Find the 8th term of the geometric sequence with the first term 2 and common ratio -3.

The solutions to the quadratic equation 3y(-2y+x)-5y(-7x+y) are y = -16x + 32x√2 and y = -16x - 32x√2

To solve the quadratic equation 3y(-2y+x)-5y(-7x+y), we first need to simplify it by distributing the terms inside the parentheses:

3y(-2y+x) = -6y² + 3xy

-5y(-7x+y) = 35xy - 5y²

Next, we can substitute these expressions back into the original equation and simplify it further:

3y(-2y+x)-5y(-7x+y) = (-6y² + 3xy) - (35xy - 5y²) = -6y² + 3xy - 35xy + 5y² = -y² - 32xy

Now, we have simplified the quadratic equation to the standard form of ax² + bx + c = 0, where a = -1, b = -32x, and c = 0. To solve for y, we can use the quadratic formula:

y = (-b ± √(b² - 4ac)) / 2a

Plugging in the values for a, b, and c, we get:

y = (-(-32x) ± √((-32x)² - 4(-1)(0))) / 2(-1) = (32x ± √(1024x²)) / (-2)

Simplifying further, we get:

y = -16x ± 32x√2

In conclusion, we can simplify the given quadratic equation by distributing the terms inside the parentheses, and then rearrange it to the standard form ax² + bx + c = 0. We can then use the quadratic formula to solve for y, and simplify the solutions.

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The value of k is given as follows:

k = 10.

The quadratic function in the context of this problem is defined as follows:

y = 3x² - 8x + 2k + 1.

The coefficients are given as follows:

a = 3, b = -8 and c = 2k + 1.

The product of the roots of  quadratic function is given as follows:

c/a.

For this problem, the product is of 7, hence the value of k is obtained as follows:

(2k + 1)/3 = 7

2k + 1 = 21

2k = 20

k = 10.

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Answer:

no not satisacl

Step-by-step explanation:

Answer:

Step-by-step explanation:

4

Answer:v-14=42

Step-by-step explanation: Since Vidya’s age is v and when it is decreased by 14, v-14=42

Answer:

Step-by-step explanation:

D 48 cubic ft

The surface area of the composite figure is 4364 sq. m.

A composite figure that consists of more than one shape. Thereby it is formed by joining two or more shapes.

In the given composite figure, we have;

i. area of one triangular surface = 1/2 x base x height

                                    = 1/2 x 25x13

                                    = 162.5

area of one of its triangular surfaces is 162.5 sq. m.

ii. area of rectangular surface 1 = length x width

                                           = 27 x 18

                                           = 486 sq. m.

iii. area of rectangular surface 2 = length x width

                               = 27 x 23

                                            = 621 sq. m.

iv. area of rectangular surface 3 = length x width

                                                     = 25 x 23

                                                     = 575 sq. m.

v. area of its base = length x width

                             = 27 x 25

                                              = 675 sq. m.

surface area of the composite figure = (2*162.5) + (2*486) + (2*621) + (2*575) + 675

                          = 4364

The surface area of the composite figure is 4364 sq. m.

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Answer:

the surface area of the cylinder is about 452.2 square centimeters.

Step-by-step explanation:

To find the surface area of a cylinder, you need to use the formula: A=2πr2+2πrh where A is the surface area, r is the radius of the circular base, and h is the height of the cylinder In this case, you are given the diameter of the base as 12 cm, so you need to divide it by 2 to get the radius: r=212​=6 cm

You are also given the height of the cylinder as 6 cm.

Plugging these values into the formula, you get: A=2π(6)2+2π(6)(6)

Simplifying, you get: A=72π+72π

Adding, you get: A=144π cm2

Using a calculator, you can approximate π as 3.14 and get: A≈452.16 cm2

Rounding to the nearest tenth, you get: A≈452.2 cm2

Emily will get a $1,040 annual pension payout from her former employer's pension plan.

Emily is not fully vested in the pension plan because she left her work after four years. She is vested in 20% of the pension plan under the graded 5-year vesting schedule.

