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We want to find an equation and the sixth term of the given geometric sequence.

The equation is: [tex]a_{n} = 4*a_{n}-1[/tex] and the sixth term is equal to 512

In a geometric sequence, each term is a constant times the previous term, so the general relation is:

[tex]a_{n} = k*a_{n}-1[/tex]

Here we can use any pair of consecutive terms to find the value of the constant, for example, if we use the first two, we have:

[tex]8 = k*2\\8/2 = 4 = k[/tex]

Now we know the value of the constant, then the general formula is: [tex]a_{n} = 4*a_{n}-1[/tex]

Now we can use this to get the sixth term:

[tex]a_{6} = 4*a_{5}-1=4*128 = 512[/tex]

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Answer:

0.000000654 kg

Step-by-step explanation:

Answer:

120

Step-by-step explanation:

3/5 of 200 = 120

Answer: Okay this is the formula for slope: y=mx+b 2 would be the slope and -1 would be the y intercept so select b.

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

90 - 50 = 40

40/8 = 5

Answer:

[tex](15 + 2x)(20 + 2x)[/tex]

Step-by-step explanation:

Given

[tex]Length= 15[/tex]

[tex]Width = 20[/tex]

[tex]Deck = x[/tex] --- on both sides

Required

An expression for total area of the pool

Because the deck will be on both sides,

the dimension of the pool will be:

[tex]L = Length + 2 * deck[/tex] --- Length

[tex]L = 15 + 2x[/tex]

[tex]W = Width + 2 * deck[/tex] --- Width

[tex]W = 20 + 2x[/tex]

The total area of the pool is calculated as:

[tex]Area = Length * Width[/tex]

[tex]A = (15 + 2x) * (20 + 2x)[/tex]

[tex]A =(15 + 2x)(20 + 2x)[/tex]

Hence, the expression is: [tex](15 + 2x)(20 + 2x)[/tex]

Answer:

1.25 meters

HOPE THIS HELPS

-Todo ❤️

Step-by-step explanation:

.5*2.5=1.25

Answer:

72

Step-by-step explanation:

Ratio:2:3=2x:3x

2x+3x=180

5x=180

x=36

m ABD=36x2=72

If it cost them $125 to rent a booth at the farmers market, then their profit will be $2816 - $125 = $2691.

Top Choice Ponce farm wants to set up a booth at a farmers market next weekend, they promise to sell their pistachios at 20% cheaper than the next cheapest farm. They plan to sell 3520 ounces of pistachios at $0.8 per ounce.

The booth rent cost them $125. To calculate the profit, they will subtract the booth cost from the total revenue of pistachios which is $2816. Therefore, their profit will be $2691. They will make this profit after paying for the Farmers Market booth.

If Top Choice Farm's pistachios are 20% cheaper than the next cheapest farm, and the next cheapest farm's pistachios cost $1 per ounce, then Top Choice Farm's pistachios will cost $1 - $1 × 20% = $0.80 per ounce.

If they sell 3520 ounces of pistachios at $0.80 per ounce, then their total revenue from pistachios will be 3520 × 0.8 = $2816

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Answer:

C 82

Step-by-step explanation:

18^(2)+80^(2)=c^(2)

Answer:

4.1667

Your welcome!

The measure of angle B is 107°.

What do similar triangles mean?

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable. Similar figures are described as items with the same shape but varying sizes, such as two or more figures.

Given a triangle, NPZ is similar to triangle HBZ.

Which can also be written as ΔNPZ ≈ ΔHBZ

So, by equating the corresponding angles that are angle P = angle B:

8x-37°=180-(2x-5+42)°

10x=180

x=18°

So, H=36-5=31°

Since the sum of all angles in a triangle is 180°, angle B can be calculated  as

B= 180°-(42+31)°

B=107°

Therefore the measure of angle B is 107 degrees

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Therefore , the solution of the given problem of tractable problem comes out be it is the most frequently encountered problem that has been discovered to be insoluble.

a process that completes a manageable task in a polynomial amount of time. The polynomial upper bound is used. If an issue cannot be resolved in a polynomial amount of time, it is referred to as being intractable. The bound's minimum is exponential.

Here,

There is no programme that can resolve the halting difficulty for sufficiently general computer programs,

making it the most frequently encountered problem that has been discovered to be insoluble.

The type of computer software we're discussing must be made clear.

Therefore , the solution of the given problem of tractable problem comes out be it is the most frequently encountered problem that has been discovered to be insoluble.

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the GPA for the current semester will be 3.5.

What is GPA?

A metric used to assess your performance throughout the course of your complete degree program is your grade point average.

The average grade point average (GPA) is a figure that represents your typical performance in classes over the course of a semester, term, or year. In line with how much you raise your overall grade point average over your time at the university, your typical GPA score will fluctuate (or, in some cases, how much you fall behind).

A pass grade is a P, an A is a grade of excellent performance worth 4 points per credit, and a B is a grade of good performance worth 3 points per credit. The grade averages do not take P grade into account.

