For the function f defined by f(x)=x^2+2x+3 find f(−x),−f(x) , and −f(−x).
Also, For the function g defined by g(x)= 55/x +3x find g(−x),−g(x), and −g(−x).

Help!

Answer:

The answer is B!

Step-by-step explanation:

The equation and the equation from scenario B are both, when simplified, g = 9.

Answer:

Option B matches the equation

Step-by-step explanation:

Equation: 34 = g + 25

A:Since we are given that The temperature on Monday was 25 degrees below zero So, in given equation there should be -25 in place of 25

So, It does not matches the equation

B: The year before, when the students were in seventh grade, there were 25 students.

Let g be the no. of students added  between seventh and eighth grade

So, Total students = 25+g

We are given that  The eighth-grade class has 34 students.

So, equation becomes : 34=g+25

It matches the equation.

C :A person bikes 34 miles on Monday

He bikes 25 miles on Tuesday.

So, Total miles =25+34

So, It does not matches the equation

D: Jack has 25 marbles.

Mary gives him 34 marbles.

Total marbles = 25+34

So, It does not matches the equation

Hence Option B matches the equation

Answer:

it will take 15 weeks for Nancy’s account to have TWICE as much money as Fred’s account

Step-by-step explanation:

Fred brown and his sister, Nancy, each have $15 in the bank

Initially both Fred and Nancy have $15

Every week Nancy plans to add $3 to her account

Let 'n' be the number of weeks she plans to add in her account

for 1 week, $3

For n weeks , its 3n

So amount of money in Nancy's account after 'n' weeks = 15 + 3n

Fret plans to add $1 to his account each week

for 1 week, $1

For n weeks , its 1n

So amount of money in Fred's account after 'n' weeks = 15 + 1n

Now we need to find out 'n' when

Nancy's account = 2 times of Fred's account

15 + 3n = 2(15+1n)

Distribute 2 inside the parenthesis

15 + 3n = 30 + 2n

Subtract 2n on both sides

15 + n = 30

Subtract 15 on both sides

n = 15

Hence, it will take 15 weeks for Nancy’s account to have TWICE as much money as Fred’s account

Answer:

The slope of the parallel line is 2/3

Step-by-step explanation:

Parallel lines have the same slope, so we need to find the slope of the line on the graph.

We can use the equation for the slope of a line

m = (y2-y1)/ (x2-x1)

   =(2-0) /(3-0)

   = 2/3

The slope of the line of the graph is 2/3  so

The slope of the parallel line is 2/3

Answer:

Step-by-step explanation:

Two points A and B are given

Using two point formula for straight lines we get

[tex]\frac{x+6}{8+6} =\frac{y-4}{9-4} \\5(x+6) = 14(y-4)\\5x+30 = 14y-56\\5x-14y+86 =0[/tex]

b) A line parallel to AB would be of the form

5x-14y +k=0

Since the line passes through (14,-6) substitute to get k

5(14)-14(-6)+k=0 Or k = -154

Line is 5x-14y-154 =0

c) A line perpendicular to AB would have form as

14x+5y =k1

Substitute (-5,-10) to get k

14(-5)+5(-10) =k1

Or k1 = -120

Hence equation is 14x+5y = -120

Answer:

sum

Step-by-step explanation:

We have that, 'The multiplication of two or more quantities may be expressed as the repeated addition of the same quantities'.

i.e. multiplication of two or more terms is equal to adding as many copies of one of them.

i.e. a × b = a + a + ... ( 'b' number of times ) = b + b + .... ( 'a' number of times )

For example,

2 × 4 = 8

2 × 4 = 2 + 2 + 2 + 2 = 8 i.e. adding 2 four times

2 × 4 =  4 + 4 = 8 i.e. adding 4 two times

or

3 × 7 = 21

3 × 7 = 3 + 3 + 3 + 3 + 3 + 3 + 3 = 21 i.e. adding 3 seven times

3 × 7 = 7 + 7 + 7 = 21 i.e. adding 7 three times.

Hence,  'The multiplication of two or more quantities may be expressed as the repeated addition of the same quantities'.

