Write the difference of the given functions (f - g)(x):
f(x) = x² + 2x - 6 and g(x) = x + 5.

Answers

Answer 1

Answer:

(f - g)(x) = x² + x - 11

General Formulas and Concepts:

Pre-Algebra

Properties

Algebra I

Combining like terms

Step-by-step explanation:

Step 1: Define

f(x) = x² + 2x - 6

g(x) = x + 5

(f - g)(x) is f(x) - g(x)

Step 2: Find

Substitute:                    (f - g)(x) = x² + 2x - 6 - (x + 5)Distribute -1:                 (f - g)(x) = x² + 2x - 6 - x - 5Combine like terms:    (f - g)(x) = x² + x - 11

Related Questions

What will be the slope of (3,-4) and (1,2)

Answers

Answer:

[tex]\boxed {m = 1}[/tex]

Step-by-step explanation:

Use the Slope Formula to determine the slope of two given points:

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

First Point: [tex](x_{1}, y_{1})[/tex]

Second Point: [tex](x_{2}, y_{2})[/tex]

-Substitute both points:

First Point: [tex](3, -4)[/tex]

Second Point: [tex](1, 2)[/tex]

[tex]m = \frac{2 + 4}{1 - 3}[/tex]

-Solve for the slope:

[tex]m = \frac{2 + 4}{1 - 3}[/tex]

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

[tex]\boxed {m = 1}[/tex]

Therefore, the slope is [tex]1[/tex].

Peter cuts lawns and makes $40 per lawn. He spends $10/day in work expenses. Write an equation in the form y = mx + b to represent this situation.

Answers

Answer: y= 40x-10 , where = number of lawns.

Step-by-step explanation:

In linear equation y= mx+b with one variable x, m= slope , b= y-intercept.

[Slope rate of change of y with respect to x, y-intercept = initial value of y at x=0]

Given: Peter cuts lawns and makes $40 per lawn.

let x = number of lawns

i.e. slope = $40

He spends $10/day in work expenses.

i.e.  y-intercept = -10  [for each day]

So equation becomes : y= 40x-10 , where = number of lawns.

Write the equation of the line that has a slope of 3 and passes through (5, 11)
y = 3x - 26
y = 3x - 38
y = 3x - 4
x = 3y - 4

Answers

Answer:

3x-4

Step-by-step explanation:

y=ax+b general type of the line

a is the slope

y=3x+b

put 5 instead of the x and put 11 instead of the y

11=15+b

b=(-4)

Equation is 3x-4

Parker has $137 in one, five, and ten dollar bills. He has just as many ten dollar bills as he has five and one dollar bills together. If he has 22 bills in all, how many of each type of bill does he have?

Answers

Step-by-step explanation:

(1$) 7+ ($5) 4 + ($10) 11=22 bills

7+20+110=137$

A small rectangle has a width of 4ft and a length of 10ft. A larger rectangle has a length of 12ft. What is the perimeter of the larger rectangle?

Answers

Answer:

48 I think

Step-by-step explanation:

12+12+12+12=48

or 12 x 4=48

Answer:

48

Step-by-step explanation:

12+12+12+12 = 48

or

12x4=48

Which of the following is a rearrangement of A
(61 +62) · h
that highlights the variable h?

Answers

Answer:

123 x h because you can't put them together but we can add the stuff that is already there so we get 123 and times h thats our answer

does anyone know ? thx

Answers

Answer:
4x-3
Explanation:
3x+2+x-5
4x-3

which expression is equivalent to 2^3 square root x^2 • square root 16x if x > 0

Answers

Answer:

A

Step-by-step explanation:

The question is actually: 2 \sqrt[3]{x^3} ·\sqrt{16x}

The expression is equivalent to option A, [tex]\rm 8x \sqrt[6]{x}[/tex].

What is an Expression?

An expression is a mathematical statement that consists of variables, constants, and mathematical operators.

