Consider the three arithmetic sequences. sequence i: 9, 13, 17, 21, . . . sequence ii: 117, 120, 123, 126, . . . sequence iii: 54, 61, 68, 75, . . . which lists the sequences in order from least common difference to greatest common difference?

The equation of tangent to the circle [tex]x^{2} +y^{2} =100[/tex] at the point  (-6,8) is -6x+8y=100.

Given the equation of circle [tex]x^{2} +y^{2} =100[/tex]

and point at which the tangent meets the circle is (-6,8).

A tangent to a circle is basically a line at point P with coordinates is a straight line that touches the circle at P. The tangent is perpendicular to the radius which joins the centre of circle to the point P.

Linear equation looks like y=mx+c.

Tangent to a circle of equation [tex]x^{2} +y^{2} =a^{2}[/tex] at (z,t) is:

xz+ty=[tex]a^{2}[/tex].

We have to just put the values in the formula above to get the equation of tangent to the circle [tex]x^{2} +y^{2} =100[/tex]  at (-6,8).

It will be as under:

x(-6)+y(8)=100

-6x+8y=100

Hence the equation of tangent to the circle at the point  (-6,8) is -6x+8y=100.

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Answer:

16

Step-by-step explanation:

6/3 = 2 postcards per day

2x8 = 16 postcards

The greatest common factor−5k2 20k − 30 is  [tex]-5(k^{2} -4k-6).[/tex]

To find the greatest common factor:

−5k2 20k − 30.

Factor the expression:   [tex]5(-k^{2} +4k-6)[/tex]

Factor the expression:   [tex]5(-k^{2} -4k+6)[/tex]

Multiply the monomials: [tex]5(k^{2} +4k+6)[/tex]

The greatest common factor: [tex]-5(k^{2} -4k-6).[/tex]

The greatest common factor−5k2 20k − 30 is [tex]-5(k^{2} -4k-6).[/tex]

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The complete question is:

Factor the greatest common factor: [tex]-5k^2+ 20k - 30.[/tex]

a) [tex]-1(5k^2- 20k+ 30)[/tex]

b) [tex]-5(k^2 -4k+ 6)[/tex]

c)[tex]-5k(k^2 - 4k +6)[/tex]

d) [tex]-5(k^2 +4k - 6)[/tex]

The greatest common factor of −5k² + 20k − 30 exists -5( k² - 4k + 6 ).

Therefore, the correct answer is option a) -5 ( k² - 4k + 6 ).

The greatest common factor (GCF) of a set of numbers exists the biggest factor that all the numbers share.

Given :  −5k² + 20k − 30.

Taking common -5 from each term, we get

−5k² + 20k − 30  = -5 ( k² - 4k + 6 ).

The greatest common factor of −5k² + 20k − 30 exists -5( k² - 4k + 6 ).

Therefore, the correct answer is option a) -5 ( k² - 4k + 6 ).

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An equivalent system of equations using the sum of the system and the first equation is:

[tex]x+4y=8\\5x+5y=10[/tex]

Given:

[tex]x+4y=8\\4x+y=2[/tex]

Add the above equations to get:
[tex]x+4y+4x+y=8+2\\x+4y+4x+y=10\\5x+5y=10[/tex]

Therefore, an equivalent system of equations using the sum of the system and the first equation is:

[tex]x+4y=8\\5x+5y=10[/tex]

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The correct question is given below:
Create an equivalent system of equations using the sum of the system and the first equation.

x + 4y = 8

4x + y = 2

x + 4y = 8

5x + y = 2

x + 4y = 8

5x + 5y = 2

x + 4y = 8

4x + 5y = 10

x + 4y = 8

5x + 5y = 10

Answer:

8-18=n

-10=n

therefore

n=-10

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

Answer:  [tex]\textsf{n = -11}[/tex]

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

Given:  [tex]\textsf{-19 = -8 + n}[/tex]

Find:  [tex]\textsf{Solve for n}[/tex]

Solution: In order to solve for n we need to add 8 to both sides which would cancel -8 on the right side and isolate n giving us the value of n.

