Josephine enlarged a picture using a photocopier the original photo was 3.5 inches by 5 inches the copy was 8.5 by 12.5 inches . What is the scale factor of the dilation?

Answer: 34

Step-by-step explanation:

[tex]a=3+2\sqrt{2} \\\\\dfrac{1}{a} =\dfrac{1}{3+2\sqrt{2}} =\dfrac{3-2\sqrt{2}}{(3+2\sqrt{2})(3-2\sqrt{2})} =\dfrac{3-2\sqrt{2}}{3^2-2^2*2} =3-2\sqrt{2}\\\\\\a+\dfrac{1}{a} =3+2\sqrt{2}+3-2\sqrt{2}=6\\\\(a+\dfrac{1}{a})^2=6^2=36=a^2+\dfrac{1}{a^2}+2\\\\\\a^2+\dfrac{1}{a^2}=36-2=34\\[/tex]

The two answers you are looking for are 16π m² and 50.24 m².

Solution:

Finding the area of the circle,

First, knowing what the area of a circle formula is:

A=πr²

Since knowing that the radius is half the length of the diameter,

If the diameter is 8, then the radius must be 4.

A=π(4)²

A=16π m²

Now, you have the first answer. If you want to express it differently,

Using 3.14 as pi,

So, therefore,

A=16(3.14)

A=50.24 m²

So, now, we can conclude that the two answers you are looking for for the area of this circle are 16π m² and/or 50.24 m².

Answer:

16pi and 50.24 m squared

Step-by-step explanation:

Step-by-step explanation:

a1 = -4 = -4/1, a2 = 8/3

r = a2/a1 = (8/3) / (-4/1) = -2/3

the formula :

an = a1. r^(n-1)

so,

an = (-4). (-2/3)^(n-1)

Step-by-step explanation:

[tex]-4, \dfrac{8}{3}, -\dfrac{16}{9}, \dfrac{32}{27}, -\dfrac{64}{81},..., (-1)^n\dfrac{2^{n + 1}}{3^{n - 1}}, ...[/tex]

a = 16

a1 = 1/6

n=9

an = a1 (r n-1)a9 = a1

a9 = 1/16 (-2 9-1)

a9 = 1/16 (-28)

a9 = 1/16 (256)

a9 = 16

I hope this helps :)

Answer:

θ = 0.9626

Step-by-step explanation:

Hi there!

We're given the hypotenuse and the leg adjacent to θ in this right triangle. To find θ, we can use the cosine ratio:

[tex]\displaystyle cos\theta=\frac{adjacent}{hypotenuse}[/tex]

Plug in the given information

[tex]\displaystyle cos\theta=\frac{4}{7}[/tex]

Use the inverse cosine ratio

[tex]\displaystyle \theta=cos^-^1(\frac{4}{7})[/tex]

Plug this into your calculator (and ensure you're solving for radians instead of degrees in the settings)

[tex]\displaystyle \theta=0.9626[/tex]

Therefore, θ = 0.9626 when rounded to four decimal places.

I hope this helps!

Answer:

theta = 0.9626 radians

Step-by-step explanation:

cos theta = a/h

cos theta = 4/7 = 0.5714

so, the angle theta = arc cos 0.5714 =

55.1520 °

in radians => 55.1520 × π / 180°

= 0.9626 radians

[tex] \sf \red {alternate \: angles}[/tex]

[tex] \huge \purple{ \underbrace{ \overbrace{Hope \: it \: helps}}}[/tex]

Answer: The antonym of multiply is divide.

Answer:

Divide

Step-by-step explanation:

Antonym simply means the opposite of the given word.

So the opposite of multiplication is division thus division is the answer.

HOPE THIS HELPED

Answer:50.000+2000+400+80+9

Step-by-step explanation:

Answer:

50.000 + 2.000 + 400 + 80 + 9

The equation to represent the length of the snake in weeks:

[tex]L=2w+26[/tex]

Given:

A snake of lenght of 26 cemtimeters grows approximately 2 centimeter long each week.

To find:

The equation to represent the length of the snake in weeks

Solution:

Let the length of the snake in' w' weeks be 'L'.

The initial length of the snake on Carlo's birthday = 26 cm

At starting very first week the length of the snake was 26 cm. And after a week the lenght of the snake becomes 28 cm and then aftertwo weeks the length becomes 30 cm and so on.

Increase in length of the snake each week = 2 cm

And increase in length of the snake in 'w' weeks = (2×w) cm

And the length of the snake in terms weeks (w) will be given by equation:

[tex]L=2\times w+ 26\\L=2w+26[/tex]

The equation to represent the length of the snake in weeks:

[tex]L=2w+26[/tex]

Learn more about equation representation here:

https://brainly.com/question/11408596

Answer:

1/24 chance

Step-by-step explanation:

To begin you would need to find the probability of picking a green sock which would be 3/9; and you could simplify this to 1/3.

