Greg is driving his motorhome. It uses 3 gallons of gas for every 21 miles he travels. Complete the table below showing the number of gallons used and the distance traveled

The nth term of this given G.P. is  [tex]T_n =5\times[3]^{n-1}[/tex].

Given that

To find

So, according to the question

We have,

            5 15 45 135​

From this G.P.

So, we know that

                        [tex]T_n =ar^{n-1}[/tex]

Where,

Now, putting the all given values

                        [tex]T_n =5\times[3]^{n-1}[/tex] -----------------(1)

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The word Inverse is used here because as the speed of traveled goes on increase, then the amount of time it takes to travel a particular distance will decrease .

The inverse variation property states that , whenever the product of values of two quantities is a constant value then there is opposite variation between these two corresponding values. Or we can also say that if the productive nature of two corresponding values is constant, then one quantity is inversely varies with second quantity.

Let say if x and y are two values and k is a constant value, then

According to inverse variation

k = xy or y = k/x

In the question here, when we double your speed, it takes half as much time to reach the destination. The word Inverse is used here because as the speed of traveled goes on increase, then the amount of time it takes to travel a particular distance will decrease .

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Answer:

Angle A is 20°

Step-by-step explanation:

The sum of the interior angles of a triangle is 180°.  

90 + 10x + x +13 = 180  Combine like terms

103 + 11x + 180  Subtract 103 from both sides

11x = 77  Divide both sides by 11

x = 7

Angle A is 13 + x.  X is 7, so 13 + 7 = 20

Answer:

como proporción de dos tipos de tela es diferente.

por lo tanto, la relación entre el número de yardas cuadradas y el costo

no es proporcional entre los dos tipos de tejido

Explicación paso a paso:

Para que una relacion sea proporcional

a:b = c:d

en otra forma

a/b = c/d

______________________________________________

Proporción para el primer tipo de tejido

costo de tela/ área de tela = 31.25/5 = 6.25

Ratio para otro tipo de tejido

costo de tela/ área de tela = 71.50/11 = 6.5

como proporción de dos tipos de tela es diferente.

por lo tanto, la relación entre el número de yardas cuadradas y el costo

no es proporcional entre los dos tipos de tejido

Step-by-step explanation:

A graph which represent the solution to this inequality is: graph B.

An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments:

Given the following inequality:

-1/4(12x + 8) ≤ -2x + 11

Opening the bracket, we have:

-3x - 2 ≤ -2x + 11

3x - 2x ≤ -11 - 2

x ≤ -13

Note: When the arrow points to the left and shaded, the inequality is either (≤).

In conclusion, a graph which represent the solution to this inequality is graph B.

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Answer: 0.22

Step-by-step explanation:

26.40/120

0.22

0.22 x 120 = 26.40

Answer:

constant

Step-by-step explanation:

Using the midpoint concept and the distance between two points, the correct statement is given by:

[tex]\sqrt{(0 - a)^2 + (2b - b)^2} = \sqrt{(2a - a)^2 + (0 - b)^2} = \sqrt{(a - 0)^2 + (b - 0)^2}[/tex]

The midpoint between two points is the halfway point between them, and is found using the mean of the coordinates.

Hence the coordinates of the midpoint of the hypotenuse are given as follows:

Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Hence the distance from the midpoint of the hypotenuse to any vertex is given by:

[tex]\sqrt{(0 - a)^2 + (2b - b)^2} = \sqrt{(2a - a)^2 + (0 - b)^2} = \sqrt{(a - 0)^2 + (b - 0)^2}[/tex]

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Step-by-step explanation:

I guess, the equation is meant to be in slope-intercept form :

y = ax + b

"a" is the slope, "b" is the y intercept (the y value when x = 0).

in a situation like this, where we have the slope and one point of the line, we can start with the point-slope form

y - y1 = a(x - x1)

"a" is again the slope, and (x1, y1) is the given point.

and then we transform this over to the slope-intercept form.

so, in our case here

y - 2 = 5/6 × (x - 5) = 5x/6 - 25/6

let's simplify this by multiplying everything by 6 :

6y - 12 = 5x - 25

6y = 5x - 13

y = 5/6 x - 13/6

or

y = 1/6 × (5x - 13)

Given data,

A piece of brass has a volume v cm'.

there were 6 cm'

mass would be 200 g

So,

We can write,

                       volume V = 6cm

                brass mass M = 200g

                        Find density d.

