Find g(x), where g(x) is the reflection across the y-axis of f(x) = -9x - 4.
Write your answer in the form mx + b, where m and b are integers.
g(x) =

Answer:

3√2

Step-by-step explanation:

[tex] \sqrt{ {(6 - 9)}^{2} + {(9 - 6)}^{2} } [/tex]

[tex] \sqrt{ {( - 3)}^{2} + {3}^{2} } [/tex]

[tex] \sqrt{9 + 9} = \sqrt{2 \times 9} = \sqrt{2} \sqrt{9} = 3 \sqrt{2} [/tex]

EXPLANATION

Given the sequence:

C. 3, 12, 27, 48, 75

First, we need to calculate the difference between terms:

12-3 = 9 27-12 = 15 48-27 = 21 75 - 28 = 27

Arithmetic relationship: 9, 15 , 21, 27

To obtain the sequence we use the following formula:

Now, we need to calculate the appropriate difference between terms:

15-9 = 6 21-25 = 6 27 - 21 = 6

So the constant difference is 6 and the nth term will be:

nth = 6n + 3

*a1=3

So, the relationship will be:

n Value Relationship

1 12 3 + (6*1 +3)

2 27 12 + (6*2 + 3)

3 48 27 + (6*3 + 3)

4 75 48 + (6*4 + 3)

5 108 75 + (6*5 + 3)

n n-1 + (6n+3) n-1 + (6n+3)

Explicit function: y = (n-1) + (6n+3)

The system of linear equations has one and only one solution.

x = 3 and y = 2.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

x - 3y = -3 _____(1)

4x + 3y = 18 ______(2)

We will solve the equation to check its solutions.

x - 3y = -3 can be written as:

x = -3 + 3y ____(3)

Putting in (2) we get,

4(-3 + 3y) + 3y = 18

-12 + 12y + 3y = 18

15y = 18 +12

15y = 30

y = 2

Putting in (3)

x = -3 + 3 x 2 = -3 + 6 = 3

x = 3

We see that,

x = 3 and y = 2

Putting in the equation it is satisfied.

x - 3y = -3

3 - 3 x 2 = -3

3 - 6 = -3

-3 = -3

4x + 3y = 18

4x3 + 3x2 = 18

12 + 6 = 18

18 = 18

Thus,

The system of linear equations has one and only one solution.

x = 3 and y = 2.

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Numerical expression: 30 - 10 - 7

In words: Elizabeth had $30, if she spent $10 to buy some pizza and $7 on a soda, how much money does she have left?

Observe the given graph carefully.

In a circle graph, the circle is divided into different sectors, each characterized by its central angle.

The complete circle measures 360 degrees. So the complete distribution (100% data) corresponds to 360 degrees.

In the given problem, we are concerned with the budget,

(a)

Consider the following,

So, one-fourth of the budget will correspond to the department which covers the 90-degree sector of the circle graph.

As observed from the graph, the most suitable department under this criteria is the Engineering Department.

Thus, Engineering Department gets approximately one-fourth of the annual budget.

(b)

Consider that the departments Engineering and support combiningly cover a little more than one-third of the area of complete circle.

Consider the following,

Note that the area covered by the department is a little more than one-third, so the corresponding percentage value must also be a little more than 33.33%.

From the available options, 40% is the value available next to 33.33%, so this should be the most suitable choice.

Thus, it can be concluded that approximately 40% of the annual budget goes to the departments Engineering and Support combined.

Therefore, option (b) is the correct choice.

The age for two men is 39.5 and 42.5.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them. Variables are the name given to these symbols because they lack set values. We frequently observe constant change in specific variables in our day-to-day situations. But the need to depict these shifting values is ongoing. These values are frequently represented in algebra by symbols such as x, y, z, p, or q, and these symbols are known as variables.

Given:

Average of 6 men = 35

Average of 4 men  = 32

So, Total age of 6 men

=6x35

=210 years

and, Total age of 4 men

=32  x 4

=128 years

Then, the remaining age for 2 people

= 210 - 128

=82 years

Let the age for two be x and y

then , x+ y=82

and x-y=3

On solving

2x =85

x=42.5 years

and y=39.5 years

Hence, the age for two men is 39.5 and 42.5.

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The slope of a ramp with a height-to-distance ratio of 1 to 12 feet is 4.76 degrees.