The multiplication of two or more quantities can be expressed as the product of the same quantities in mathematics.

Multiplication is a fundamental arithmetic operation that combines two or more numbers to find their total value. It represents repeated addition and is denoted by the "×" or "*" symbol. For example, multiplying 5 by 3 results in 5 * 3 = 15, indicating that the value is added five times.

In mathematics, the multiplication of two or more quantities may be expressed as the product of the same quantities. For example, if you multiply 2 by 3, the product is 6. This concept of multiplication applies to all quantities, whether they are numbers or variables.

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Expand

4x - 28 = 0.3x + 0.6 + 2.11

Simplify 0.3x + 0.6 + 2.11 to 0.3x + 2.71

4x - 28 = 0.3x + 2.71

Add 28 to both sides

4x = 0.3x + 2.71 + 28

Simplify 0.3x + 2.71 + 28 to 0.3x + 30.71

4x = 0.3x + 30.71

Subtract 0.3x from both sides

4x - 0.3x = 30.71

Simplify 4x - 0.3x to 3.7x

3.7x = 30.71

Divide both sides by 3.7

x = 30.71/3.7

Simplify 30.71/3.7 to 8.3

x = 8.3

The length of the rectangular playground can be determined using the conversion of the area formula, Length = Area ÷ Width. Substituting the values provided gives us Length = 3,162 ÷ 51.

The subject of this question is mathematics, more specifically, the topic involves calculating the dimensions of a rectangle when given the area and one side length. In this case, the student is asked to determine the length of a rectangular playground that has an area of 3,162 square meters and a known width of 51 meters.

The area of a rectangle is calculated by multiplying its length by its width, according to the formula: Area = Length x Width. This can be rearranged to find Length, resulting in: Length = Area ÷ Width.

Plugging in the values provided, we find the length by using the rearranged formula:

Length = 3,162 ÷ 51

With these calculations, we would find our answer for the length of the playground.

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Answer:

{- 5, - 4, 2 }

Step-by-step explanation:

the range is the corresponding values of y ( output) from the given set in ascending order without repeats

ANSWER:

EXPLANATION:

[tex]\frac{1}{3}(9-6m)+\frac{1}{4}(12m-8)\\\text{Distribute.}\\3 - 2m + 3m - 2\\\text{Simplify.}\\m + 1[/tex]

Answer:

I belive it is m +1

Step-by-step explanation:

The first hing you need to do is distribute, and then combine like terms.

Answer:

I would solve for x in the first equation.  X in the first equation has a coefficient of 1, unlike y in the second equation which has a coefficient of 2.  I do not have to divide to solve for my variable.

Step-by-step explanation:

I would solve for x in the first equation.  X in the first equation has a coefficient of 1, unlike y in the second equation which has a coefficient of 2.

x-3y =1

Add 3y to each side

x = 1+3y

Then substitute this into the second equation.

Max would have to subtract 7x from each side and then divide by 2

7x+2y =7

2y = -7x+7

y = -7x/2 + 7/2

This makes the math complicated when it is substituted into the first equation because we are multiplying by 3.  We will have fractions.

Answer:

Jerry solved the system of equations.

x minus 3 y = 1. 7 x + 2 y = 7.

As the first step, he decided to solve for y in the second equation because it had the smallest number as a coefficient. Max told him that there was a more efficient way. What reason can Max give for his statement?

The variable x in the first equation has a coefficient of one so there will be fewer steps to the solution.

The variable x in the second equation has a coefficient of 7 so it will be easy to divide 7 by 7.

The variable y in the second equation has a coefficient of 2 so it will be easy to divide the entire equation by 2.

The variable x in the second equation has the largest coefficient. When dividing by 7, the solution will be a smaller number.

correct answer is AAAAA

Answer:

86

Step-by-step explanation:

Subtract 322 from 408

8-2=6

we cant subtract 2 from zero so we take 1 from the next

10-2=8

3-30

86

Hope this helps! (Brainliest please!)

Answer:

6.24 feet (to nearest hundredth)

Step-by-step explanation:

Use the Pythagoras Theorem:-

20^2 = x^2 + 19^2     where x = height of the loading dock.

x^2 = 20^2 - 19^2 =  39

x =  √39

= 6.2449 feet

The height of the loading dock is found to be approximately 6.24 feet.