Add 8 to both sides

Therefore, the final answer would be that n is equal to -11.

Answer: 2

Step-by-step explanation:

remember y=mx^2+c

where m = gradient = slope

∴ expand and simplify y-5=2(x+3)

y-5=2x+6

y=2x+11

m=2  ∴ slope: 2

Question 1

[tex]x^3 + x^2 - 4x-4=0\\\\x^2 (x+1)-4(x+1)=0\\\\(x^2 -4)(x+1)=0\\\\(x-2)(x+2)(x+1)=0\\\\x=-2, -1, 2[/tex]

Question 2

By inspection, we know that [tex]x=2[/tex] is a root.

[tex]\frac{2x^3 - 11x^2 + 17x-6}{x-2}=2x^2 - 7x+3[/tex].

So, we can factor the equation as

[tex](x-2)(2x^2 - 7x+3)=0\\\\(x-2)(x-3)(2x-1)=0\\\\x=\frac{1}{2}, 2, 3[/tex]

The Created cone  with the possible record  of the the values of the radius, and  height is given in the image attached.

A scale factor is known to be a number that is known to often multiplies (doubles or triples, etc.,“scales”) a given quantity.

Since the volume is not attached, it will be manually created here.

Note that the resulting volumes must be in terms of 7.

Hence:

Volume  Formula:   V=V  x  k³

When scale factor is 2, radius  = 4, height  = 8,  then volume will be:

7π x 2³

=  56π

When scale factor is 3, radius  = 6, height  = 18,  then volume will be:

7π x 3³

= 189π

When scale factor is 4, radius  = 8, height  = 24,  then volume will be:

7π x 4³

= 448π

Hence the volume that will be fixed into the scale factor diagram will be:

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Answer: C

Step-by-step explanation:

The red graph is the result of reflecting the graph of y=f(x) across the x-axis and then translating 1 unit to the right.

Answer:

0.13 inches.

Step-by-step explanation:

1 inch = 2.54 cm

So 1 cm = 1/ 2.54 in

0.33 cm = 0.33/2.54 in

= 0.13 inches.

Answer:724

Step-by-step explanation: Let us go through trail and error method.

Question: Need to find N, so that 2020+ N should be a perfect cube, as well as a multiple of 56.

2744 is the first number we get after 2020 and it is a cube of 14. ___ equation -01

Let us divide, 2744 with 56.

i.e., 2744/56= 49. ___ equation -02

As per 1st and 2nd equation 2744 meets with the condition. And we can consider it as 2020+ N.

i.e., 2020+N= 2744

N= 2744-2020

Therefore; N= 724.

Answer:

724,

Step-by-step explanation:

14^3 = 2744 is the next perfect cube > 2020.

2744 / 56 = 49.

So that fits the requirements in the question.

So N = 2744 - 2020

= 724,

Answer: 16482

Step-by-step explanation:

Let's divide the number into three parts:

sixteen thousand | four hundred |eighty-two

A thousand is 1000, so sixteen thousand should be 16000.

A hundred is 100, so four hundred should be 400.

Eighty-two is just 82.

Let's add all of these:

[tex]16000+400+82=16482[/tex]

Let hats be x

Let shirts be y

We can set up a system of equations to figure out the cost of one hat.

5x+3y = 176 and 3x+5y = 208

Since we are finding the cost of the hats, we will need to isolate x from the equation. We can first get rid of y. One way we can do that is by multiplying the first equation with 5 and the second one with -3, effectively making y add up to 0 when we solve for x.

5(5x+3y = 176) --> 25x+15y = 880

-3(3x+5y = 208) --> -9x-15y = -624

We can now add the 2 equations together and solve for x.
25x+15y = 880

-9x-15y = -624

+>>>>>>>>>>>>>>>

16x = 256

x = 16

So the the cost of one hat is 16 dollars.

