Find the nth term of this quadratic sequence
2, 8, 18, 32, 50

The will be A'(0, 20),  B'(20, 10) and  '(-10, 0). Transformation is the  of a point from its to a. Types of transformation are reflection, translation, rotation and dilation.

What is transformation?
When a function is transformed, the graph's curve either "moves to the left/right/up/down," "expands or compresses," or "reflects." For instance, by simply moving the graph of the function g(x) = x2 up by 3 units, the graph of the function f(x) = x2 + 3 is obtained. Function transformations are very useful for graphing functions without having to start from scratch because they allow you to move, expand, compress, or reflect the curve. In this article, we will examine the guidelines for function transformations as well as examples of how to transform various function types.

Let ABC be a   with coordinates A(0, 2), B(2, 1), C(-1, 0).

The coordinate of points A, B, C will change by below rule

(x, y)↔(10x, 10y)        

where 10 is the scale factor.

∴A(0, 2) ↔A'(0, 20)

B(2, 1) ↔B'(20, 10)

C(-1,0) ↔C'(-10, 0)

Hence,   will be A'(0, 20) ,B'(20, 10)  and C'(-10, 0)

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Answer:

  -4, -2, 4

Step-by-step explanation:

You want the roots of the polynomial x³ +2x² -16x -32.

The polynomial can be factored by grouping:

  x³ +2x² -16x -32

  = (x³ +2x²) -(16x +32) . . . . . . group pairs of terms

  = x²(x +2) -16(x +2) . . . . . . . . factor each group

  = (x² -16)(x +2) . . . . . . . . . . . . factor out the common factor

Now, the difference of squares can be factored:

  = (x -4)(x +4)(x +2)

The zero product rule tells us the roots are the values of x that make the factors zero:

  x -4 = 0   ⇒   x = 4

  x +4 = 0   ⇒   x = -4

  x +2 = 0   ⇒   x = -2

The roots of the polynomial are {-4, -2, 4}.

__

Additional comment

The factorization of the difference of squares is a special form:

  a² -b² = (a +b)(a -b)

Answer:

-2, -4, and 4 are the correct answers on edge

Step-by-step explanation:

Answer:

C, B

Step-by-step explanation:

[tex]x^2+6x+6=0 \\ \\ x=\frac{-6 \pm \sqrt{6^2-4(6)}}{2(1)} \\ \\ x=-3 \pm \sqrt{3} \\ \\ \sqrt{3} \approx 1.7 \implies -5<-3-\sqrt{3}<-4, -2<-3+\sqrt{3}<-1[/tex]

The specification as an absolute value inequality is l w - 18 l ≤ 0.1.

Given:

A furniture maker uses the specification 17.9≤w≤18.1 for the width w in inches of a desk drawer.

m = 17.9 + 18.1 / 2

= 36/2

= 18

t = 18.1 - 17.9

= 0.2/2

= 0.1

l w - 18 l ≤ 0.1

Therefore The specification as an absolute value inequality is l w - 18 l ≤ 0.1.

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The sum using the distributive property is 75

From the question, we have the following expression

30 + 45

Rewrite the given expression as follows

This is represented using

(30 + 45)

Factor out 5 from the expression

So, we have the following representation

30 + 45 = 5(6 + 9)

The above means that 5 is the GCF of the sum expression 30 + 45

This represents the GCF

Solving further, we have

30 + 45 = 5 * 15

Evaluate

30 + 45 = 75

Hence, the sum is 75

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Answer:

x = 2

Step-by-step explanation:

8x - 21 - 5x = - 15 ( collect like terms on left side )

3x - 21 = - 15 ( add 21 to both sides so numeric values on right side )

3x = 6 ( isolate x by dividing both sides by 3 )

x = 2

The area of the quadrilateral is = 15 square units.

acc to our quesstion-

hence,The area of the quadrilateral is = 15 square units.