To solve this problem, we will use the Pythagorean theorem, which is applicable when we have a right triangle. The theorem states:

a² + b² = c²

Here:

a is the height of the loading dock (which we need to find).

b is the base of the ramp (19 feet).

c is the length of the ramp (20 feet).

We can set up the equation as follows:

a² + 19² = 20²

a² + 361 = 400

a² = 39

a = √39 ≈ 6.24 feet

Thus, the height of the loading dock is approximately 6.24 feet.

Answer:

19 i think

Step-by-step explanation:

Answer:

The students baked at least 19 pies.

Step-by-step explanation:

We know that each of the pies were cut into 8 pieces. Since the students sold at least 224 pieces of pie, we can use these equations to figure out how many pies were sold and how many were made by the students.

Total number of pies = total number of slices sold/number of slices per pie

Total number of pies = 224/8

Total number of pies = 28

Pies made by students= total number of pies-pies made by school cafeteria

Pies made by students= 28-9

Pies made by students= 19

Answer:

3.3

Step-by-step explanation:

To find the amount of gasoline when Deborah's tank is 1/4 full, divide the tank's full capacity (13.2 gallons) by 4, which results in 3.3 gallons of gasoline in the tank at 1/4 full.

To find out how many gallons of gasoline Deborah's car has when the tank is 1/4 full, we need to calculate 1/4 of the total capacity of the tank. Since the tank holds 13.2 gallons when full, the amount of gasoline at 1/4 full is calculated as follows:

Therefore, when Deborah's gas gauge indicates that the tank is 1/4 full, it contains 3.3 gallons of gasoline.

[tex]-3x+2y=11\qquad\text{add 3x to both sides}\\\\2y=3x+11\qquad\text{divide both sides by 2}\\\\y=\dfrac{3}{2}x+\dfrac{11}{2}\\\\for\ x=1\to y=\dfrac{3}{2}(1)+\dfrac{11}{2}=\dfrac{3}{2}+\dfrac{11}{2}=\dfrac{14}{2}=7\to(1,\ 7)\\\\for\ x=-3\to y=\dfrac{3}{2}(-3)+\dfrac{11}{2}=-\dfrac{9}{2}+\dfrac{11}{2}=\dfrac{2}{2}=1\to(-3,\ 1)\\\\for\ x=-5\to y=\dfrac{3}{2}(-5)+\dfrac{11}{2}=-\dfrac{15}{2}+\dfrac{11}{2}=-\dfrac{4}{2}=-2\to(-5,\ -2)[/tex]

Answer: h = -16t^2 + 120t + 2

Answer:

9.2 hours for the total drive

To determine how long it took for an object to travel 230 miles at 25 miles per hour, divide the distance by the speed, which results in 9.2 hours.

This problem is a straightforward application of the formula for calculating time when distance and speed are known. The formula is Time = Distance ÷ Speed.

In this case, the distance (d) is 230 miles and the speed (v) is 25 miles per hour. Using the formula:

Therefore, it took 9.2 hours for the object to travel a distance of 230 miles at a speed of 25 miles per hour.

Answer:

55

Step-by-step explanation:

Add from left to right

1+2+3+4+5+6+7+8+9+10

3 +3+4+5+6+7+8+9+10

6+4+5+6+7+8+9+10

10+5+6+7+8+9+10

15+6+7+8+9+10

21+7+8+9+10

28+8+9+10

36+9+10

45+10

55

Answer:

option B

Given : |x + 4| < 5

A. –5 > x + 4 < 5

B. –5 < x + 4 < 5

C. x + 4 < 5 and x + 4 < –5

D. x + 4 < 5 or x + 4 < –5

In general , |x|< n where n is positive

Then we translate to -n < x < n

|x + 4| < 5

5 is positive, so we translate the given absolute inequality to

-5 < x+4 < 5

So option B is correct

let's say Artaud's age is "x", its opposite will then be -x, so

[tex]\bf \stackrel{\textit{opposite of his age plus 40}}{-x+40}~~\stackrel{is}{=}~~28\implies -x+40-28=0 \\\\\\ -x+12=0\implies \boxed{12=x}[/tex]

Answer:

12 years old

Step-by-step explanation:

28 - 40 = -12

Note that -12 is the opposite of 12.