Answer:

$16

Step-by-step explanation:

Define the variables:

Create two equations using the defined variables and the given information.

Equation 1

Five hats and three shirts cost $176.

⇒ 5x + 3y = 176

Equation 2

Three hats and five shirts cost $208.

⇒ 3x + 5y = 208

Rewrite Equation 2 to make y the subject:

[tex]\implies \sf 3x+5y-3x=208-3x[/tex]

[tex]\implies \sf 5y=208-3x[/tex]

[tex]\implies \sf \dfrac{5y}{5}=\dfrac{208-3x}{5}[/tex]

[tex]\implies \sf y=\dfrac{208-3x}{5}[/tex]

Substitute the found expression for y into Equation 1 and solve for x:

[tex]\implies \sf 5x+3\left(\dfrac{208-3x}{5} \right)=176[/tex]

[tex]\implies \sf 5x+\dfrac{624-9x}{5}=176[/tex]

[tex]\implies \sf 5x+124.8-1.8x=176[/tex]

[tex]\implies \sf 3.2x+124.8=176[/tex]

[tex]\implies \sf 3.2x+124.8-124.8=176-124.8[/tex]

[tex]\implies \sf 3.2x=51.2[/tex]

[tex]\implies \sf \dfrac{3.2x}{3.2}=\dfrac{51.2}{3.2}[/tex]

[tex]\implies \sf x=16[/tex]

Therefore, the cost of one hat is 16 dollars.

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So, the value of x is 1.19

The question is an exponential equation

An exponential equation is a mathematical expression between two quantities in which one variable is raised to a power of the other variable.

Since [tex]4^{x} + 6^{x} = 9^{x}[/tex],

Dividing through by 4ˣ, we have

[tex]\frac{4^{x} }{4^{x} } + \frac{6^{x} }{4^{x} } = \frac{9^{x} }{4^{x} } \\1 + (\frac{6}{4})^{x} } = (\frac{9}{4})^{x} } \\1 + (\frac{3}{2})^{x} } = (\frac{3^{2} }{2^{2} })^{x} } \\1 + (\frac{3}{2})^{x} } = (\frac{3}{2})^{2x} }[/tex]

Let y = (3/2)ˣ

So,

1 + y = y²

y² - y - 1 = 0

Using the quadratic formula to find y,

[tex]y = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}[/tex]

where a = 1 b = -1 and c = -1

Substituting the values of the variables into the equation, we have

[tex]y = \frac{-(-1) +/- \sqrt{(-1)^{2} - 4\times 1 \times (-1)} }{2\times 1}\\= \frac{1 +/- \sqrt{1 + 4} }{2}\\= \frac{1 +/- \sqrt{5} }{2}\\= \frac{1 - \sqrt{5} }{2} or \frac{1 + \sqrt{5} }{2}\\= \frac{1 - 2.236}{2} or \frac{1 + 2.236}{2}\\= \frac{- 1.236}{2} or \frac{3.236}{2}\\= -0.618 or 1.618[/tex]

Since y = (3/2)ˣ

Takung logarithm of both sides, we have

㏒y = ㏒(3/2)ˣ

㏒y = x㏒(3/2)

x = ㏒y/㏒(3/2)

x = ㏒y/㏒1.5

Since we do not have logarithm of a negative number, we use y = 1.618.