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Step-by-step explanation:

[tex]2(x - 3) {}^{2} - 12 = 116 \\ [/tex]

[tex]2 \times ( {x}^{2} - 6x + 9) - 12 = 116[/tex]

[tex] {2x}^{2} - 12x + 18 - 12 = 116[/tex]

[tex] {2x}^{2} - 12x - 110 = 0[/tex]

[tex] {x}^{2} - 6x - 55 = 0[/tex]

[tex] {x}^{2} - 11x + 5x - 55 = 0[/tex]

[tex]x(x - 11) + 5(x - 11) = 0[/tex]

[tex](x +5 )(x - 11) = 0[/tex]

Answer:

  19%

Step-by-step explanation:

You want the probability a student is a senior, given that they are female.

The table indicates that 3 +4 +6 +3 = 16 students are female. Of those, 3 are seniors. The desired probability is ...

  P(senior | female) = N(senior & female)/N(senior) = 3/16 = 0.1875

The probability that a female student is a senior is about 19%.

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The value of m in the angle (6m - 12)° is m = 17 , the correct option is (b) .

In the question ,

it is given that ,

the triangle WZY is cut by the bisector ZX ,

and also given that ZW and ZY are congruent ,

that means ZW = ZY

Based on the characteristics of the triangle given ,

we can conclude that triangle WYZ is an isosceles triangle ,

that means , triangle WXZ = triangle YXZ

So ,  ∠YXZ = ∠WXZ = 90°

given that ∠YXZ = (6m - 12)°

So , (6m - 12)° = 90°

6m - 12 = 90

6m = 90 + 12

6m = 102

m = 102/6

m = 17

Therefore , the value of m in the angle (6m - 12)° is m = 17 .

The given question is incomplete , the complete question is

Triangle W Z Y is cut by bisector Z X. The lengths of sides Z W and Z Y are congruent. ZX bisects ∠WZY. If the measure of ∠YXZ is (6m – 12)°, what is the value of m?

(a) 6

(b) 17

(c) 90

(d) 102

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Answer:

17

Step-by-step explanation:

i got it right on edge 2022

Answer:

Step-by-step explanation:

As described in the hint:

The product is:

This is a quadratic expression ax² + bx + c with the leading coefficient of a = - 1, b = 20 and c = 0.

It has a maximum and no minimum value since a < 0.

The x-coordinate of the maximum is the vertex which is x = - b/2a.

The x- coordinate of the vertex is:

The maximum value itself is:

Answer:

10 and 10.

[tex]f(x)=-x^2+20x[/tex]

Maximum value of the function is 100.

Step-by-step explanation:

Two numbers whose sum is a positive integer, and whose product is the maximum possible value have to be two positive integers.

Pairs of positive integers whose sum is 20:

The pair of numbers whose product is the maximum possible value is the pair of numbers that are closest to each other.  

Therefore the pair of numbers is 10 and 10:

[tex]\implies x = 10[/tex]

[tex]\implies 20 - x = 10[/tex]

Form a quadratic function by multiplying:

[tex]\implies f(x)=x(20-x)[/tex]

[tex]\implies f(x)=20x-x^2[/tex]

[tex]\implies f(x)=-x^2+20x[/tex]

The maximum value of the function is the y-value of its vertex.

[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]

To convert the function to vertex form, complete the square.

Factor out negative 1:

[tex]\implies f(x)=-(x^2-20x)[/tex]

Add and subtract the square of half the coefficient of the term in x:

[tex]\implies f(x)=-\left(x^2-20x+\left(\dfrac{-20}{2}\right)^2-\left(\dfrac{-20}{2}\right)^2\right)[/tex]

[tex]\implies f(x)=-(x^2-20x+100-100)[/tex]

[tex]\implies f(x)=-(x^2-20x+100)+100[/tex]

Factor the perfect square trinomial:

[tex]\implies f(x)=-(x-10)^2+100[/tex]

Therefore, the vertex of the function is (10, 100), and so the maximum value of the function is 100.

The equation that would give the amount each month, given a certain number of text messages is 27 + 0.43t.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Let the number of text messages be represented as t.

Since BobbyLou's cell company charges $27 a month for voice service plus $0.43 for each text message. The amount will be:

= 27 + (0.43 × t)

= 27 + 0.43t

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Quotient is 2x³ +x² -4x+3 for (2x⁴ – 3x³ – 6x² + 11x + 8) ÷ (x – 2)

A division is a process of splitting a specific amount into equal parts.

