Find the 7th term of the geometric sequence -2, 6, -18, 54, -162, ...

Answer:

Edge = 2.5

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

Given: a*b=2a-3b

To find: 2*(-3)

Solution:

Numbers that are used for counting are known as natural numbers. Number along with the digit 0 are known as whole numbers.

In the question, [tex]*[/tex] is used to define relation between a and b as [tex]a*b=2a-3b[/tex]

To find 2*(-3), use the given condition: a*b=2a-3b

Put [tex]a=2,b=-3[/tex]

[tex]2*(-3)=2(2)-3(-3)=4+9=13[/tex]

Given that a*b = 2a-3b,then 2*(-3)=​ 13

The given binary operation is:

a*b = 2a  -  3b

Applying this binary operation to 2*(-3), we are going to substitute a = 2 and b = -3 into the binary operation a*b = 2a  -  3b

If a = 2 and b = -3:

2*(-3)  =  2(2)  -  3(-3)

2*(-3)  =  4   +  9

2*(-3)  =  13

Therefore, given that a*b = 2a-3b,then 2*(-3)=​ 13

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Step-by-step explanation:

4 + (27 - 12 * 2) / 2

4 + (27 - 24) / 2

4 + 3/2

5 1/2

Answer:

5 1/2

Step-by-step explanation:

4 + (27 - 12 ∙ 2) ÷ 2=

4 + (27 - 24) ÷ 2=

4 + 3/2= 5 1/2

Step-by-step explanation:

do you mean --8 plus 31

Answer:

135°

Step-by-step explanation:

You want QRT. So if you look at it you have a straight line, which equals 180°. you already have an angle at 45° so all you do is 180-45 and that equals 135°

Answer:

x=6

Step-by-step explanation:

11, 3, x, x+2, 5, 10

in ascending order the data points:

Step-by-step explanation:

6a

Sn = n/2 [2a + (n-1) d]

(2Sn)/ n = 2a + (n - 1) d

2a + (n-1) d = (2Sn)/n

(n-1) d = (2Sn - 2a)/n

[tex]d = \frac{2sn \: - 2a}{(n(n - 1))} [/tex]

[tex]d = \frac{2(sn - a)}{ {n}^{2} - n} [/tex]

6b

[tex]d = \frac{2(56 - 25)}{ {32}^{2} - 32} [/tex]

d = ¹/16

7a.

E = (mv²)/2 + mgh

E = m( v²/2 + gh)

E/m = v²/2 + gh

E/m - gh = v²/2

2(E/m - gh) = v²

so

[tex]v = \sqrt{2( \frac{e}{m} - gh)}[/tex]

7b.

[tex]v = \sqrt{2( \frac{4900}{20} - 9.8 \times 15)}[/tex]

v = 14 m/s

Answer:

Y=1/2x-3

Step-by-step explanation:

Down 3 at the y-axis and up 1 right 2.

Answer:

Search Results

Featured snippet from the web

Odd and even square numbers

As all even square numbers are divisible by 4, the even numbers of the form 4n + 2 are not square numbers. As all odd square numbers are of the form 4n + 1, the odd numbers of the form 4n + 3 are not square numbers.

Step-by-step explanation:

Answer:

6 plus .1 plus .007

6 times 1 plus 1 times .1 plus 5 times .01

Step-by-step explanation:

Hope this helps

Answer:

y = 4 - x/2

Step-by-step explanation:

Since the line passes through the points A(8,0) and B(4,6), we find that gradient of that lime m = (y₂ - y₁)/(x₂ - x₁) where (8,0) = (x₁, y₁) and (-4,6) = (x₂, y₂).

So, m = (6 - 0)/(-4 - 8) = 6/-12 = = -1/2.

Since the line passes through the point (0,4), the equation of the line is

m = (y - y₃)/(x - x₃) where (x₃, y₃) = (0,4)

So, -1/2 = (y - 4)/(x - 0)

            = (y - 4)/x

    -x/2 = y - 4

         y = 4 - x/2

which is the equation of the line.