Define Density :

Density, mass of a unit volume of a material substance. The formula for density is d = M/V, where d is density, M is mass, and V is volume. Density is commonly expressed in units of grams per cubic centi meter.

                                  d = M/V

Where,

M: It is the mass

V: It is the volume

According to the data of the statement we have:

                                [tex]V = 6 cm^{1}[/tex]

                                [tex]M = 200g[/tex]

So, the density is given by:

                                d = M/V

                                d = [tex]\frac{200g}{6cm^{1} }[/tex]

                                d = [tex]33.33\frac{g}{cm^{1} }[/tex]

Therefore,

The density of the brass ornament is d = [tex]33.33\frac{g}{cm^{1} }[/tex]

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If the total price is $307.32 and tip rate is 20%, the original price given the total amount and tip rate is $256.10

What is the sum of the percentage of the original price and tip rate?

First and foremost, the tip rate is an added layer on the original price of 100%, which means that when the original price and the tip rate are added together, it gives 120%, hence, the total price of $307.32 is 120% of the original price

120% of original price=$307.32

1% of original price=$307.32/120

1% of original price=$2.561

100% of original price=$2.561*100

100% of original price=$256.10

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In the expression 2x + 5 at x = 3 Brett is wrong as the correct answer is 11.

An expression is written in the form of numbers and variables with arithmetic operations.

According to the given question we have to evaluate 2x + 5 at x = 3 and match our answer with Brett which is 41.

To obtain the value of 2x + 5 at x = 3, we have to substitute x with 3 in the given expression which is,

= 2(3) + 5

= 6 + 5.

= 11.

So, our answer is correct which is 11 and Brett is wrong.

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Two consecutive asymptotes are θ = - π / 20 and θ = 3π / 20 and the period is π / 5.

In this question we must look for two consecutive vertical asymptotes related to a trigonometric function. A function becomes undefined when its denominator is zero. Now we proceed to simplify the expression by trigonometric formulas:

y = 4 · csc (5θ - 3π / 4)

y = 4 / sin (5θ - 3π / 4)

y = 4 / (sin 5θ · cos 3π / 4 - cos 5θ · sin 3π / 4)

y = 4 / [(- √2 / 2) · sin 5θ - (√2 / 2) · cos 5θ]

The function is undefined for (- √2 / 2) · sin 5θ - (√2 / 2) · cos 5θ = 0:

(- √2 / 2) · sin 5θ - (√2 / 2) · cos 5θ = 0

(- √2 / 2) · sin 5θ = (√2 / 2) · cos 5θ

- sin 5θ = cos 5θ

tan 5θ = - 1

5θ = - π / 4 + i · π

θ =  - π / 20 + i · π / 5

θ = (π / 5) · (- 1 / 4 + i)

There are two consecutive asymptotes:

i = 0

θ = - π / 20

i = 1

θ = 3π / 20

And the period is ΔT = 3π / 20 - (- π / 20) = π / 5.

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Answer:

y = 3 and x = 4

Step-by-step explanation:

Let's solve your system by substitution.

6x+5y=39;3x+5y=27

Step: Solve6x+5y=39for x:

6x+5y=39

6x+5y+−5y=39+−5y(Add -5y to both sides)

6x=−5y+39

6x/6=−5y+39/6

(Divide both sides by 6)

x=−5/6y+13/2

Step: Substitute −5/6y+13/2 for x in 3x+5y=27:

3x+5y=27

3(−5/6y+13/2)+5y=27

5/2y+39/2=27(Simplify both sides of the equation)

5/2y+39/2+−39/2=27+−39/2

(Add (-39)/2 to both sides)

5/2y=15/2

5/2y/5/2=15/2/5/2

(Divide both sides by 5/2)

y=3

Step: Substitute 3 for y in x=−5/6y+13/2:

x=−5/6y+13/2

x=−5/6(3)+13/2

x=4(Simplify both sides of the equation)

Answer:

the answer is false because it will always be a odd number

Answer:

Step-by-step explanation:

well, first you have to add the number to an even number 4+17=21

21 is not an even number 12+17=29 which is also an odd number

answer B is false.

