This figure shows three identical spherical billiard balls of diameter 6 cm inside an equilateral triangular frame.
Work out the perimeter of the frame, leaving your answer
in surd form.

Answer:

The second answer

Step-by-step explanation:

Answer:

-3 ± √41

Step-by-step explanation:

Numerator of Quadratic Formula

⇒ -3 ± √(-3)² + 4(2)(-4)

⇒ -3 ± √9 + 32

⇒ -3 ± √41

Answer:

A = 8 and B = 6

Step-by-step explanation:

Since (B = A - 2), we can substitute (A - 2) in for the "B" variable in the first equation to isolate "A".

(A - 5)² + (B - 3)² = 18                                 ----->  Original equation

(A - 5)² + ((A - 2) - 3)² = 18                         ----->  Plug in B = A - 2

(A - 5)² + (A - 5)² = 18                                ----->  Subtract

(A² - 10A + 25) + (A² - 10A + 25) = 18       ----->  Expand parentheses

2A² - 20A + 50 = 18                                 ------>  Add like terms

2A² - 20A + 32 = 0                                   ----->   Subtract 18 from both sides

2(A² - 10A + 16) = 0                                   -----> Remove common factor

2(A - 2)(A - 8) = 0                                      -----> Factor within parentheses

A = 2                                                         -----> Find A - 2 = 0

A = 8                                                        -----> Find A - 8 = 0

Since "A" gave two possible values, we need to plug them into both equations to see which value gives reasonable "B" values.

When A = 2:

B = A - 2                           -----> Original equation

B = 2 - 2                           -----> Plug in A = 2

B = 0                               -----> Subtract

(A - 5)² + (B - 3)² = 18       -----> Original equation

(2 - 5)² + (B - 3)² = 18       ------>  Plug in A = 2

(-3)² + (B - 3)² = 18           -----> Subtract within first parentheses

9 + (B - 3)² = 18               -----> Square value within first parentheses

(B - 3)² = 9                      ----->  Subtract 9 from both sides

B - 3 = 3                          ----->  Take square root of both sides

B = 6                               ----->  Add 3 to both sides

When A = 8:

B = A - 2                         -----> Original equation

B = 8 - 2                         -----> Plug in A = 8

B = 6                             -----> Subtract

(A - 5)² + (B - 3)² = 18       -----> Original equation

(8 - 5)² + (B - 3)² = 18       ------>  Plug in A = 8

(3)² + (B - 3)² = 18            -----> Subtract within first parentheses

9 + (B - 3)² = 18               -----> Square value within first parentheses

(B - 3)² = 9                      ----->  Subtract 9 from both sides

B - 3 = 3                          ----->  Take square root of both sides

B = 6                               ----->  Add 3 to both sides

As you can see, when A = 2, there are two possible values of "B" depending on the equation. However, when A = 8, both equations give a "B" value of B = 6. Therefore, A = 8 and B = 6 are the answers.

Answer: 3 apples

Step-by-step explanation:

Given:

12 red apples

15 green apples

8 people

Freida

..............................................................................................................................................

12 + 15 = 27

Since she is going to give the apples equally among 8 people,

27 / 8 = 3 remainder 3

Each of the 8 people will get 3 apples each.

Freida will get the remaining 3 apples.

Answer:

[tex]\huge 3w^2\sqrt[4]{2\:w^{3}}[/tex]

Step-by-step explanation:

Answer:

180

Step-by-step explanation:

(10×11)+(10×7)=110+70

The area of the kite is expressed as 1/2 × (Product of its diagonals)

In this case, we have;

Therefore, when we substitute the diagonals in the formula, we get;

When simplified, we get;

Therefore, the area of the kite is 180 ft².

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A can with a radius of 60 mm and a height of 160 mm. Then the surface area of the cylinder will be 1808640 mm³.

The lateral surface area of a cylinder is also called the curved surface area of the cylinder.

Suppose that:

Radius of the considered cylinder = 'r' units

Height of the considered cylinder = 'h' units

Then, the lateral surface area of that cylinder is:

SA = πr²h

A can with a radius of 60 mm and a height of 160 mm. Then the surface area of the cylinder will be

SA = π x (60)²  x 160

SA = 3.14 x 3600 x 160

SA = 1808640 mm³

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Answer:

x<7

Step-by-step explanation:

-3(x - 4) > -2x + 5 Distribute

-3x+12>-2x+5  Subtract 12 from both sides

-3x>-2x-7 Add 2 to both sides

-5x>-7 Simplify

x<7

Answer:

x < 7.

Step-by-step explanation:

-3(x - 4) > -2x + 5

-3x + 12 > -2x + 5

-3x + 2x > 5 - 12

-x  > -7      Note: we divide by -1 so the sign flips:

x < 7.      

There are total 15 dogs, 27 cats, and 3 ferrets were adopted if the ratio of dogs to ferrets was 5:1. The ratio of cats to dogs was 9:5.

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

We have:

An animal shelter had 45 animals adopted over one week. The ratio of dogs to ferrets was 5:1. The ratio of cats to dogs was 9:5.

