What is the value of x in the equation 2(x−3)+9=3(x+1)+x?

x = −3
x = −1
x = 0
x = 3

[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]\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

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:

y = 5x

Step-by-step explanation:

The equation to do this is y = mx + b.

b is y intercept which is 0

m is the slope, which is 5

y = 5x + 0 or y = 5x

Answer:

y=5x

Step-by-step explanation:

So we have the points (0,0) and (2,10) that are on the line.

The slope can be calculate the slope by finding the rise and the run, and then putting the rise/run.

If you want to use the graph to count the rise, you can.  If you start at 0 and need to get to 10, then you need to rise 10 units.

If you want to use the graph to count the run, you can. If you start at 0 and need to get to 2, then you need to run 2 units.

So the slope is 10/2=5.

Or, if you didn't want to count, you could use the slope formula for a line given two points on that line.

That is the formula is [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].

There is another format for that formula that might be easier to remember.  Just line the points up and subtract vertically. Then put 2nd difference over 1st difference.

So let's do that also:

(  2  ,  10)

-(  0   ,   0)

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

  2           10

So the slope is 10/2=5.

Now you can get the same answer if you had done it the other way:

 ( 0 ,   0)

- ( 2 ,  10)

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

 -2      -10

So the slope is -10/-2=5.

You get the same number either way.

So the slope-intercept form of a line is y=mx+b.

m is the slope and b is the y-intercept.

We found m which is 5.

If you look at the graph, you see the line goes through the y-axis at y=0 so the y-intercept, b, is 0.

The equation of the line here is y=5x+0 or just simply y=5x.

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:

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:

ok seems easy *ahem*

x=26

Step-by-step explanation:

*MLG intensufys*

Answer:

15) 300%

Step-by-step explanation:

15)

Let the item originally cost n dollars.

The new incorrect price is (n-.6n).

So we want to find k such that (n-.6n)+k(n-.6n)=n+.6n

since we actually wanted it to be (n+.6n).

So we have (n-.6n)+k(n-.6n)=n+.6n

Distribute:

n-.6n+kn-.6nk=n+.6n

Subtract n on both sides

  -.6n+kn-.6nk=.6n

We are trying to solve for k. So add .6n on both sides:

kn-.6nk=1.2n

Divide both sides by n:

k-.6k=1.2

.4k=1.2

Divide both sides by .4

k=1.2/.4

k=3

So 3=300%.

The incorrect price must be increased by 300% to get to the proper new price.

Here is an example:

Something cost $600.

It was reduce by 60% which means it cost 600-.6(600)=600-360=240

This was the wrong price.

We needed it to be increased by 60% which would have been 600+360=960.

So we need to figure out what to increase I wrong price 240 to to get to our right price of 960.

240+k(240)=960

1+k=960/240

1+k=4

k=3

So 240*300%+240 would give me my 960.

16) Speed=distance/time

In the first half hour, she traveled 5 miles (8:30 to 9).

In 1/3 hour she traveled (5-2)=3 miles (9 to 9:20).

We are told not to do anything where she stayed still.

In the last half hour, she traveled (2-0)=2 miles (9:30 to 10).

The average speed=[tex]\frac{5+3+2}{\frac{1}{2}+\frac{1}{3}+\frac{1}{2}}=\frac{10}{\frac{4}{3}}=\frac{10(3)}{4}=\frac{30}{4}=\frac{15}{2}=7\frac{1}{2}[/tex].

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:

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:

Step-by-step explanation:

6x^2+5x+1=0

Descr= b^2-4ac

Descr= 25-24=1

X1= (-b+√descr)/2a = (-5+1)/12= -1/3

X2= (-b-√descr)/2a = (-5-1)/12= -1/2

Answer:

see explanation

Step-by-step explanation:

Given

6x² + 5x + 1 = 0

To factorise the quadratic

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

The factors are + 3 and + 2

Use these factors to split the x- term

6x² + 3x + 2x + 1 = 0 ← ( factor the first/second and third/fourth terms )

3x(2x + 1) + 1 (2x + 1) = 0 ← factor out (2x + 1) from each term

(2x  1)(3x + 1) = 0

Equate each factor to zero and solve for x

2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = - [tex]\frac{1}{2}[/tex]

3x + 1 = 0 ⇒ 3x = - 1 ⇒ x = - [tex]\frac{1}{3}[/tex]

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:

Answer:

12.9

Step-by-step explanation:

!!!!