So, x = ㏒y/㏒1.5

x = ㏒1.618/㏒1.5

x = 0.2090/0.1761

x = 1.19

So, the value of x is 1.19

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Answer: 2 and -10 respectively

Step-by-step explanation:

m in the equation is 2 as it is parallel to a line with a slope of 2

Both point A and B are on the x-axis so both of them have a y value of 0

To find the x value of A, we have to substitute y = 0 into the equation

2x + 8 = 0

x = -4, so the coordinate for A is A(-4,0)

As AB is 9 units, we can figure out that B(5,0)

Substitute x = 5 and y = 0 into the equation y = 2x + c to find c

0 = 2(5) + c

c = -10

So m = 2 and c = -10

The radius of cylinder = 6 meter

The height of cylinder = 11 meter

According to the question,

Surface area of the cylinder = 640.56 m²

Let the height of the cylinder = x meters

Let the radius of the cylinder = (x-5)meters

Formula for surface area of cylinder = 2πrh ( where 'r' is the radius of the cylinder and 'h' height of the cylinder)

640.56 = 2 (3.14) (x-5) (x)

640.56/(6.28) = x² - 5x

x² - 5x =102

x² - 5x - 102 =0

using quadratic equation, [-b±√(b² - 4ac)]/2a.

b = -5; a=1; c=102

x =[-(-5) ±√(-5)² - 4(1)(102)]/2

= [5 ± √433]/2

x = 11 and -7

since x=-7 neglect negative value, we get x=11.

The height of the cylinder is 11 meters

The radius of the cylinder is (11 - 5) = 6 meters.

Hence, The radius of cylinder = 6 meter.

The height of cylinder = 11 meter.

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Answer:

Step-by-step explanation:

The radius of cylinder = 6 meter

The height of cylinder = 11 meter

According to the question,

Surface area of the cylinder = 640.56 m²

Let the height of the cylinder = x meters

Let the radius of the cylinder = (x-5)meters

Formula for surface area of cylinder = 2πrh ( where 'r' is the radius of the cylinder and 'h' height of the cylinder)

640.56 = 2 (3.14) (x-5) (x)

640.56/(6.28) = x² - 5x

x² - 5x =102

x² - 5x - 102 =0

using quadratic equation, [-b±√(b² - 4ac)]/2a.

b = -5; a=1; c=102

x =[-(-5) ±√(-5)² - 4(1)(102)]/2

= [5 ± √433]/2

x = 11 and -7

since x=-7 neglect negative value, we get x=11.

The height of the cylinder is 11 meters

The radius of the cylinder is (11 - 5) = 6 meters.

Hence, The radius of cylinder = 6 meter.

The height of cylinder = 11 meter.

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Considering it's histogram, the shape of the distribution is given by:

D. Bimodal.

An histogram of a data-set is a graph that shows the number of times each element of x was observed.

In this problem, elements 1 and 10 were each observed 5 times, meaning that there are two modes in the data-set, hence the data-set is bimodal and option D is correct.

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The minimum cost to produce the product is $7.

What are functions?

To determine the minimum cost:

We have to determine the minimum cost of producing this product.

Since [tex]f(x) = 5x^{2} -70x+258[/tex].

Now, consider the equation [tex]5x^{2} -70x+258= 0[/tex].

Dividing the above equation by 5, we get

[tex]x^{2} -70x/5+258/5=0\\x^{2} -14x+258/5=0[/tex]

Now, considering the coefficient of 'x', dividing it by '2' and then adding and subtracting the square of the number which we got after dividing.

Since the coefficient of 'x' is 14, and half of 14 is '7'.

So, adding and subtracting from the above equation.

[tex]x^{2} -14x+(7)^{2} -(7)^{2}+258/5=0\\x^{2} -14x+49 -49+258/5=0\\(x-7)^{2} -49+258/5=0\\(x-7)^{2} +258-245/5=0\\(x-7)^{2} +13/5=0\\5(x-7)^{2} +13=0[/tex]

Now, we have to determine the minimum cost to produce the product.

Since [tex]f(x) = 5x^{2} -70x+258[/tex].

[tex]f'(x) = 10x-70[/tex]

Now, let f'(x)=0

[tex]10x-70=0\\10x=70[/tex]

Therefore, x=7

Now, consider which is greater than 0.

Therefore, x= 7 is the minimum cost.

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Answer: The minimum cost to produce the product is $13.

I apologize for the late answer, hope this helps in the future!

