Write an equation for the nth term of the geometric sequences. Then Find a6


A. 2, 8, 32, 128,.

B. 0. 6, -3, 15, -75,.

C. -1/8, -1/4, -1/2, -1,.

D. 0. 1, 0. 9, 8. 1, 72. 9,

The solution is Option B.

Number of seats for the students is given by the equation A = 231 seats

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.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of seats for the students be A

Now , the equation will be

The total number of buses = 3 buses

The total number of seats on each buses = 80 seats

So , the total number of seats = number of buses x number of seats on each buses

Substituting the values in the equation , we get

The total number of seats = 80 x 3

The total number of seats = 240 seats

Now , the teachers has 3 seats each on 3 buses

So , the number of seats for teachers = 3 x 3 = 9 seats

And , the remaining number of seats = total number of seats of students

The total number of seats for students A = total number of seats - number of seats for teachers

Substituting the values in the equation , we get

The total number of seats for students A = 240 - 9

The total number of seats for students A = 231 seats

Therefore , the value of A is 231 seats

Hence , the number of seats for students is 231 seats

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Ramona’s mistake was she just substituted the 8.5 for the wrong variable.

From given conditions:

Ramona used the regression equation y = 444x - 21.29,  

where x represents height and y represents shoe size,

According to Romana her answer is incorrect as a man who is -17.52 inches tall does not predict the approximate height of a man.

The 8.5 refer to shoes size, not height.

So substituting 8.5 for the x-variable is wrong, because x refers to height and y represents shoe size.

Therefore, Ramon just substituted the 8.5 for the wrong variable. She must replace 8.5 for y-variable, because that's the right one for shoe size.

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The triangle is an acute triangle using the Pythagorean theorem.

Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We have,

The sides of a triangle are 68, 61, and 46.

Note:

When the sum of the squares of two sides of a triangle is equal to the square of the hypotenuse, the triangle is a right triangle.

When the sum of the squares of two sides of a triangle is less than the square of the hypotenuse, the triangle is an obtuse triangle.

When the sum of the squares of two sides of a triangle is greater than the square of the hypotenuse, the triangle is an acute triangle.

Now,

68² = 4624

46² = 2116

61² = 3721

We see that,

We can never have a right triangle or an obtuse triangle.

The possible combination.

61² + 68² > 46²

61² + 46² > 68²

68² + 46² > 61²

Thus,

The triangle is an acute triangle.

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The width of the picture frame with the given area would be = 3.9in

A frame is a structure that can be a rectangle or a square shape which is used to display a picture.

The area of the frame = 60in²

The width of the frame = x

The height of the frame = 4x

The area of a rectangle = length×width

That is ; 60 = X × 4x

60 = 4x²

make X the subject of formula;

X = √60/4

X = √15

X = 3.9 in.

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Answer:

m = 2

Step-by-step explanation:

Slope = rise / run or (y2 - y1) / ( x2 - x1)

Let's pick 2 points (0,0) (1,2)

We see the y increase by 2 and the x increase by 1, so the slope is

m = 2

The equation of the line in the attached graph in slope intercept form is written as

The slope, m of the linear function is calculated using the points on the graph (1, -4) and  (2, -10)

m = (y₀ - y₁) / (x₀ - x₁)

plugging in the values and evaluating

m = (-10 + 4) / (2 - 1)

m = (-6) / (1)

m = -6

equation passing through point (2, -10), using the point slope formula

(y - y₁) = m (x - x₁)

y - (-10) = -6(x - 2)

y + 10 = -6x + 12

rearranging the equation

y = -6x + 12 - 10

y = -6x + 2

The equation of the line in slope intercept form is written as y = -6x + 2

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Answer:

A, B, F

Step-by-step explanation:

Divide both sides of -4x<20 by 4, and we have A

Multiply both sides of -4x<20 by -1, since -1 is a negative number, we reverse the inequality, and we have B

Multiply both sides of -x<5 (A) by -1, since -1 is a negative number, we reverse the inequality, and we have F

As you can see, we turned the fraction 10100 into its decimal representation, 0.1, in a single simple computation.

