}{6}\ km=\frac{19}{6}\ km[/tex]

Time taken[tex]=\frac{1}{4}\ hour[/tex]

[tex]Speed=\frac{Distance}{Time}\\\Rightarrow\ Speed=\frac{\frac{19}{6}}{\frac{1}{4}}\\\\=\frac{19\times4}{6}\\\\=\frac{38}{ 3}\\\\=12\frac{2}{3}\ km/hour[/tex]

Therefore, the average speed of Harvey the wonder hamster is[tex]12\frac{2}{3}\ km/hour[/tex].

A basketball team has eight boys and four girls on the roster. The boys average 12 points each. The team averages 136 points as a whole. How many points does each girl average?

Answers

8 x 12 = 96

136-96 =40

40/4 = 10

 each girl averages 10 points

The girls average about 10 points a game
the boys have 8 player 
EX. 12x8=96 
136-96=40
There are four girls so 40 is divided evenly so the answer is 10 points a game

If a point is equidistant from the two sides of an angle, then it is:

A. on the perpendicular bisector.
B. the vertex of the angle.
C. on the angle bisector.
D. on one side of the angle.

Answers

on the bisector.it means its dividing the the sides of the angle into two equal parts

A point is equidistant from the two sides of an angle, then it is option (C) on the angle bisector is the correct answer.

What is angle bisector theorem?

An angle bisector is a straight line drawn from the vertex of a triangle to its opposite side in such a way, that it divides the angle into two equal or congruent angles.

For the given situation,

Any point that is on the angle bisector is an equal distance ("equidistant") from the two sides of the angle.

A point which is always equidistant from all the sides is the point of intersection of internal angle bisectors.

Hence we can conclude that a point is equidistant from the two sides of an angle, then it is option (C) on the angle bisector is the correct answer.

Learn more about angle bisector theorem here

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a washer and dryer cost $978 combined the washer cost $78 more than the dryer what is the cost of the dryer

Answers

the cost of the dryer is 528

Answer:

$450

Step-by-step explanation:

2x+78=978

2x=900     [subtract 78 from both sides]

x=450        [divide both sides by 2]

what is 561 divided by 3

Answers

561 divided by 3 is .... 187

Diana made a recipe that yields 6 and 1 over 2 cups. If each serving is 1 over 4 cup, which expression will help Diana determine the number of servings her recipe will yield? 6 and 1 over 2 ⋅ 1 over 4 6 and 1 over 2 ÷ 1 over 4 6 and 1 over 2 + 1 over 4 6 and 1 over 2 − 1 over 4

Answers

six and a half divided by one over four

Answer:

6 and 1 over 2 ÷ 1 over 4

Step-by-step explanation:

Given,

The total cups in a recipe =  6 and 1 over 2 cups

[tex]=6\frac{1}{2}\text{ cups}[/tex]

Also, the cups in each serving =  1 over 4 cup

[tex]=\frac{1}{4}\text{ cups}[/tex]

Hence, the number of servings = [tex]\frac{\text{total cups in a recipe}}{\text{cups in each serving}}[/tex]

[tex]=\frac{6\frac{1}{2}}{\frac{1}{4}}[/tex]

= 6 and 1 over 2 ÷ 1 over 4

Second option is correct.

Cual es el minimo comu multiplo de 81,27,9



Answers

La respuesta es 81.

Eso es porque
81*1= 81,
27*3=81,
y 9*9=81.

The map shows Santa Cruz Boulevard and the construction site for the new town hall. Find the equation of a “street” that passes through the building site and is parallel to Santa Cruz Boulevard.

Answers

y=1/2x-1 is the answer that is parallel

Answer:

the equation of a “street” that passes through the building site and is parallel to Santa Cruz Boulevard[tex]y=\frac{x}{2}+4[/tex]

Step-by-step explanation:

The slope is find by 2 points on line [tex](x_1,y_1)\,\text{and}\,(y_2,y_2)[/tex] is calculated as; [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Equation of line is in slope-intercept form is written as;

          [tex](y-y_1)=m(x_2-x_1)[/tex]

We can easily take two points from given graphs are

(2,5) and (6,7)

The slope of line is;

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{7-5}{6-2}[/tex]

[tex]m=\frac{2}{4}[/tex]

[tex]m=\frac{1}{2}[/tex]

the slope of line is [tex]\frac{1}{2}[/tex]

Now, find the equation of line with the  slope-intercept form

[tex](y-y_1)=m(x-x_1)[/tex]

[tex](y-5)=\frac{1}{2}(x-2)[/tex]

Add both the sides by 5 in above expression,

[tex]y=\frac{1}{2}(x-2)+5[/tex]

[tex]y=\frac{x}{2}-1+5[/tex]

[tex]y=\frac{x}{2}+4[/tex]

Therefore, the equation of a “street” that passes through the building site and is parallel to Santa Cruz Boulevard[tex]y=\frac{x}{2}+4[/tex]

Solve 5^x=81. 2
Round to the nearest ten-thousandth.

