If x is in west of y and y is in north of z, towards which direction of x is z?

Answer:

if she would sell it for what it is worth now she would make $36.50

Step-by-step explanation:

0.75 x 83 = 62.5

62.5 + 8.75 = 71

71 is how much it is worth now

71 - 34.5 = 36.5

36.50 is how much she would make

Answer:

$36,50

Step-by-step explanation:

That is correct to me. You do those exact steps to arrive at that answer.

Answer:

The probability of selecting a black card or a 6 = 7/13

Step-by-step explanation:

In this question we have given two events. When two events can not occur at the same time,it is known as mutually exclusive event.

According to the question we need to find out the probability of black card or 6. So we can write it as:

P(black card or 6):

The probability of selecting a black card = 26/52

The probability of selecting a 6 = 4/52

And the probability of selecting both = 2/52.

So we will apply the formula of compound probability:

P(black card or 6)=P(black card)+P(6)-P(black card and 6)

Now substitute the values:

P(black card or 6)= 26/52+4/52-2/52

P(black card or 6)=26+4-2/52

P(black card or 6)=30-2/52

P(black card or 6)=28/52

P(black card or 6)=7/13.

Hence the probability of selecting a black card or a 6 = 7/13 ....

Answer:

[tex]l=\frac{P}{2}-w[/tex].

Step-by-step explanation:

The perimeter of a rectangle is the sum of it's side lengths.

A rectangle has 4 sides where it's opposite sides are congruent.

So if one side has measurement w, then there is another side that has measurement w.

If there is one side that has measurement l, then there is another side that has measurement l.

So if you add w+w+l+l you get 2w+2l.

They are giving us that the perimeter is P, so P=2w+2l.

we are being asking to solve for l.

P=2w+2l

First step: Isolate term that contains the l, so get 2l by itself first.

We are going to subtract 2w on both sides giving us:

P-2w=2l

2l=P-2w

Now that we have 2l by itself it is time to perform the last step in getting l by itself.

Second step: Divide both sides by 2.

This gives us:

l=(P-2w)/2

You may separate the fraction like so:

[tex]l=\frac{P-2w}{2}=\frac{P}{2}-\frac{2w}{2}=\frac{P}{2}-w[/tex].

I don't know your options but I have solve for l in terms of P and w

and got [tex]l=\frac{P}{2}-w[/tex].

Please let me know if you have further questions with this problem.

G. 7,500 cubic feet

Answer:

The correct option is B) [tex]f(x)=-5x+250[/tex].

Step-by-step explanation:

Consider the provided information.

let x represents the number of weeks and y represents the fixed cars.

During week 10 of the recall, the manufacturer fixed 200 cars.

Thus, the ordered pair can be made with the help of the above data is: (10,200).

In week 15, the manufacturer fixed 175 cars.

Thus, the ordered pair can be made with the help of above data is: (15,175)

Now use two point slope formula: [tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

Substitute the [tex](x_1,y_1)=(10,200)\ \text{and}\ (x_2,y_2)=(15,175)[/tex] in the above formula.

[tex]y-200=\frac{175-200}{15-10}(x-10)[/tex]

[tex]y-200=\frac{-25}{5}(x-10)[/tex]

[tex]y-200=-5(x-10)[/tex]

[tex]y-200=-5x+50[/tex]

[tex]y=-5x+250[/tex]

Which also can be written as:

[tex]f(x)=-5x+250[/tex]

Hence, the correct option is B) [tex]f(x)=-5x+250[/tex].

Answer:

64 : 1

Step-by-step explanation:

Given 2 similar cylinders with linear ratio = a : b then

volume ratio = a³ : b³

Here the height ratio = 4 : 1, hence

volume ratio = 4³ : 1³ = 64 : 1

There are 5 20% in 100% ( 20 x 5 = 100)

So 10% of a number would be 12 x 5 = 60

Then there are 10 10% in 100% ( 10 x 10 = 100).

So if 10% = 60, then 100% = 60 x 10 = 600.

The starting value is 600

600 x 10% = 600 x 0.1 = 60

60 x 20% = 60 x 0.2 = 12

Now you have the starting value you can calculate the other answer:

600 x 20% = 600 x 0.20 = 120

120 x 10% = 120 x 0.10 = 12

The answer would be 12

Answer:

12

Step-by-step explanation:

Long Answer:

"20% of 10% of a number is 12" translates to:

.2 (times) .1 (times) x         =   12

of translated to times.