You can test to see if a diagram made using digital tools is a construction or just a drawing based on estimation by C. Look to see just how accurate the diagram appears. If needed, measure the screen using a ruler and protractor.

The phrase "digital construction" is understood to refer to the use of digital technologies to improve and improve the quality of construction.

In this case, you can test to see if a diagram made using digital tools is a construction or just a drawing based on estimation by looking to see just how accurate the diagram appears. If needed, measure the screen using a ruler and protractor.

In conclusion, the correct option is C.

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How can you test to see if a diagram made using digital tools is a construction or just a drawing based on estimation? O Digital tools cannot be used to make a construction. Construction tools are limited to only straightedge and compass. O Look to see just how accurate the diagram appears. If needed, measure the screen using a ruler and protractor. O Drag a free point to see if the construction changes. Restart your computer and see if the diagram is found in the same location.

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{3 - 4^2 + \dfrac{6}{2}}[/tex]

[tex]\mathsf{= 3 - 4\times 4 + \dfrac{6}{2}}[/tex]

[tex]\mathsf{= 3 - 16 + \dfrac{6}{2}}[/tex]

[tex]\mathsf{= -13 + \dfrac{6}{2}}[/tex]

[tex]\mathsf{= -13 + 3}[/tex]

[tex]\mathsf{= -10}[/tex]

[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{-10}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

10

4 plus 6 is equal to 10 there you go

The rational function with the given characteristics is [tex]f(x) = \frac{3x + 1}{x - 4} [/tex].

Any function that can be expressed mathematically as a rational fraction—an algebraic fraction in which both the numerator and the denominator are polynomials—is referred to as a rational function. The polynomials' coefficients don't have to be rational numbers,they can be found in any field K.

given that a vertical asymptote at x=-4.

A horizontal asymptote at y=3.

The denominator of the function cancels for this value and the numerator does not cancel at this value if the rational function has a vertical asymptote at x=4.

[tex]f(x) = \frac{p(x)}{(x - 4)} [/tex]

The degree of the numbered variable is equal to the degree of the denominator if the rational function has a horizontal asymptote at y=3, and the coefficient of the higher degree variable is three times larger.

Hence,

[tex]f(x) = \frac{3x + 1}{x - 4} [/tex]

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Answer:

-2x-5=4x-29

-2x-4x=-29+5

-6x =-24

x=-24/-6

x=4

hence proved

Answer:

[tex]0.243243[/tex]

The inverse of function f( x ) = ( 2x - 3)² is [tex]y=\frac{\pm\sqrt{x} +3}{2}[/tex].

A function that can reverse into another function is known as an inverse function or anti-function. A function takes in values, applies specific operations to them, and produces an output. In order to find y when x is swapped with another variable, we must first determine the inverse function. On the other hand, the inverse function and the original function likewise have interchangeable domains and ranges.

We have the function,

f(x) = y = ( 2x - 3 )²

x = ( 2y - 3 )²

2y - 3 = ±√x

Adding 3 from each side.

2y - 3 + 3 = ±√x + 3

2y = ±√x + 3

Dividing each side of the equation by 2.

[tex]y=\frac{\pm\sqrt{x} +3}{2}[/tex]

Hence, the inverse of function f( x ) = ( 2x - 3 )² is [tex]y=\frac{\pm\sqrt{x} +3}{2}[/tex].

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Answer:

line

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

Hey there!

In order to find which description of the graph matches the problem, we must first create an equation or an inequality

So, we need to find how much more people the company needs to reach their goal to generate at least $7,300 in monthly revenue

We know that each person adds $300 to the already total of $5,500 per month

Now we can form the equation with this knowledge

[tex]300x + 5,500 \geq 7,300[/tex] where x is the number of people

Now we can simplify the equation

[tex]300x\geq 7500 - 5500\\ 300x\geq 2000\\x\geq 6.67[/tex]

Since we cannot have 6.67th of a person, we must round down because it means that we need more than 6 people

If we round up, it means that you need more 7 people in order to get $7,300 which isn't true

This means, you need more than 6 salespeople per month in order to meet the monthly quota of $7,300 in monthly revenue

Now that we know this, we can make a graph, or find the correct description of the graph

Since they need more than 6 people, the dot that sits on 6 in the number line will not be filled in, indicating that you need more than 6 salespeople

And since we need MORE, not LESS, the line will be pointing to the right

So, the correct answer would be D.

