Find whether the following expressions are functions in the ranges they are defined.

The factors of the expression x² 4x 3 are (x + 3)(x − 3).

Factor is a number that can be multiplied to produce another number. Factors are used to find the greatest common factor (GCF) and least common multiple (LCM) of two or more numbers. Factors are also used in equations to find solutions and in algebra to solve polynomials. Factors are also important in computing, since they are used to identify prime numbers and prime factorisation.

This is determined by using the factoring technique called factoring by grouping.

First, the expression is written in two groups: x2 and 4x 3. Then, each group must be factored. For the first group, the factors are x and x, since any number multiplied by itself results in the number itself. For the second group, the factors are 4 and 3, since 4 multiplied by 3 equals 12.

Next, the two factors of each group must be multiplied together. The product of x and 4 is 4x, and the product of x and 3 is 3x. The product of 4 and 3 is 12.

Finally, the two groups of factors are combined to form the final expression: (x + 3)(x − 3).

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The function G(x) = 3 tan(x) does not have a minimum value.

The relative extremas of a function are the values of x for which the derivative of the function assumes a value of zero.

The extremas are classified as local minimum or local maximum, as follows:

The tangent function does not have a local minimum, as it is increasing over it's entire domain.

The function G(x) = 3 tan(x) is a vertical stretch by a factor of 3 of the tangent function, which changes only the range, thus the function continues without a local minimum.

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Answer:

6kilometers ,8 kilometers,10kilometers

The solution to the system of equations is x = 4 and y = 5.

3x + 2y = 7

y = 3x - 11

Substitute 3x - 11 for y in the first equation:

3x + 2(3x - 11) = 7

Simplify:

3x + 6x - 22 = 7

Combine like terms:

9x - 22 = 7

Add 22 to both sides:

9x = 29

Divide both sides by 9:

x = 29/9

x = 4

Change x in the second equation to 4:

y = 3(4) - 11

Simplify:

y = 12 - 11

y = 1

The solution to the system of equations is x = 4 and y = 1.

The solution to the system of equations 3x + 2y = 7 and y = 3x - 11 is x = 4 and y = 1. To solve this system, we first substituted 3x - 11 for y in the first equation. We then simplified the equation and combined like terms to get 9x - 22 = 7. We then added 22 to both sides, divided both sides by 9, and got x = 29/9 which is x = 4. We then substituted 4 for x in the second equation, simplified, and got y = 1. Thus, the solution to the system of equations is x = 4 and y = 1.

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Answer:D. 1 and 2

Step-by-step explanation:

Domain cannot repeat

The simplified expression for its perimeter and area are 8x.

The perimeter of a square is the sum of the lengths of all the sides of a square. Thus, by summing the lengths of a square's four sides, we can get its perimeter.

An equal number of sides make up a square. As a result, the side of a square is added four times to determine the square's perimeter.

The formula for finding the Perimeter of square = 4*a

= 4 * 2x

= 8x

Perimeter of square = 8x

Hence, the simplified expression for its perimeter is 8x

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Answer:

v = 7

Step-by-step explanation:

Divide both sides by 4 to isolate v

28/4 = 4v/4

v = 7

Step-by-step explanation:

y=k/x

y=20, x=2

Substitute this first to get "k"

20=k/2

k=40

Value of y when x=10... is now

y= 40/10

y=4.

Answer:

C. [tex]4\frac{2}{3}[/tex]

Step-by-step explanation:

One way of approaching this problem is to multiply the numbers the numerators together and then divide by the denominator to receive the quotient and the remainder.

Firstly 6 can be written as a fraction like so: [tex]\frac{6}{1}[/tex] because 6 divided by 1 is equal to 6.

To multiply two fractions together, we simply multiply the numerators and multiply the denominators:

[tex]\frac{7}{9}* \frac{6}{1} =\frac{7*6}{9*1}[/tex]

Which gives us the improper fraction of: [tex]\frac{42}{9}[/tex]

Next, we find the highest multiple of 9 which is smaller than 42. If we write out the multiples of 9 we will find that it is 36:

1x9=9, 2x9=18, 3x9=27, 4x9=36, 5x9=45

Since we know that at least 4 whole 9s go into 42 we can conclude that the coefficient of the fraction will be 4.

