Find g(x), where g(x) is the reflection across the x-axis of f(x)=3x–9

By the Centroid Theorem, we can conclude that the length of a segment of the median from a vertex to a centroid is equal to the two-thirds of the length of the median from that vertex.

What is Centroid Theorem?

The point that may be used to represent the centre of a one- or two-dimensional figure, with all points' distances from this point adding up to zero. centre of mass is comparable. also known as the median point Geometry. the location where a triangle's medians meet.

The common endpoint of two or more rays or line segments Vertex typically means a corner or a point where lines meet.

Here given that,

The length of a segment from a vertex to the centroid is the length of the median from that vertex.

So, the length of a segment from a vertex to the centroid is  which is the median of that vertex.

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The required equation of a line is y = 9/5 (4x - 12)

Given-

The point from which the line passes through is (3,2)

The slope of the given line m is -4/5.

Equation of the line

The linear equation of a line can be represented by a set of points on a graph using the equation of the line.

The standard form of the line passing through the point x₁, y₁

The slope m is given by,

m = (y - y₁) / (x - x₁)

Put the values of points and slope in the above equation, we get,

-4/5 = (y - 2) / (x - 3)

-4/5(x - 3) = y -2

-4x/5 + 12/5 = y - 2

-1/5 (4x - 12) + 2 = y

y = 9/5 (4x - 12)

The linear equation of a line can be represented by a set of points on a graph using the equation of the line. The following equation depicts a line that crosses (3, 2) and has a slope of -4/5: y = 9/5 (4x - 12)

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As per the given options, one which does not have a unit price of $24 for one sweater is $38 for 2 sweaters. Hence, option A is correct.

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.

Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.

As per the information in the question,

The unit price of the sweater is $24.

Now, let's check the options for a unit price of the sweater.

1.

$38 for 2 sweaters

So, the unit price = 38/2 = $19, it does not have the unit price of $24 for one sweater.

2.

$72 for 3 sweaters

So, the unit price = 72/3 = $24, so this is correct.

3.

$96 for 4 sweaters

So, the unit price = 96/4 = $24, this one is correct.

4.

$120 for 5 sweaters

So, the unit price = 120/5 = $24, this one is also correct.

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Your question seems incomplete, the complete question may be:

Which of the following does NOT have a unit price of $24 for one sweater?

$38 for 2 sweaters

$72 for 3 sweaters

$96 for 4 sweaters

$120 for 5 sweaters

In polynomial, x - 2 is not a factor f(x) [By factor theorem]

What is Polynomials ?

Sums of terms with the pattern kxn—where k is any positive integer and n is an arbitrary number—are known as polynomials.

                    For instance, the polynomial 3x+2x-5. a description of polynomials. In this video, basic terms like terms, degrees, standard form, monomial, binomial, and trinomial are covered.

p(x) = 4x^3 + 10x^2 - 6x - 20  

put x = -2 in equation

p(x) = 4 * (-2)³ + 10 * ( -2)² - 6 * -2 - 20

       = 4 *  -8 + 10 * 4 + 12 - 20

        = -32 + 40 + 12 - 20

        = 52 - 52

        = - 2

p(x) ≠ 0

Which is not equal to zero

x - 2 is not a factor f(x) [By factor theorem]

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Answer:

3(n+4)=18

Step-by-step explanation:

Answer:3(n+4)=18

Step-by-step explanation:

The sum of 4 and a number is 4+n

Three times the sum of 4 and a number is 3(4+n)

is means equal sign

3(n+4)=18

1/3x+3/4+2/3x-1/4-2/3x=0.66666...x+0.5

Answer: 1/2 * 6 = 3

Step-by-step explanation:

Answer:

81

Step-by-step explanation:

Area is multiplying all side

9 x 9 = 81

Answer:

Step-by-step explanation:

Aub, probability, set theory and discrete math?

Answer:

  3)  260 ft

Step-by-step explanation:

You want the perimeter of a rectangle 55 ft by 75 ft.

The equation for the perimeter of a rectangle is ...

  P = 2(L +W)

For the given rectangle, the perimeter is ...

  P = 2(75 ft +55 ft) = 2(130 ft) = 260 ft

Maya needs 260 feet of fencing to put fence around her rectangular yard.

The polygons from the figure given below that are similar are Polygon B and Polygon C .

In the question ,

it is given that there are three polygons ,

we have to check which polygons are similar ,

to find the similarity we compare the length of all the polygons .