Combine ratio dogs:ferrets:cats = 5:1:9

Let's suppose the number of ferrets is x then:

5x + x + 9x = 45

15x = 45

x = 3

Ferrets x = 3

Dogs = 5x = 5(3) = 15

Cats = 9x = 9(3) = 27

Thus, there are total 15 dogs, 27 cats, and 3 ferrets were adopted if the ratio of dogs to ferrets was 5:1. The ratio of cats to dogs was 9:5.

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Answer:

  14

Step-by-step explanation:

A hexadecimal (base 16) number can have any of 16 digits. Conventionally, digits 0–9 are used, along with letters A–F. The letters are assigned the values ...

  A = 10

  B = 11

  C = 12

  D = 13

  E = 14

  F = 15

Answer:

Step-by-step explanation:

Comment

If you do not have a graphing calculator the best thing to use is Desmos. Desmos is free -- anyone can use it and and the graphs can be used here on Brainly.  I've downloaded the graph for you.

There are a couple of things you should notice.

The most downward point is (-5,-3)

The largest root is x =   -2

The smallest root is x = - 8

Notice the roots are the opposite of what you are given. You will eventually learn how to do all of these things.

Answer:

12

Step-by-step explanation

Answer:

1, 2, 3, 6, 13, 26, 39, 78

Step-by-step explanation:

The factors of a number are the numbers that "go into" 78 "evenly" that is, without a remainder. You can make a factor tree or divide to find the prime factors. Any combination "goes into" 78. That's why we'll include 6 and 26 on this list.

1×78

2×39

3×26

6×13

all make 78!

Answer:

90

bc i don't care about this

The equation of plane containing the points ABC is 13x+y-18z = 1035.

A plane in 3D coordinate space is determined by a point and a vector that is perpendicular to the plane. The equation of plane is defined as the position vectors and the Cartesian product of the vector perpendicular to the plane.

For the given situation,

The plane containing the points

A(10, 5, -50), B(15, 30, -45) and C(-5, 20, -60).

The equation of the plane in the form r.n=d can be represented as

[tex](r-a).[(b-a)[/tex] × [tex](c-a)]=0[/tex] ------ (1)

Let r = xi + yj +zk

a = 10i + 5j - 50k

b = 15i + 30j - 45k

c = -5i + 20j - 60k

[tex](r-a)=(x-10)i+(y-5)j+(z+50)k[/tex] ------- (2)

[tex](b-a)=(15-10)i+(30-5)j+(-45-(50))k[/tex]

⇒ [tex](b-a)=5i+25j+5k[/tex]

[tex](c-a)=(-5-10)i+(20-5)j+(-60-(50))k[/tex]

⇒ [tex](c-a)=-15i+15j-10k[/tex]

Now, [tex](b-a)[/tex] × [tex](c-a)[/tex]

⇒ [tex](5i+25j+5k)[/tex] × [tex](-15i+15j-10k)[/tex]

⇒ [tex]\begin{vmatrix}i&j&k\\5&25&5\\-15&15&-10\end{vmatrix}[/tex]

⇒ [tex]i(-250-75)-j(-50+75)+k(75+375)[/tex]

⇒ [tex]-325i-25j+450k[/tex] -------- (3)

Substitute all values in equation 1,

⇒ [tex][(x-10)i+(y-5)j+(z+50)k].[(-325i-25j+450k)]=0[/tex]

⇒ [tex]-325(x-10)-25(y-5)+450(z+50)=0[/tex]

⇒ [tex]-325x+3250-25y+125+450z+22500=0[/tex]

⇒ [tex]-325x-25y+450z=-22500-3250-125[/tex]

⇒ [tex]-325x-25y+450z=-25875[/tex]

On dividing by 25 and multiply with negative sign on both sides,

⇒ [tex]13x+y-18z=1035[/tex]

Hence we can conclude that the equation of plane containing the points ABC is 13x+y-18z = 1035.

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There are 142506 different selections of twenty-five pastries

The given parameters are:

The number of different selections is calculated using:

[tex]C(n + r - 1,r) = \frac{(n + r - 1)!}{r!(n - 1)!}[/tex]

The above formula is used because repetitions are allowed.

So, we have:

[tex]C(6 + 25 - 1,25) = \frac{(6 + 25 - 1)!}{25!(6 - 1)!}[/tex]

Evaluate the sum and difference

[tex]C(30,25) = \frac{30!}{25!5!}[/tex]

Evaluate the expression

C(30,25) = 142506

Hence, there are 142506 different selections of twenty-five pastries

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Answer:

Step-by-step explanation:

Answer:

x=11800

Step-by-step explanation:

make a proportion:

2360/.2=X/1

2360(1)=.2x

x=11800

Answer:

Circle

Step-by-step explanation:

Answer:

6. The number is [tex]-5[/tex]

7. The two numbers are [tex]10[/tex] and [tex]11[/tex]

Step-by-step explanation:

Question six can be re-worded to create the following expression:

[tex]-2=\frac{4x+10}{5}[/tex]

Solve for x to find the number:

[tex]-2=\frac{4x+10}{5}\\-10=4x+10\\-20=4x\\\frac{-20}{4} = x\\-5 = x[/tex]

