Find the next three terms in each geometric sequence. 54, 162, 486, ...

Answer:

h = 9.9

b = 4.6

Step-by-step explanation:

The first triangle is an isosceles right triangle
The base leg = vertical leg = 7

diagonal = 7√2 = 9.9  (rounded to nearest tenth)

h = 9.9

For the 30-60-90 triangle
if the vertical leg is x, the base leg = vertical leg / √3 = 8/√3 = 4.6

b = 4.6

The total amount of yards are 4(1/8).

To find the total amount of fabric Tanya used, we need to add the amount of fabric she used for the dress and the amount of fabric she used for the jacket.

Tanya used 3(3/8) yards of fabric for the dress and 1(1/3) yards of fabric for the jacket. We can add these two amounts by finding a common denominator for the fractions and adding the whole numbers:

3(3/8) + 1(1/3) = 3(9/24) + 1(8/24)

=> 3(17/24)

Therefore, Tanya used a total of 3(17/24) yards of fabric. This can be simplified to:

=> 3(17/24) = 4(1/8)

So the answer is A. 4(1/8).

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Area is calculated using length measurements, specifically measurements of two dimensions of a flat or planar shape, such as length and width. The resulting value represents the amount of space occupied by the shape on a flat surface.

Area is commonly measured in square units such as square metres ([tex]m^{2}[/tex]), square feet ([tex]ft^{2}[/tex]), square inches ([tex]in^{2}[/tex]), and so on.

To calculate the area of a flat shape, multiply its length and width by the appropriate unit of measurement.

Area = Length x Width

Similarly, to find the area of a circular surface, we would use the formula for the area of a circle:

Area = π x (Radius)^2

[tex]Area = \pi . (r)^2[/tex]

where π is the mathematical constant pi, and the radius is half the diameter:

So, area is a measure of the amount of space occupied by a flat or planar shape and is calculated using length measurements.

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Exponents laws are

[tex]a^n . a^m = a^{n + m}[/tex]

[tex]a^n / a^m[/tex] = [tex]a^{n - m}[/tex]

Exponent laws are important to use because they will help us to simplify complex expressions easier.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Exponents are written in the form [tex]a^n[/tex]

Where n can be any real numbers.

Now,

a = 2

For n = 0, 1, 2, 3, -1, -2, -3

We get,

[tex]2^0[/tex] = 1

2² =  2 x 2 = 4

2³ = 2 x 2 x 2 = 8

[tex]2^{-1}[/tex] = 1/2

[tex]2^{-2}[/tex]  = 1/(2 x 2) = 1/4

[tex]2^{-3}[/tex] = 1/(2 x 2 x 2) = 1/8

Exponents laws are:

[tex]a^n . a^m = a^{n + m}[/tex]

[tex]a^n / a^m[/tex] = [tex]a^{n - m}[/tex]

Thus,

Exponent laws are important to use because they will help us to simplify complex expressions easier.

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Answer:

ABCD is a kite, therefore, ΔAEC is a right Δ

Step-by-step explanation:

Look at ΔABD and ΔACD, they both have the same side AD, AB = AC while BD = CD. Therefore ΔABD and ΔACD are congruent or basically the same triangle.

Both ΔABD and ΔACD will form a quadrilateral, which can be called a kite.

Definition: A kite is a quadrilateral with two pairs of adjacent sides, congruent.

Therefore, a kite has perpendicular diagonals, where one bisects the other.

So AD is perpendicular to BC

so the angles AEC, ABD, DEC, DEB are all right angles.

Hope this helps.

The vertex form of a quadratic function is given by:

f(x) = a(x - h)^2 + k

where (h, k) is the vertex of the parabola.

Since the graph of f(x) = x^2 was translated 6 units to the left to create the graph of g, the vertex of g is at the point (h - 6, k).

The vertex of f(x) = x^2 is at (0, 0), so the vertex of g is at (-6, 0).