20%=.20 or .2

10%=.10   or .1

number translated to variable.

is translated to equals.

We have the following equation to solve:

[tex].2 \cdot .1 \cdot x=12[/tex]

Simplifying the .2 times .1 part:

[tex].02 \cdot x=12[/tex]

Divide both sides by .02:

[tex]x=\frac{12}{.02}[/tex]

[tex]x=600[/tex]

Now it ask for "what is 10% of 20% of the same number?"

Multiplication is communicative and I wouldn't have done all of this work if I had seen them just switch the 10% and 20% around.  The answer is 12.

But for fun since we already done all of this work!

"10% of 20% of 600" translates to:

.1 (times) .2 (times) 600

[tex].1 \cdot .2 \cdot 600[/tex]

[tex].02 \cdot 600[/tex]

[tex]12[/tex].

Short Answer:

.2(.1)x=12 so .1(.2)x=12

Multiplication is commutative is the reason the answer is 12.

Answer:

D. 31.42

Step-by-step explanation:

you can look up a calculator and it gives you the answer!

The circumference of a circle with a radius of 5 units is,

⇒ Circumference = 31.4 units

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The radius of circle = 5 units

Now,

Circumference = 2πr

Here, r = 5

⇒ Circumference = 2 × 3.14 × 5

⇒ Circumference = 31.4 units

Thus, The circumference of a circle with a radius of 5 units is,

⇒ Circumference = 31.4 units

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To solve this problem, we need to find the values of w and I. We can set up a system of equations based on the given information and solve for w and I.

The subject of this question is Mathematics and the grade level is Middle School. To solve this problem, we are given the cost of a wallet-sized portrait (w) and the cost of an 8" x 10" portrait (I). We are also given the prices for two different packages.

The Basic Package includes 30 wallet-sized photos and 1 8" x 10" portrait. The cost of the package is $17.65.

The Deluxe Package includes 20 wallet-sized photos and 3 8" x 10" portraits. The cost of the package is $25.65.

To find the value of w and I, we can set up a system of equations based on the given information:

1. 30w + I = 17.65

2. 20w + 3I = 25.65

By solving this system of equations, we can find the values of w and I.

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The variables w and I represent the cost of wallet-sized and 8 x 10 portraits. The basic and deluxe packages are defined, including the quantities and costs of photos.

The subject of this question is Mathematics. It involves the cost of different portrait packages offered by a photo studio.

The question asks for the definitions of variables w and I, which represent the cost of wallet-sized and 8 x 10 portraits, respectively.

Mathematically, the basic package includes 30 wallet-sized photos and 1 8 x 10 portrait for a cost of $17.65.

The deluxe package includes 20 wallet-sized photos and 3 8 x 10 portraits for a cost of $25.65.

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Answer:

Angle CAB.

Step-by-step explanation:

Angle PMN is congruent to Angle CAB.

All we have to do is follow the markers to determine the order to put the letter.

P has the double marker.

C has the double marker.

Since P came first, you put C first.

M has the triple marker.

A has the triple marker.

Since M came second, you put A second.

N has the single marker.

B has the single marker.

Since N came third, you put B third.

Answer:

Thus the last row has 119 seats.

The total number of seats in 24 rows = 1476

Step-by-step explanation:

The number of seats in each row make an arithmetic series. We will use arithmetic equation to find the number of seats in last row:

An = a1+ (n-1)d

An = 4+(24-1)5  

An = 4 + (23)(5)  

An = 4 + 115  

An = 119

Thus the last row has 119 seats.

Now to find the sum of seats we will apply the formula:

Sn = n(a1 + an)/2

Sn = 24(4+119)/2  

Sn = 24(123) /2  

Sn = 1476 .....

The total number of seats in 24 rows = 1476....

Answer:

1476 seats

Step-by-step explanation:

We are given that each row in a baseball stadium has five more seats than the row below it. Given that there are four seats in the first row, we are to find the total number of seats in the first 24 rows.

For this, we can use arithmetic sequence:

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

[tex]a_n = 4+(24-1)5[/tex]

[tex]a_n=119[/tex]

Now that we know the number of seats in the last row, we will plug the value to find total seats in first 24 rows:

[tex]S_n=\frac{24(4+119)}{2}[/tex]

[tex]S_n=1476[/tex]

Therefore, there are 1476 seats in the first 24 rows.