After that you need to find the probability of picking a purple sock out of the 8 left, which would provide you with 1/8. To find the probability of both you would multiply 1/8 by 1/3 to find the combined probability which would leave you with 1/24.

9514 1404 393

Answer:

  20 years

Step-by-step explanation:

The interest earned is found using the formula ...

  I = Prt

where principal P is invested at rate r for t years. Solving for t, we find ...

  t = I/(Pr) = $900/($1500×0.03) = 900/45

  t = 20

You must leave the money in the account for 20 years to earn $900 in interest.

Answer:

[tex] \frac{x + 11}{8} = - 3 \\ x + 11 = - 3 .8 \\ x = - 24 - 11 \\ x = - 33[/tex]

maaf jika salah

Answer:

x=-35

Step-by-step explanation:

x+11=-3*8

x+11=-24

x=-24-11

x=-35

Answer:

(x-1.5)^2 -2.25

Step-by-step explanation:

divide 3 by 2 which is 1.5

(x-1.5)^2 -2.25

Answers:

12. 2 3/5+1 4/6 = (2+1)+(3/5+4/6) = 3+19/15 = 64/15

13. 2/4*4/6 = 8/24 = 1/3

14. 3/4*3/6 = 9/24 = 3/8

15. 2/6*4/6 = 8/36 = 2/9

16. 2/4*1/6 = 2/24 = 1/12

17. 3/4/1/6 = 18/4 = 9/2

18. 3/4/2/4 = 12/8 = 3/2

19. 3/6/4/6 = 18/24 = 3/4

20. 5/7+2/7 = 7/7 = 1

21. 4/5+5/7 = 53/35

22. 3/5+5/5 = 8/5

23. 1/6-1/6 = 0

24. 3/7-2/3 = -5/21

25. 3/5-2/7 = 11/35

Answer:

e) and f) doesn't exist.

Step-by-step explanation:

Other you can see in picture.

Answer:

... uhh I'm only in middle school but uhh I think 25??

Answer:

Step-by-step explanation:

buzhou一=12212+13。8.12+13.8=25.8          25.8x9.4=?242.52242.522

The area of the trapezoid is given by A = 121.26 feet²

The Trapezoid is a 4 sided polygon. Two sides of the shape are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid.

There are three types of trapezoids , and those are given below:

a) Isosceles Trapezoid

b) Scalene Trapezoid

c) Right Trapezoid

The area of the Trapezoid is given by

Area of Trapezoid = ( ( a + b ) h ) / 2

where , a = shorter base of trapezium

b = longer base of trapezium

h = height of trapezium

Given data ,

Let the area of the trapezoid be represented as A

Now , the equation will be

Let the height of the trapezium be H = 9.4 feet

The shorter base of the trapezium a = 12 feet

The longer base of the trapezium b = 13.8 feet

Now , Area of Trapezoid = ( ( a + b ) h ) / 2

On simplifying the equation , we get

Area of Trapezium A = ( ( 13.8 + 12 ) 9.4 ) / 2

Area of Trapezium A = 121.26 feet²

Hence , the area of trapezium is 121.26 feet²

To learn more about area of trapezium click :

https://brainly.com/question/12221769

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Answer:

20000

Step-by-step explanation:

Answer:

X= –10

[tex] \frac{1}{2} x - 5 = - 10 \\ \frac{1}{2} x = - 10 + 5 \\ \frac{1}{2} x = - 5 \\ x = - 5 \times 2 \\ x = - 10[/tex]

I hope I helped you^_^

Answer:

x< -4/1 or x > 6/5

If our answers are different, just say so :)

Answer:

If it goes to the left it becomes in the hundredths place meaning it decreases

Step-by-step explanation:

Answer:

B: $0.60

Step-by-step explanation:

4x+6=8.40

4x=2.40

2.40 / 4 = .6

.6 = 0.60 or 60 cents

Answer:$0.60

Step-by-step explanation:

A bag a kibble is 6$

Subtract the cost for the kibble to the cost of all products.

  $8.40

-  $6.00  

  $2.40...  is the cost for all 4 cans of cat food.

Then divide $2.40 by 4... That will be B) $0.60

Answer:

x= –4/5 , x= 2

Step-by-step explanation:

5x²-6x-14=-6

5x² –6x –14 +6=0

5x²–6x –8=0

(5x+4)(x-2)=0

x=–4/5

x=2

Hi! I'm happy to help!

To solve this, we simply have to replace x with the given values.

First, we have -14, let's apply that:

(5·(-14²))-(6·(-14))-14=

Now, let's solve (using the order of operations):

(5·(-14²))-(6·(-14))-14=

(5·196)-(6·(-14))-14=

980-(6·(-14))-14=

980-(-84)-14=

980+84-14=

1064-14=

1050=

1050≠-6

Option 1 is incorrect.