Since the vertex is at (-6, 0), the equation of g in vertex form is:

g(x) = a(x + 6)^2 + 0

We can find the value of "a" by using another point on the parabola. For example, if we know that g(-3) = 9, then we can substitute these values into the equation and solve for "a":

9 = a(-3 + 6)^2

9 = 9a

a = 1

So the equation of g in vertex form is:

g(x) = (x + 6)^2

Therefore, the value of the car after three years is approximately $9,484.

Percent is a term used to represent a fraction of 100. It is denoted by the symbol "%". Percentages are commonly used to express proportions, ratios or fractions in terms of parts per hundred. The word "percent" comes from the Latin phrase "per centum," which means "by the hundred." Percentages are commonly used in everyday life, such as in calculating taxes, discounts, interest rates, and in comparing statistics, among others.

Here,

The exponential decay model for the value of the car after ⁿ years can be written as:

v = 22500 * (0.75)ⁿ

where 22500 is the initial value of the car, and (0.75)ⁿ represents the value after ⁿ years with a 25% annual decrease.

To find the value of the car after three years, we can substitute n = 3 into the equation:

v = 22500 * (0.75)³

v = 22500 * 0.421875

v = 9484.375

Rounding this to the nearest dollar amount, we get:

v ≈ $9,484

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The solution set for this equation is {4}, since 4 is the only value that makes the equation true.

You have done a great job of explaining how to check if the numbers 3 and 2 are part of the solution set for the equation 13 = 2x + 5. You correctly substituted each number in for x and simplified the equation to see if it was true or false. You found that both numbers resulted in a false equation, so they are not part of the solution set.

One thing to note is that the solution set for an equation is the set of all values that make the equation true. So, in order to find the solution set for this equation, you would need to solve for x. Here is how you would do that:

13 = 2x + 5

Subtract 5 from both sides of the equation:

8 = 2x

Divide both sides of the equation by 2:

4 = x

So, the solution set for this equation is {4}, since 4 is the only value that makes the equation true.

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The volume of a cylinder with a diameter of 34 m and a height of 27 m is 24501.42 m³.

A cylinder is a three-dimensional figure that has a rectangular body but is rolled up which gives it a round shape with two circles for its top and bottom. We see a lot of cylinders around us all the time.

Here, we have been told that the diameter of the cylinder is 34 which means that the radius is 34/2 = 17 m.

Furthermore, we have also been told that the height of the cylinder is 27 m.

We already know that the volume of a cylinder can be calculated using

= πr²h

Using the values, we get -

= 3.14 * 17 * 17 * 27

= 24501.42 m³.

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The value of the equation f(x)=-3x+5 at f(-2) is 11.

An equal sign ("=") links two expressions together to form an equation. The two expressions on either side of the equals sign are referred to as the "left-hand side" and "right-hand side" of the equation. The right side of an equation is typically assumed to be zero. As we can balance this by deducting the expression on the right from the expressions on both sides, this won't reduce the generality.

The given equation is f(x)=-3x+5.

Substitute the value of x = -2 in the equation to find f(-2).

f(x)=-3x+5

f(-2) = -3(-2) + 5

f(-2) = 6 + 5

f(-2) = 11

Hence, the value of the equation f(x)=-3x+5 at f(-2) is 11.

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The angle of polygons is an important concept in geometry and can be calculated using the formula (n-2) x 180. Quadrilaterals are a specific type of polygon with four sides and four angles, and their interior angles can be found by dividing the sum of the interior angles by the number of sides.

The angle of polygons is an important concept in geometry. A polygon is a closed shape with three or more sides, and the angles of a polygon are the interior angles formed by the sides. Quadrilaterals are a specific type of polygon with four sides and four angles.

To find the sum of the interior angles of a polygon, you can use the formula (n-2) x 180, where n is the number of sides. For example, a quadrilateral has four sides, so the sum of its interior angles would be (4-2) x 180 = 360 degrees.

