Find the 8th term of the geometric sequence 4, -12,36,...

Given:

Scale factor [tex]s=\dfrac{1}{3}[/tex]

Center of dilation = (4,2)

To find:

The coordinates of the points C' and A.

Solution:

We know that, if a figure is dilated with a scale factor k and the center of dilation is at the point (a,b), then

[tex](x,y)\to (k(x-a)+a,k(y-b)+b)[/tex]

The scale factor is [tex]\dfrac{1}{3}[/tex] and the center of dilation is at (4,2).

[tex](x,y)\to (\dfrac{1}{3}(x-4)+4,\dfrac{1}{3}(y-2)+2)[/tex]            ...(i)

Suppose the vertices of red triangle are A(m,n), B(10,14) and C(-2,11).

Using rule (i), we get

[tex]C(-2,11)\to C'(\dfrac{1}{3}(-2-4)+4,\dfrac{1}{3}(11-2)+2)[/tex]

[tex]C(-2,11)\to C'(\dfrac{1}{3}(-6)+4,\dfrac{1}{3}(9)+2)[/tex]

[tex]C(-2,11)\to C'(-2+4,3+2)[/tex]

[tex]C(-2,11)\to C'(2,5)[/tex]

Hence, the coordinates of Point C' are C'(2,5).

Let us assume that point A is A(m,n).

Using rule (i), we get

[tex]A(m,n)\to A'(\dfrac{1}{3}(m-4)+4,\dfrac{1}{3}(n-2)+2)[/tex]

From the given figure it is clear that the image of point A is (8,4).

[tex]A'(\dfrac{1}{3}(m-4)+4,\dfrac{1}{3}(n-2)+2)=A'(8,4)[/tex]

On comparing both sides, we get

[tex]\dfrac{1}{3}(m-4)+4=8[/tex]

[tex]\dfrac{1}{3}(m-4)=8-4[/tex]

[tex](m-4)=3(4)[/tex]

[tex]m=12+4[/tex]

[tex]m=16[/tex]

And,

[tex]\dfrac{1}{3}(n-2)+2=4[/tex]

[tex]\dfrac{1}{3}(n-2)=4-2[/tex]

[tex](n-2)=3(2)[/tex]

[tex]n=6+2[/tex]

[tex]n=8[/tex]

Therefore, the coordinates of point A are (16,8).

Answer:

x = 1

y = 2

Step-by-step explanation:

the intersecting point is (1,2)

Answer:

I love Math anyways  

the ans is in the picture with the steps  

(hope it helps can i plz have brainlist :D hehe)

Step-by-step explanation:

Answer:

no clue

Step-by-step explanation:

lol

Answer:

b) 2017

c) Quarter 2

Step-by-step explanation:

the americans scored twice in the last period although the soviet team dominated second period, after that the americans finally took the lead

(this is english not math change your question when you have to do this again)

Answer:

10

Step-by-step explanation:

i just kno it if it's not 10 it -11 okkkkkk

Answer:

NI and HN

Step-by-step explanation:

The segments are both marked with a congruency mark.

Answer:

Yes, this is a right triangle.

Step-by-step explanation:

If you look more closely, you can notice that it is a 3-4-5 Pythagorean triple and it was multiplied by 3 to get 9-12-15.

Or you can do it using the Pythagorean Theorem directly:

9^2 + 12^2 = 15^2

and that is true.

Answer:

yes it is.

Step-by-step explanation:

pythagorean theorem. A^2 + B^2 = C^2

Ex 9^2 + 12^2 = 15^2

Answer:

Opposite sides are equal in length and opposite angles are equal in measure. To find the area of a parallelogram, multiply the base by the height. The formula is: A = B * H where B is the base, H is the height, and * means multiply.

I hope it's helpful!

Answer:

4.415525546*10 to the power of 15

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

5x + 3y = 95

8x + 6y = 170

x = 10 ; y = 15

Step-by-step explanation:

Let :

x = pack of juice boxes

y = pack of water bottles

Pack of juice box = $5

Pack of water bottles = $3

Amount of money spent :

5x + 3y = $95

Number of drinks purchased :

8x + 6y = 170

Using both equations ;

5x + 3y = 95 - - - (1)

8x + 6y = 170 - - - (2)

Multiply (1) by 6 and (2) by 3

30x + 18y = 570

24x + 18y = 510

Subtract :

6x = 60

x = 60 / 6

x = 10

Put x = 10 in (1)

5(10) + 3y = 95

50 + 3y = 95

3y = 95 - 50

3y = 45

y = 45 / 3

y = 15

x = 10 ; y = 15

Answer:

102.4

Step-by-step explanation:

hope that helps beautiful ;-)

Answer: The slope is 2/3.

Step-by-step explanation: From (-1,6) to (-7,-3), the x goes up 6, and the y goes down 9. This makes the fraction -6/9. This would reduce to -2/3, but the direction the slop is headed is upwards to the right, meaning it's a positive slope.

Answer:

4

Step-by-step explanation:

Because the common multiple of 6 and 8 is 24 which is the amount of pencils.

1/8 x 3 equals 24 (3 because 3 times 8 gives 24)

1/6 x 4 equals 24 (4 because 4 times 6 gives 24)

Answer:

8.06 feet

Step-by-step explanation:

use the Pythagorean theorem

9^2 = 4^2 + x^2

81 =16 +x^2

x^2 = 65

x = 8.06 feet

Answer:

c > 38.5

Step-by-step explanation:

14c > 600 - 61

14c > 539

c > 38.5

Answer:

[tex]16[/tex]

Step-by-step explanation:

Substituting [tex]a=2[/tex] and [tex]b=3[/tex] into [tex](a^{b}+b^{a})-1[/tex] gives us:

[tex](a^{b}+b^{a})-1[/tex]

[tex]=(2^{3} +3^{2})-1[/tex] (Substitute given values into expression)

[tex]=(8+9)-1[/tex] (Evaluate exponents)

[tex]=17-1[/tex] (Evaluate expression in parentheses)

[tex]=16[/tex] (Simplify)

Hope this helps!

Answer:

16

Step-by-step explanation:

Given

([tex]a^{b}[/tex] + [tex]b^{a}[/tex] ) - 1 ← substitute a = 2, b = 3

= (2³ + 3²) - 1

= (8 + 9) - 1

= 17 - 1

= 16

Answer:

We conclude that the train can travel 2240 miles in 16 hours.

Step-by-step explanation:

Given that a  super train traveled 420 miles in 3 hours.

Step 1 of 2

Determine distance per hour

Important Tip:

Distance per hour = Distance Covered / Time taken

              = 420 / 3

              = 140 miles per hour

Step 2 of 2

Determine the distance traveled in 16 hours

We already know that a super train travels 140 miles per hour. In other words, the speed of the super train is 140 miles per hour.

Important Tip:

Distance traveled in 16 hours = Distance per hour × 16

                                                 =  140 × 16

                                                 = 2240 miles

Conclusion:

Therefore, we conclude that the train can travel 2240 miles in 16 hours.

Answer:

$3,993

Step-by-step explanation:

Answe

Step-by-step explanation:

Here goes the answer. Please mark brainliest.

Answer:

multiply both sides by 17

your supposed to do the opposite of the symbol given

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

12x = 36

simply 12 will go to the other side and switches to the opposite sign for example + will be -

× will br ÷

so 36 ÷ 12 =3

x = 3

Answer:

slope=2x, y-intercept=-3

Step-by-step explanation:

When in slope intercept, the slope (m) is always the x (and whatever number is in front of it), and the y-intercept (b) is at the end of the equation.