The length of AC is approximately 12.9cm

Given the following identity

Using the SOH CAH TOA identity

sin 40 = AC/20

AC = 20sin40

AC = 20(0.6428)

AC = 12.9cm

Hence the length of AC is approximately 12.9cm

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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.

G. 7,500 cubic feet

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:

The expression which gives the probability that she will select two red cubes = 5/12 * 4/11 ....

Step-by-step explanation:

According to the statement there are 4 red cubes and 7 white cubes.

The total number of cubes are = 7+5 = 12

If she picks up one red cube then the number of ways of picking up red cubes out of 12 is = 5/12

If she picks up 2nd red cube then  the number of ways of picking up 2nd red cube = 4/11

Therefore the expression which gives the probability that she will select two red cubes = 5/12 * 4/11 ....

Answer:

Yes, C is correct.

Step-by-step explanation:

Answer:

Multiply both sides of the equation by 1/3

Step-by-step explanation:

3x^2+18x=21

The first step is to get the x term with a coefficient of 1, so divide by 3 on both sides of the equation

This is the same as multiplying by 1/3

1/3 * (3x^2+18x)=21*1/3

x^2 +6x = 7

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:

3 tyres

Step-by-step explanation:

56/4=14

14*3=42

Answer:

3 tyres he will fill.....

Answer:

Option B: 81y^4-16x^2, the difference of squares

Step-by-step explanation:

we know that

The Difference of Squares is two terms that are squared and separated by a subtraction sign

so

[tex](a+b)(a-b)=(a^{2}-b^{2})[/tex]

In this problem we have

[tex](9y^{2}-4x)(9y^{2}+4x)[/tex]

Let

[tex]a=9y^{2}[/tex]

[tex]b=4x[/tex]

so

[tex]a^{2}=(9y^{2})^{2}=81y^{4}[/tex]

[tex]b^{2}=(4x)^{2}=16x^{2}[/tex]

substitute

[tex](9y^{2}-4x)(9y^{2}+4x)=81y^{4}-16x^{2}[/tex]

Answer: b

Step-by-step explanation: edge 2022

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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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.

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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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:

[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]

Answer:

B is a function.

Step-by-step explanation:

A relation that is a set of points is a function if all the x's are different.  Each ordered pair in the set (excluding the duplicates if any) all have to have a distinct x.

For example if someone ask you if this is a function they are trying to trick you:

{(4,5),(1,3),(4,5)}.

They are trying to trick you because they listed the element (4,5) twice.

The set is really {(4,5),(1,3)}.

This would be a function because all the x's are distinct, ex 4 is different than 1.

Let's look at your choices:

A This is not a function because you have two pairs with the same x-coordinate.

B This is a function.  There are no repeats of any x,

C This is not a function because you have 11 as x twice.

D This is not a function because x=3 happens twice.

If the same x happens more than once than it isn't a function.  

Answer:

b

Step-by-step explanation:

took test

Answer:

The approximate volume of the sphere= 4187  cubic units

Step-by-step explanation:

Points to remember

Volume of sphere = (4/3)πr³

Where 'r' radius of sphere

To find the volume of sphere

It is given that the radius of the sphere is 10 units. ,

Here radius r = 10 units

Volume =  (4/3)πr³

 =  (4/3) * 3.14 * 10³

 =  (4/3) * 3140

 =  4186.666 ≈  4187  cubic units

Answer:

Option C.

Step-by-step explanation:

Radius of the sphere is given as 10 units.

We have to calculate the volume of this sphere.

Since formula to measure the volume of sphere is V = [tex]\frac{4}{3}\pi r^{3}[/tex]

V =  [tex]\frac{4}{3}\pi 10^{3}[/tex]

  =  [tex]\frac{4}{3}(3.14)(10^{3})[/tex]

  = 4186.67

  ≈ 4187 cubic units.

Option C. is the answer.