I need help with the question plzzzz

The arithmetic sequence's fifth term is therefore 84.

An arithmetic sequence's nth term is determined by a = a + (n - 1)d. So, enter the values a = 2 and d = 3 into the formula to determine the nth term.

The formula to determine the nth term of an arithmetic series is a = a1 + (n - 1)d if a1 is the first term and d is the common difference.

In the mathematical sequence, 84 is the fifth term.

The process for calculating value

An arithmetic sequence's nth term can be calculated using the following formula:

Tn = a + (n -1)d

Where;

First term is a.

N words are present.

d is the typical difference

We must substitute nas 5's value in order to find the fifth term.

T5 = 4 + (5-1) 20

T5 = 4 + 4(20) (20)

the bracket be expanded

T5 = 4 + 80

T5 = 84

The arithmetic sequence's fifth term is therefore 84.

The complete question is,

4 is the initial term and 20 is the constant difference in an arithmetic series. Discover the sequence's sixth phrase.

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Answer:

From top to bottom:

Simplify

Combine like terms

Subtract 3x from both sides

Add 14 on both sides

Step-by-step explanation:

Hope this helps

Answer:

$0.35 per minute

Step-by-step explanation:

Answer:

0.35 per minute

Step-by-step explanation:It was on my quiz and I got it right

The rate of interest is 73%.

What is the annual rate?

The term annual percentage rate of charge refers to the interest rate for an entire year rather than just a monthly fee or rate as applied on a loan, mortgage loan, credit card, etc. It can also be referred to as a nominal APR or an effective APR. It is an annual rate of a finance charge.

Given that 1 dollar to grow to X dollars in 2 years is given by the formula X = (1+r) ².

A dollar to triple in 2 years.

Thus putting X = 3 in X = (1+r) ²

3 = (1+r) ²

Take square root on both sides:

√3 = 1 + r

Subtract 1 from both sides:

r = √3 - 1

r = 0.73

r = 73%

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Answer:

Step-by-step explanation:

2 steps

     3.7 = x +(-5) , add 5 to both sides

3.7+ 5 = x + (-5) +5

    8.7 = x , combine like terms

or 1 step

  3.7 = x +(-5), add 5 to both sides and combine like terms

  8.7 = x

Answer:

Step-by-step explanation:

Given equation:

Solve:

Answer:

9.25% - [2, 3]

Step-by-step explanation:

If someone purchases a shirt that costs $49.99 in Nashville, they would be required to pay 9.25% in sales tax. This would be calculated by taking the pre-tax value of $49.99, then multiplying it by 0.0925, which is equal to the sales tax of $4.57. In total, the shirt would cost $54.56 with the sales tax included [1]. In comparison, the use tax rate is equal to the sales tax rate, so the use tax rate for this shirt would be 9.25% in Nashville, as well [2, 3].

Answer:

1. The possible roots are ±1, ±2, ±3, ±6. These are the factors of the trailing constant (6) divided by the factors of the leading coefficient (1). When the leading coefficient is 1, the possible roots are the factors of the constant

2. The polynomial is easier to evaluate when it is written in Horner form:

 f(x) = ((x -4)x +1)x +6

To show that 2 is a zero, we want to find f(2):

 f(2) = ((2 -4)2 +1)2 +6 = (-4 +1)2 +6 = -6 +6 = 0

 f(2) = 0, so 2 is one of the zeros of this function

3.  Using synthetic division (attached) or polynomial long division, we can divide the given polynomial by (x-2) to find the remaining factors. This division gives (x^2 -2x -3), which can be factored as (x -3)(x +1), so the three actual roots are ...

 x = 2 (from above), x = 3, x = -1 (from our factorization)

4. In factored form, the polynomial can be written ...

 f(x) = (x +1)(x -2)(x -3)

The first factor was found from the fact that 2 was given as a zero of the function. For any zero "a", a factor of the polynomial is (x-a).

The remaining factors were found by factoring the quadratic trinomial that resulted from the division of f(x) by x-2. That trinomial is x^2 -2x -3.

There are a number of methods that can be used to factor x^2 -2x -3. Again, the rational root theorem can help. It suggests that ±1 and ±3 are possible roots.

Answer:

Should be the first answer, x=5

Step-by-step explanation:

This would flip the graph and the square would land on top of where it currently is.