The expression is [tex]\rm 2\sqrt[3]{x^2} . \sqrt{16x}[/tex]

The expression can be simplified as

[tex]\rm = 2 . 4 x^{2/3} x^{1/2}\\\\\=8 x ^{ 7/6}\\\\\\ = 8x x^{1/6}\\\\= 8x \sqrt[6]{x}[/tex]

Therefore, the expression is equivalent to option A, [tex]\rm 8x \sqrt[6]{x}[/tex].

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Select the correct locations on the graph. Select the lines that represent functions.

Answers

Answer:

bruh there isnt a graph or anything we cant answer it

Step-by-step explanation:

Answer:

where is it

Step-by-step explanation:

whose method can be used to verify the distributive property was correctly applied expression

A. zoes method
B.latoyas method
C. christinas method
D. Rhodas method​

Answers

answer:
D: Rhodas method

Sandra wrote p(x) = 30x + 5x2 in vertex form. Her work is below. 1. p(x) = 5x2 + 30x 2. p(x) = 5(x2 + 6x) 3. (six-halves) squared = 9; 4. p(x) = 5(x2 + 6x + 9) – 5(9) 5. p(x) = 5(x + 3)2 – 45 Describe Sandra’s function. What is the vertex of this function? Is it a maximum or a minimum? What is the axis of symmetry of this function?

Answers

Answer: 1st question• (-3, -45)

2nd question• x= -3

Step-by-step explanation:

just did it on edge

The vertex of the function p(x) = 30x^2 + 5x^2 is (-3,-45), and it is a minimum

The description of the function

The function is given as:

p(x) = 30x^2 + 5x^2

The description of the function is that the function is a quadratic function

The vertex

From the question, we have:

p(x) = 5(x + 3)^2 – 45

A quadratic function represented as: p(x) = a(x - h)^2 + h has the vertex (h,k)

This means that the vertex is (-3,-45), and it is a minimum because a is positive i.e. a = 5

The axis of symmetry

This is the x-coordinate of the vertex.

Hence, the axis of symmetry is x = -3

Read more about quadratic functions at:

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What is the y-intercept. Describe how you know in both the table and the graph.

Answers

Answer:

(4,0)

Step-by-step explanation:

the y-intercept is 4 because when the x value is 0 the y value is 4 on both the graph and table

Adult tickets to a basketball game cost $5. Student tickets cost $1. A total of $2,791 was collected on the sale of 1,275 tickets. How many of each type of ticket were sold?

Answers

9514 1404 393

Answer:

379 adult tickets896 student tickets

Step-by-step explanation:

Let 'a' represent the number of adult tickets sold. Then (1275-a) is the number of student tickets sold. The total revenue was ...

  5a +1(1275 -a) = 2791

  4a = 1516 . . . subtract 1275 and simplify

  a = 379 . . . . . divide by 4

  1275-a = 896

379 adult and 896 student tickets were sold.

Question 6 of 10
Which of the following are solutions to the equation below?
Check all that apply
2x2 + 6x = 20
A. -5
B. 20
C. -2
D. 1
E. 2
F -10

Answers

b , e , a are the correct answers

Answer:

-5 and 2

Step-by-step explanation:

Find the rate of change of the linear function
shown in the graph, Then find the initial value.
The rate of change is

Answers

Answer:

6

Step-by-step explanation:

dfsfads

On the number line, a point was moved from -7 to -3. Which of the following problems describes this move?
-7 + 3 = -4
-7-4 = -3
-7-3 = -10
-7+ 4 = -3

Answers

Answer:

-7+-3=-4

Step-by-step explanation:

Which statement is true about perpendicular lines?

Help please!!

Answers

Answer:

The answer is that they intersect at the right angles 90°

Answer:

they intersect at right angles (90 degrees)

Step-by-step explanation:

Question 2 (1 point)
A video game has three villains who appear on screen at different intervals. One villain appears every 2 seconds, a second villain appears every
19 seconds, and a third villain appears every 10 seconds. How much time passes between the occasions when all three villains appear at the
same time?