Any number of equal portions, or parts of a whole, are described by fractions. Fractions in standard English indicate the number of pieces of a specific size. 8, 3/4 of .Part of an entire is a fraction. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. When a fraction is true, its numerator is smaller than its denominator.

With 100 as the denominator, decimal fractions in the hundredth place are written. We shall discover how each square is split into 100 equal sections in this section. A tenth is a portion that is just partially shaded. The fraction is expressed as 1/100 in decimal form.

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The number of grams of sugar that would be in a 200 ml glass of juice, given the carton, is 13. 2 grams of sugar

In a 250 ml glass of juice, we would see 16. 5 g of sugar. Given this information, we can find the amount of sugar in a 200 ml of juice by using direct proportion.

The amount of sugar in 200 ml of juice is :

= ( Amount of sugar in 250 ml x Quantity of juice ) / Quantity of base quantity of juice

= ( 16. 5 x 200 ) / 250

= 3, 300 / 250

= 13. 2 grams of sugar

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Answer:

49a + 28

Step-by-step explanation:

Answer:

49a+28

Step-by-step explanation:

49a+26+11–3–6

49a+26+11-9

49a+26+2

49a+28

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The domain is the set of years, which is {1, 2, 3, 4}, and the range is the set of values, which is {25000, 21250, 13750, 10000}. The ordered pairs of this function are (1, 25000), (2, 21250), (3, 13750), (4, 10000).

The relation described above can be expressed as a set of ordered pairs by calculating the value of the car for each year based on the depreciation rate. Let's calculate the value of the car for each year:

Year 1: 25000

Year 2: 25000 - 3,750

= 21250

Year 3: 21250 - 3,750

= 13750

Year 4: 13750 - 3,750

= 10000

Therefore, the ordered pairs of this relation are

: (1, 25000), (2, 21250), (3, 13750), (4, 10000).

The domain of this relation is the set of years, which is {1, 2, 3, 4}, and the range is the set of values, which is

{25000, 21250, 13750, 10000}.

This relation is a function because each input (year) is associated with one output (value).

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The measure of the angle of the shaded sector with an area of 65 cm² is 74.5°

An equation is used to show the relationship between numbers and variables.

The area of a two dimensional shape is the amount of space it occupies.

The area of a sector in a circle is given by:

Area = (Ф/360) * π * radius²

Where Ф is the sector angle

Given that sector area is 65 cm², radius is 10 cm, hence:

Area = (Ф/360) * π * radius²

Substituting gives:

65 = (Ф/360) * π * 10²

Ф = 74.5°

The measure of the angle is 74.5°

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The solutions of the quadratic equation 3x² − x + 8 = 0 are as follows;

x = 0.1667 + 1.6245i

x = 0.1667 - 1.6245i

In Mathematics, the standard form of a quadratic equation is given by this mathematical expression;

ax² + bx + c = 0

Mathematically, the quadratic formula is modeled or represented by this mathematical expression:

[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]

From the information provided above, we can logically deduce the following data values (parameters);

3x² − x + 8 = 0

Where:

Substituting the data values (parameters) into the quadratic formula, we have the following;

[tex]x = \frac{-(-1)\; \pm \;\sqrt{(-1)^2 - 4(3)(8)}}{2(3)}\\\\x = \frac{1\; \pm \;\sqrt{1\; - \;4(3)(8)}}{2(3)}\\\\x = \frac{1\; \pm \;\sqrt{1\; - \;96}}{6}[/tex]

x = (1 ± √95)/6

x = (1 + √95)/6 = 0.1667 + 1.6245i

or

x = (1 - √71)/6 = 0.1667 - 1.6245i

In conclusion, i represents a complex number.

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Complete Question:

Find the solutions of the quadratic equation 3x² − x + 8 = 0.

Answer:

[B] 6²

Step-by-step explanation:

Given:

[tex]\frac{6^4\cdot \:6^3}{6^5}[/tex]

Solve:

Add the exponents - [tex]6^4 \times 6^3=6^7[/tex]

Now we have - [tex]\frac{6^7}{6^5}[/tex]

Exponent Rule: [tex]\frac{x^a}{x^b}=x^{a-b}[/tex]

Which means - [tex]\frac{6^7}{6^5}=6^{7-5}[/tex]

Subtract the exponent - [tex]6^2[/tex]

Hence, the answer is [B] 6²

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Kate needs to buy 453.6 ft2 of mulch for her 12 ft radius garden, which is equal to 76.3 cubic feet when multiplied by the desired depth.