Answer: (I'm sorry if this is not the right answer)

The width = 8 meters

Step-by-step explanation:

The length: a (m)

The width: b (m)

We cannot have a negative length and a negative width: a>b>0

Eq. I: a=2b-4

Eq. II: ab=96

Substitute the value of a from Eq. I into Eq. II: (2b-4).b=96

Solve for b:

(2b-4).b=96

2\(b^{2}\)-4b-96=0

\(b^{2}\)-2b-48=0

\(b^{2}\)+6b-8b-48=0

b.(b+6)-8.(b+6)=0

(b+6).(b-8)=0

b=8; b=-6

As mentioned above, b>0. Therefore, b=8

Conclusion: if the area of the rectangle is 96 square meters then its width is 8 meters.

The width of the given rectangle is 8 units.

A rectangle is a geometrical figure in which opposite sides are equal.

The angle between any two consecutive sides will be 90 degrees.

Area of rectangle = length × width.

Perimeter of rectangle = 2( length + width).

Let's say the length of the rectangle is L and the width is W

Given that,

The length of a rectangle is four meters less than twice its width.

So,

L = 2W - 4

And,

Area = 96 square meter

LW = 96

Now by substituting

2W² - 4W = 96

W² - 2W - 48 = 0

W² -8W + 6W - 48 = 0

W(W - 8) + 6(W - 8) = 0

(W + 6)(W - 8) = 0

W = 8, -6 since distance cannot be negative so it will be 6 meters.

Hence "The width of the given rectangle is 8 units".

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Answer:

15

Step-by-step explanation:

let the number=x

⅔x=18

2x=54

x=27

Now 5/9 of the number=5/9×27

=5×3=15

Answer:

\(-8\sqrt{6}\)

Step-by-step explanation:

\(4i\sqrt{-24} \\\\=4i\sqrt{24} \sqrt{-1} \\\\=4i\sqrt{2^{3}*3 } \sqrt{-1} \\\\=4i(2)\sqrt{6} (i)\\\\=4*2i^{2} \sqrt{6} \\\\=8(-1)\sqrt{6} \\\\=-8\sqrt{6}\)

The simplification of the given function as complex number would be -8√6 .

Simplification involves proceeding with the pending operations in the expression. Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form. Simplification usually involves making the expression simple and easy to use later.

We have been given a function as complex number that is  4i√-24

We can also write it as;

4i√24 √-1

=  4i√2³ 3 √-1

=  4i (2) √6 (i)

Then simplify;

= 4 2i² √6

= 8  (-1)√6

= -8 √6

Therefore, the simplification of the given function as complex number would be -8√6 .

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Answer:

\(\textsf{1.} \quad x=-6, \quad x=6\)

\(\textsf{2.} \quad x=-5, \quad x=2\)

\(\textsf{3.} \quad x=-3, \quad x=7\)

\(\textsf{4.} \quad x=\dfrac{-5 +\sqrt{57} }{4}, \quad x=\dfrac{-5 -\sqrt{57} }{4}\)

\(\textsf{5.} \quad x=\dfrac{7+ \sqrt{309} }{10}, \quad x=\dfrac{7-\sqrt{309} }{10}\)

Step-by-step explanation:

Method: Extracting the Square Root

\(\begin{aligned}& \textsf{Given}: & x^2 & = 36\\& \textsf{Square root both sides}: & \sqrt{x^2} & = \sqrt{36}\\& \textsf{Simplify}: & x & = \pm 6\\&\textsf{Solution}:&x& = -6, 6\end{aligned}\)

Method: Factoring

\(\begin{aligned}& \textsf{Given}: & x^2+3x-10 & = 0\\& \textsf{Split the middle term}: & x^2+5x-2x-10 & = 0\\& \textsf{Factor the first two and the last two terms}: & x(x+5)-2(x+5)&=0\\& \textsf{Factor out the common term $(x+5)$}: & (x-2)(x+5)&=0\\& \textsf{Apply the zero-product property}: & (x-2)=0 \implies x&=2\\ &&(x+5)=0 \implies x&=-5\\ & \textsf{Solution}: & x&=-5,2\end{aligned}\)

Method: Factoring

\(\begin{aligned}& \textsf{Given}: & x^2-4x-21 & = 0\\& \textsf{Split the middle term}: & x^2-7x+3x-21 & = 0\\& \textsf{Factor the first two and the last two terms}: & x(x-7)+3(x-7)&=0\\& \textsf{Factor out the common term $(x-7)$}: & (x+3)(x-7)&=0\\& \textsf{Apply the zero-product property}: & (x+3)=0 \implies x&=-3\\&&(x-7)=0 \implies x&=7\\& \textsf{Solution}: & x & = -3, 7\end{aligned}\)