Answers

Answer:

3 minutes tens seconds or 190 seconds

Step-by-step explanation:

Find the LCM.

ILL MARK U BRAINLIEST IF U DO THIS AND GET IT RIGHT

Answers

Answer:

Step-by-step explanation:

1.

The x's and y's will shift to the right and upward. This will make the shape larger because we are multiplying each point (x, y) by 2 [2(x, y)]. The new shape is similar since it is practically the same exact figure with a different scale. Furthermore, the angle measurements are congruent.

2. This will shift the x's and the y's upward and to the right making the shape larger although the shape will be stretched and will not be similar in terms of angle measures and other factors.

3. This will make the figure larger although the angle measurements will not be preserved and a new shape will form. This will not be similar from the original one since it will be stretched and the angles measurements are not congruent..

A baseball camp is held at a complex that has 6 baseball diamonds. The coaches would like each diamond to have the same number of campers. Use divisibility rules to determine whether this is possible if 152 kids show up for the camp.

Answers

Answer:

Using divisibility rules, it is impossible to have exactly the same number of kids in each of the diamonds

Step-by-step explanation:

Here, we want to use divisibility rule to check for the possibility of 152 kids showing for the kids

Since we need exactly equal number of kids in each of the diamonds, we are going to test the possibilities that we can share 152 to have the same number of campers in each of the diamond

Mathematically 152/6 = 25.3333

Since we have a remainder for the division, it is impossible to share the campers equally in the six diamonds if 152 kids show up for the camp

WILL GIVE BRAINLIEST!!!!! Given the equation y = x – 2, you substitute 3 for y. Check all true statements below.
A. You replaced y with 3 temporarily.
B. This is wrong because you can only substitute for x.
C. The equation becomes 3 = x – 2
D. The value of x is 5.
E. The equation y = x – 2 is still true, just with specific values.

Answers

Answer:

y=x-2

a. 3=x-2

b. this isn't wrong??

c. 3=x-2

d. add 2 to both side so taht x is on its own so 5=x

e. yes

Answer:

C and E

Step-by-step explanation:

Im not entirely sure about A, because you are substituting so technically you changed it but the equation is still true (just as E says) but with more specific values.

B is not right because you can replace either y or x

D is not right because if you switch the equation to get the value of x you would make x= -3-2 which would be -5, not 5.

Hope this helped :)

Solve for x. 3(5 + 4x) = 75

Answers

Answer:

3(5+4x) = 75

Step-by-step explanation:

Step 1: Distribute. --> 3(5+4x) = 75

                                   15 + 12x =75

Step 2: Find X. ---> 15 + 12x = 75

                               -15            -15

                                      12x = 60

Step 3: Divide.                12      12

Answer: x = 5

Answer:

X=5

Step-by-step explanation:

I need to know 2/7 divided by 6 =

Answers

it’s an irrational number just use a call

Answer: 1/21

[tex]\frac{2}{7}:6=\frac{2}{7}.\frac{1}{6}=\frac{2}{42}=\frac{1}{21}[/tex]

Step-by-step explanation:

17 points
Jeremy drove 18.04 miles on Monday, 18.4 miles on Tuesday, 17.68 miles
on Wednesday, and 17.86 miles on Thursday. Which shows the distances
written in order from greatest to least? *
17.68, 17,86, 18.04, 18.4
18.04, 18.4, 17.86, 17.68
17.86, 17.68, 18.4, 18.04
O 18.4, 18.04, 17.86, 17.68

Answers

Answer:

D. 18.4, 18.04, 17.86, 17.68

Step-by-step explanation:

Very Easy!

Mrs. Wally cut a 21 foot long ribbon into four equal lengths. How many feet long was each length of ribbon

Answers

the answer is:

Each equal length of ribbon is 5.25 ft

Step-by-step explanation:

21 divided by 4 is 5.25

To find the number of distributed quantities division operator is used. Each length of ribbon was 5.25 foot long.

What is division ?