Artaud is 12

Step-by-step explanation:

Parent function f(x) = x

g(x)= -3(x-4) + 1

If any number added or subtracted with x  then graph moves left or right

Here 4 is subtracted from x, so graph move 4 units to the right

If any number added or subtracted at the end then  graph move up or down

Here 1 is added at the end, so graph move 1 unit up.

g(x) = -f(x), for negative sign the graph reflects across x axis

We have negative sign at first, so the graph reflects over x axis

The graph of [tex]\( g(x) \)[/tex] is the result of these transformations applied to the graph of the parent function [tex]\( f(x) \)[/tex].

The sequence of transformations that transforms the graph of the parent function [tex]\( f(x) = x \)[/tex] into the graph of the function [tex]\( g(x) = -3(x-4)+1 \)[/tex] involves a reflection across the x-axis, a horizontal shift, a vertical stretch, and a vertical shift.

1. Reflection across the x-axis: The negative sign in front of the function[tex]\( g(x) \)[/tex]indicates a reflection across the x-axis. This means that for every point \( (x, y) \) on the graph of [tex]\( f(x) \)[/tex], there will be a corresponding point [tex]\( (x, -y) \)[/tex] on the graph of [tex]\( g(x) \)[/tex].

2. Horizontal shift: The expression [tex]\( (x-4) \)[/tex] inside the function [tex]\( g(x) \)[/tex]indicates a horizontal shift to the right by 4 units. This means that every point on the graph of [tex]\( f(x) \)[/tex] is moved 4 units to the right along the x-axis to get the graph of [tex]\( g(x) \).[/tex]

3. Vertical stretch: The coefficient 3 in [tex]\( -3(x-4) \)[/tex] indicates a vertical stretch by a factor of 3. This means that for every point [tex]\( (x, y) \)[/tex] on the graph of the reflected function[tex]\( -f(x) \)[/tex], the y-coordinate is multiplied by 3 to get the corresponding point [tex]\( (x, 3y) \)[/tex] on the graph of [tex]\( g(x) \)[/tex].

4. Vertical shift: Finally, the[tex]\( +1 \)[/tex] at the end of the function [tex]\( g(x) \)[/tex]indicates a vertical shift upwards by 1 unit. This means that every point on the graph of [tex]\( -3f(x-4) \)[/tex] is moved 1 unit up along the y-axis to get the graph of [tex]\( g(x) \).[/tex]

Putting it all together, the sequence of transformations is as follows:

 - Start with the parent function [tex]\( f(x) = x \).[/tex]

- Reflect the graph across the x-axis to get [tex]\( -f(x) \).[/tex]

- Shift the graph 4 units to the right to get [tex]\( -f(x-4) \).[/tex]

- Stretch the graph vertically by a factor of 3 to get [tex]\( -3f(x-4) \).[/tex]

- Shift the graph 1 unit upwards to get [tex]\( -3f(x-4) + 1 \),[/tex] which is the function [tex]\( g(x) \)[/tex].

Therefore, the graph of [tex]\( g(x) \)[/tex] is the result of these transformations applied to the graph of the parent function [tex]\( f(x) \)[/tex].

The solution to (x-2)(x+10)=13 is x can be either 3 or -11, therefore the problem has 2 solutions.

Answer:

x = 3 or  x = -11

Hope This Helps!

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                     - Innverted

Answer:

B. 51 in²

Step-by-step explanation:

π14²= 615.752160104 (find total circle area)

30/360= 1/12 (calculate fraction size the section would be of the entire circle)

615.752160104/12= 51.3126800087 (the slice's area)

Answer:

51

Step-by-step explanation:

Answer:

A 25¢ per piece

Step-by-step explanation:

To find the unit price, we take the dollar amount and divide by the number of pieces

$2.25 / 9 pieces

$.25 per piece