The slope or gradient of a line in mathematics is a number that describes both the direction and the steepness of the line. The tangent relation or the height-to-distance ratio helps to determine the slope of the line.

It is given that the height-to-distance ratio of a slope is given as 1 to 12 feet.

So,

[tex]\tan \alpha = 1/12\\\alpha= \tan^{-1}1/12\\\alpha= 4.76^\circ[/tex]

So, the slope of the ramp is about 4.76 degrees.

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The probability that a randomly selected person in the country enjoys cooking or shopping or both will be;

⇒ P (C ∪ S) = 0.76

What is mean by Probability?

The term probability refers to the likelihood of an event occurring.

Given that;

48% of people in a certain country like to cook.

And, 54% of people in the country like to shop, while 26% enjoy both activities.

Now,

Probability to like the cook P (C) = 48%

Probability to like the shop P (S) = 54%

Probability to like the both activity P (C∩S) = 26%

So, Probability to like the both activity P (C ∪ S) is calculated as;

P (C ∪ S) = P (C) + P (S) - P (C ∩ S)

P (C ∪ S) = 48% + 54% - 26%

P (C ∪ S) = 102% - 26%

P (C ∪ S) = 76%

P (C ∪ S) = 0.76

Thus, The probability that a randomly selected person in the country enjoys cooking or shopping or both will be;

⇒ P (C ∪ S) = 0.76

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The function that represents the cost function is c(x) = 75 + 0.25x

To find the cost function c(x), we have to write a linear equation or linear function to represent this.

The cost function can be expressed as a function of the number of copies made which can be represented as

[tex]c(x) = 75 + 0.25x[/tex]

The cost of printing x number of pages is c(x) = 75 + 0.25x

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Answer:

1.50t + 3 < 9

Step-by-step explanation:

each taki is $1.50

each Gatorade is $3 and he only bought one so its $3.

total cost of taking and Gatorade is less than $9

Answer:

1.50t + 3 < 9

Step-by-step explanation

each taki is $1.50

each Gatorade is $3 and he only bought one so its $3.

the total cost of taking and Gatorade is less than $9

Step 1

Rearrange the expression to bring like terms together.

Step 2

Simplify to get the final answer

Hence the right answer is option C

Given:

The distance to the door from your desk is d meters.

Your first step is 1/6 that distance =

Each successive step is 1/6 the previous distance.

so, the second step =

The third step =

And so on,

So, for the step number n, the formula will be :

So, for 8 steps

You will have traveled =

For 12 steps =

For 20 steps =

For n steps =

The equation for g(x) is g(x) = x²-3

When x=0, f(x)= 0 and so has a vertex at (0,0)

Given that g(x) is a shifter version of f(x) and has a vertex at (0,-3), g(x) must be shifted down the y axis such that g(x)= x2+c when x=0 and g(x)= -3 -3=0+c c=-3 when x=3.

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Given:

The objective is to find hte value of x.

The value of x can be calculated by basic proportionality theorem.

Thus, the required equation is obtained.

The value of x is,

Hence, the value of x is 10.5

Answer: C

Step-by-step explanation: A is definitely not correct. not b. not d

The money was distributing un equally. Because of the great depression, the lower classes made less money

The slope can be calculated as the quotient between the difference in the y-coordinates of two points, and the difference in the x-coordinates of the same two points.

We pick any 2 known points, like (0,2) and (5,4).

We calculate the slope as:

Answer:

The slope is m=2/5=0.4

(7,-8)

1) Considering that f(x-2) is a transformation of f(x). Precisely, a horizontal translation to the right.

2) So, we can write out the following:

Note that a horizontal translation just "pushes to the right". So there was no vertical shift.

3) Hence, the answer is (7,-8)

If a quadrilateral is a parallelogram, then its opposite sides are congruent therefore:

Using the distance formula:

Step 2:

The diagonals are given by:

Answer:

9 is the answer

Answer: 9 cubes

Step-by-step explanation:

9 * 9 is 81 which makes the floor of it

since its a cube, we multiply 81 by 9, giving 729

4.6

1) Since 3/4x = 3.45, then we can solve it for x

3/4x = 3.45 Multiply both sides by 4 to eliminate the fraction

3x =13.80 Divide both sides by 3

x= 4.6

2) So x is equal to 4.6, and that is the answer

A histogram is a representation that organizes a group of data points into specified ranges.