(2x⁴ – 3x³ – 6x² + 11x + 8) ÷ (x – 2)

Let f(x)=2x⁴ – 3x³ – 6x² + 11x + 8

and g(x)=x-2

We need to divide the f(x) by g(x),

f(x)=g(x)× (2x³ +x² -4x+3)+16

If we equate the above equation with division algorithm which says,

a=bq+r

f(x)=g(x)q(x)+r(x)

so quotient is 2x³ +x² -4x+3

Hence quotient is 2x³ +x² -4x+3 for (2x⁴ – 3x³ – 6x² + 11x + 8) ÷ (x – 2)

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Answer:

1.81 inches

Step-by-step explanation:

Answer:

A = 7.5 in^2

Step-by-step explanation:

the formula for a triangles area is [(h)(b)]/2

2.5 is the h (height) and 6 is the b (base)

first multiply h and b

2.5 * 6 = 15

now divide by 2

15 / 2 = 7.5

that is your answer

Answer:

2nd one

Step-by-step explanation:

You can see that at the end, it is +5. That means it is to the left, NOT the right. So the second one is correct.

The given equation written in standard form is 8x - 14y = 26

From the question, we are to write the given linear equation is standard form.

From the given information, the given linear equation is

8x = 26 + 14y

The standard form of linear equation is given as

Ax + By = C

Where x and y are the variables

A, B, and C are the constants

Now, we will write the given equation in standard form

8x = 26 + 14y

Subtract 14y from both sides of the equation

8x - 14y = 26 + 14y - 14y

8x - 14y = 26

Hence, the equation is 8x - 14y = 26

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The 42nd term of the sequence is 248

What is Arithmetic Progression?

Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value.

The furmula is [tex]a_{n}[/tex]=a + (n - 1 )d

where a = The first form of A.P

n = Number of terms given to find

d = Common difference between each terms

Given,

a = 2

n = 42

d = 6

Now,

[tex]a_{42\\[/tex] = 2 + (42 - 1)6

[tex]a_{42}[/tex] = 2 + (41)6

[tex]a_{42}[/tex] = 2+ 246

Therefore, for 42nd term

[tex]a_{42}[/tex] = 248

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Answer:

15% and 40%

Step-by-step explanation:

22500/150000 is 15/100 or 15%

60000/150000 is 40/100 or 40%

Answer:

150 plates

Step-by-step explanation:

if 1 stack = 10 plates then

15 stacks =?

15×10 =150

Answer:

150

Step-by-step explanation:

If 1 stack = 10 plates all you have to do is figure out how 1 changes to 15 ( in this case multiply). You tyen multiply 10 by 15 which equals to 150.

The mathematical sentence that expresses the given information is the number of players who left the team, denoted by p, are 43 less than the number of players at the start of the season or p = 52-43.

According to the question,

We have the following information:

A football team had 52 players at the start of the season, but then some players left the team. After that, the team had 43 players.

Now, let's take the number of players who left the team to be p.

So, we have the following expression:

p = 52-43

p = 9

Hence, the mathematical sentence that expresses the given information is the number of players who left the team, denoted by p, are 43 less than the number of players at the start of the season.

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The number of integers between 1 and 2022 inclusive that are multiples of 11 but not multiples of 3, using arithmetic sequences, is of:

122.

An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.

The nth term of an arithmetic sequence is given by the rule presented as follows:

[tex]a_n = a_1 + (n - 1)d[/tex]

In which [tex]a_1[/tex] is the first term of the arithmetic sequence.

The sequence composed by the integer multiples of 11 between 1 and 2022 are given as follows:

(11, 22, ..., 2013)

The first term and the common ratio of the sequence are given as follows:

[tex]a_1 = 11, d = 11[/tex]

The number of terms is obtained as follows:

2013 = 11 + 11(n - 1)

11n = 2013

n = 2013/11

n = 183.

The sequence composed by terms that are multiples of 11 and of 3 is given by:

(33, 66, ..., 2013).