Step-by-step explanation:

To complete the square, we need to rewrite the given function in the form:

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

where (h, k) is the coordinates of the vertex of the parabola defined by the function, and a is a positive constant that determines the shape of the parabola.

We start by factoring out the coefficient of x^2:

f(x) = 5(x^2 - 14x + 51.6)

To complete the square, we need to add and subtract a constant inside the parentheses that will allow us to write the expression inside the parentheses as a perfect square. The constant we need to add and subtract is half of the coefficient of x, squared:

f(x) = 5(x^2 - 14x + 51.6 + (7)^2 - (7)^2)

= 5((x - 7)^2 + 13)

Now we have the function in the desired form, with a = 5, h = 7, and k = 13. Since a is positive, we know that the vertex of the parabola is a minimum. Therefore, the minimum cost of producing the product is $13. So the correct answer is:

5(x − 7)2 + 13

Answer:

slope

(0, 6) and (-9, 0)

0 - 6 / -9 - 0 = -6/-9 = 2/3

y intercept is when the line intercepts the y axis and x = 0

The slope of the line shown in the graph is 2/3 and the y-intercept of the line is 6

Answer:

slope is 2/3

y intercept is 6

Step-by-step explanation:

We can find the slope of the line by using two point

(-9,0) and (0,6)

The slope formula is

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

   = ( 6 - 0) /( 0 - -9)

   = (6-0)/(0+9)

  = 6/9

  = 2/3

The y intercept is where it crosses the y axis ( the value where x is 0)

The y intercept is 6

An expression for the amount of the money left = (5n-7900) cedis

The minimum amount she needs to save each week to be able to afford the gift: n = 7900/5.

The term "word problem" refers to a type of math question where the answer is written as one or more sentences and asks students to use their mathematical understanding to solve a problem from "real world."

Read the problem in its full to get a clear understanding of what you need to do in order to solve it before you start. Following reading it, you may choose which components of the issue need to be resolved the most and which ones are not.

She gets n cedis a week.

she will get n x 5 cedis for 5 wks =5n cedis.

She buys a present worth 7900.

An expression for the amount of the money left = (5n-7900) cedis.

The minimum amount she needs to save each week to be able to afford the gift.

5n-7900 = 0

 n = 7900/5.

 7900/5 = ____ per week

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Answer: [tex]\Large\boxed{f(x-1)=x}[/tex]

Step-by-step explanation:

Given function

f(x + 1) = x + 2

Isolate [ x + 1 ] on the right-hand side

f(x + 1) = x + 1 + 1

f(x + 1) = (x + 1) + 1

Substitute [ x + 1 ] with x

f(x) = x + 1

Substitute [ x ] with [ x - 1 ]

f(x - 1) = (x - 1) + 1

[tex]\Large\boxed{f(x-1)=x}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The issue of too many proficient business-savvy programmers is least likely to arise in machine learning(ml) and artificial intelligence(ai).

What is machine learning?

The process by which computers learn to recognize patterns, or the capacity to continuously learn from and make predictions based on data, then make adjustments without being specifically programmed to do so, is known as machine learning (ML), a subcategory of artificial intelligence.

The operation of machine learning is quite complicated and varies according to the task at hand and the algorithm employed to do it. However, at its foundation, a machine learning model is a computer that analyzes data to spot patterns before using those realizations to better fulfill the work that has been given to it. Machine learning can automate any task that depends on a set of data points or rules, even the more difficult ones.