To find the fraction itself, we must find the remainder which we can do by subtracting 36 from 42: 42-36 = 6

The remainder is the numerator of the fraction as there are 6 ninths left over after we have divided 42 by 9.

Therefore our answer is [tex]4\frac{6}{9}[/tex]

If we divide 6 and 9 by 3 we will find that 6/9 is equivalent to 2/3 therefore our final answer is [tex]4\frac{2}{3}[/tex].

Option C is correct.

Answer:

30.25

Step-by-step explanation:

The coordinates of the point P on the directed line segment that partitions the segment into a ratio of 2 to 3 is the ordered pair (3, 0).

In this scenario, we would use line ratio to determine the coordinates of the point P on the directed line segment that partitions the segment into a ratio of 3 to 2.

In Mathematics, line ratio can be used to determine the coordinates of the point P and this is modeled by this mathematical expression:

P(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

Substituting the given parameters into the line ratio formula, we have;

P(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

P(x, y) = [(2(9) + 3(-1))/(2 + 3)],  [(2(6) + 3(-4))/(2 + 3)]

P(x, y) = [(18 - 3)/(5)],  [(12 - 12)/5]

P(x, y) = [15/5],  [0/5]

P(x, y) = [3, 0]

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Complete Question:

Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A(-1, -4), B(9, 6); to 3. The coordinates of P are?

Answer:

$53.33

Step-by-step explanation:

A whole (100%)- 25% is 0.75

x*0.75=40

/0.75 /0.75

x=53.33333

round to the 2 decimal since this is money

Therefore the original sale price was $53.33

Have a nice day and I hope this helped. :D

Answer:

I got 2.527. And the 7 repeats I’m wasn’t sure if you wanted it in a fraction but it shouldn’t be difficult to convert if you have a calculator with that function

Step-by-step explanation:

Answer:

130^2 or 130 meters squared

Step-by-step explanation:

I decomposed the figure, then found the area of the decomposed figures then found the sum of them.

FIGURE A:

3 x 3 = 9

= 9^2

FIGURE B:

11 x 11 = 121

= 121 meters^2

So 121 + 9 = 130

= 130 meters^2

REMEMBER!!!!

THE FORMULA FOR AREA IS LENGTH * WIDTH = AREA

Answer: 2/12 (1/6 simplified)

Step-by-step explanation:

5+4+3=12

2 marbles of the same color

2/12

2/2=1

12/2=6

Answer:

1,121.44 or 1,121.4 (nearest tenth)

Step-by-step explanation:

l = 16.8

w = 8.9

h = 16

A  = 2(lw + wh + lh)

2((16.8)(8.9) + (8.9)(16) + (16.8)(16))

2(149.52 + 142.4 + 268.8)

560.72(2)

Answer:

Below

Step-by-step explanation:

SA = 2(w x l + h x l + h w)

= 2(8.9 x 16.8 + 16 x 16.8 + 16 x 8.9)

= 1,121.44 m2

With rounding = 1,121.4 m2

Hope this helps!

The solution of the expression 3x² - 4 = 0 is x = ±2/√3.

The term expression in math is defined as a sentence with a minimum of two numbers or variables and at least one math operation

Here we have the expression 3x² - 4 = 0.

Now, we have to solve this one by using the following steps:

First we have to add 4 to both sides of the equation, then we get the expression as,

=> 3x² = 4

Now, we have to Divide each term by 3 and simplify, then we get

=> x² = 4/3

Then we have to take the specified root of both sides of the equation to eliminate the exponent on the left side,

=> x = √4/3

When we simplify this one further, then we get

=> x = ±2/√3.

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A graph shows lap time (seconds) labeled 82 to 98 on the horizontal axis and the number of laps on the vertical axis. 1 lap was 82 to 84 seconds.  4 laps were 84 to 86 seconds. 2 laps were 86 to 88 seconds. 4 laps were 88 to 90 seconds. 6 laps were 90 to 92 seconds. 5 laps were 92 to 94 seconds. 2 laps were 94 to 96 seconds. 0 laps were 96 to 98 seconds

What is endurance race?

A type of motorsport racing known as endurance racing is designed to test both the participants' and the equipment's endurance. Teams of several drivers attempt to travel a long distance in a single race while being allowed to change drivers at any time.

The given table is attached below.

