Find the 9th term of the geometric sequence 9,27,81...

Answer:

r=2

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

68=3(6r−1)−7(1−3r)

68=(3)(6r)+(3)(−1)+(−7)(1)+(−7)(−3r)(Distribute)

68=18r+−3+−7+21r

68=(18r+21r)+(−3+−7)(Combine Like Terms)

68=39r+−10

68=39r−10

Step 2: Flip the equation.

39r−10=68

Step 3: Add 10 to both sides.

39r−10+10=68+10

39r=78

Step 4: Divide both sides by 39.

39r/39=78/39

r=2

Answer: (-3,2)

Step-by-step explanation:

Answer:

(-3, 2)

Step-by-step explanation:

There are two methods on finding the vertex. The one I will be using is the faster version.

y=2x^{2}+12x+20

a=2   b=12   c=20

First use the formula -b/2a.

-(12)/2(2)=

=-12/4=-3

-3 is the x-coordinate.

Plug in -3 into the equation for x.

y=2(-3)^{2}+12(-3)+20

y=2(9)+12(-3)+20

y=18-36+20

y=2

The y-coordinate is 2

Use (x, y) for the vertex.

x=-3

y=2

The vertex is (-3, 2)

Hope this helps!

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Using limits and numeric value, we have that lim x -> 0 f(f(x)) is closest to:

c. 3.

f(f(x)) is a composite function, hence:

A limit is the value that a function f(x) tends as x tends to a value. It there are no undetermined values, we can just verify the numeric value from the graph, but with undetermined values, there are multiple things to look at.

For this function, looking at the graph, we have that:

This means that option c is the closest approximation for the limit of the function.

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c

in an arithmetic expression

Answer:

Below.

Step-by-step explanation:

3x² - 1 = 0

3x² = 1

x² = 1/3

x = ±√(1/3)

  = -1/√3, 1/√3.

So, -1/√3 is a zero of 3x² - 1 .

Yes, x = -1/√3 is a zero of the polynomial 3x² - 1 because substituting the value results in zero, confirming its solution to the equation.

To verify whether x = -1/√3 is a zero of the polynomial 3x² - 1, we need to substitute this value into the polynomial and check if it results in zero.

Given polynomial: 3x² - 1

Now, substitute x = -1/√3 into the polynomial:

3(-1/√3)² - 1

Now, simplify:

3(1/3) - 1

1 - 1

The result is zero. Since the expression evaluates to zero when x = -1/√3, this means that x = -1/√3 is indeed a zero of the polynomial 3x² - 1.

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It would take 21 8/ 12 seconds to fill 2 tires

Proportion can be defined as the comparison between two numbers or elements

It is also an equation with two ratios draw equal to each other.

From the information given,

If 31/ 3 tires (10/ 3 ) tires is filled in 3 1/4 seconds ( 13/ 4)

Then 2 tires = x seconds

cross multiply

x = 13 / 4 × 2 ÷ 10/ 3

x = 26/ 4 × 3/ 10

x = 260/ 12

x = 21 8/ 12 seconds

Thus, it would take 21 8/ 12 seconds to fill

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The plane can fly 384 miles in 3/5 hours.

An airplane can cruise at 570 miles per hour.

We have to find the distance travelled by airplane in 4/3 hours.

Distance = Speed x Time

Distance = 640 x 3/5

Distance = 128 x 3

Distance = 384 miles

Hence, The plane can fly 384 miles in 3/5 hours.

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The scale of the drawing by using proportion is 3 : 5.

According to the given question.

Melissa drew a scale drawing of a city.

The width of the park in the drawing is 36 inches.

And the actual width of the park is 60 yards.

As we know that, a proportion is a fraction of a total amount, and the measures are related using a rule of three.

Therefore, the scale of the drawing by using proportion

= 36iches/ 60 yards

= 3/5

= 3 : 5

Hence, the scale of the drawing by using proportion is 3 : 5.

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The measure of angle J is 116°

Linear pair of angles are angles formed when two lines intersect at a single point.

Angles are said to be linear if they are adjacent to each other with the intersection of the two lines.

Note that the sum of angles of a linear pair is equal to 180°.

From the information given, we have that;

But we have the expression as;

Angle R + Angle J = 180°

substitute the values into the equation

3x - 5 + 5x + 1 = 180°

collect like terms

8x - 4 = 180°

8x = 180 + 4

8x = 184

To determine the value of x, divide both sides by the 8

8x/8 = 184/8

Divide through

x = 23

But we have that;

Angle J = 5x + 1

Angle J = 5(23) + 1

Angle J = 115 + 1

Angle J = 116°

Thus, the measure of angle J is 116°

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$32 money will she have after five bets.