X≈????

Answers

Is that 5^x=81.2?

5^x=81.2  take the natural log of both sides

xln5=ln81.2  divide both sides by ln5

x=ln81.2/ln5

x≈2.7320  (to nearest ten-thousandth)

If you just meant 5^x=81, the process is the same

5^x=81  take the natural log of both sides

xln5=ln81  divide both sides by ln5

x=ln81/ln5

x≈2.7304  (to nearest ten-thousandth)


what is the decimal representation of 27/100?

Answers

Your Answer Is...

.27

Glad I Could Help, And Good Luck!

My Brainly Name: AnonymousGiantsFan
.27 is the answer

since 100/100 = 1.0 obviously 27/100 = .27

what is the converse to the following conditional statement if x=12 then 2x-5=19

Answers

The converse means to simply switch the two given statements or facts.
For the given conditional statement, the converse will be:
if 2x-5=19, then x=12
Now we need to check whether the converse is true or not:
2x-5=19
2x=19+5=24
x=24/2=12
Thus, the converse is true
Extra note:
When the converse of the conditional statement is found to be true, then this statement is said to be a bi-conditional statement and we write the converse as follows:
2x-5=19 if and only if x=12

Final answer:

The converse of the given conditional statement 'if x=12 then 2x-5=19' is 'if 2x-5=19, then x=12'. To verify its truth, we solve for x when 2x-5 equals 19, resulting in x equaling 12, thus showing that in this instance, the converse is true.

Explanation:

The converse of a conditional statement is formed by swapping the hypothesis and the conclusion of the original statement. For the statement 'if x=12 then 2x-5=19', its converse would be 'if 2x-5=19, then x=12'. To test the validity of the converse, we substitute the value of x back into the equation 2x-5 and check if it equals 19 when x=12.

However, we need to be cautious because the converse of a true conditional statement is not always true. To determine the truth of the converse, one must check if every instance where 2x-5 equals 19 also means that x must be equal to 12. If there is even a single case where 2x-5 is 19 and x is not 12, then the converse is not true.

For instance, let's test the converse: If we solve the equation 2x-5=19 for x, we get:

x = (19+5)/2

x = 24/2

x = 12

Therefore, for this specific case, the original statement and the converse are both true.

M to the second power equals 49. Is it 7?

Answers

M^2 = 49
M^2 = 7^2
M = -7 and M = 7
yes because the square root of 49 is 7

In a line of students, Jenna is number 8. The teacher says that a rule for a number pattern is add 4. The first student in line says the first term, 7. What number should Jenna say?

Answers

Jenna should say 35

Hope this helps!

Jaime drew a square that has sides that are whole numbers of centimeters. Which could not be the area of Jaime's square? A. 25cm2 B. 36cm2 C. 50cm2 D. 64cm2

Answers

Final answer:

To find the area of a square, we use the formula A = s², where A represents the area and s represents the length of a side. Evaluating the options, the area that could not be Jaime's square is C. 50cm².

Explanation:

To find the area of a square, we need to multiply the length of one side by itself. So, the formula for the area of a square is A = s², where A represents the area and s represents the length of a side. We can evaluate the given options using this formula:

A. 25cm²: This could be the area of Jaime's square since 5² = 25.B. 36cm²: This could be the area of Jaime's square since 6² = 36.C. 50cm²: This could not be the area of Jaime's square since there is no whole number that can be squared to give 50.D. 64cm²: This could be the area of Jaime's square since 8² = 64.

Therefore, the answer is C. 50cm².

In a group of 60 students, 12 students take Algebra I, 18 students take Algebra II, and 8 students take both subjects. How many students don't take either of these subjects?

Answers

well if 12.students tAke algebra I and 18 tAke algebra II and 8 of these students are in both classes, that means we are actually counting these.8 students twice. So it would appear there are 30 but minus the 8 we counted twice and we get 22. So 60 - 22 = 38
12-8=4.
18-8=10.
10+4+8=22
60-22=38

Melanie has a piece of cloth 12 and 1/3 yards long. How many 3/4 yard-long pieces can be cut from the cloth?