The first term and the common ratio of the sequence are given as follows:

[tex]a_1 = 33, d = 33[/tex]

The number of terms is obtained as follows:

2013 = 33 + 33(n - 1)

33n = 2013

n = 2013/33

n = 61.

Hence the number of integers that are multiples of 11 but not 3 is given by:

183 - 61 = 122.

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Answer:

(g-7)^3

Step-by-step explanation:

(x-y)^3 = x^3 - y^3

In this case you are solving for y, or 343

The cube root of 343 is 7

g^3 - 7^3 = (g-7)^3

(g-7)^3

Step-by-step explanation:

g³-343=0

g³=343

g=³√343

g=7

g³-7³=0

(g-7)^3=0

6 liters of brand A fruit punch must be mixed with 9 L of brand b fruit punch.

Let x=liters of Brand A fruit punch to be mixed with 9 liters of Brand B fruit punch.

x + 9 = liters of mixture.

20%(x) + 9*40% = 32%(x+9)

20/100 x + 9*40/100 = 32/100 (x+9)

0.2x + 360/100 = 0.32x + 9*0.32

0.2x + 3.6 = 0.32x + 2.88

0.12x = 3.6 - 2.88

0.12x = 0.72

divide by 0.12 on both sides

x = 0.72/0.12

= 72/100/12/100

= 72/12

= 6 liters.

Therefore 6 liters of brand A fruit punch must be mixed with 9 L of brand b fruit punch.

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A 98% confidence interval estimate of the mean wake time for a population with zopiclone treatments is 74.26 to 125.54.

What is a confidence interval?

A confidence interval (CI) is a range of values that, with a particular level of certainty, is likely to encompass a population value. A population mean that sits between an upper and lower interval is frequently stated as a percentage.

Here,

From the standard normal table, the z-critical value at 98% confidence interval is 2.33 so,

98%C.I. = µ ± z * σ /   n = 98.90 ± 2.33 * 42.30 / sqrt of 16  = 98.90 ± 24.64 = 74.26 to 125.54

The mean wake time of 102.80 minutes before the treatment due to the mean wake time of 102.80 minutes included in the 98% confidence interval which is between 74.26 and 125.54. Zopiclone does not appear effective.

Hence, A 98% confidence interval estimate of the mean wake time for a population with zopiclone treatments is 74.26 to 125.54.

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a) The smallest number is 2

b) The first quartile Q1 is 12

c) The median is 16

d) Third quartile Q3 is 33

e)The  largest number is 39

What Is Quartile Formula?

To divide a set of observations into four equal pieces, use the quartile formula. The median and the first term are where the first quartile is located. The median represents the middle quartile. The third quartile represents the midway value that falls between the median and the last term.

Given data set:

19, 39, 9, 33, 15, 16, 2, 33, 16

Arrange the data in ascending order:

2, 9 ,15 ,16 ,16 ,19 ,33 ,33 ,39

a) Smallest number: 2

b) The first quartile Q1 :

  number of terms=n=9

Q1= (n+1)/4 th term

Q1= (9+1)/4 = 2.5th terms

This means, Q1=mean of 2nd and 3rd terms= (9+15)/2 = 12

c) Median:

M=(n+1)/2 th term = (9+1)/2 =5th term = 16

d) Third quartile Q3:

Q3= 3[(n+1)/4] th term

Q3= 3[(9+1)/4] = 7.5th terms

This means, Q3=mean of 7th and 8th terms= (33+33)/2 = 33

e) largest number : 39

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The equivalent fraction is 40x⁷ of the given expression 8x⁴ × 5x³.

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

The expression is given in the question as:

8x⁴ × 5x³

We have to determine the equivalent fraction of the given expression.

⇒ 8x⁴ × 5x³

⇒ 8 × 5 × x⁴× x³

Multiply the coefficients in the above expression,

⇒ 40 × x⁴× x³

Add the exponents in the above expression,

⇒ 40 × x⁴⁺³

⇒ 40x⁷

Thus, the equivalent fraction is 40x⁷ of the given expression 8x⁴ × 5x³.

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