What  is a linear equation?

starting amount = $1

she doubles her money on her each bet.

So, when she makes her first bet , her money doubles and keep doubling

on every bet of the previous amount .

Money she makes on her first bet =  2 * 1 = $2

Money she makes on her second bet =  2 * 2 = $4

money on third bet = 2 * 4 = $8

money on fourth bet =  2 * 8 = $16

money on fifth bet =  2 * 16 = $32

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Answer:-12

Step-by-step explanation:  -4b=48      b=48/-4        b=-12

hope it helps

Answer:

x = 3

Step-by-step explanation:

Hello!

Solve for x by isolating the variable

The value of x is 3.

Answer:

(0,-2)?

Step-by-step explanation:

The equation of line passing through the point (4, 6) and parallel to x axis is y = 6.

According to the given question.

A line which is passes through the point (4, 6).

And also parallel to x-axis.

As we know that, the equation of line parallel to the x-axis, cuts the y-axis at the point (0, b) is y = b.

Since, the line is passing through the point (4, 6) and parallel to x-axis, cuts the y-axis at the point (0, 6).

As per the formula, the equation of line passing through the point (4, 6) and parallel to x axis is y = 6.

Hence, the equation of line passing through the point (4, 6) and parallel to x axis is y = 6.

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The leading term, the degree of the polynomial is  −6x3 is 3rd degree and coefficient −6.

Option (C) is correct.

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables .It is  is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.

Given:

The given expression is

−6x3

We have to find the  polynomial by degree and tell the leading coefficient.

According to given question we have

The leading term of a polynomial is the term with the highest degree.

The leading coefficient of a polynomial is the coefficient of the leading term.

The degree of a polynomial is the highest degree of its terms.

Hence, the leading term, the degree of the polynomial is  −6x3 is 3rd degree and coefficient −6.

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The point (1,1) represents 1+i in the two dimensional complex plane. Absolute value of 1+i = [tex]\sqrt{2}[/tex].

Given the complex number, z = 1+i

The general form of a complex plane is x+iy, where x and y are real numbers.

We can place any complex number into a two-dimensional complex plane with two axes - X and Y.

For z = 1+i, x = 1 and y = 1. So the point (1,1) will represent z = 1+i in the two dimensional complex plane.

The absolute value of a complex number z = x+iy is given by ,

|z| = [tex]\sqrt{x^2+y^2}[/tex]

So for z = 1+i, |z| =  [tex]\sqrt{1^2+1^2}=\sqrt{2}[/tex]

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The distance between the two points as depicted on the graph is:

√5.

Given, the points are:

(1,2) = (x₁,y₁) and

(3,1) = (x₂,y₂)

We know that distance between two points is:

d = √(x₂-x₁)²+(y₂-y₁)²

d = √(3-1)²+(1-2)²

d = √(2)²+(-1)²

d = √4+1

d = √5

Hence we get the distance between two given points as √5

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Answer:

Domain: x > -4

Range: y > -1

Step-by-step explanation:

Domain is the points on the x axis that could be vaild for that line.

Range is the points on the y axis that could be valid for that line.

Answer:

pamachino ala iscola iyo kapito binisimo bambena ilina

The function rule for g(x) is (x₊6)² ₋ 5. According to the given data we apply the translations onto the graph and from the graph we determine the function of g(x).

Given, the function of f(x)  = x²

The base graph is moved up or down in the y-axis direction when a graph is vertically translated. Each point on a graph is moved k units up the graph to translate it vertically. Shifting the f (x) k units vertically will allow you to sketch the equation g (x) = f (x) + k.

The graph of g(x) is f(x) translated to 6 units left and down 5 unit.

Draw the translations onto the graph. In the given graph provided, the yellow curve indicates the function g(x).

therefore g(x) = (x₊6)² ₋ 5 is the function from the graph.

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The percentage of the company’s employees are both female and over 6 feet tall is 3.75%

Let the total number of employees in the given company be x. So, the number of female employees in the company are : 75% × x

Number of female employees in company = 0.75x

Now, calculating number of female employees that over 6 feet tall = 0.75x × 5%

The number of female employees that over 6 feet tall = 0.0375x

Percentage of the company’s employees are both female and over 6 feet tall = percentage of female and tall employees ÷ total number of employees × 100

Percentage of the company’s employees are both female and over 6 feet tall = (0.0375x÷x)×100

Percentage of the company’s employees are both female and over 6 feet tall = 3.75%

Therefore, the percentage of the company’s employees are both female and over 6 feet tall is 3.75%

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Another way to write this rule is (x, y) = (x - 8, y + 4)

The translation rule is given as:

T–8, 4(x, y).