We can use the following formula to compute Emily's annual pension:

Annual pension = (final average income) x (service years) x (2% multiplier)

Emily's final average income in this scenario was $65,000, and she worked for 4 years. As a result, her annual pension would be:

Annual pension = ($65,000) multiplied by (4 years) multiplied by 2%

Pension = $5,200 per year

Emily, on the other hand, is only vested in 20% of her pension plan because she quit her work before the entire 5-year vesting term. As a result, her real pension payment will be:

Annual pension = ($65,000) multiplied by (4 years) multiplied by 2%

Pension = $5,200 per year

Emily, on the other hand, is only vested in 20% of her pension plan because she quit her work before the entire 5-year vesting term. As a result, her real pension payment will be:

(vested percentage) x (annual pension) equals pension payment

(20% of $5,200) equals pension payout

$1,040 in pension payments

As a result, Emily will get a $1,040 annual pension payout from her former employer's pension plan.

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The angles and percentages have been calculated as shown below.

A pie chart for the information about the different make of cars is shown below.

For the total number of car makes, we have the following:

Total make of cars = 12 + 8 + 8 + 2 + 10

Total make of cars = 40.

Next, we would determine the angles and percentage as follows;

Toyota

12/40 × 360 = 108°

12/40 × 100 = 30%.

Nissan

8/40 × 360 = 72°

8/40 × 100 = 20%.

Datsun

8/40 × 360 = 72°

8/40 × 100 = 20%.

Volvo

2/40 × 360 = 18°

2/40 × 100 = 5%.

Peugeot

10/40 × 360 = 90°

10/40 × 100 = 25%.

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Answer:

here

Step-by-step explanation:

Answer:

Explanation:

-5 -4 -3 -2 -1 0 1 2 3 4 5

The distance will be in the decimal form is :41.34

Consider the triangle :

Where “a” is the perpendicular,

“b” is the base,

“c” is the hypotenuse.

According to the definition, the Pythagoras Theorem formula is given as:

[tex]Hypotenuse^2 = Perpendicular^2 + Base^2[/tex]

[tex]c^2 = a^2 + b^2[/tex]

We have the points are:

15,-17 and -20, -5

To find the distance between them.

The distance of x- axis is:

15 - (-20)

= 15 + 20

= 35

The distance of y- axis is:

|17 - 5| = |-22| = 22

We can now use the Pythagorean theorem (a²+b²=c²) with our imaginary triangle:

[tex]x^2+y^2=(distance)^2[/tex]

[tex]35^2+22^2=distance^2[/tex]

[tex]1709= distance^2\\Distance = \sqrt{1709}[/tex]

In decimal form the distance would be around 41.34.

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Note that the estimated time it will take to cause hearing loss at 106 decibels is 0.0625 hours or 3 minutes, 75 seconds.

The formula used is:


Exposure Time = 8/ 2^((dBA-85)/3)

Since the decibel (dBA) given is 106


Exposure Time = 8/ 2^((106-85)/3)

= 8/2^1
= 8/ 128

= 0.0625 hours or 3 minutes, 75 seconds.

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The length of piece of fabric is 6 cm.

Since, Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

Given that, Karen was cutting out some fabric for a friend. She cut a piece that was 6 centimeters wide and had an area of 36 square cm.

Here, area of rectangular shaped fabric is Area =Length × Width

36=Length × 6

Length =6 cm

Therefore, the length of piece of fabric is 6 cm.

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The expression shows the distance between the points -2.8, 1.6 is |x-y| units

When two numbers are pointed on the number line and they are x and y, then the expression to represent the difference between those two numbers is |x-y|

Let x = -2.8 and y = 1.6

Therefore, the distance between those two points is given by;

|x-y|

= |-2.8-1.6|

= |-4.4|

= 4.4 units.

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The expression that is equivalent to [tex]5^{-10}/(5^4)(5^0)[/tex] is [tex]5^{-14[/tex].

We can simplify the expression using the rules of exponents, which state that when we divide two powers with the same base,

we can subtract their exponents, and when we multiply two powers with the same base, we can add their exponents.

Also, any number raised to the power of zero is equal to 1.

Using these rules, we have:

[tex]5^{-10} / (5^4)(5^0) \\= 5^{-10} / (5^4) \\= 5^{-10-4}\\ = 5^{-14[/tex]

Therefore, the expression that is equivalent to [tex]5^{-10}/(5^4)(5^0)[/tex] is [tex]5^{-14[/tex].

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It will take Boris approximately 4.02 years to have enough money for his project if he invests $6000 now at an annual rate of 7%, compounded quarterly.