Each individual angle of a quadrilateral can be found by dividing the sum of the interior angles by the number of sides. So for a quadrilateral, each angle would be 360/4 = 90 degrees.

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The equation that the graph of the systems of equations solve is:

x^2 - 2x + 3 = 2x^2 - 4x + 3

This is the second equation listed.

The conversion mass value of the kilograms to pounds is given by

( 103.635 ) pounds.

Standard formula which relates these two quantities of mass are represented as :

One kilogram is equal to 2.205 pounds

After substituting the standard relation between the kilograms and the pounds we get the required value,

1 kilogram = 2.205 pounds

⇒ 47 kilograms = ( 47 ) × ( 2.205 ) pounds

⇒ 47 kilograms = ( 103.635 ) pounds

Therefore, the converted value of 47 kilograms into the pounds is written as  ( 103.635 ) pounds.

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Answer:  the awnser is 43

Step-by-step explanation:

Answer:

30 X 4=yhhvvihddthjgyujjnbbbvvvukgdddsxgjooi

The given integral is solved by using integration by parts. And the required answer for the integral of x lnx is [tex]\int x\ln (x) \;dx=\frac{1}{2}x^2\ln x-\frac{1}{4}x^2+C[/tex].

Integration by parts is a special method that is used when we have to integrate the product of two functions. This method is also called the product rule for integration. Using this method, we consider the integral of x ln x as the product of two functions such as x and ln x. This is solved by using the formula, [tex]\int u\;dv = uv- \int v\;du[/tex].

Let's take u = ln x, dv = x dx, [tex]v=\frac{1}{2}x^2[/tex], [tex]du =\frac{1}{x}dx[/tex]. Then,

[tex]\begin{aligned}\int u\;dv &= uv- \int v\;du\\\int \ln x \cdot xdx&=\ln x\times \frac{x^2}{2}-\int \frac{x^2}{2}\times\frac{1}{x}dx\\&=\frac{1}{2}x^2\ln x-\frac{1}{2}\int xdx\\&=\frac{1}{2}x^2\ln x-\left[\frac{1}{2}\times\frac{1}{2}x^2\right]+C\\&=\frac{1}{2}x^2\ln x-\frac{1}{4}x^2+C\end{aligned}[/tex]

The required answer is [tex]\int x\ln (x) \;dx=\frac{1}{2}x^2\ln x-\frac{1}{4}x^2+C[/tex].

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The price for 5 pounds of honey is $13.32.

Unitary method is a mathematical technique used to solve problems related to proportions and ratios.

To find the price for 5 pounds of honey, we can use a proportion:

Price of 3 pounds of honey / 3 = Price of 1 pound of honey

We can use this equation to find the price of 1 pound of honey, and then multiply by 5 to find the price of 5 pounds of honey.

Price of 3 pounds of honey / 3 = 7.99 / 3

Price of 1 pound of honey = 2.6633 (rounded to 4 decimal places)

Price of 5 pounds of honey = 2.6633 x 5 = $13.32 (rounded to 2 decimal places)

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Answer:

Below

Step-by-step explanation:

Volume of a cone = 1/3  pi  r^2 h

      4125 pi             = 1/3 pi r^2 h

                       4125  = 1/3 r^2 h  <===if diameter =30  then radius = 15 units

                         4125 = 1/3 (15)^2 h

                            4125 / (1/3 * 15^2) = h = 55 units

The fraction of the value given as 125% can be expressed by the term of  125% = 5/4.

A ratio in which the total value is always 100 is a ratio, and a percentage is a portion of that ratio.

To represent a portion of a whole, we utilise fractions. Now, we must translate a percentage to a fraction.

Use the instructions below to convert 125% to a fraction:

First, add the percent sign.

Divide the supplied percentage by 100 to express it as a fraction.

As a result, we can write as 125/100.

To simplify the fraction, divide the numerator and denominator by their respective HCFs.

Now, 125 percent can be expressed as 125/100.