Answer:

B

Step-by-step explanation:

Answer: 10.99 + 1.25x

Step-by-step explanation:

The cost of a large pizza is $10.99 and each additional topping costs $1.25. The expression that can be used to calculate the cost of a pizza when x toppings are added will be:

Cost of pizza + (number of additional toppings × 1.25)

Since x toppings are included, this will be:

= 10.99 + (1.25 × x)

= 10.99 + 1.25x

Answer:

12

Step-by-step explanation:

n*30=360

n=360/30

n=12

Answer:

Janice converted a mixed number to the wrong improper fraction.

Step-by-step explanation:

1 batch of stew uses 1 and 2/3 lb meat

Total amount of meat used - 10 and 5/6 lb

x = number of stew batches made

To get number of batches made, divide total meat used by the amount of meat each batch requires:

x = 10 5/6 ÷ 1 2/3

convert mixed fractions to improper fractions:

x = (10x6+5)/6 ÷ (1x3+2)/3

x = 65/6 ÷ 5/3

The fraction in bold numbers is where Janice got it wrong. She changed 1 2/3 to 5/2. (From the question: 10 and StartFraction 5 over 6 EndFraction divided by 1 and two-thirds = StartFraction 65 over 6 EndFraction divided by five halves). 1 2/3 converted to an improper fraction is 5/3. From this point going forward, the calculations are wrong.

Answer:

A

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

1/4 +11/4

(1+11)/4

12/4

3

Answer:

=3

Step-by-step explanation:

The correct answer to this question is =3. I added the steps down below. I also added a attachment that refer to a number line for this question.

1: =1/4+11/4

2: =1+11/4

3: 12/4

4: =3

Answer: =3

Number line attached.

Hope this helps.

Answer:

OG, OC, TG, TC, VG, VC

Step-by-step explanation:

Soups: O, T, V

Salads: G, C

For each soup, he can choose 2 salads.

OG, OC, TG, TC, VG, VC

The sample space represents all the possible ways to choose one soup and one salad is {OG, OC, TG, TC, VG, VC}.

Sample space is the set of all the possible values or the outcomes of a event.

Let suppose the coin are tossed two times. Then the set of possible outcome or sample space of it can be given as,

[tex]S=\{HH,HT,TH,TT\}[/tex]

Here, H denotes the head and T denotes the tail part of the coin.

A customer at a restaurant can choose a soup and a salad from the menu choices shown.

For this menu the customer choose one onion as soup and one garden as salad which can be represented as (OG). Similarly, the sample space of his choice can be,

[tex]\{OG, OC, TG, TC, VG, VC\}[/tex]

Thus, the sample space represents all the possible ways to choose one soup and one salad is {OG, OC, TG, TC, VG, VC}.

Learn more about the sample space here;

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#SPJ2

Answer:

126

Step-by-step explanation:

The probability is 90/500 = 18%

So, from 700 customers,

700 * 18%  = 700 * 18/100 = 126

Therefore, 126 customers will be selected on saturday.

1. x =5

2. x = 7

3. p = 12

4. m=2

5. z = 10

Answer:

Below in bold.

Step-by-step explanation:

1) 4x - 7 = 13

4x = 20

x = 20/4

x = 5.

2)  3x + 4 = 25

3x = 21

x = 7.

3) p/3 + 5 = 9

p/3 = 9 -5 = 4

Multiply both sides by 3:

p =  3*4

p = 12.

4)   m/5 + 2 = 12/5

Multiply through by 5:

m + 10 = 12

m = 12 -10

m = 2.

5) 4z/5 - 2 = 6

4z/5 = 8

Cross multiply:

4z = 5*8

4z = 40

z = 10.