MAT 003, CHM 131a, and ACA 122 each have three, one, and two credits. Thus, the final score is 3 + 1 + 1 = 5. P in MAT 003, B in CHM 131a, and A in ACA 122 are the grades she receives.

GPA can be calculated by

GPA = (  3 × 1 + 4 × 1)/ 5

GPA = ( 3 + 4)/ 5

GPA = 3.5

Hence the GPA for the current semester will be 3.5.

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[tex]-7x < 35[/tex]

Divide both sides by -7:

[tex]\dfrac{-7x}{-7} < \dfrac{35}{-7}[/tex]

Since we are dividing by a negative number, the sign will reverse.

[tex]\fbox{x} > \fbox{-5}[/tex]

The solution to the given inequality is x > -5 which represents a set of all real numbers x that are greater than -5.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

The inequality is given in the question, as follows:

-7x < 35

To solve the inequality -7x < 35, we first need to isolate the variable (x) on one side of the inequality.

We will divide both sides of the inequality by -7 (since -7 is being multiplied by x on the left side).

However, when we divide or multiply both sides of an inequality by a negative number, we must reverse the inequality symbol. So the inequality becomes:

x > -5

This inequality can be read as "x is greater than -5." It is the solution set of all real numbers x that is greater than -5.

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The equation for the side of the line that contains the first two vertices' opposite side is 3x+y=12

Given that,

Three of a parallelogram's vertices have the coordinates (-3, 4), (-2, 1), and (2, 6).

We have to find what is the equation for the side of the line that contains the first two vertices' opposite side.

We know that,

The equation of the line is

y=mx+b

Here, we find m and d

Take the points (-3,4) (-2,1)

m = y₂-y₁ / x₂-x₁

m = 1 - 4 / -2-(-3)

m = -3 / 1

m = -3

Now take point (2,6)

6 = -3(2) + b

6 = -6 + b

6 + 6 = b

12 = b

We get m =-3 and b=12

The equation will be y=-3x+12

3x+y=12

Therefore, the equation for the side of the line that contains the first two vertices' opposite side is 3x+y=12

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The vertex of V' had a preimage of V(0, 3) as V' has a dilation of 3.

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

Given, On a coordinate plane, polygon S'T'U'V' has points (- 2, 4), (- 4, 1),

(- 2, - 2), and (0, 1) with a dilation rule  DO,1/3 (x, y) to [(1/3)x, (1/3)y].

Therefore, The coordinates of the vertex V had a preimage of,

3(V'), which is 3(0, 1) = (0, 3).

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The 7th term of the geometric sequence is 3675/64.

A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a constant called the common ratio.

The 7th term of a geometric sequence can be found using the formula:

a_n = a_1 * (r)^(n-1) where a_1 is the first term of the sequence, r is the common ratio, and n is the position of the term in the sequence.

Given that the common ratio is 3/2 and the first term is 5, we can substitute these values into the formula:

a_7 = 5 * (3/2)^(7-1)

After solving the expression we get:

a_7 = 5 * (3/2)^6 = 5* (243/64) = 15*243/64 = 3675/64

So the 7th term of the geometric sequence is 3675/64.

Therefore, the 7th term of the geometric sequence is 3675/64.

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When there are 10 identically sized parking spaces in each row of the grocery store parking lot, the solution is 3.192 width.

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal." The three main types of linear equations are the slope-intercept form, standard form, and point-slope form. An equals sign is a part of a mathematical expression referred to as an equation. A lot of equations include algebra. In math, algebra is employed when you don't know the precise amount to calculate.

given

The grocery store is 31.92 wide overall, with 10 equally wide parking spaces.

If you assume that the width of these 10 parking spaces is equal to the width of the grocery store as a whole, you will have:

10x=31.92

on both sides of the equation, multiply by 10.

10x/10 = 31.92/10

x = 3.192

When there are 10 identically sized parking spaces in each row of the grocery store parking lot, the solution is 3.192 width.

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Answer:

17.3 miles / gallon

Step-by-step explanation:

Rates can be represented in different forms, such as speed (meters per second) or water flow rate (liters per minute or second)

Given information from the question,

2 gallons = 34.6 miles

1 gallon = 34.6 ÷ 2 = 17.3 miles / gallon

1. The area of two concentric circles with radii 28 cm and 18 cm is 460π cm^2.

2. If the perimeter and the area of the circle are numerically equal then find the radius of the circle is 2 units.

What are concentric circles?

Concentric circles are those that share a common centre but have differing radii. It is described as two or more circles with the same centre, in other words.

The radii of two concentric circles are 28 cm and 18 cm.

The bigger circle has a radius of r1=28 cm and the smaller circle has the radius of r2=18 cm.

Area of two concentric circles is -

A = π[(r1)^2-(r2)^2]

A = π[(28)^2-(18)^2]

A = π[(28+18)(28-18)]

A = π[46 × 10]

A = 460π cm^2

Therefore, the area of concentric circle is 460π cm^2.