Answer:

One other zero is 2+3i

Step-by-step explanation:

If 2-3i is a zero and all the coefficients of the polynomial function is real, then the conjugate of 2-3i is also a zero.

The conjugate of (a+b) is (a-b).

The conjugate of (a-b) is (a+b).

The conjugate of (2-3i) is (2+3i) so 2+3i is also a zero.

Ok so we have two zeros 2-3i and 2+3i.

This means that (x-(2-3i)) and (x-(2+3i)) are factors of the given polynomial.

I'm going to find the product of these factors (x-(2-3i)) and (x-(2+3i)).

(x-(2-3i))(x-(2+3i))

Foil!

First: x(x)=x^2

Outer: x*-(2+3i)=-x(2+3i)

Inner:  -(2-3i)(x)=-x(2-3i)

Last:  (2-3i)(2+3i)=4-9i^2 (You can just do first and last when multiplying conjugates)

---------------------------------Add together:

x^2 + -x(2+3i) + -x(2-3i) + (4-9i^2)

Simplifying:

x^2-2x-3ix-2x+3ix+4+9  (since i^2=-1)

x^2-4x+13                     (since -3ix+3ix=0)

So x^2-4x+13 is a factor of the given polynomial.

I'm going to do long division to find another factor.

Hopefully we get a remainder of 0 because we are saying it is a factor of the given polynomial.

                x^2+1

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

x^2-4x+13|  x^4-4x^3+14x^2-4x+13                    

              -( x^4-4x^3+ 13x^2)

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

                                 x^2-4x+13

                               -(x^2-4x+13)

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

                                    0

So the other factor is x^2+1.

To find the zeros of x^2+1, you set x^2+1 to 0 and solve for x.

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

[tex]x^2=-1[/tex]

[tex]x=\pm \sqrt{-1}[/tex]

[tex]x=\pm i[/tex]

So the zeros are i, -i , 2-3i , 2+3i

The zeros of a function are the points where the function cross the x-axis.

One other zero of [tex]\mathbf{f(x) = x^4 - 4x^3 + 14x^2 - 4x + 13}[/tex] is 2 + 3i.

The zero of [tex]\mathbf{f(x) = x^4 - 4x^3 + 14x^2 - 4x + 13}[/tex] is given as:

[tex]\mathbf{Zero = 2 - 3i}[/tex]

The above number is a complex number.

If a complex number a + bi is the zero of a function f(x), then the conjugate a - bi is also the zero of f(x).

This means that, one other zero of [tex]\mathbf{f(x) = x^4 - 4x^3 + 14x^2 - 4x + 13}[/tex] is 2 + 3i.

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Answer:

Step-by-step explanation:

[tex]f(x)=x^2-x-2\\\\\text{The zeros are for}\ f(x)=0:\\\\x^2-x-2=0\\\\x^2-2x+x-2=0\\\\x(x-2)+1(x-2)=0\\\\(x-2)(x+1)=0\iff x-2=0\ \vee\ x+1=0\\\\x-2=0\qquad\text{add 2 to both sides}\\x=2\\\\x+1=0\qquad\text{subtract 1 from both sides}\\x=-1[/tex]

Answer:

Rounding to nearest hundredths gives us r=0.06.

So r is about 6%.

Step-by-step explanation:

So we are given:

[tex]A=P(1+r)^t[/tex]

where

[tex]A=2300[/tex]

[tex]P=1600[/tex]

[tex]t=6[/tex].

[tex]A=P(1+r)^t[/tex]

[tex]2300=1600(1+r)^6[/tex]

Divide both sides by 1600:

[tex]\frac{2300}{1600}=(1+r)^6[/tex]

Simplify:

[tex]\frac{23}{16}=(1+r)^6[/tex]

Take the 6th root of both sides:

[tex]\sqrt[6]{\frac{23}{16}}=1+r[/tex]

Subtract 1 on both sides:

[tex]\sqrt[6]{\frac{23}{16}}-1=r[/tex]

So the exact solution is [tex]r=\sqrt[6]{\frac{23}{16}}-1[/tex]

Most likely we are asked to round to a certain place value.

I'm going to put my value for r into my calculator.

r=0.062350864

Rounding to nearest hundredths gives us r=0.06.