Method: Quadratic  Formula

\(\boxed{\begin{minipage}{4 cm}\begin{center}\underline{Quadratic Formula}\end{center}\\\\\begin{center}$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\end{center}\\\\\\\begin{center}when $ax^2+bx+c=0$\end{center}\end{minipage}}\)

Given:

\(5x-4=-2x^2\)

Rearrange into standard form by adding 2x² to both sides:

\(\implies 2x^2+5x-4=0\)

Therefore:

\(a=2, \quad b=5, \quad c=-4\)

Substitute the values into the quadratic formula and solve for x:

\(\implies x=\dfrac{-5 \pm \sqrt{5^2-4(2)(-4)} }{2(2)}\)

\(\implies x=\dfrac{-5 \pm \sqrt{25+32} }{4}\)

\(\implies x=\dfrac{-5 \pm \sqrt{57} }{4}\)

Therefore, the solutions are:

\(x=\dfrac{-5 +\sqrt{57} }{4}, \quad x=\dfrac{-5 -\sqrt{57} }{4}\)

Method: Quadratic  Formula

\(\boxed{\begin{minipage}{4 cm}\begin{center}\underline{Quadratic Formula}\end{center}\\\\\begin{center}$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\end{center}\\\\\\\begin{center}when $ax^2+bx+c=0$\end{center}\end{minipage}}\)

Given:

\(5x^2-7x-13=0\)

Therefore:

\(a=5, \quad b=-7, \quad c=-13\)

Substitute the values into the quadratic formula and solve for x:

\(\implies x=\dfrac{-(-7) \pm \sqrt{(-7)^2-4(5)(-13)} }{2(5)}\)

\(\implies x=\dfrac{7 \pm \sqrt{49+260} }{10}\)

\(\implies x=\dfrac{7 \pm \sqrt{309} }{10}\)

Therefore, the solutions are:

\(x=\dfrac{7+ \sqrt{309} }{10}, \quad x=\dfrac{7-\sqrt{309} }{10}\)

The equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.

To find an equation in slope-intercept form that passes through the point (1, -2) and is perpendicular to the given equation y = 5x + 4, we need to determine the slope of the perpendicular line.

The given equation y = 5x + 4 is already in slope-intercept form (y = mx + b), where m represents the slope. In this case, the slope of the given line is 5.

To find the slope of a line perpendicular to this, we use the fact that the product of the slopes of two perpendicular lines is -1. So, the slope of the perpendicular line can be found by taking the negative reciprocal of the slope of the given line.

The negative reciprocal of 5 is -1/5.

Now that we have the slope (-1/5) and a point (1, -2), we can use the point-slope form of the equation:

y - y1 = m(x - x1)

Substituting the values:

y - (-2) = (-1/5)(x - 1)

Simplifying:

y + 2 = (-1/5)(x - 1)

To convert the equation into slope-intercept form (y = mx + b), we need to simplify it further:

y + 2 = (-1/5)x + 1/5

Subtracting 2 from both sides:

y = (-1/5)x + 1/5 - 2

Combining the constants:

y = (-1/5)x - 9/5

Therefore, the equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.

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Answer: -7

Step-by-step explanation:

Hi ;-)

\(y=15 \ and \ x=5\\\\(y-9)+(3+x)=(15-9)+(3+5)=6+8=\boxed{14}\)

Answer:

14

Step-by-step explanation:

(y-9)+(3+x)

(15-9)+(3+5)

6+8

14

Answer:

She buys 9 adult tickets and 4

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

Polygons=2d Shapes

Not all 2d shapes are 4-sided.

Answer: True

Step-by-step explanation:

Polygons can have 3 or more sides so they can be defined also as quadrilaterals depending on the shapes because a quad is 4

Answer:

use the sine rule

Step-by-step explanation:

Answer:

a. The number of light bulbs that burn out in the next year in a room with 19 bulbs: is a discrete random variable.

b. The usual mode of transportation of people in City Upper A: is not a random variable because its outcome isn't numerical.

c. The number of statistics students now doing their homework: is a discrete random variable.

d. The number of home runs in a baseball game: is a discrete random variable.

e. The exact time it takes to evaluate 67 plus 29: is a continuous random variable.

f. The height of a randomly selected person: is a continuous random variable.