Answers

This is a division problem. First, get 12 1/3 into fraction form instead of mixed number form to make your life easier;  
[tex]12 \frac{1}{3} = \frac{36}{3} + \frac{1}{3} = \frac{37}{3} [/tex]  
Now, divide the two fractions. Since this is fraction division, the reciprocal is flipped and the two fractions multiplied.  
[tex] \frac{37}{3} * \frac{4}{3} = \frac{148}{9} = 16 \frac{4}{9} [/tex]  
The answer from the fraction division is 16 and four-ninths, but because you need a whole number as an answer,  
the answer is 16 pieces.

Answer: 16 pieces

Step-by-step explanation:

To get the number of pieces, we simply divide 12 1/3 by 3/4

12 1/3 ÷ 3/4

but 12 1/3 = 37/ 4 ( converting to improper fraction)

12 1/3 ÷ 3/4

=37/ 3 ÷ 3/4

= 37/3 × 4/3

= 148/9

= 16. 44444

= 16 approximately

Therefore we can get 16 pieces of yard from the cloth

The table shows the ratio of caramel corn to hot pepper corn in a bag. What is the constant of proportionality?

Hot Pepper Corn | Caramel Corn
 5_______________8
10 _____________ 16
15______________ 24

Answers

Ratio is merely the fraction of two terms. For example, when you cook a recipe, you are given a ration of 1 cup of milk is to two eggs. In this case, the ratio of milk to eggs is 1/2 or 1:2. 

For this problem,let's divide each row of values to get the ratio. The ratio for all of this pair of values must coincide with each other. The solution is as followsL

Hot Popcorn Corn/Caramel Corn
5/8 = 5/8
10/16 = 5/8
15/24 = 5/8

Therefore, the ratio is 5/8. It can also be in decimal form which is equal to 0.625.

What is the solution to the equation x + 8.5 = 64.5? 7.6 48 56 73

Answers

The solution to x + 8.5 = 64.5 is 56.

    x + 8.5 = 64.5
       - 8.5   - 8.5
---------------------------
    x = 56


Simplifying
x + 8.5 = 64.5
 
Reorder the terms:
8.5 + x = 64.5
 
Solving
8.5 + x = 64.5

Solving for variable 'x'.
 
Move all terms containing x to the left, all other terms to the right.

Add '-8.5' to each side of the equation. 
8.5 + -8.5 + x = 64.5 + -8.5
 
Combine like terms:
8.5 + -8.5 = 0.0
 0.0 + x = 64.5 + -8.5
 x = 64.5 + -8.5
 
Combine like terms: 64.5 + -8.5 = 56
x = 56
 
Simplifying x = 56

Which of the binomials below is a factor of this trinomial? x2 - 5x - 36 A. x + 4 B. x - 4 C. x2 + 7 D. x - 7

Answers

Option A is correct, x+4 is the binomial factor of the given trinomial x² - 5x - 36

What is Polynomial?

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

The given trinomial is  x² - 5x - 36

Now we have to factorize the given polynomial.

x² - 9x +4x - 36

x(x-9)+4(x-9)

(x+4)(x-9)

The factorial form of the trinomial  x² - 5x - 36 is (x+4)(x-9)

So x+4 is the binomial factor of the given trinomial.

Hence, Option A is correct, x+4 is the binomial factor of the given trinomial x² - 5x - 36

To learn more on Polynomials click:

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simplify this expression x^8 y^-26

Answers

x^33 is the expression x^8 y^-26/x^14y^-5*x^-39y^-21 simplified 

A set of equations is given below: Equation E: c = 2d + 1 Equation F: c = 3d + 7 Which statement describes a step that can be used to find the solution to the set of equations? (1 point)


Equation F can be written as c = 3(c – 1) + 7.
Equation F can be written as c = 2(c – 7) + 1.
Equation F can be written as d + 1 = 3d + 7.
Equation F can be written as 2d + 1 = 3d + 7.

Answers

Equation F can be written as 2d + 1 = 3d + 7

What process can you use to help you write a system of linear equations when dealing with mixture problems

Answers

First, you have to understand the mixture problem. You cannot solve any problem without understanding it first. You should have a good comprehension of the problem. Then, you need to have the set up. Usually, mixture problems have three amounts. Two of those are usually the amounts being mixed and the third is the mixed amounts. Then, you need to identify the "x" or the variable. You need to assign the x properly to the problem. Let us say for example that you need to have 15 liters of mixture. Then you put some x liters to the other component of mixture. Therefore, the other component would be "15 – x liters". Then finally, solve the equation and you will eventually get with the right amount.