When the given fraction is simplified, we obtain

[Dividing the numerator and denominator by their HCF, which is 25]: 125/100 = 5/ 4

Hence, the fraction of 125% is 5/4.

Using a percent to fraction calculator is another way to confirm.

Hence, the fraction of 125% is 5/4.

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For the defined function  f(t)=e^rt and g(t)=e^st where r is not equal to s it was proved that the f and g are linearly independent function in F(r,r).

For the defined function f and g we have,

f(t)=e^rt

g(t)=e^st

Where r is not equal to s.

To prove f and g are linearly independent function we need,

f( t) ± g(t) = 0

Substitute the value of f(t) and g(t) we get,

⇒ e^rt ± e^st  = 0

⇒ e^rt ( 1 ± e^( s - r )t = 0

This implies ,

e^rt = 0 or ( 1 ± e^( s - r )t = 0

But e^rt is always greater than zero for all the values of r and t.

e^rt = 0 is not possible.

If ( 1 ± e^( s - r )t = 0

This is possible if and only if r = s .

Which is against the given condition.

Therefore, f(t) and g(t) are linearly independent function in f( r , r).

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The above question is incomplete, the complete question is:

Let f, g, element F(r,r) be the function defined by f(t)=e^rt and g(t)=e^st, where r cannot equal s. prove that f and g are linearly independent in F(r,r).

Answer:

Step-by-step explanation:

5 seconds later acceleration of the car is 6m/h^2

We know that the initial velocity of a car is 50 mph.

In the end, the final velocity of a car is 80 mph.

The time difference is 5 seconds.

For the calculation of the acceleration, we have this formula,

α = δv/t

so here, according to our data, velocity and time are,

u = 50 mph

v = 80 mph

t = 5 s

Finally, the acceleration of the car can be calculated by,

α = (80 - 50) / 5

α = 30 / 5

α = 6 m/h^2

From the above calculations, the car's acceleration is 6 m/h^2.

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The value of millimeter in inches can be calculated by simply dividing the millimeter by 25.4 so 125 mm is 4.921 inches.

Unit conversion is the process of converting the measurement of a given amount between various units, often by multiplicative conversion factors that alter the value of the measured quantity without altering its effects.

Converting from millimetres to inches

Between millimetres (mm) and inches (in)

Calculation of Inches (dec) in Inches (frac) in Feet plus Inches ft mm to inches

* The value is rounded to the nearest 1/64 fraction for the inches fraction.

How to change metric units to inches

Inches are equal to 0.03937007874 millimetres in length:

1mm = (1/25.4)″ = 0.03937007874″

The distance d in millimetres (mm) divided by 25.4 gives the distance d in inches (′′):

d(″) = d(mm) / 25.4

Example of 20 mm converted to inches:

d(″) = 125mm / 25.4 = 4.92126″

How many millimetres are in one inch

0.03937 inches are equal to one millimetre:

1mm is equal to 1mm / 25.4mm/in = 0.03937in.

What is the millimetre to inch conversion

25.4 millimetres make up one inch.

1 inch Equals 25.4 millimetres per inch.

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Equation for 6 halves of pears is 1/2 x 6 = 3

The factor of a number is a number that divides the given number completely without any remainder. The factors of a number can be positive or negative.

Every factor is divisor of that number but every divisor is not a factor of that number.

Given, in the picture,

half of 6 pears

One half of pear can be denoted as = 1/2

Now,

equation of 6 half pears.

= 1/2 x 6

= 4

Hence, equation for 6 half pears can be written as 1/2 × 6 = 3.

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A regression line is defined as an estimate of the line that describes the actual line, which is unknown. It represents a linear relationship between the two variables, that is the dependent and the independent variable.

In other words, the equation of the regression line is used to estimate the value of the dependent variable from a specified value of the independent variable.

Correlation coefficient is used to determine the strength of linear association between two variables, that is the dependent and the independent variable. (Correlation shows what kind of relation two variables have.)

