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SashulF [63]
2 years ago
12

What are the values of a, and r of the geometric series?

Mathematics
1 answer:
Charra [1.4K]2 years ago
7 0
A. A= ray and r=2
That’s the answer
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The green triangle is a dilation of the red triangle with a scale factor of s=1/3 and the center of dilation is at the point (4,
klasskru [66]

Given:

The scale factor is s=\dfrac{1}{3} and the center of dilation is at the point (4,2).

Red is original figure and green is dilated figure.

To find:

The coordinates of point C' and point A.

Solution:

Rule of dilation: If a figure is dilated with a scale factor k and the center of dilation is at the point (a,b), then

(x,y)\to (k(x-a)+a,k(y-b)+b)

According to the given information, the scale factor is \dfrac{1}{3} and the center of dilation is at (4,2).

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

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

Using (i), we get

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

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

C(-2,11)\to C'(-2+4,3+2)

C(-2,11)\to C'(2,5)

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

We assumed that point A is A(m,n).

Using (i), we get

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

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

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

On comparing both sides, we get

\dfrac{1}{3}(m-4)+4=8

\dfrac{1}{3}(m-4)=8-4

(m-4)=3(4)

m=12+4

m=16

And,

\dfrac{1}{3}(n-2)+2=4

\dfrac{1}{3}(n-2)=4-2

(n-2)=3(2)

n=6+2

n=8

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

5 0
3 years ago
Please Help! Given triangles ABC and DEF, which statement explains a way to determine if the two figures are similar?
forsale [732]

Answer:

A

Step-by-step explanation:

i took the test

5 0
3 years ago
Read 2 more answers
7. The following clues are given about a bucket of bubble gum.
scZoUnD [109]

There were 472 pieces of bubble gum in the bucket

Step-by-step explanation:

The following clues are given about a bucket of bubble gum

1. There are between 400 - 500 pieces of gum in the bucket

2. The bubble gum was purchased in 4 equally-sized bags

3. The product of all the digits is 56

Let us explain how to solve the problem

∵ The number of the pieces of gum is between 400 and 500

∴ The number of pieces is 3-digit number and its hundred digit is 4

∵ The product of all digits is 56

∵ One of the digit is 4

∵ 56 ÷ 4 = 14

∴ The product of the ten digit and the one digit is 14

∵ 14 = 2 × 7

∴ The ten digit and the one digit are 2 and 7 or 7 and 2

- If the ten digit is 2 and the one digit is 7

∴ The number of pieces is 427

∵ The bubble gum was purchased in 4 equally-sized bags

- That means there were 4 pieces of bubble gum in each bag

∴ The number of pieces must divisible by 4

- The number is divisible by 4 if it is an even number and the number

 formed from the ten digit and one digit is divisible by 4

∵ 427 is an odd number

∴ 427 not divisible by 4

- If the ten digit is 7 and the one digit is 2

∴ The number of pieces is 472

∵ 472 is an even number

∵ 72 divisible by 4

∴ 472 is divisible by 4

∴ There are 472 pieces of gum in the bucket

There were 472 pieces of bubble gum in the bucket

Learn more:

You can learn more about digits in brainly.com/question/547255

#LearnwithBrainly

7 0
3 years ago
What is the solution to the equation -3d/a^2-2d-8 + 3/d-4 = -2/ d+2
Alex73 [517]

Answer:

d=1

Step-by-step explanation:

\frac{-3d}{d^2-2d-8} +\frac{3}{d-4} =\frac{-2}{d+2}

Lets factor the denominator d^2 -2d-8

d^2 - 2d - 8 = (d-4)(d+2)

\frac{-3d}{(d-4)(d+2)} +\frac{3}{d-4} =\frac{-2}{d+2}

Now make the denominators same

LCD: (d-4)(d+2)

\frac{-3d}{(d-4)(d+2)} +\frac{3(d+2)}{(d-4)(d+2)} =\frac{-2(d-4)}{(d+2)(d-4)}

Denominators are same on both sides

So equate the numerators

-3d +3(d+2) = -2(d-4)

-3d +3d +6 = -2d +8

6 = -2d + 8

subtract 8 on both sides

-2 = -2d

So d=1




3 0
3 years ago
Read 2 more answers
In his free time, Gary spends 13 hours per week on the Internet and 13 hours per week playing video games. If Gary has five hour
goldenfox [79]
<span>Gary spend 13 hours per week on the Internet and 13 hours on video games Gary has 5 hours of free time each day,
 so total free time in a week=> 7*5=35 hours
Now he spends 13+13 hours on the internet and games=28 hours Percentage free time spent on games and internet
 

26/35 (that is a fraction) x100 =</span><span>74.285714 
</span>so round your answer
6 0
3 years ago
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