Answer:

The solution of the given two simultaneous equation

A( 3 ,6)  and  [tex]B(\frac{1}{2} ,\frac{17}{2} )[/tex]

The intersecting points of given two simultaneous equations are

A( 3 ,6)  and  [tex]B(\frac{1}{2} ,\frac{17}{2} )[/tex]

Step-by-step explanation:

Explanation:-

Step(i):-

Given  simultaneous equation

        y  =  9-x    ...(i)

      y   = 2 x² +4 x+6 ..(ii)

Equating (i) and (ii) equations , we get

      9 -x =  2 x² +4 x+6

 ⇒    2 x² +4 x + 6- 9 +x =0

 ⇒  2 x² + 5 x - 3 =0

  ⇒ 2 x² +6 x -x -3 =0

⇒   2 x ( x +3) -1 ( x+3) =0

⇒    (2 x -1 ) ( x+3) =0

⇒    (2 x -1 ) = 0   and   ( x +3 ) =0

    [tex]2 x =1[/tex]    and   x = -3

      x = 1/2 and x =3

Step(ii):-

  x = 3  ⇒ y = 9 - 3 =6

   A( 3 ,6)

 [tex]x = \frac{1}{2} , y = 9 - \frac{1}{2} = \frac{17}{2}[/tex]

[tex]B(\frac{1}{2} ,\frac{17}{2} )[/tex]

Final answer:-

The intersecting points of two simultaneous equations are

A( 3 ,6)  and  [tex]B(\frac{1}{2} ,\frac{17}{2} )[/tex]

The solution of the given two simultaneous equation

A( 3 ,6)  and  [tex]B(\frac{1}{2} ,\frac{17}{2} )[/tex]

The solution to the given simultaneous equation is (1/2, 8 1/2) and (-3, 12)

From the question,

We are to solve the given simultaneous equations

The given equations are

y = 9-x                ---------- (1)

y = 2x²+4x+6    ---------- (2)

Substitute equation (1) into equation (2)

y = 2x²+4x+6

That is

9-x = 2x²+4x+6

Simplifying, we get

0 = 2x² +4x +x +6 -9

0 = 2x² +5x -3

∴ 2x² +5x -3 = 0

Now, solving the quadratic equation

2x²+6x -x -3 = 0

Factorizing

2x(x+3) -1(x+3) = 0

Then, we get

(2x -1)(x+3) = 0

∴ 2x - 1 = 0 OR x + 3 = 0

2x = 1 OR x = -3

∴ x = 1/2 OR x = -3

Now, substitute the values of x into equation (1) to determine the values of y

y = 9-x

When x = 1/2

y = 9 - 1/2

y = 8 1/2

and when x = -3

y = 9 --3

y = 9+3

y = 12

Hence, the solution to the given simultaneous equation is (1/2, 8 1/2) and (-3, 12)

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Answer:

a) The equation of the parabola

                        [tex]y = \frac{-x^{2} }{4} +5[/tex]

Step-by-step explanation:

Explanation:-

Step(i):-

Given the directrix of the parabola y = 6

Focus of the parabola S(0,4)

The standard equation of the parabola

                  ( x- h)² = 4 a (y-k)

(h,k) is the vertex of the parabola

Axis of the parabola is parallel to y-axis

Given the directrix of the parabola y = 6

The directrix of the parabola y = k -a = 6

                                k-a =6 ...(i)

The focus of the parabola

                         S( h , K+a) = (0,4)

so   h = 0 and K+a =4

                          K+a =4 ....(ii)

Step(ii):-

Solving (i) and (ii) equations , we get

    Adding (i) and (ii) equations and we get

     K-a + k+a = 6 +4

               2 K = 10

                  K =5

Substitute   K =5 in equation (i)

             K -a =6

            5 -a =6

            5-6 =a

            a = -1

Step(iii):-

we have (h,k) =( 0,5)  and a = -1

The equation of the  parabola

                                 ( x- h)² = 4 a (y-k)

                                 ( x- 0)² = 4 (-1) (y-5)

                                x²  = -4 y + 20

                              -4 y =   x²  - 20

dividing '-4' on both sides, we get

                         [tex]y = \frac{x^{2} }{-4} +\frac{-20}{-4}[/tex]