The number of laps in the range 82 to 84 seconds = 1

The number of laps in the range 84 to 86 seconds = 4

The number of laps in the range 86 to 88 seconds = 2

The number of laps in the range 88 to 90 seconds = 4

The number of laps in the range 90 to 92 seconds = 6

The number of laps in the range 92 to 94 seconds = 5

The number of laps in the range 94 to 96 seconds = 2

The number of laps in the range 96 to 98 seconds = 0

Therefore, the histogram that represents Blanca's lap times for the three days of practice is described as follows;

A graph shows lap time (seconds) labeled 82 to 98 on the horizontal axis and the number of laps on the vertical axis. 1 lap was 82 to 84 seconds.  4 laps were 84 to 86 seconds. 2 laps were 86 to 88 seconds. 4 laps were 88 to 90 seconds. 6 laps were 90 to 92 seconds. 5 laps were 92 to 94 seconds. 2 laps were 94 to 96 seconds. 0 laps were 96 to 98 seconds.

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Answer:A

Step-by-step explanation:

Answer:

7y

Step-by-step explanation:

Answer:

D. 24

Step-by-step explanation:

substitute -4 for x:

f(-4)=20-(-4)

f(-4)=24

Answer:

The standard odds of drawing a jack, king, etc is always 1 in 13 from a shuffled 52 card deck. 4 suits,13 cards each, 1 jack for each suit

Step-by-step explanation:

Answer:

Half of 40 is 20(new radius)

20^2 = 400

400 x 3.14 = 1256 meters^2

Formula of area of a circle:

πr2

pi(3.14 or 22/7 whatever they tell you to use for pi) x radius(half of your diameter or your given radius) being squared(^2 to the power of 2)

The answer is D) If one angle is a right angle, then the frame must be rectangular,

An angle is a measure of the amount of rotation between two lines or planes. It is measured in degrees or radians. Angles are formed by the intersection of two lines, called the sides of the angle, and a point, called the vertex of the angle. There are different types of angles such as acute angle, right angle, obtuse angle, and straight angle.

A rectangle is a four-sided polygon with four right angles. It has opposite sides that are parallel and congruent, and the opposite angles are also congruent. A rectangle can be defined by its length and width or by the coordinates of its vertices. Rectangles are a special case of parallelograms, which have opposite sides parallel but not necessarily congruent. The special properties of rectangles make them a popular shape in design and construction, such as in building and engineering.

A rectangle is defined as a four-sided polygon with four right angles. Opposite sides of a rectangle are congruent, but adjacent sides may or may not be congruent. Therefore, A and B are not sufficient to prove that the frame is a rectangle. Also, two adjacent angles being supplementary does not guarantee that the frame is a rectangle. The only way to be sure that the frame is a rectangle is if it has one right angle, this is the only way to ensure that all angles are right angles. Therefore, D) is the correct answer.

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The graph of y is a straight line parallel to the x−axis through the point (0,-2)

Now, According to the question:

What is slope and example?

Whenever the equation of a line is written in the form y = mx + b, it is called the slope-intercept form of the equation. The m is the slope of the line. And b is the b in the point that is the y-intercept (0, b). For example, for the equation y = 3x – 7, the slope is 3, and the y-intercept is (0, −7).

The given equation is Y = -2

y = -2 is a line in which all points have the y-value -2. The line has a slope of 0 (horizontal line) since the y-value does not change for any value of x.

The point-intercept form for the equation of a line is:

y = mx + b

We can write y = -2

As y = 0x - 2;

slope = 0, y-intercept = -2

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Answer:

O  A. 8

Step-by-step explanation:

the line is 180, so subtract 140 to get 5x. 5x = 40 so divide by 5

180 - 140 = 5x

         40 = 5x

          /5    /5

            8 = x

Answer: X=8

Step-by-step explanation:

it is a 180 degree angle total.

180=5x+140

subtract 140 from both sides

40=5x

divide by 5 on both sides

8=x

Answer:

12 feet !!

Step-by-step explanation:

its the onlt one that can fit into a car

Answer:

Plz give

Step-by-step explanation:

Expressions have no equal sign while Equations have the equal sign

Answer: x=8

Step-by-step explanation:

3(x+4) = 36

3x+12= 36

3x-12= -12

3x = 24

— —

3 3

X=8