Next, let's substitute 14 for x:

(5·14²)-(6·14)-14=

Now, let's solve:

(5·14²)-(6·14)-14=

(5·196)-(6·14)-14=

980-(6·14)-14=

980-84-14=

896-14=

880=

880≠-6

Option 2 is incorrect.

Now, let's substitute -7 for x:

(5·(-7²))-(6·(-7))-14=

Now, let's solve:

(5·(-7²))-(6·(-7))-14=

(5·49)-(6·(-7))-14=

245-(6·(-7))-14=

245-(-42)-14=

245+42-14=

287-14=

273=

273≠-6

Option 3 is incorrect.

Now, let's substitute 7 for x:

(5·7²)-(6·7)-14=

Now, let's solve:

(5·49)-(6·7)-14=

245-(6·7)-14=

245-42-14=

203-14=

189=

189≠-6

Option 4 is incorrect.

Now, let's substitute -2 for x, and solve:

(5·(-2²))-(6·(-2))-14=

(5·4)-(6·(-2))-14=

20-(6·(-2))-14=

20-(-12)-14=

20+12-14=

32-14=

18=

18≠-6

Option 5 is incorrect.

Now, let's substitute 2 for x and solve:

(5·2²)-(6·2)-14=

(5·4)-(6·2)-14=

20-(6·2)-14=

20-12-14=

8-14=

-6=

-6=-6

Option 6 is correct.

Now, let's substitute -1 for x and solve:

(5·(-1²))-(6·(-1))-14=

(5·1)-(6·(-1))-14=

5-(6·(-1))-14=

5-(-6)-14=

5+6-14=

11-14=

-3=

-3≠-6

Option 7 is incorrect.

Now, let's substitute 1 for x and solve:

(5·1²)-(6·1)-14=

5-(6·1)-14=

5-6-14=

-1-14=

-15=

-15≠-6

Option 8 is incorrect.

Now, let's substitute -4/5 for x and solve:

(5·(-4/5²))-(6·(-4/5))-14=

(5·0.64)-(6·(-4/5))-14=

3.2-(6·(-4/5))-14=

3.2-(-4.8)-14=

3.2+4.8-14=

8-14=

-6=

-6=-6

Option 9 is correct.

Now let's substitute 4/5 for x and solve:

(5·4/5²)-(6·4/5)-14=

(5·0.64)-(6·4/5)-14=

3.2-(6·4/5)-14=

3.2-4.8-14=

-1.6-14

-15.6

-15.6≠-6

Option 10 is incorrect.

To summarize, you should pick option 6, and option 9.

I hope this was helpful, keep learning! :D

Answer:

This formula can also be written as \(y - {y}_{1} = m\left(x - {x}_{1}\right)\). The standard form of the straight line equation is \(y = mx + c\) where \(m\) is the gradient and \(c\) is the \(y\)-intercept.

The profitability of the restaurant is when the function gives a value greater than 0. The franchise does not make a profit after 5, 3, 2 or 1 month of opening.

Given that:

[tex]P(t) = t^4 - 9t^3 + 24t^2 - 20t[/tex]

To calculate the profit, we simply substitute the values of t in the above equation.

(a) 5 months

This means [tex]t =5[/tex]

So, we have:

[tex]P(5) = 5^4 - 9\times 5^3 + 24 \times 5^2 - 20 \times 5[/tex]

[tex]P(5) = 0[/tex]

(b) 3 months

This means that [tex]t=3[/tex]

So, we have:

[tex]P(3) = 3^4 - 9 \times 3^3 + 24 \times 3^2 - 20 \times 3[/tex]

[tex]P(3) = -6[/tex]

(c) 2 months

This means that [tex]t = 2[/tex]

So, we have:

[tex]P(2) = 2^4 - 9 \times 2^3 + 24 \times 2^2 - 20 \times 2[/tex]

[tex]P(2) = 0[/tex]

(d) 1 month

This means that [tex]t = 1[/tex]

So, we have:

[tex]P(1) = 1^4 - 9 \times 1^3 + 24 \times 1^2 - 20 \times 1[/tex]

[tex]P(1) = -4[/tex]

For the restaurant to make a profit, the equation has to give a positive value. Since none of the values of t gives a positive value for P(t).

Then, we can say the franchise does not make a profit after 5, 3, 2 or 1 month of opening.

Read more about functions at:

https://brainly.com/question/24314573

Answer:

40%

Step-by-step explanation:

40+30+70=140

180-140= 40

Answer:

9680 ft^2

Step-by-step explanation:

1 acre = 43,560 ft^2

(2/9) acre = (2/9)*43,560 ft^2

(2/9) acre = 9680 ft^2