Step-by-step explanation:

A random variable often used in statistics and probability, is a variable that has its possible values as numerical outcomes of a random experiment or phenomenon. It is usually denoted by a capital letter, such as X.

In statistics and probability, random variables are either continuous or discrete.

1. A continuous random variable is a variable that has its possible values as an infinite value, meaning it cannot be counted.

Example are the height of a randomly selected person, time it take to move from Texas to New York city, etc.

2. A discrete random variable is a variable that has its possible values as a finite value, meaning it can be counted.

Examples are the number of light bulbs that burn out in the next year in a room with 19 bulbs, the number of chicken in a district etc.

Answer:

A random variable in statistics can be loosely defined as a variable whose values depend on the outcome of a random phenomenon. These variables are variables that can be the results of an experiment not yet performed, or the results of an already performed experiment whose already existing result is uncertain.

A discrete random variable is finite and has a countable range of values.

A continuous random variable takes on numerical values in an interval of values and has no countable range of value.

a. The number of light bulbs that burn out in the next year in a room with 19 bulbs---   discrete random variable

b. The usual mode of transportation of people in City Upper A---  

not a random variable

c. The number of statistics students now doing their homework ---   discrete random variable

d. The number of home runs in a baseball game ---   discrete random variable

e. The exact time it takes to evaluate 67 plus 29 ---   continuous random variable

f. The height of a randomly selected person---   continuous random variable

Answer:

Bases

Step-by-step explanation:

Answer:

x = -1,375

y = -5

Step-by-step explanation:

{-8x + y = 6, / : (-1)

{-8x + 3y = -14;

Multiply the first equation by -1, so that we could eliminate 8x:

+ {8x - y = -6,

{-8x + 3y = -14;

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

4y = - 20 / : 4

y = -5

Now, make x the subject from the first equation (you can do it from the 2nd one instead):

8x = -6 + y / : 8

x = -0,75 + 0,125y

x = -0,75 + 0,125 × (-5) = -0,75 - 0,625 = -1,375

Answer:

Step-by-step explanation:

\(x=\frac{-(-9)\pm\sqrt{(-9)^2-4(2)(4)} }{2 \times 2} \\x=\frac{9\pm\sqrt{81-32} }{4} \\x=\frac{9\pm\sqrt{49} }{4} \\x=\frac{9 \pm 7}{4} \\either~x=\frac{9+7}{4} =\frac{16}{4} =4\\or\\x=\frac{9-7}{4} =\frac{2}{4} =\frac{1}{2}\)

We have to find the 80% confidence interval for a population proportion.

The sample size is n = 362 and the number of successes is X = 54.

Then, the sample proportion is p = 0.149171.

The standard error of the proportion is:

The critical z-value for a 80% confidence interval is z = 1.281552.

Then, the lower and upper bounds of the confidence interval are:

As the we need to express it as a trilinear inequality, we can write the 80% confidence interval for the population proportion (π) as:

Answer: 0.125 < π < 0.173

Answer:

C

Step-by-step explanation:

The equation y=Mx + b, where b is the y intercept

Answer:

The vertex of the function is at (–3,–16)

The graph is increasing on the interval x > –3

The graph is positive only on the intervals where x < –7 and where

x > 1.

Step-by-step explanation:

The graph of \(f(x)=(x-1)(x+7)\) has clear zeroes at \(x=1\) and \(x=-7\), showing that \(f(x) > 0\) when \(x < -7\) and \(x > 1\). To determine where the vertex is, we can complete the square:

\(f(x)=(x-1)(x+7)\\y=x^2+6x-7\\y+16=x^2+6x-7+16\\y+16=x^2+6x+9\\y+16=(x+3)^2\\y=(x+3)^2-16\)

So, we can see the vertex is (-3,-16), meaning that where \(x > -3\), the function will be increasing on that interval

Answer:

1st one

Step-by-step explanation:

because it is

Answer:

Option 1

Step-by-step explanation:

In the first one, the first number is lower than -2, the second is between -1 and 0, and 1+1/6 is of course bigger than 0 and smaller than 1+5/6, so it's the right answer.

The second one is the first one reversed, so it's ordered from greatest to lowest.

The third one has a negative number on both ends, but positives in the middle, so it cannot be ordered lowest to greatest. Same with the last one.