The above means that

x = x - 8

y = y + 4

Express as a transformation rule

So, we have

(x - 8, y + 4)

Rewrite as:

(x, y) = (x - 8, y + 4)

Hence, another way to write this rule is (x, y) = (x - 8, y + 4)

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The answer is expressed in terms of unit vectors  x^ and y^ as B = B (cos θ  x ^ + sin θ  y ^)

For expressing the magnetic field B in terms of vectors we need to know the magnitude of the magnetic field and the angle between them.

the angle we have is with respect to the positive side of the x-axis, let's use trigonometry.

cos θ = Bₓ / B

sin θ =  / B

Bx = B cosθ

By = B sinθ

hence the resulting vector is

 B = Bₓ i ^ + [tex]B_{y}[/tex] j^

The unit vectors are

x ^ = i ^

y ^ = j ^

The answer is expressed in terms of unit vectors  x^ and y^ as B = B (cos θ  x ^ + sin θ  y ^)

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Answer:

y=2

Step-by-step explanation:

The domain of the function is -2 ≤ x < -5 and the range is -2 < y < 1

The domain of the function is the set of input values of the graph

The range of a function is the set of output values of the graph.

The graph represents the given parameters

On the graph, we have the following endpoints

Closed circle at (-2, -1)

Open circle at (-5, -2)

Maximum = (0, 1)

The domain

The definition of the domain implies that the domain of a function is the set of x values of the graph.

Recall that

Closed circle at (-2, -1)

Open circle at (-5, -2)

Maximum = (0, 1)

Remove the maximum

Closed circle at (-2, -1)

Open circle at (-5, -2)

Remove the y coordinates

So, we have

Closed circle at (-2)

Open circle at (-5)

Combine the x values

-2 ≤ x < -5

The range

The definition of the range implies that the range of a function is the set of y values of the graph.

Recall that

Closed circle at (-2, -1)

Open circle at (-5, -2)

Maximum = (0, 1)

Remove the smaller larger y value of the endpoints)

Open circle at (-5, -2)

Maximum = (0, 1)

Remove the x coordinates

So, we have

Open circle at (-2)

Maximum = (1)

Combine the y values

-2 < y < 1

Hence, the domain of the function is -2 ≤ x < -5 and the range is -2 < y < 1

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You can make 106.67 L of 25% v/v acid solution by mixing 6.67 L of pure acid with 100 L of 20% v/v acid solution.

Acids are a type of chemical that can either absorb electrons or give off protons or hydrogen ions. An anion and a cation can form in water when a hydrogen atom that is bonded to an acid releases (dissociates). How acidic a substance is and how acidic its solution pH is depends on how many hydrogen ions it produces.

The word acid stems from the Latin words acidus or acere, which suggest "sour," because one of the characteristics of acids in water is a sour taste (e.g., vinegar or lemon juice).

How thoroughly an acid splits into its ions after being dissolved in water indicates whether it is strong or weak. A strong acid, like hydrochloric acid, completely dissociates into its ions in water.

100 liters * (20/100) = 20 liters acid

Let's assume that the number x represents the amount of pure acid you need to add to your initial solution. The volume of acid will increase by x because you are working with pure acid.

V(acid) = 20 +x

V(solution) = 100+ x

As a result, the percent concentration by volume of the target solution will be equal to

{V(acid)/V(solution)} * 100 = 25%

{(20+x)/(100+x)} * 100 = 25%

(20 +x) 100 = 25(100+x)

2000+100x = 2500 + 25x

75 x = 500

x = 6.67 liters

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The committee can be selected by combinatorial argument  in

[tex]\sum ^{n}_{k=1} k(^n_k).[/tex] ways.

A counting-based argument is known as a combinatorial argument or combinatorial proof. This line of reasoning has previously been used, for instance in the section on Stirling numbers of the second sort.

By initially selecting k individuals from our group of n, we can then choose one of those k individuals to serve as the committee's chairperson.

A number of methods for completing the first task, k methods for completing the second task, and so on. ways to create a k-member committee with a chairperson.

[tex]\sum ^{n}_{k=1} k(^n_k).[/tex] is the number of methods to construct a committee with a chairman of size less than or equal to n can be found by adding up over 1≤k≤n.

A committee of size less than or equal to n can also be formed with a chairperson by selecting the chairperson first, followed by the members of the committee. The chairperson can be chosen from among n options. The picker has two options for the remaining n-1 individuals: to include them or not. We therefore have n options for the chairperson, 2 options for the following, 2 options for the following, etc. These can be multiplied together to give us [tex]n2^{n-1}[/tex], which is a proof of the identity.

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