The simplified form of the expression is -17x⁴ -13x³ - 13x

From the question, we are to simplify the given expression

The given expression is

(-3x⁴ - 5x - x³) + (-12x³ -8x -14x⁴)

To simplify the expression,

First clear the parentheses

(-3x⁴ - 5x - x³) + (-12x³ -8x -14x⁴)

-3x⁴ - 5x - x³ -12x³ - 8x - 14x⁴

Collect like terms

-3x⁴ - 14x⁴ - x³ -12x³ - 8x - 5x

Simplify further

-17x⁴ -13x³ - 13x

Hence, the simplified form of the expression is -17x⁴ -13x³ - 13x

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Answer:

Step-by-step explanation:

1.

IF THE SHADED REGION IS THE WANTED AREA then the inequality is

y > 2x + 1

BUT IF THE SHADED REGION IS THE UNWANTED AREA then the in equality is

y < 2x + 1

2.

You have to figure out the equation of the dotted line.

Since the line is dotted, it means less than or greater than, it cant be less than equals to or greater than equal to

The gradient of the line is 2 as

rise / run = 14/7 = 2

and y intercept is 1

y > 2x + 1

3.

this is used in economics and for planning to maximize profits and minimize costs.

It depends on what you mean "simplify". Chances are the goal here is to resolve any exponents that are improper fractions, meaning we don't want exponents larger than 1, like 4/3, for instance, but smaller than 1, like 2/3, is okay.

Now, by the distributive property of exponentiation,

[tex]\left(x^4 y\right)^{2/3} = \left(x^4\right)^{2/3} y^{2/3}[/tex]

Since [tex](x^a)^b = x^{ab}[/tex], we have

[tex]\left(x^4 y\right)^{2/3} = x^{4\cdot2/3} y^{2/3} = x^{8/3} y^{2/3}[/tex]

Convert the improper fraction to a mixed number.

[tex]\dfrac83 = 3 + \dfrac23[/tex]

Then we can write

[tex]x^{8/3} = x^{3 + 2/3} = x^3 x^{2/3}[/tex]

since [tex]x^{a+b}=x^ax^b[/tex].

Finally, we group together the factors with the same power.

[tex]\left(x^4 y\right)^{2/3} = x^3 x^{2/3} y^{2/3} = \boxed{x^3 (xy)^{2/3}}[/tex]

Answer:

[tex]x \geq 7[/tex]

Step-by-step explanation:

First inequality

[tex]-27 > -4x - 7\\\to 4x > 20\\\to x > 5[/tex]

Second inequality

[tex]-35 \geq -4x - 7\\\to 4x \geq 28\\\to x \geq 7[/tex]

We are given that x is greater than 5 and greater or equal to 7.
We can summarize this down to [tex]x \geq 7[/tex]

Answer:

Inequality notation: [7, ∞)

Number Line:

7 (closed dot), point towards positive infinity.

Step-by-step explanation:

-27 > -4x - 7 and -35 ≥ -4x - 7

+7            +7         +7            +7

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

-20 > -4x               -28 ≥ -4x

÷-4     ÷-4                ÷-4   ÷-4

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

5 < x                        7 ≤ x or x ≥ 7

Inequality notation includes the numbers that are included or the"≥" symbol.

Number line:

                                      --------->

<------------------------------|------------>

                                    7

I hope this helps!

The rate at which Riya is applying the mulch to the garden is 250000:1.

It should be noted that rate is simply used to show the relationship between two things. A rate in mathematics is the comparison of two related values expressed in different units. The numerator of the ratio expresses the corresponding rate of change in the dependent variable if the denominator of the ratio is written as a single unit of one of these quantities and it is assumed that this quantity may be modified systematically (i.e., is an independent variable).

Per unit of time is a frequent sort of rate, and examples include speed, heart rate, and flux. Exchange rates, literacy rates, and electric field ratios are examples of ratios with a non-time denominator (in volts per meter).

From the information, Riya is applying mulch to the garden and she applied at a rate of 250000cm³ for every m² of space.

Therefore, the rate at which Riya is applying the mulch to the garden is 250000:1.

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