Kate needs to purchase 453.6 cubic feet of mulch for her garden. To figure this out, she needs to first calculate the area of her garden using the formula A = πr2, where A is the area of the garden and r is the radius. In this case, the area of Kate’s garden is 453.6 ft2. For example, if she wants to put down 2 inches of mulch, she would need to purchase 453.6 ft2 x 0.167 ft = 76.3 cubic feet. This calculation can be adjusted depending on the depth of mulch desired. For example, if Kate wants to put down 3 inches of mulch, she would need to purchase

453.6 ft2 x 0.25 ft = 113.4 cubic feet

A = πr2

A = π(12)2

A = 453.6 ft2

Mulch = A x depth

Mulch = 453.6 ft2 x 0.167 ft

Mulch = 76.3 cubic feet

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Answer:

Step-by-step explanation:

(9x-12)-(5x-7)=9x-12-5x+7=9x-5x-12+7=4x-5

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The commission from selling each pair of shoe is $5 while that from selling each boot is $15

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Let x represent the commission earned from selling each pair of shoe and y represent the commission from selling each pair of boot.

Cooper sold 2 pairs of shoes and 10 pairs of boots, earning $160 in commission. Hence:

2x + 10y = 160    (1)

Also, he sold 4 pairs of shoes and 10 pairs of boots, earning a total commission of $170, hence:

4x + 10y = 170    (2)

From both equations:

x = 5, y = 15

The commission from selling each pair of shoe is $5

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Answer:

w = -11/6

Step-by-step explanation:

-8 5/9 = 4 2/3w

-8 5/9  = -77/9

4 2/3 = 14/3

So, our equation is

-77/9 = 14/3w

Divided  both sides by 14/3

w = -11/6

Answer:

B. x ≥ 1

Step-by-step explanation:

Answer:

Sales=8571$

Commission=11.2% of Sales

=11.2/100 × 8571$

=(11.2×8571)/100 $

=959.952$ Which is nearly equal to 960$.

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The area of the rectangle is 69.12 square inches.

We know that for a rectangle of length L and width W, the area is given by the formula:

A = L*W

Here we know that the length is 14.4 inches, then:

L = 14.4 in

And the width is one-third of that length, then we can write:

W = (1/3)*L

Replacing the value of L, we will get:

W = (1/3)*14.4 inches

W = 4.8 inches.

Then the area of the rectangle is:

A=  (4.8 in)*(14.4 in) = 69.12 in²

That is the area of the rectangle.

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The degree of the polynomial as calculated from the given data7x³ + 5x + 4x⁵ + 2x² is 5 .

The given polynomial is  7x³ + 5x + 4x⁵ + 2x²

To find the degree of the polynomial we will write the equation down in the descending power of x

which is ,

4x⁵ + 7x³ + 2x² + 5x

Here , the highest power of the variable that appears with nonzero coefficient is 5.

So ,degree of the polynomial is said to be 5.

The hightest power of the variable in a polynomial is known as the degree of the polynomial. A polynomial expression is made up of constants and variables.

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yes it  is the same as that of all students at Faber GPAs as 2.32 and lower will mean that a track team athlete will be recommended for extra tutoring and population is 2.3* student number

What is the definition of a population?

In ordinary usage, a population is a distinct group of individuals with shared citizenship, identity, or characteristics. In statistics, a population is a representative sample of a larger group of people (or even things) with one or more characteristics in common.

When the distribution is normal, we use the z-score formula.

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

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f(x)=[tex]x^{2}[/tex]-x-4 + g(x)=x+4 = the product is with process [tex]x^2+7 x+8$$[/tex] . It is the solution of f(x) and g (x) .