Answer:

10 possible teams.

Step-by-step explanation:

5C2

=5!/(5-2)!2!

=5!/3!2!

=5*4*3*2*1/3*2*1*2*1

=5*4/2*1

=20/2

=10

Therefore answer is 10 possible teams....

Answer:

B

Step-by-step explanation:

The x- intercepts are the points on the x- axis where the graph crosses.

That is (- 3, 0), (1, 0) and (2, 0) → set B

Answer:

D. (1,0), (2,0), (-3,0), and (0,6)

Step-by-step explanation:

Answer:

c=2

The remainder is 7.

Step-by-step explanation:

They want you to subtract those last two lines:

[tex]0x^4+0x^3-5x^2-18x[/tex]

[tex]-(0x^4+0x^3-5x^2-20x)[/tex]

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

[tex]0x^4+0x^3+0x^2+2x[/tex].

2x comes from doing -18-(-20) or -18+20.

Then you bring down the +15 so you have 2x+15 below that last bar in the picture.

Anyways, you then need to find how many times x goes into 2x or what times x gives you 2x?

Hopefully you say 2 here and put that as c.

Now anything you put above the bar has to be multiplied to your divisor so 2(x+4)=2x+8.

We want to see what's left over from subtract (2x+15) and (2x+8). That gives you a remainder of 15-8=7.

Here are my steps for this division:

           4x^3+2x^2-5x+2

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

 x+4| 4x^4+18x^3+3x^2-18x+15

       -(4x^4+16x^3)

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

                    2x^3+3x^2-18x+15

                  -(2x^3+8x^2)

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

                              -5x^2-18x+15

                           -( -5x^2-20x)

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

                                        2x+15

                                     -(  2x+8)

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

                                                7

c=2

The remainder is 7.

Answer:

Step-by-step explanation:

A square and quadrilateral share the properties of having parallel opposite sides, being closed plane figures and having four sides. Not all quadrilaterals have right angles and equal side lengths like squares.

A square and a quadrilateral share several properties due to the fact that a square is a specific type of quadrilateral. The following statements are true: Both shapes always have opposite sides that are parallel, Both shapes are closed plane figures, and Both figures always have four sides. Not all quadrilaterals have right angles or equal length sides, so those properties are unique to squares and not shared with all quadrilaterals.

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Answer:

3 tyres

Step-by-step explanation:

56/4=14

14*3=42

Answer:

3 tyres he will fill.....

Answer:

[tex]\frac{4}{3}[/tex]

Step-by-step explanation:

Simplify your first fraction.

[tex]\frac{12}{6} =2[/tex]

Solve by multiplying your numerators against each other and your denominators against each other.

[tex]\frac{2}{1} *\frac{2}{3} =\frac{4}{3}[/tex]

Answer: 4/3

Step-by-step explanation: You can start off by simplifying 12/6 to 2/1. Then, you can multiply.

2/1 x 2/3 = 4/3

Multiply the numerators. 2x2=4.

Multiply the denominators. 1x3=3

Answer: Step 3

Step-by-step explanation:

He should have divided 8 by 2 and then added it to 49.

In the third step, Rahul made his first mistake. Simplification is to be done using the BODMAS rule.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

Rahul simplified an expression. His work is shown below.

The expression is given below.

7 (8.5 - 1.5) + 8 / 2

Step 1. 7 (7) + 8 / 2

Step 2. 49 + 8 / 2

Step 3. 49 + 4

Step 4. 53

In the third step, Rahul made his first mistake.

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Answer:

see explanation

Step-by-step explanation:

We require to rationalise the denominator by multiplying the numerator and denominator by the complex conjugate of the denominator.

The conjugate of 5 + 3i is 5 - 3i

noting that i² = - 1, hence

[tex]\frac{(9-6i)(5-3i)}{(5+3i)(5-3i)}[/tex] ← expand factors

= [tex]\frac{45-57i+18i^2}{25-9i^2}[/tex]

= [tex]\frac{45-57i-18}{25+9}[/tex]

= [tex]\frac{27-57i}{34}[/tex]

= [tex]\frac{27}{34}[/tex] - [tex]\frac{57}{34}[/tex] i ← quotient

Final answer:

To find the quotient of 9-6i and 5+3i, multiply both the numerator and the denominator by the conjugate of the denominator 5-3i. Simplify by using the distributive property and knowing that i^2 equals -1. The final quotient is 27/34 - 57i/34.