                          [tex]y = \frac{-x^{2} }{4} +5[/tex]

Final answer:-

The equation of the parabola

                        [tex]y = \frac{-x^{2} }{4} +5[/tex]

Answer:

In this problem, we have three vertices, namely:

A(-2,2) , B(-2,4) , C(0,0)

Our transformation rule is (x+3,y-2) and this rule forms the image A'B'C'. So:

Step-by-step explanation:

A'=(-2+3,2-2)=(1,0)

B'=(-2+3,4-2)=(1,2)

C'=(0+3,0-2)=(3,-2)

Taking a look in the First Figure, we can see the two triangles. The red one is the triangle ABC and the blue one is A'B'C'. In the Second Figure, the corresponding vertices have been connected with line segments, as indicated the green lines. The characteristics of those three lines are two, namely:

They are parallel.

They have the same length.

Answer: a=-2, b=7/2

Step-by-step explanation:

To solve for a and b, we can use the elimination method for these system of equations.

3a+2b=1

a+2b=5

Since there is a 2b in both equations, we can subtrac the 2 equations.

2a=-4

a=-2

Now that we have found a, we can plug it into ay of the equations to find b.

-2+2b=5

2b=7

b=7/2

Answer:

x=9

y=5

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

Answer:

x=62.

Step-by-step explanation:

2x +4=128

2x=128-4

2x=124

x= 62

I'm guessing the second derivative is for y with respect to x, i.e.

[tex]\dfrac{\mathrm d^2y}{\mathrm dx^2}[/tex]

Compute the first derivative. By the chain rule,

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm d\theta}\dfrac{\mathrm d\theta}{\mathrm dx}=\dfrac{\frac{\mathrm dy}{\mathrm d\theta}}{\frac{\mathrm dx}{\mathrm d\theta}}[/tex]

We have

[tex]y=b\sin\theta\implies\dfrac{\mathrm dy}{\mathrm d\theta}=b\cos\theta[/tex]

[tex]x=a\cos\theta\implies\dfrac{\mathrm dx}{\mathrm d\theta}=-a\sin\theta[/tex]

and so

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{b\cos\theta}{-a\sin\theta}=-\dfrac ba\cot\theta[/tex]

Now compute the second derivative. Notice that [tex]\frac{\mathrm dy}{\mathrm dx}[/tex] is a function of [tex]\theta[/tex]; so denote it by [tex]f(\theta)[/tex]. Then

[tex]\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm df}{\mathrm dx}[/tex]

By the chain rule,

[tex]\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm df}{\mathrm d\theta}\dfrac{\mathrm d\theta}{\mathrm dx}=\dfrac{\frac{\mathrm df}{\mathrm d\theta}}{\frac{\mathrm dx}{\mathrm d\theta}}[/tex]

We have

[tex]f=-\dfrac ba\cot\theta\implies\dfrac{\mathrm df}{\mathrm d\theta}=\dfrac ba\csc^2\theta[/tex]

and so the second derivative is

[tex]\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\frac ba\csc^2\theta}{-a\sin\theta}=-\dfrac b{a^2}\csc^3\theta[/tex]

Answer:

44/51

Step-by-step explanation:

1 5/6 ÷ 2 1/8

Change to improper fractions

1 5/6 = (6*1+5)/6 = 11/6

2 1/8 = (8*2 +1) /8 = 17/8

11/6 ÷17/8

Copy dot flip

11/6 * 8/17

11/17 * 8/6

11/17 *4/3

44/51

Answer: 400 units

Step-by-step explanation:

Volume=1/3a^2h

=1/3(10)^2(12)

=400

The correct answer is 400. I had the same question on a test I took not to long ago.

Answer:

4/5

Step-by-step explanation:

y = mx + b

4/5 = m = slope

Answer:

The slope is 4/5.

Step-by-step explanation:

It's a linear equation. Which means that you can graph a "line" out of it.

The format is y=mx+b

mx=slope

b= y-intercept.

The slope is 4/5.