Question seven can be solved by first listing the constraints (assuming x is smaller than y):

To get the numbers, we can create a system of linear equations. First, solve for [tex]y[/tex] in each expression:

[tex]y = x+1[/tex]

[tex]2y = 3x-8\\y = \frac{3}{2}x - 4[/tex]

Solve for [tex]x[/tex]:

[tex]x+ 1 = \frac{3}{2}x - 4\\x + 5 = \frac{3}{2}x\\5 = \frac{3}{2}x - x\\5 = \frac{1}{2}x\\10 = x[/tex]

Solve for [tex]y[/tex]:

[tex]y = x + 1\\y = 10 + 1\\y= 11[/tex]

Answer:

see explanation

Step-by-step explanation:

(6)

let n be the number then the sum of 4 times the number and 10 is 4n + 10

so

[tex]\frac{4n+10}{5}[/tex] = - 2 ( multiply both sides by 5 to clear the fraction )

4n + 10 = - 10 ( subtract 10 from both sides )

4n = - 20 ( divide both sides by 4 )

n = - 5

(7)

let the consecutive integers be n and n + 1 , then

3n = 2(n + 1) - 8 ← distribute parenthesis and simplify right side

3n = 2n + 2 - 8

3n = 2n - 6 ( subtract 2n from both sides )

n = - 6 and n + 1 = - 6 + 1 = - 5

the 2 integers are - 6 and - 5

Answer:

sqrt(13)

Step-by-step explanation:

The entire base is 4, so 1/2 of the base is 2

We can use the pythagorean theorem

a^2 = b^2 = c^2

2^2 + 3^2 = x^2

4+9 = x^2

13 = x^2

Taking the square root of each side

sqrt(13) = x

Check the picture below.

Answer:

6.5

Step-by-step explanation:

9.1^2-6.4^2 is 41.85

square root of that is 6.469...

Answer:The answer is 12.0321

Step-by-step explanation:

Answer:

C. 54 tens

Step-by-step explanation:

54×10=540

54tens=540

Answer:

54 tens

Step-by-step explanation:

This is like regular multiplication, sort of.

54 x 10= 540

540=54

Let's consider all the trig identities, to help us with the problem:

   ⇒ (look at the attached image for help with that)

After looking at all the trig identity, let's look at the problem given to us:

 ⇒ cos(θ) = [tex]\frac{5}{13}[/tex]

    ⇒ we know that sec(θ) = 1 / cos(θ) = 1 / (5/13) = 13/5

Thus: sec(θ) = 13/5, which just so happens to be Choice (D)

Answer: sec(θ) = 13/5 or Choice (D)

Hope that helps!

Using the dot plot, the correct option regarding the group that appears to have the longer average forearm length is:

Group A, because seven children have a forearm length longer than 12 inches

A dot plot shows the number of times each measure appears in the data-set.

In this problem, Group A has 3 students with forearm length of 14 inches, while group B have none. Group A also has more students with forearm length of 13 inches, and less of 11 and 12(lower values). Hence the correct option is given by:

Group A, because seven children have a forearm length longer than 12 inches.

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The depreciated value of the car after 12 years that Kyle buys for $58,000 today, which declines 23% annually, will be $2,520.

Depreciation is the reduction or decrease in the value of an asset over time.

Depreciation occurs because an asset is put to use, and undergoes wear and tear.

The current price of the car = $58,000

The annual depreciation rate = 23%

The depreciated value after one year = 0.77 (1 - 23%)

Let the number of years of depreciation = x

The worth of the car after 12 years = 58,000 x 0.77^x

= 58,000 x 0.77^12

= 58,000 x 0.04344

= $2,519.52

= $2,520

The car's depreciated value can be modeled by the exponential function (decay) abˣ, which yields $2,520 in this situation.

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Answer is 105 degrees.

Explanation:

Given two parallel lines AB and CD and a transversal cutting the two lines.

We know that when a transversal cuts two parallel line,

i) corresponding angles would be equal

ii) Interior angles total to 180

iii) alternate angles are equal.

In the picture given we have corresponding angles as

(2,6) .  Hence angle 2 = angle 6.

Angle 6 = 75 (given)

Hence angle 2 =75.

Angles 1 and 2 are supplementary because they form a linear pair.

Hence angle 1 = 180-75

Angle 1 =105

Answer:

see explanation

Step-by-step explanation:

the sum of the 3 angles in the triangle = 180° , then

∠ BAC + 51° + 90° = 180°

∠ BAC + 141° = 180° ( subtract 141° from both sides )

∠ BAC = 39°

using the tangent ratio in the right triangle

tan51° = [tex]\frac{opposite}{adjacent }[/tex] = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{AC}{12.8}[/tex] ( multiply both sides by 12.8 )

12.8 × tan51° = AC , then

AC ≈ 15.8 ( to 1 dec. place )

using the cosine ratio in the right triangle

cos51° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{12.8}{AB}[/tex] ( multiply both sides by AB )

AB × cos51° = 12.8 ( divide both sides by cos51° )

AB = [tex]\frac{12.8}{cos51}[/tex] ≈ 20.3 ( to 1 dec. place )