[tex]$$f(x)=x^2-x-4, g(x)=x+4: x^2+7 x+8$$$$\begin{aligned}& \text { Find } f \circ g \text { given } f(x)=x^2-x-4, g(x)=x+4 \\& f \circ g=f(g(x)) \\& g(x)=x+4 \\& =f(x+4)\end{aligned}$$$$\begin{aligned}& f(x+4): \quad x^2+7 x+8 \\& =x^2+7 x+8\end{aligned}$$[/tex]

When a number is multiplied by another number, its products can be found. Because 9 x 3 Equals 27, for instance, 27 is a product of 9 and 3. What you get when you multiply two numbers together is their product. As a result, the product of three and four is twelve, followed by five and four, and so on.

A number that is obtained by multiplying two or more other numbers together is referred to in mathematics as a product. For instance, the result of multiplying 2 by 5 is 10 when the two numbers are combined. Byproducts include things like straw from grain harvesting operations, salt from desalination plants, sawdust from sawmills, and manure from feedlot operations.

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On solving the provided question, we can say that by having the equation 15 attendees were at the party

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

let x = number of attendees

[tex]2x[/tex] + 20 = number of slices 5(x-5) = [tex]2x[/tex] - 20

[tex]5x[/tex] - 25 = [tex]2x[/tex] + 20

[tex]3x[/tex] = 45

[tex]x[/tex] = 15

[tex]2x[/tex] + 20 = 50 slices

15 attendees

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The dimensions of a different sector with the same area and perimeter are An alternative sector's radius is 6.42 inches. An alternative sector has an arc length of 16.52 inches.

The distance between two places along a segment of a curve is known as the arc length.

Sector radius, r = 8.26 inches

Sector arc length = 12.84 inches

Sector perimeter = 2r + length of the arc

The specified sector's perimeter is equal to 2 x 8.26 x 12.84 x 29.36 inches.

The circle's circumference is 2 + 8.26 + 16.52.

The specified circle's area is A = 8.262 * 68.2276.

Sector area, A = 53.0292 inch2

Consequently, we have;

2R plus A equals 29.36 inches

A·R = 53.0292 × 2

that provides;

R² + 53.0292 = 14.68·R

R² - 14.68·R + 53.0292 = 0

using a graphing calculator to factor yields;

(R - 6.42)·(R - 8.26) = 0

R = 6.42 or R = 8.26

R = 8.26 is the measurement for the first sector.

Due to the distinctions between the sectors, we have;

R = 6.42 inches is the radius of the other sector.

The length of the arc, A = 29.36 - 2R

∴ A = 29.36 - 2 × 6.42 = 16.52

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Answer:

Step-by-step explanation:

We know that , the equation of line when the slope and the coordinates are given is:

y - y1 = m(x - x1)

where x1 = 4 , y1 = -6 and m = 1/2

therefore, y -(-6) = 1/2(x - 4)

y + 6 = x/2 - 2

6+2 = x/2 - y

8 = x - 2y/2

16 = x - 2y

required equation : x-2y-16=0

x = 448, which is the greatest of these integers.

Positive, negative, and zero are all examples of integers.

The Latin word "integer" signifies "whole" or "intact."

As a result, fractions and decimals are not included in integers.

All whole numbers and negative numbers are considered integers.

This means that if we combine negative numbers with whole numbers, a collection of integers results.

An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion.

Here are a few instances of integers: -5, 0, 1, 5, 8, 97, and 3,043. a collection of numbers, denoted by the symbol Z.

According to our question-

added together =1341

x +  x-1 + x-2 =1341

3x-3  = 1341

3x = 1344

x = 448

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Answer:

[tex](x,y)\rightarrow(1,2)[/tex]

Step-by-step explanation:

Multiply first equation by 3 to help cancel out the "y" variable:

[tex]\displaystyle \left \{ {{x+y=3} \atop {x-3y=-5}} \right.\\\\\rightarrow \left \{ {{3x+3y=9} \atop {x-3y=-5}} \right.[/tex]

Combine system of equations on both sides:

[tex](3x+3y)+(x-3y)=9+(-5)\\4x=9-5\\4x=4\\x=1[/tex]

Thus,

[tex]x+y=3\\1+y=3\\y=2[/tex]