If there are 8 boys and 56 girls in a room, fill out all of the possible ratios of boys to girls that could be made.

Answer:

10 terms

Step-by-step explanation:

equate the sum formula to 55 and solve for n

[tex]\frac{1}{2}[/tex] n(n + 1) = 55 ( multiply both sides by 2 to clear the fraction )

n(n + 1) = 110 ← distribute parenthesis on left side

n² + n = 110 ( subtract 110 from both sides )

n² + n - 110 = 0 ← in standard form

Consider the factors of the constant term (- 110) which sum to give the coefficient of the n- term (+ 1)

the factors are + 11 and - 10 , since

11 × - 10 = - 110 and 11 - 10 = + 1 , then

(n + 11)(n - 10) = 0 ← in factored form

equate each factor to zero and solve for n

n + 11 = 0 ⇒ n = - 11

n - 10 = 0 ⇒ n = 10

However, n > 0 , then n = 10

number of terms which sum to 55 is 10

Answer:

x = 0, y = 4

Step-by-step explanation:

1 pen = x dollars

4 pen = 4x

1 ruler = y dollars

5 rulers = 5y

now,

a) = 5y + 4x = 20

2x + 4y = 16

Now,

2x + 4y = 16

or, 2x = 16 - 4y

or, x = (16 - 4y)/2

Now,

5y + 4x = 20

or, 5y + 4{(16 - 4y)/2} = 20

or, (10y + 64 - 16y) = 40

or, 64 - 6y = 40

or, 64 - 40 = 6y

or, 6y = 24

so, y = 4

now,

x = (16 - 4(4))/2

or, x =(16 - 16)/2

so, x = 0

The  speed on the plane is 104mph while that of the wind is 78mph

The formula for calculating distance is expressed as:

Speed = Distance/Time

If the plane is flying with the wind;

3(r+ w) = 312

r + w = 104 ................... 1

If against the wind

4(r - w )= 312

r- w = 78 .................. 2

Add both equations

2r = 104  + 78

2r = 182

r = 91

Since r + w = 104

w = 104 - 91

w = 13

Speed on the plane  = r + w  = 91 + 13 = 104mi/hr

Speed on the wind = 91 - 13 = 78mi/hr

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Answer:

It should look like the graphs above.

Hope this helps!

Answer:

8x-3

Step-by-step explanation:

I hope it helps you

Answer:

6 meters

Step-by-step explanation:

[tex]A=a^2+2a\sqrt{\frac{a^2}{4}+h^2} [/tex]is the formula that you use

h=vertical altitude and

a=side length of the base

[tex]85=5^2+(2*5)\sqrt{\frac{25}{4}+h^2}[/tex]

[tex]85-25=10\sqrt{\frac{25}{4}+h^2}[/tex]

[tex]\frac{60}{10}=\sqrt{\frac{25}{4}+h^2}[/tex]

[tex]6=\sqrt{\frac{25}{4}+h^2}[/tex]

[tex]36=\frac{25}{4}+h^2[/tex]

[tex]36-\frac{25}{4}=h^2[/tex]

[tex]36-6.25=h^2[/tex]

[tex]29.75=h^2[/tex]

Vertical altitude (h) and [tex]\frac{1}{2}a[/tex] and the slant height form a right triangle with the slant height being the hypotenuse

[tex]h^2+(2.5)^2=s^2 [/tex]where s=slant height

[tex]29.75+6.25=s^2[/tex]

[tex]36=s^2[/tex]

s=6 meters

Answer:

slant height = 6 meters

Step-by-step explanation:

surface area of pyramid: 2bs + b²

2*5*s + 5² = 85

10s = 85 - 25

10s = 60

s = 6

The slant height is 6 meters.

Answer:

20.428571

Step-by-step explanation:

C=(22/7)d

C=(22/7)6.5

C=20.428571

Answer:

20.4285714289

or ≈20.4

Step-by-step explanation:

2*pi*r

radius = diameter/2 = 6.5/2

r=3.25

22/7=3.1428571429

2*3.1428571429*3.25

Answer:

[tex]-26x^2+56x-15[/tex]

Step-by-step explanation:

[tex]3x(-2x + 7) - 5(x - 1)(4x - 3)[/tex]

Expand the brackets:

[tex]\implies -6x^2+21x-5(4x^2-7x+3)[/tex]

[tex]\implies -6x^2+21x-20x^2 +35x-15[/tex]

Collect like terms:

[tex]\implies -6x^2-20x^2+21x +35x-15[/tex]

Combine like terms:

[tex]\implies -26x^2+56x-15[/tex]

Answer:

Step-by-step explanation:

This is late reply. You can try searching online next time you need an answer in a hurry - most questions have been asked before: like here https://brainly.com/question/11412899

3x(-2x + 7) - 5(x - 1)(4x - 3)

= (-6x^2 + 21x) - 5(4x^2- 7x +3)

= -6x^2 + 21x - 20x^2 + 35x - 15

= -26x^2 + 56x -15

Answer:

28 miles

Step-by-step explanation:

308/11 = 28 miles per gallon of gas

The domain of the function is the real number and the range of the function is (-∞, 6].

The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

The function f(x) = -x² - 4x + 2

The function can be written as

[tex]\rm f(x) = -x^2- 4x +2\\\\f(x) = -x^{2}- 4x - 4 + 4 +2 \\\\f(x) = -(x^{2} +4x +4) + 6\\\\f(x) = -(x+ 2)^2 + 6[/tex]

The domain is the real number and the range is (-∞, 6].