Division is a mathematical operation used to divide a number into equal parts. When a number is divided by another number, a quotient and remainder is obtained.

Given length of ribbon = 21 foot

Number of parts it has to be divided = 4.

So, to get the length of each part divide the total length by 4.

Thus, the length of each part is 21/4 = 5.25 foot.

Hence,  the length Mrs. Wally' s each ribbon is 5.25 foot.

To know more about division click on,

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Please help me---------------------------

Answers

Answer:

Using the graph, just look at the exact spot where the lines are intersecting and that point is the solution.

The solution is: (1.2, -1.6)

Step-by-step explanation:

You can also test this by plugging the values of the point into both equations.

Tyler is conducting a science experiment. He is observing the effects of
low temperatures on bacteria. He cools one sample to -55˚C and
another to -80˚C. What is the difference between the two
temperatures?

Answers

Answer:

Your answer is -25

Step-by-step explanation:

First, you figure out what to do for the equation.

In this case we you would subtract because it says "what is the difference" which means to subtract.

So -55 subtracted by -80 = -25

Kevin has a rectangular
swimming pools that is 12
feet by 16 feet. He wants
to put a rope diagonally
across the pool. How long
does the rope need to
be?

Answers

Answer:

20 feet long

Step-by-step explanation:

To solve this you need to use the Pythagorean theorum, [tex]a^2+b^2=c^2[/tex], where c is the length of rope needed and A and B are the side lengths. Think of it like a right triangle.

So, the equation is

[tex]12^2+16^2=c^2[/tex]

Which is then

[tex]144+256=c^2[/tex]

[tex]c^2=400[/tex]

And the possible values of c are 20 and -20.

From here we know the answer cannot be -20 because you cannot have a negatively long length of rope, so the answer must be 20 feet.

Answer:

20 feet

Step-by-step explanation:

Use Pythagoras's theorem.

[tex]A^{2}+B^{2} =C^{2} \\12^{2} +16^{2}= C^{2} \\400 = C^{2} \\\sqrt{400}= \sqrt{C^{2}\\\\[/tex]

20 = C

4)
Ben, Joe and Alex bought flowers for their girlfriends at the same store.
Ben bought 5 roses, 8 daisies, and 2 carnations for $14.50. Alex bought
3 roses, 12 daisies, and 1 carnation for $14.00. Joe bought 10 roses, 1 daisy
and 3 carnations for $17.25. How much was one rose and one carnation?
rose:
carnation:

Answers

Answer:

1 rose cost $1.5

1 carnation cost $0.5

Step-by-step explanation:

Let the price for one rose be r, price for one daisies be d and the price for one carnation be c

For Ben;

5r + 8d + 2c = 14.5

For Alex

3r + 12d + c = 14

For Joe

10r + d + 3c = 17.25

From equation iii;

d = 17.25- 10r - 3c

Insert this into the first two equations;

5r + 8(17.25-10r-3c) + 2c = 14.5

5r + 138 - 80r -24c + 2c = 14.5

-75r -22c = -123.5

Thus;

75r + 22c = 123.5

Insert the formula for d in the second equation;

3r + 12(17.25-10r-3c) + c = 14

3r + 207 - 120r -36c + c = 14

-117r-35c = 14-207

117r + 35c = 193

So we have two equations to solve simultaneously;

75r + 22c = 123.5

117r + 35c = 193

Multiply first equation by 35 and second by 22

2625r + 770c = 4322.5

2574r + 780c = 4246

Subtract second from first

51r = 76.5

r = 76.5/51

r = 1.5

Insert this in the equation below;

75r + 22c = 123.5

75(1.5) + 22c = 123.5

112.5 + 22c = 123.5

22c = 123.5-112.5

22c = 11

c = 11/22

c = 0.5

BB is paid straight commission at a rate of 9.35%. last week he sold $6000. How much money did he make?
A. 6900.00
B. 56100
C. 4551.00
D. 451.00

Answers

Answer

how much is like saying time the this

Step-by-step explanation:

60,000 time 9.35%= 56100

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