For the given data:

4, 18 , 20, 17, 16, 23, 19, 14, 8, 8, 6, 12, 20, 14, 18

Answer: it would be D because m∠NSO+m∠OSL+m∠LSM+m∠MSN=360°  

and m∠LSM+m∠SML+m∠MLS≠360° doesnt equal 360 degrees so that one is wrong ∠LSM≅∠NSM is a false statement same with m∠LSO+m∠MSO=180° its false so it would be (D)

hope i helped

Step-by-step explanation:

Solution:

Let x be the number of antifreeze solution. Thus;

We would solve for x;

Hence, the amount needs to be drained out is;

Answer: 1.15 gallon

Using percentages, we can conclude that the total cost of the meal is approximately $33.

So, the total cost of the meal:

Sales tax on the bill: 9%

18% tip of the bill:

Total cost of meal: $27.5277 + $5 = $32.5277

Therefore, using percentages, we can conclude that the total cost of the meal is approximately $33.

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Answer:

29,378 people

Step-by-step explanation:

[tex]28337 \times {1.0121}^{3} = 29378[/tex]

Distance is the total movement of an object without any regard to direction. Total distance jogged by Linsey is 420 yards.

What is distance?

Distance is the total movement of an object without any regard to direction

Given data

vertex 1 is at ( -4, - 1)

vertex 2 is at ( - 4, 5)

vertex 3 is at (2,5)

vertex 4 is at ( 2, -1 )

Lindseys jogs along the edge of the park in order from vertex 1 to the vertex 2 , vertex 2 to vertex 3 and vertex 3 to vertex 4 and then back to vertex 1. One unit in the coordinate grid is 20 yards.

Let us calculate distance vertex 1 and vertex 2of (-4,-1) and (-4,5)

x₁=-4,x₂=-4, y₂=5, y₁=-1

Distance=√(x₂-x₁)²+(y₂-y₁)²

Substitute the values x₁=-4,x₂=-4, y₂=5, y₁=-1 in distance formula

=√(-4+4)²+(5-(-1))²

=√6²

=6

Since 1 one unit on the coordinate gride equal 20 yd.

so 6×20=120 yards.

Now for four vertices we get 4×120=480 yards.

So total distance jogged by Linsey is 420 yards.

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Answer:

Explanation:

To complete the table, we need to replace each value of x and calculate the value of y.

So, if x = - 16, y is equal to:

If x = -8, y is equal to:

If x = 0, y is equal to:

If x = 8, y is equal to:

If x = 16, y is equal to:

So, the complete table is:

x y

-16 -8

-8 -5

0 -2

8 1

16 4

Finally, we can graph the table, so:

The first error Rafael made was that he made six arcs instead of taking the perpendicular bisector of the diameter and then making 4 arcs.

A square is constructed first by taking the perpendicular bisector of the diameter and making the four arcs and then joining them to make the square.

The blue car has traveled the greater distance on one gallon of gasoline

The formula for calculating the unit rate is expressed as shown:

For the blue car

Distance = 39.5miles

Gallons of gasoline = 1.25 gallons

Get the unit rate:

The unit rate of the blue car as a mixed fraction is 31 3/5 miles per gallon

For the red car

Distance traveled = 22.4 miles

Gallons of gasoline = 0.8 gallons of gasoline

Get the unit rate of the red car;

From the unit rates, we can see that the blue car has traveled the greater distance on one gallon of gasoline since its unit rate is greater than that of the red car.

The most appropriate choice for speed will be given by-

Speed of the flying carpet is 15.2 mph

What is speed?

The distance travelled by the body per unit time is called speed of the body.

If d is the distance travelled by the body and t is the time taken, then

speed = [tex]\frac{d}{t}[/tex]

Speed is a scalar quantity as the direction is not taken into account.

Here,

Let the speed of the flying carpet be [tex]x[/tex] miles

A flying carpet flies 2.4 miles with the wind

Time taken flying with the wind = [tex]\frac{2.4}{x +4}[/tex]

The flying carpet flies 1.4 miles against the wind

Time taken flying against the wind = [tex]\frac{1.4}{x - 4}[/tex]

By the problem,

                         [tex]\frac{2.4}{x +4} = \frac{1.4}{x-4}[/tex]  

                         [tex]2.4(x - 4) = 1.4(x + 4)\\2.4 x - 9.6 = 1.4 x + 5.6\\2.4 x - 1.4 x = 9.6 + 5.6\\[/tex]

                          [tex]x = 15.2[/tex] mph

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