More about the function link is given below.

https://brainly.com/question/5245372

Answer:

184cm^2

Step-by-step explanation:

(5+5+6) * 10 = 160

6*4 = 24

160+24=184

there are 2 triangles so I am assuming they have the same dimensions

Answer:

[tex]x-11[/tex]

Step-by-step explanation:

Let the number be x

Then we have,

x-11

The 12th term of the given geometric sequence is equal to -8,388,608.

Given the following sequence:

A geometric sequence can be defined as a series of real and natural numbers that are generally calculated by multiplying the next number by the same number each time.

Mathematically, a geometric sequence is given by the expression:

[tex]a_n =a_1r^{n-1}[/tex]

Where:

Substituting the given parameters into the formula, we have;

[tex]a_{12} =2 \times -4^{12-1}\\\\a_{12} =2 \times -4^{11}\\\\a_{12} =2 \times -4194304[/tex]

12th term = -8,388,608.

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graph of the linear function y = 5 is attached below. which is true for all the values of x.

a function whose equation is of the form y = ax + b, where a and b are constants, a does not equal zero, and x is any real number, and whose graph is a straight line.

Given a linear function y = 5 here

The graph of that linear function will be a straight line that is attached below.

this function will be the same for all the values of x. since it is not dependent on the variable x

it will pass through points (0, 5),  (1, 5),  (-6, 5),  (5, 5),  (-9, 5),.... and so on.

therefore, Below is a graph of the linear function at y = 5. This holds true regardless of x's value.

Learn more about linear functions here:

https://brainly.com/question/20286983

#SPJ2

Answer:

x = 18

Step-by-step explanation:

So there is two ways, but I'm going with the way I remember

1/6 x = 3

1x/6 = 3 multiply by 1

x/6 = 3 then multiply by 6

x = 18

Answer:

you just have to calm down and search it online it helps sometimes

A:

4 seconds per centimer:

30cms               15 cms

----------------       -------------

2 minutes           1 minute

1 minute= 60 seconds

15 cms                       1cm

-----------------     =     ----------------

60 seconds              4seconds

B: 15 cms per minute

30cms/2minutes

(divide by 2 to get speed for one minute)

15cm/1 minute

Answer:

4 X 3= 12

6 X 3= 18

Please mark as Brainliest

Answer:

12

Step-by-step explanation:

View the question mark as x then cross multiply

18×4= 6×x

72= 6x

x is 12

Both Josan and Adama must have to earn 6 credits for they to have the same amount of play time.

An equation is an expression used to show the relationship between two or more numbers and variables.

Let z represent the number of credits they must earn to have the same amount of play time. Hence:

5z + 6(5) = 10z

5z = 30

z = 6

Both Josan and Adama must have to earn 6 credits for they to have the same amount of play time.

Find out more on Equation at: https://brainly.com/question/2972832

Answer:

5(z+6) −  10=10z

Step-by-step explanation:

Step-by-step explanation:

[tex] \frac{1}{2} (11ft + 17ft) \times 12ft \\ \frac{1}{2} \times 28ft \times 12ft \\ divide \: 28 \: by \: 2 \\ 14ft \times 12ft = 168 {ft }^{2} \\ answer = 168 {ft}^{2} [/tex]

Answer:

s=sqrt(60) => the second one is the correct answer.

Step-by-step explanation:

It’s given that A=60.

Formula: A=s^2.

=> s=sqrt(A)=sqrt(60)

[tex]3^{-4}=\dfrac{1}{3^4} =\dfrac{1}{81}[/tex]

The steps for completing a W-4 form include the following:

A W-4 form can be defined as an internal revenue service (IRS) tax form which is used to indicate the correct federal income tax that should be withheld from an employee's paycheck in the United States of America.

After an employee fills a W-4 form, it must be submitted to the internal revenue service (IRS) by the employer.

Basically, the steps for completing a W-4 form include the following:

Step 1: You should provide your information such as name, address, Social Security Number (SSN).

Step 2: You should indicate that Addison has one job only.

Step 3: You should indicate whether or not Addison has dependents.

Step 4: You should state that there is no need to have any additional taxes withheld from Addison's paycheck.

Step 5: You should provide a signature and date.

Read more on W-4 form here: https://brainly.com/question/15507745

Answer:

Step-by-step explanation:

Parallel lines have the same slope, so if the slope of the given line is 2, the slope of the "new" line is also 2, and the slope-intercept equation becomes:

y = 2x + b.  

Here you seem to have a "misprint," as "(3, -2)2 is not a valid expresion.

Supposing that y ou meant (3, -2), then our equation becomes

-2 = 2(3) + b, or -8 = b.

The desired equation is then y = 2x - 8

If this is not what you expected, please focus on your (3, -2)2 and rewrite it properly.

Answer:

x= - 8/3

Step-by-step explanation:

1- Multiply the monomials

2- Combine like terms

3- Rearrange variables to the left side of the equation

4- Divide both sides of the equation by the coefficient of the variable

5- Cross out the common factor

Answer:

1.35

Step-by-step explanation:

the explanation to the question is in the photo I sent

rounding off to the nearest tenth

then the final answer is 1.4

Answer:

2x² - 3x

Step-by-step explanation:

multiply the outside with the inside brackets

x × 2x = 2x²

x × (-3) = -3x

Answer:

x(2x-3)

Step-by-step explanation:

x(2x-3)

x times 2x equals 2x².

x times -3 is -3x.

2x²-3x.