The formula for perimeter of the circle is 2πr, and the formula for the area of the circle is πr^2, where r is the radius of the circle.

Now, according to the data given the perimeter and area of the two circles are equal.

So, the equation will be 2πr = πr^2.

2πr = πr^2

2π = πr

r = 2 units

Therefore, the radius is 2 units.

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1. If radii of two concentric circle are 28 cm and 18 cm respectively. Find the area of the concentric circles.

2. If the perimeter and the area of the circle are numerically equal then find the radius of the circle​.

Answer:

12%

Step-by-step explanation:

Answer:

The location would be between 4 and 5.

Step-by-step explanation:

The square root of 19 would be around 4.3. So you would put a mark between the two lines that are in between the 4 and 5.

The slope of a line is a measure of its steepness and can be calculated using the formula:

slope = (y2 - y1) / (x2 - x1)

In this case, the points (0,3) and (36,0) represent the coordinates of two points on the ramp. To find the slope of the ramp, we can plug these values into the formula:

slope = (0 - 3) / (36 - 0) = -3 / 36 = -1/12

The slope of the ramp is -1/12. This indicates that the ramp is relatively flat, as a negative slope means that the line is sloping downward.

To find the slope of the second ramp, represented by the function g(x) = -1/4x + 2, we can take the derivative of the function. The derivative of a function represents the slope of the function at any given point, and it is calculated using the formula:

derivative = f(x) = -1/4

The derivative of the function g(x) is a constant value of -1/4, which means that the slope of the second ramp is also -1/4. This is a steeper slope than the first ramp, as the value of the derivative is larger in magnitude.

Answer:

A=16.3 ft²

Step-by-step explanation:

we are given a composite figure, composing of a triangle and a semicircle

first, let's find the area of the triangle

we are given the height (5 ft) and the base of the triangle (4 ft)

the formula for the area of the triangle is given as bh/2, where b is the base and h is the height

substitute the known values into the formula

[tex]A_{triangle}[/tex]=bh/2

[tex]A_{triangle}[/tex]=(5*4)/2

[tex]A_{triangle}[/tex]=20/2=10 ft²

so the area of the triangle is 10 ft²

now to find the area of the semicircle:

the area of a semicircle is half the area of a circle; the area of a circle is given as πr², where r is the radius. Therefore, the area of a semicircle is (πr²)/2

4 ft isn't just the base of the triangle; it's also the diameter of the semicircle

however, we need the radius

the radius is half the diameter value

r=d/2

r=4/2

r=2 ft

so the radius is 4 feet

now find the area of the semicircle. Don't substitute for π just yet.

[tex]A_{semicircle}[/tex]=(πr²)/2

[tex]A_{semicircle}[/tex]=(π*2²)/2

[tex]A_{semicircle}[/tex]=4π/2

[tex]A_{semicircle}[/tex]=2π

π is often substituted as 3.14 or 22/7

so if we used 3.14 for instance:

[tex]A_{semicircle}[/tex]=6.28; rounded to the nearest tenth, that's 6.3 ft²

now add the two areas together to get the area of the composite figure

[tex]A_{compositefigure}[/tex]=[tex]A_{triangle}[/tex]+[tex]A_{semicircle}[/tex]

[tex]A_{compositefigure}[/tex]=10+6.3=16.3 ft²

Hope this helps! Good luck on your assignment!!

Each person present in Mrs. Nunez's class is going to receive 1/6th part of the cake when they get it cut.

Mr. Nunez brought 2 ½ cakes for 15 people which means, 2 ½ cakes will be equally divided into 15 pieces and distributed to each person. Since 2 ½ is a mixed fraction we have to convert it into a regular fraction which will be equal to 5/2. So, the amount of cake a person will receive is equal to (5/2)/15 which is 1/6, which is roughly 0.167 part of the whole cake.

The given problem has been solved by using the properties of fractions.

The complete question that you might be looking for is-

Mrs. Nunez brought 2 1/2 cake to school for her class. If there are 15 people in the class, including Mr. Nine, how much of the cake will each person receive?

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Answer:

6x+10

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

6x + 10

Step-by-step explanation:

2(3x + 5)

Distribute the 2.

When distributing, multiply the outside term(s) by the inside term(s).

2 * 3x = 6x

2 * 5 = 10

Combine them to get

6x + 10.

The sprinkler should be set to rotate through  the angle 6.42 degrees.

What is an angle?

Two lines intersect at a location, creating an angle. An "angle" is the term used to describe the width of the "opening" between these two rays. Angles are used in the design of buildings, roadways, and sports venues by engineers and architects.

r =  50 yards

Area, A = 140 square yards

Θ = angle

A= (Θ /360) πr²

140 = (Θ /360) * 3.14 * 50*50

Θ = (140*360)/(3.14*25*100) = 6.42 degrees

The sprinkler should be set to rotate through  the angle 6.42 degrees.

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