Explanation:

To find the quotient of the complex numbers 9-6i divided by 5+3i, we must multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of 5+3i is 5-3i. So, the process is as follows:

Thus, the quotient is 27/34 - 57i/34 or approximately 0.7941 - 1.6765i.

Answer:

1) y=6

Step-by-step explanation:

The equation y=mx+b is called slope-intercept because it tells us the slope,m, and y-intercept ,b.

The equation y=a is a horizontal line and goes through a on the y-axis.  Horizontal lines have a slope of zero.

The equation x=b is a vertical line and goes through b on the x-axis.

Vertical lines have an undefined slope.

1) y=6 is horizontal so it's slope is 0

2) x=6 is vertical so it's slope is undefined

3) y=2x has slope 2

4) x+y=1 can be put into the form y=mx+b to determine the slope.

Subtract x on both sides:

       y=-x+1

The slope is -1.

Answer:

= 1/59049 ....

Step-by-step explanation:

9 to the 2 = 9^2 = 9*9 = 81

9 to the 7 = 9^7= 9*9*9*9*9*9*9 = 4782969

Now simplify the values by table of 9

=81/ 4782969

=9/531441

=1/59049 ....

Step-by-step explanation:

9 to the 2ND power is 81

9 to the 7th power is 4,782,969

81 divided by 81 is 1

4,782,969 divided by 81 is 59,049

so the final answer is 1

59,049

Answer:

x = 2.68, x = -0.186

Step-by-step explanation:

We are given the following equation that we are to solve:

[tex] 2 x ^ 2 - 1 = 5 x [/tex]

Rearranging this quadratic equation to get:

[tex] 2 x ^ 2 -5 x - 1 = 0 [/tex]

Solving it by using the quadratic formula as we cannot find any factors for it.

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

[tex]x=\frac{-(-5) \pm (-5)^2-4(2)(-1)}{2(2)}[/tex]

[tex]x=\frac{5 \pm\sqrt{25+8} }{4}[/tex]

[tex]x=\frac{5+\sqrt{33} }{4}[/tex], [tex]x=\frac{5-\sqrt{33} }{4}[/tex]

x = 2.68, x = -0.186

Answer:

x = 2.68, x = -0.186 is the answer , i got a 100% on my test

Step-by-step explanation:

b) -4

- 8x +4 =36

First, we subtract 4 from 36 to get 32

36-4=32

-8x=32

Since a negative times a negative equals a positive, then the answer has to be negative because 36 is positive.

32 divided by 8 = 4

B) -4

Answer:

The answer is B, x=-4

Step-by-step explanation:

-8x + 4 = 36

-8x - 4 = 36 - 4

-8x = 32

-8x/-8 = 32/-8

x = -4

Answer:

Part A) Annual [tex]\$66,480.95[/tex]  

Part B) Semiannual [tex]\$66,862.38[/tex]  

Part C) Monthly [tex]\$67,195.44[/tex]  

Part D) Daily [tex]\$67,261.54[/tex]

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

Part A)

Annual

in this problem we have  

[tex]t=5\ years\\ P=\$47,400\\ r=0.07\\n=1[/tex]

 substitute in the formula above  

 [tex]A=47,400(1+\frac{0.07}{1})^{1*5} \\A=47,400(1.07)^{5}\\A=\$66,480.95[/tex]

Part B)

Semiannual

in this problem we have  

[tex]t=5\ years\\ P=\$47,400\\ r=0.07\\n=2[/tex]

 substitute in the formula above  

[tex]A=47,400(1+\frac{0.07}{2})^{2*5} \\A=47,400(1.035)^{10}\\A=\$66,862.38[/tex]

 Part C)

Monthly

in this problem we have  

[tex]t=5\ years\\ P=\$47,400\\ r=0.07\\n=12[/tex]  

substitute in the formula above  

[tex]A=47,400(1+\frac{0.07}{12})^{12*5}\\A=47,400(1.0058)^{60}\\A=\$67,195.44[/tex]

 Part D)

Daily

in this problem we have  

[tex]t=5\ years\\ P=\$47,400\\ r=0.07\\n=365[/tex] 

substitute in the formula above  

[tex]A=47,400(1+\frac{0.07}{365})^{365*5}\\A=47,400(1.0002)^{1,825}\\A=\$67,261.54[/tex]

Answer:

Yes, C is correct.