Let us first check for  Polygon A and Polygon B ,

105/120 = 7/8

80/90 = 8/9.

and  105/120 ≠ 80/90 ,

So , Sides are not in proportion for Polygons A and B.

Hence , the Polygons A and B are not Similar.

Let us check for Polygon A and C .

105/100 = 21/20

80/75 = 16/15.

and 105/100 ≠ 80/75

So , sides are not in proportion for Polygons A and C.

Hence , the Polygons A and C are Non Similar.

Now  for Polygon B and C .

120/100 = 6/5.

90/75 = 6/5.

and  120/100 = 90/75 = 6/5

So , Sides are in proportion for Polygons B and C .

Hence , the Polygons B and Polygon C are Similar.

Therefore , the Polygon B and Polygon C are similar .

The given question is incomplete , the complete question is

Which pairs of rectangles are similar polygons ? select similar or not similar for each pair of rectangles from the figure given below .

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Answer:

x = 17

Step-by-step explanation:

x + 6 + 7x + 4 + 2x = 180  Combine like terms

10x + 10 = 180  Subtract 10 from both sides

10x = 170  Divide both sides by 10

x = 17

x = 17

1. Add the numbers

x + 6 + 7x + 4 + 2x = 180

x + 10 + 7x + 2x = 180

2. Combine like terms

x + 10 + 7x + 2x = 180

10x + 10 = 180

3. Subtract 10 from both sides

10x + 10 = 180

10x + 10 - 10 = 180 - 10

4. Simplify

Subtract the numbers:

10x + 10 - 10 = 180 - 10

10x = 180 - 10

Subtract the numbers:

10x = 180 - 10

10x = 170

5. Divide both sides by the same factor

10x = 170

[tex]\frac{10x}{10}[/tex] = [tex]\frac{170}{10}[/tex]

6. Simplify

Cancel terms that are in both the numerator and denominator:

[tex]\frac{10x}{10}[/tex] = [tex]\frac{170}{10}[/tex]

x = [tex]\frac{170}{10}[/tex]

Divide the numbers:

x = [tex]\frac{170}{10}[/tex]

x = 17

x = 17

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

To find the gas unit used in baking of cookies, we plug the values into the given equation: g = t, g = 12. Thus, the gas unit used is 12.

Organic gas usage or production is measured in "gas units." It is frequently employed to estimate the price of natural gas for a predetermined time period, such as a month or a year.

British thermal units (BTUs), a measure of the energy content of natural gas, are the industry standard for quantifying this fuel. One BTU is the amount of heat necessary to raise the temperature of one pound of water by one degree Fahrenheit.

To compute the gas unit for a given time period, the total amount of natural gas used or generated is first converted into BTUs.

How to solve?

To find the gas unit used, we plug the values into the given equation:

g = t, g = 12. Thus, the gas unit used is 12.

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- 6x + 15 < 10 - 5x , are correct representations of the inequality .

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. [1] The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:

The symbol a b indicates that an is smaller than b.

When a > b is used, it indicates that an is bigger than b.

A is not equivalent to b in any scenario. Since an is strictly less than or strictly greater than b, these relationships are known as stringent inequalities[1]. Equivalence is not considered.

There are two forms of inequality relations that are not strict, in contrast to strict inequalities:

The indication of an or b denotes that.

According to our question-

The difference is 5 (-3(2x - 5)). (2 - x)

First, make each side simpler.

∵ -3(2x - 5) = -3(2x) + -3(-5) (-5)

Recall that (+)=(-)

∴ -3(2x - 5) = - 6x + 15

∵ 5(2 - x) = 5(2) + 5(-x) (-x)

Recall that (+)(-) = (-)

∴ 5(2 - x) = 10 - 5x

∴ - 6x + 15 < 10 - 5x

Take 15 away from both sides.

∴ - 6x < -5 - 5x

5 times on both sides

∴ - x < - 5

Because the coefficient of x is negative, you must change the inequality's sign when you divide both sides by it.

The x coefficient is -1.

∴ Add -1 to both sides.

∴ x > 5

The appropriate answers are:

- 6x + 15 < 10 - 5x

Hence, - 6x + 15 < 10 - 5x , are correct representations of the inequality .