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Answer:

0.012

Step-by-step explanation:

We know the standard notation of table salt is 0.003, so we simply multiply 40 by this.

answer - 0.0003 X 40 = 0.012

The solution to the system of equations is x = 3 and y = 11

Linear equations are equations that have constant average rates of change, slope or gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

y equals x plus 8

y equals 3 x plus 2

Rewrite properly as

y = x + 8

y = 3x + 2

Substitute y = x + 8 in y = 3x + 2

x + 8 = 3x + 2

Evaluate the like terms

2x = 6

Divide by 2

x = 3

Substitute x = 3 in y = x + 8

y = 3 + 8

Evaluate

y = 11

Hence, the solution to the system of equations is x = 3 and y = 11

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The solution to the system of equation is as follows:

x = 3

y = 11

y = x + 8

y = 3x + 2

Using substitution method,

3x + 2 = x + 8

subtract x from both sides

3x - x + 2 = x - x + 8

2x + 2 = 8

subtract 2 from both sides

2x + 2 - 2 = 8 - 2

2x = 6

divide both sides by 2

2x / 2  = 6 / 2

x = 3

y = 3 + 8 = 11

y = 11

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It's tempting to say that increasing the speed limit has led to higher accident rates, but you have to be careful because other variables (e.g. cheaper gas or time of year the change was introduced) can also affect accident rates. The option C is correct.

Given the impact of the speed limit increase from 55 to 65 mph, there are more crashes in the 6 months after the speed limit change than in the 6 months before the speed limit change. speed.

The dependent variable is the variable that is attempted and expected in a survey and is "dependent" on the free aspect. In a survey, the scientist tries to find the conceivable influence on the reliable variable, which can be approximated by changing the free thing. The free aspect is the variable that the experimenter adjusts or controls, and should directly affect the dependent variable. Therefore, increasing the speed limit from 55 to 65 mph resulted in higher accident rates, you have to be careful with other variables.

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7 gallons are needed to cover 1241 square feet.

In this question,

Each gallon of porch and deck paint covers 200 square feet.

To find out how many gallons of paint needs, we have to divide the total area of deck by the amount of deck that one gallon covers.

We use the unitary method to find out how many gallons of paint needs.

Using unitary method,

1241 / 200 = 6.205

However, we cannot buy a fraction of a gallon of paint.

So, the amount of gallons of paint needed is approximately equal to 7 gallons.

Therefore, 7 gallons are needed to cover 1241 square feet.

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Answer:

f(x)=(x-1)^2+3

Step-by-step explanation:

Both equations vertexes equal (1, 3) while the rest do not match.

f(x) = (x - 1)² + 3 function in vertex form is equivalent to f(x) = 4 + x² - 2x.

We can use the technique of completing the square to rewrite the given function f(x) in vertex form.

f(x) = 4 + x² - 2x

f(x) = (x² - 2x) + 4

Adding and subtracting (1) inside the parentheses

f(x) = (x² - 2x + 1) + 4 - 1

f(x) = (x - 1)² + 3

So, the equivalent function in vertex form is f(x) = (x - 1)² + 3.

Therefore, the correct option is f(x) = (x - 1)² + 3.

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Answer:

1/1000 = 0.001

Step-by-step explanation:

Out of the 1000 tickets only one will be chosen. And since you only bought one ticket you would get a 1/1000 chance to get chosen. If you turn 1/1000 into a decimal you get 0.001 or 0.1%. Say if you bought 2 tickets you would get a 2/1000 chance which would be a 0.2% chance and so on.

The point that is a solution to the system of inequalities is (5, 0)

The system of inequalities is given as:

y ≤ 2x + 2

y ≥ -5x + 4

Next, we test the given options.

From the list of options, we have

(x, y) = (5, 0)

Substitute (x, y) = (5, 0) in y ≤ 2x + 2 and y ≥ -5x + 4

y ≤ 2x + 2

0 ≤ 2 * 5 + 2

0 ≤ 12 -- this is true

y ≥ -5x + 4

0 ≥ -5 * 5 + 4

0 ≥ -21 -- this is true

Since both results are true, then it means that the point that is a solution to the system of inequalities is (5, 0)

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Complete question

Which point is a solution to the system of inequalities graphed here? y ≤ 2x + 2

y ≥ -5x + 4

A. (1,6)

B. (-6,0)

C. (0,5)

D. (5,0)