The formula for compound interest is:

[tex]A = P(1 + \dfrac{r}{n})^{(nt)}[/tex]

where A is the future value of the investment, P is the principal amount invested, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, Boris has invested $6000 at an annual interest rate of 7%, compounded quarterly. Therefore, we have:

P = 6000

r = 0.07 (since 7% is the annual interest rate)

n = 4 (since the interest is compounded quarterly)

A = 8058

We can solve for t by rearranging the formula:

[tex]t =\dfrac{ ln(\dfrac{A}{P})} { n ln(1 + \dfrac{r}{n})}[/tex]

Substituting the values we have:

[tex]t = \dfrac{ln(\dfrac{8058}{6000}) }{ [4 ln(1 + \dfrac{0.07}{4})]}[/tex]

t ≈ 4.02 years

Therefore, it will take Boris approximately 4.02 years to have enough money for his project if he invests $6000 now at an annual rate of 7%, compounded quarterly.

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The function represented by the graph given is equivalent to -

g(x) = (x - 4)².

The function plotted represents a quadratic equation. A quadratic equation has a degree of 2. The given function is shifted to the left by 4 units. This means that the following transformation will take place on the x - coordinate of each and every point lying on the graph -

f(x, y) → f(x - 4, y)

So, we can write the function as -

g(x) = (x - 4)²

So, the function represented by the graph given is equivalent to -

g(x) = (x - 4)²

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Answer:

The area of composite shapes is the area that is covered by any composite shape. The composite shape is a shape in which some polygons are put together to form a required shape. These shapes or figures can be made up of a combination of triangles, squares, quadrilaterals, etc.

explanation:

By the following steps mentioned below, we can calculate the area of the composite shapes.

Step 1: Break the compound shape into basic shapes.

Step 2: Find the area of each and every basic shape.

Step 3: Add all the areas of basic shapes together.

Step 4: Represent the answer in square units.

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Answer: -2

Step-by-step explanation:

You can see it clearly passes through an origin consisting of -2

Answer:

Step-by-step explanation:

A -5        

By solving it as a sequence, it will take 9 years for the club to plant 54 flowers in the courtyard.

The number of years will it take for 54 flowers to grow in the courtyard is determined by solving the planting method as a sequence.

The nth term of the sequence Z is given by:

Z = a1 + (n-1)d

where Z = 54

a1 = 6

n = ?

d = d

Solving for n:

54 = 6 + (n - 1) * 6

48 = (n - 1) * 6

8 = n - 1

n = 8 + 1

n = 9

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Answer:

y + 5 = 3y - 1

2y = 6, so y = 3

4x - 2 = x + 10

3x = 12, so x = 4

Answer:

to the nearest tenth)?

First, we need to find the volume of the cylinder. Since we have the height and are trying to find the radius, we can use the formula for the volume of a cylinder:

V = πr^2h

where V is the volume, r is the radius, and h is the height.

We don't know the volume of the cylinder, but we can use the volume of the cone and the fact that the cone and cylinder share a base to find the radius. The volume of a cone is given by:

V = (1/3)πr^2h

where V is the volume, r is the radius, and h is the height.

We know that the height of the cone is 9 meters and its volume is 57 cubic meters, so we can set up an equation:

57 = (1/3)πr^2(9)

Simplifying, we get:

19 = πr^2

Dividing both sides by π and taking the square root, we get:

r ≈ 2.2

Therefore, the radius of the cylinder is about 2.2 meters (rounded to the nearest tenth).

Answer:

1/3 foot longer

Step-by-step explanation:

2/3-1/3=1/3

The sum of the first 9 terms of the arithmetic sequence is 81.

An arithmetic sequence is an ordered set of numbers that have a common difference between each consecutive term.

To calculate the sum of the first 9 terms of the arithmetic sequence, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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Answer: 44 degrees

Step-by-step explanation: 59+77+x=180

x=44

Answer: 6 ≤ x ≤ 11

Step-by-step explanation:

Let x be the number of additional outfits that can be packed in the suitcase.

The suitcase will fit at most 11 outfits, which means that x cannot be greater than 11 outfits.

On the other hand, 5 outfits have already been packed, so the number of additional outfits that can be packed is at least 6.

Therefore, the inequality that represents this situation is 6 ≤ x ≤ 11.