Regression line's important use is to make predictions about the values of y for a given x-value.

Hence option a is correct.

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August is the eighth month of the year. Depending on the region and culture, August is known for a variety of historical and cultural events, as well as natural occurrences.

August is noted in the United States for National Women's Equality Day (August 26th), which honors the enactment of the 19th Amendment to the United States Constitution, which granted women the right to vote.

The Perseid meteor shower, which happens yearly between late July and late August and is visible from many parts of the world, is also celebrated in August.

August is connected with the harvest season in several cultures and is commemorated with numerous festivals and rituals.

August is also a popular month for vacations and travel, particularly in the Northern Hemisphere, where it corresponds with the summer season.

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Answer:

x = 14°

z = 74°

Step-by-step explanation:

10x - 34° = 106° ( A.I.A )

x = 72°

106° + z = 180° ( linear pair axiom )

z = 74°

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Answer:

x=14°

z= 74°

Step-by-step explanation:

Here

(10x-34)°= 106°

since the Vertically Opposite Angle are equal.

so solving for it.

First, we can add 34° to both sides of the equation to get:

10x° - 34°+ 34° = 106° + 34°

Simplifying the left side gives:

10x° = 140°

Then we can divide both sides of the equation by 10 to get:

x = 14°

Again

z+106°=180°

since the sum of angle in the linear pair is equal to 180°

solving for it

we can subtract 106° from both sides of the equation to get:

z + 106° - 106° = 180° - 106°

Simplifying the left side gives:

z = 74°

Answer:

+x+=+3+

+y+=+-.9%2A%28+3+%2B+3+%29%2A%28+3+-+3+%29+

+y+=+-.9%2A6%2A0+

+y+=+0+

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

The distance between ( -3, 0 ) and ( 3, 0 )

is +3+-%28-3%29+=+6+

The width of the arch at ground level is 6 ft

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

Here's the plot of the equation:

Step-by-step explanation:

The dimensions square must be cut if the volume of the box is to be 189 cubic inches is  9 * 7 * 3.

The mathematical concept of volume represents the amount of three-dimensional space that an object or closed surface takes up. Volume is measured in cubic units like m³, cm³, in³, etc.

The dimension of the box will be:

= L * W* H

=(15-2x)*(13-2x)*x

The volume:

x(15-2x)*(13-2x) = 189

x(195 - 56x + 4x²) = 189

4x³ - 56x² + 195x - 189 = 0

Hopefully it's an integer, we know it's a low value

Try x=3 using synthetic division

we get ,  3 as the solution or or root of the equation.

Check x = 3, the side of the cut out squares

(15-6)(13-6)  3 = 189

9 * 7 * 3 = 189 cu/in

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According to the Empirical Rule, approximately 68% of the data in a normal distribution will fall within ±1 standard deviation of the mean. The correct option is (d) 68%

The Empirical Rule is a statistical rule of thumb that describes the approximate proportions of data that fall within a certain number of standard deviations from the mean in a normal distribution.

The Empirical Rule states that for a normal distribution:

About 68% of the data will fall within 1 standard deviation of the mean

About 95% of the data will fall within 2 standard deviations of the mean

About 99.7% of the data will fall within 3 standard deviations of the mean

Therefore, option (b) 68 is the correct answer.

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The weighted average of the given numbers 1 and 6 is 2.

What is a weighted average?

A weighted average is the average of a set of integers with different associated "weights" or values. The weighted average can be calculated by multiplying each value by its weight, then adding the results.

We are given two numbers as 1 and 6.

The formula of weighted average is as follows

Weighted average = (first number x weight of first number) + (second number x weight of second number)

We are given weights as four-fifths on the first number and one-fifth on the second number.

So,

⇒Weighted average = (1 x 4/5) + (6 x 1/5)

⇒Weighted average = 4/5 + 6/5

⇒Weighted average = 10/5

⇒Weighted average = 2

Hence, the weighted average of the given numbers 1 and 6 is 2.

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