Step-by-step explanation:

[tex]\bf \qquad \qquad \textit{combined proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with \underline{z}} \end{array}\implies y=\cfrac{kx}{z}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf \stackrel{\textit{"x" varies with}}{x}~~=~~k\stackrel{\textit{inverse of "r"}}{\cfrac{1}{r}}\cdot \stackrel{\stackrel{\textit{inverse of}~\hfill }{\textit{square of a sum}}}{\cfrac{1}{(y+z)^2}}~\hfill x=\cfrac{k}{r(y+z)^2}[/tex]

The variation: x varies jointly with the inverse of r and the inverse of the square of the sum of y and z is,  [tex]x = \frac{1}{r + y^{2} + z^{2} }[/tex]

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

the variation,

x varies jointly with the inverse of r

And the inverse of the square of the sum of y and z

[tex]x = \frac{1}{r + y^{2} + z^{2} }[/tex]

Therefore, the general formula  [tex]x = \frac{1}{r + y^{2} + z^{2} }[/tex]

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Answer:

[tex]a_n=7 \cdot (-3)^{n-1}[/tex]

Step-by-step explanation:

The explicit form for a geometric sequence is [tex]a_n=a_1 \cdot r^{n-1}[/tex] where [tex]a_1[/tex] is the first term and [tex]r[/tex] is the common ratio.

We have the following given:

[tex]a_2=-21[/tex]

[tex]a_5=567[/tex].

We also know that [tex]a_2=a_1 \cdot r[/tex] while [tex]a_5=a_1 \cdot r_4[/tex].

So if we do 5th term divided by second term we get:

[tex]\frac{a_1 \cdot r_4}{a_1 \cdot r}=\frac{567}{-21}[/tex]

Simplifying both sides:

[tex]r^3=-27[/tex]

Cube root both sides:

[tex]r=-3[/tex]

The common ratio, r, is -3.

Now we need to find the first term.

That shouldn't be too hard here since we know the second term which is -21.

We know that first term times the common ratio will give us the second term.

So we are solving the equation:

[tex]a_1 \cdot r=a_2[/tex].

[tex]a_1 \cdot (-3)=-21[/tex]

Dividing both sides by -3 gives us [tex]a_1=7[/tex].

So the equation is in it's explicit form is:

[tex]a_n=7 \cdot (-3)^{n-1}[/tex]

Check it!

Plugging in 2 should gives us a result of -21.

[tex]a_2=7 \cdot (-3)^{2-1}[/tex]

[tex]a_2=7 \cdot (-3)^1[/tex]

[tex]a_2=7 \cdot (-3)[/tex]

[tex]a_2=-21[/tex]

That checks out!

Plugging in 5 should give us a result of 567.

[tex]a_5=7 \cdot (-3)^{5-1}[/tex]

[tex]a_5=7 \cdot (-3)^4[/tex]

[tex]a_5=7 \cdot 81[/tex]

[tex]a_5=567[/tex]

The checks out!

Our equation works!

Final answer:

To find the nth term formula of a geometric sequence with given terms, divide one term by the other to find the common ratio, and then solve for the first term. For this sequence, the nth term is [tex]a_{n}= 7 (-3)^{n-1}[/tex].

Explanation:

To find an equation for the nth term of a geometric sequence where the second and fifth terms are -21 and 567, respectively, we must determine the common ratio (r) and the first term (a1) of the sequence. For a geometric sequence, the nth term is given by the formula [tex]a_{n}= a_{1} (r)^{n-1}[/tex].

Since the second term a2 is -21 and the fifth term a5 is 567, we can set up the following equations using the geometric sequence formula:

[tex]a_{2}[/tex] =  [tex]a_{1}[/tex] x r = -21

[tex]a_{5}[/tex] =  [tex]a_{1}[/tex] x [tex]r_{4}[/tex] = 567

Dividing the second equation by the first gives us:

[tex]r_{3}[/tex] = 567 / -21 = -27

Thus, the common ratio r is -3. Now using [tex]a_{2} =a_{1} r[/tex] , we find that [tex]a_{1}[/tex] = -21 / (-3) = 7. Therefore, the nth term of the sequence is:

[tex]a_{n}= 7 (-3)^{n-1}[/tex]