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The distance between the point (-3,7) and the line y=1/3x-2 is  11.0 units

Distance shows how long it is between a point and another

We can do this by drawing a segment that is perpendicular to the line

the given equation is 1/3x-2

The slope here is 1/3 That is slope =3

From the equation of slope=intercept form = y=mx+c

put m=3 to have

y=3x+c

From the given coordinates (-3,7)

7=3(-3)+c

7+9=c

c=16

This implies that y=3x+16

Find the line where the equation intersect  the line

⇒3x+16=1/3x-2

Rearrange the equation

8x/3=-18

Make x the subject. x=6.75

Recall that y=1/3(6.75)-2

y=2.25

The second coordinates are (6.75,2.25) and first (-3,7)

The distance is given by

d=[tex]\sqrt({X_{2}-X_{1})^{2} +(Y_{2}-Y_{1} )^{2} }[/tex]

d= √(6.75+3)²+(2.25-7)²

d=√9.75²+(-4.75)²

d=√95.0625+22.5625

d=√117.625

d=10.8455059817

Therefore the distance is 11 units

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The rate of change of Area of the circle of ripples when radius is 24 inches is  602.88  in²/sec  .

In the question ,

it is given that ,

a rock dropped in pond causes a circular waves of ripples ,

the rate at which the radius is increasing (dr/dt) = 4 in/sec .

let the radius of the circular ripples is = r ,

the area of the circular ripples is ; A = πr² ,

differentiating Area with respect to time(t) is ,

dA/dt = π×2r×(dr/dt)

to find the rate of change of area when the radius of circle is 24 inches ;

substituting dr/dt = 4 and r = 24 ,

we get ,

dA/dt = π×2×24×4

= 192×3.14    .

= 602.88 in²/sec

Therefore , the rate of change of Area is = 602.88  in²/sec   .

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Answer: No, they are not inverses of one another.

=======================================================

Explanation:

There are at least 3 methods we can use to prove the functions aren't inverses of each other.

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

Method 1

Let's say we plugged x = 0 into f(x).

[tex]f(\text{x}) = 2\text{x}+1\\\\f(0) = 2*0+1\\\\f(0) = 1\\\\[/tex]

The input x = 0 leads to the output y = 1.

Then let's treat y = 1 as the input of the g(x) function, so we'll plug x = 1 into here.

[tex]g(\text{x}) = -2\text{x}-1\\\\g(1) = -2*1-1\\\\g(1) = -3\\\\[/tex]

If g(x) was the inverse of f(x), then the g(1) output value should be 0 to get us back where we started. However, we get an output of -3 instead.

This is sufficient evidence to conclude that f(x) and g(x) are not inverses of each other. We only need one counter-example to disprove this claim.

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

Method 2

Recall that if f(x) and g(x) are inverses of each other, then we have the following two properties

The left hand side of each equation involves the concept of "function composition".

Let's see what f(g(x)) is equal to in this case.

[tex]f(\text{x}) = 2\text{x}+1\\\\f(g(\text{x})) = 2(g(\text{x}))+1\\\\f(g(\text{x})) = 2(-2\text{x}-1)+1\\\\f(g(\text{x})) = -4\text{x}-2+1\\\\f(g(\text{x})) = -4\text{x}-1\\\\[/tex]

We do not get an output of simply x only, so this is another way to see how we don't have inverses.

Through similar steps, you should find that [tex]g(f(\text{x})) = -4\text{x}-3[/tex] which is further confirmation that f(x) and g(x) are not inverses of each other.

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

Method 3

Let's ignore g(x) for now. We'll start with f(x) and find the inverse of it.

The process involves this basic outline:

So,

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

Unfortunately we do not end up with -2x-1 as the actual inverse.

So if [tex]g(\text{x}) = \frac{\text{x}-1}{2}[/tex] was the case, then f(x) and g(x) would be inverses of each other.

Through similar steps, the inverse of [tex]g(\text{x}) = -2\text{x}-1\\\\[/tex] is [tex]g^{-1}(\text{x}) = -\frac{\text{x}+1}{2}\\\\[/tex]

Answer:

C) 300

Step-by-step explanation:

Butter cookies :-

2 x 50 = 100 cookies

Choco chip cookies

4x 100 = 200 cookies

Total cookies :-

100 + 200 = 300

I hope my answer helps you.

The APR for this loan is equal to 468%.

In Mathematics, APR is an abbreviation for annual percentage rate and it can be defined as a measure of an amount of money based on a yearly rate of interest, which a borrower must pay on a loan or credit card.