Which expression represents the composition [f o g](x) for the functions below? f(x) = 2x + 3 g(x) = x – 6
2x – 9
2x – 3
2x – 15
2x2 – 9x – 18

Answers

The answer would be 2x-9. If you need help to see how to work it out, let me know 

Answer:

Option A is correct

2x-9

Step-by-step explanation:

Given the functions:

f(x) = 2x + 3

g(x) = x -6

We have to find  [f o g](x).

[tex][fog](x) = f[g(x)][/tex]

Substitute the function g(x),

[tex][fog](x) = f[x-6][/tex]

Replace the value of x with x-6 in f(x) we have;

[tex][fog](x) =2(x-6)+3[/tex]

⇒[tex][fog](x) =2x-12+3[/tex]

⇒[tex][fog](x) =2x-9[/tex]

Therefore, the value of [tex][fog](x)[/tex] is, 2x-9

A number minus 25 is equal 51

Answers

A number (x) minus 25 (-25) is equal to (=) 51 (51).
Rewrite everything only in parenthesis.
x - 25 = 51

Now, we can solve.

To solve for x, we need for it to be on one side by itself. However, x is subtrating 25. To get rid of -25, we must perform the opposite order of operations.

Remember, what you do to one side of an equation, you must do to the other.

Add 25 to both sides.
-25 + 25 = 0
51 + 25 = 76.

We are now left with:
x = 76.

I hope this helps!
  x − 25 = 51 .

 This is the expression that would be written; in which "x" refers to the particular number.

To solve for that number, one would add 25 to EACH SIDE of the equation; to isolate "x" (the particular number to be solved for) on ONE SIDE of the equation; and to solve for "x" (that particular number) ; AS FOLLOWS:
_________________________________
   x − 25 = 51 ;

  Add 25 to each side of the equation; 

  x − 25 + 25 = 51 + 25 ;

   to get: 
 
            x = 76. 
____________________________________________
The particular number is:  " 76 " .
____________________________________________

The probability of drawing a blue card is 5/11 what is the probability of NOT drawing a blue card?

Answers

The probability of not drawing one is 6/11
To get the probability of not drawing a blue card, you have to subtract 5 from 11 which is 6. So, the probability of not drawing a blue card is 6/11.

Which of the following best describes the expression 7(x + 9)?

A.) The product of a constant factor 7 and a 2-term factor x + 9

B.) the sum of a constant factor 7 and a 2-term factor x + 9

C.) the sum of a constant factors 7 and x + 9

D.) the product of a constant factors 7 and x + 9

Answers

The product of a constant factor 7 and a 2-term factor (x + 9)

A.

got it right on my test, flvs

A ship traveled for 4 hours heading east and for 3 hours heading north. If the total distance traveled was 149 miles, and the ship traveled 3 miles per hour faster heading north, at what speed was the ship traveling east?

Answers

d=vt,   distance is equal to velocity times time.

4v+3(v+3)=149 perform indicated multiplication

4v+3v+9=149  combine like terms on left side

7v+9=149  subtract 9 from both sides

7v=140  divide both sides by 7

v=20

So the ship traveled at a speed of 20 mph when heading east.

BEST ANSWER GETS BRAINLIEST
Frank is surveying shoppers about their use of the new food court in a mall. Which question in his survey is a statistical question?

A. How many hours do you spend at the food court each month?

B. Where is the food court located in the mall?

C. How many restaurants are there in the food court?

D. Who is the manager of the food court?

Answers

A. is a statistical answer because it is asking for a number from each person (in this case, number of hours), which provides him with statistics. So the answer to this question is answer A.

Answer:


Step-by-step explanation:

The answer to this question is answer A.

Help me please asap :(

Answers

This is a fairly tedious problem. The only way to solve that I see is to simply list out all the possible cases and go through each one by one. You'll use the triangle inequality theorem to see if the triangles can be formed. The theorem says that a+b > c must be true for all sets of pairs. In other words, take any two sides and add them up. The sum must be greater than the third side. 

Going through all the combos possible (that I could find), this is what I got
Blue9,Green7,Orange4
Blue9,Green7,Purple12
Blue9,Green7,Red3
Blue9,Green7,Yellow5
Blue9,Orange4,Purple12
Blue9,Purple12,Yellow5
Green7,Orange4,Yellow5
Green7,Red3,Yellow5
Orange4,Red3,Yellow5

In all, I count 9 cases. So the answer to problem 1 is 9.

-----------------------------------------------------------

For problem 2, the best way may be to pick two segments at a time instead of one. However, I have a feeling that will take just as long as the first method. I haven't tried it out. Even though going through the rods one at a time takes a while, it's probably the best option so you don't overlook any cases. 


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