Mathematically, the annual percentage rate (APR) of a loan can be calculated by using this formula:

APR = [((simple interest/principal)/n) × 365] × 100

Where:

n represents the number of days.

Note: n is equal to 14 days (2 weeks).

Next, we would determine the FC for this loan as follows;

FC = $295 - $250

FC = $45.

For the two-week period, we have;

Interest = 45/250

Interest = 0.18.

Therefore, the annual percentage rate (APR) of this loan is given by;

APR = 0.18 × 52/2

APR = 468%.

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Answer:

x = you sold

y = friend sold

---

x + y = 58

x = y + 14

---

put the system of linear equations into the standard form:

---

x + y = 58

x - y = 14

x= you sold 36

y= friend sold 22

Step-by-step explanation:

Answer:

95

Step-by-step explanation:

He might use the equation y = (3/2) x to determine how much flour he required for the cake.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance.

Equations come in a variety of forms, including linear, quadratic, cubic, etc.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" symbol in it.

According to our question-

Accordingly, we require 2.3 cups of sugar for every cup of flour.

It also means that you need 3 1/2 cups of flour for every cup of sugar.

Therefore, if x cups of sugar and y cups of flour, respectively, are used:

y = (3/2) x.

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Answer:f - 1 ( x ) to show the final answer. Verify if f−1(x)=x2+1 f - 1 ( x ) = x 2 + 1 is the inverse of f(x)=2x−2 f ( x ) = 2 x - 2 .

Answer:4x+4

Step-by-step explanation:

6-3= 3+1= 4 =4x+4

Answer: -3x³ - 6x²  + 8x

Step-by-step explanation:

      In standard form, we order the terms in a polynomial with the highest degree on the left down to the lowest degree on the right. Make sure to keep the positive or negative "attached" to the mathematical term you are moving.

    Given;

8x - 6x² - 3x³

    3 > 2 > 1, so we will reorder:

-3x³ - 6x²  + 8x

-3x^3-6x^2+8x is the standard form of polynomial 8x-6x^2-3x^3.

Often, we arrange the terms in a polynomial in standard form in which the term with the highest degree is first and is followed by the other terms in order of decreasing powers.

The first term of a polynomial in this form is called the leading term, and the coefficient in this term is called the leading coefficient.

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Using trigonometric ratio, the length of BE is 10 units, the value of sin B is 0.64 and cos B is 0.64 respectively

This is the ratio between the angles and sides of a right-angle triangle. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

In this problem, we have that

1)

Using tangent of B

tan B = opposite / adjacent

tan B = NE / BE

3/4 = 7.5 / BE

BE = 7.5 / 0.75

BE = 10

2)

To find sin B, we need to calculate the hypothenuse of the triangle which we will use Pythagoras's theorem

NB² = BE² + NE²

NB² = 10² + 7.5²

NB = 12.5

sin B = NE / NB

sin B = 7.5 / 12.5

B = sin⁻¹ (7.5 / 12.5)

B = 0.64

3)

cos B = BE / NB

cos B = 10 / 12.5

B = cos⁻¹ (10/12.5)

B = 0.64

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Answer: Yes, it is linear expression

Step-by-step explanation:

The equation is y=mx + b

Here we have 7x, which we have the slope

We don't see the y-intercept, so it is 0

Answer:

The Answer is 6.

Step-by-step explanation:

12x = 72

12 x 6 = 72

X = 6 because 6 can go into 72 12 times

Answer:

x = 6

Step-by-step explanation:

following the working through

substitute y = - x + 2 into the other equation

5x - 7y = 58

5x - 7(- x + 2) = 58 ← distribute parenthesis by - 7

5x + 7x - 14 = 58

12x - 14 = 58 ( add 14 to both sides )

12x = 72 ( divide both sides by 12 )

x = [tex]\frac{72}{12}[/tex] = 6

substitute x = 6 into y = - x + 2

y = - 6 + 2 = - 4

The function h(x) is the result of two rigid transformations, reflecting the function f(x) about the x-axis and translating it vertically 7 units down.

In this problem we must determine the difference between the quadratic functions f(x) = x² and h(x) = - x² - 7, we can infer the change necessary to derive h(x) by means of rigid transformations, that is, transformations applied on a function such that the features of the functions are conserved.

All the rigid transformations required to transform f(x) into h(x) are listed below:

Now we proceed to plot the two functions. From the graph we noticed that h(x) is the result of reflecting f(x) about the x-axis and translating 7 units in the -y direction.

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