The surface area of a cube is 27^2. Calculate the length of the sides of the cube

$560-$500

=$500

therefore, other roommate will be paying $500 per month

f is a function defined by

{(-3, 1), (-2, 2), (-1, -3), (0, -1), (1, 3), (2, -2), (3, 0)}

so f (1) = 3. Then

h (g (i (j (f (1))))) = h (g (i (j (3))))

j is defined by

{(-3, 0), (-2, 1), (-1, 2), (0, -1), (1, -2), (2, 3), (3, -3)}

so j (3) = -3, and

h (g (i (j (f (1))))) = h (g (i (-3)))

And so on. Next you have i (-3) = 2, then g (2) = 0, and finally, h (0) = 0, so your answer is correct.

Answer:

[tex]x-4=0\: and\: x-2=0[/tex]

Step-by-step explanation:

[tex]x^{2} -6x+8-0[/tex]

[tex]x^{2} -4x-2x+8-0[/tex]

[tex]x(x-4)-2(x-4)=0[/tex]

[tex](x-4)(x-2)=0[/tex]

[tex]x-4=0[/tex] and [tex]x-2=0[/tex]

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OAmalOHopeO

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The valid conclusions for the quadratic equation x² - 6x + 8 = 0 are:

x - 4 = 0 and x - 2 = 0

Option D is the correct answer.

We have,

Quadratic equation x² - 6x + 8 = 0.

Now,

To solve the quadratic equation x² - 6x + 8 = 0, we can use the quadratic formula, which states that:

x = (-b ± √(b² - 4ac)) / (2a)

where a, b, and c are the coefficients of the quadratic equation.

In this case,

a = 1, b = -6, and c = 8.

Substituting these values into the quadratic formula, we get:

x = (-(-6) ± √((-6)² - 4(1)(8))) / (2(1))

x = (6 ± √(36 - 32)) / 2

x = (6 ± √(4)) / 2

x = (6 + 2) / 2 or x = (6 - 2) / 2

x = 4 or x = 2

Therefore,

The valid conclusions for the quadratic equation x² - 6x + 8 = 0 are:

x - 4 = 0 and x - 2 = 0

because the roots of the equation are x = 4 and x = 2,

which can be written in factored form as (x - 4)(x - 2) = 0.

Learn more about quadratic equations here:

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Let y be a solution to the given differential equation,

[tex]y' = xy[/tex]

where

[tex]\displaystyle y = \sum_{n=0}^\infty c_n x^n \\\\ y' = \sum_{n=0}^\infty nc_nx^{n-1} = \sum_{n=1}^\infty nc_nx^{n-1} = \sum_{n=0}^\infty (n+1)c_{n+1}x^n[/tex]

Substituting these series into the DE gives

[tex]\displaystyle \sum_{n=0}^\infty (n+1)c_{n+1}x^n = x\sum_{n=0}^\infty c_nx^n \\\\ \sum_{n=0}^\infty (n+1)c_{n+1}x^n = \sum_{n=0}^\infty c_nx^{n+1} \\\\ \sum_{n=0}^\infty (n+1)c_{n+1}x^n = \sum_{n=1}^\infty c_{n-1}x^n \\\\ c_1 + \sum_{n=1}^\infty (n+1)c_{n+1}x^n = \sum_{n=1}^\infty c_{n-1}x^n \\\\ c_1 + \sum_{n=1}^\infty \bigg((n+1)c_{n+1}-c_{n-1}\bigg)x^n = 0[/tex]

Then the coefficients [tex]c_n[/tex] in the series solution are governed by the recurrence,

[tex]\begin{cases}c_0 = c_0 \\ c_1 = 0 \\ (n+1)c_{n+1}-c_{n-1} = 0&\text{for }n\ge1\end{cases}[/tex]

We have

[tex](n+1)c_{n+1}-c_{n-1} = 0 \implies nc_n - c_{n-2} = 0 \implies c_n = \dfrac{c_{n-2}}n[/tex]

so it follows that [tex]c_1=c_3=c_5=\cdots = 0[/tex], while

[tex]c_0 = \dfrac{c_0}1 = \dfrac{c_0}{2^0\times0!} \\\\ c_2 = \dfrac{c_0}2 = \dfrac{c_0}{2^1\times1!}\\\\ c_4 = \dfrac{c_2}4 = \dfrac{c_0}{2\times4} = \dfrac{c_0}{2^2\times2!}\\\\ c_6 = \dfrac{c_4}6 = \dfrac{c_0}{2\times4\times6} = \dfrac{c_0}{2^3\times3!}[/tex]

and so on, with the general n-th coefficient being

[tex]c_n = \begin{cases}0&\text{if }n\text{ is odd} \\ \dfrac{c_0}{2^{n/2}\left(\frac n2\right)!} &\text{if }n\text{ is even}\end{cases}[/tex]

Then the power series solution is

[tex]\displaystyle y(x) = c_0 \sum_{n=0}^\infty \frac{x^n}{2^{n/2}\left(\frac n2\right)!} = c_0 \sum_{n=0}^\infty \frac1{\left(\frac n2\right)!} \left(\frac x{\sqrt2}\right)^n[/tex]

but this doesn't tell the whole story because it doesn't capture the odd-index-is-zero case.

More concisely: let n = 2k for integers k ≥ 0. Then

[tex]\displaystyle y(x) = c_0 \sum_{k=0}^\infty \frac{x^{2k}}{2^k k!} = c_0 \sum_{k=0}^\infty \frac1{k!} \left(\frac{x^2}2\right)^k[/tex]

and as a bonus, it's easier to get an exact solution for this DE,

[tex]y(x) = c_0e^{x^2/2}[/tex]

Answer:

the correct answer is 3 m............

Answer:

27

Step-by-step explanation:

Answer:

£0.50

Step-by-step explanation:

t = one cup of tea

c = one piece of cake

t + c = £1.10

2t + c = £1.70

the cost increases by £0.60 (£1.70 - £1.10) when you order one more cup of tea which means that one cup of tea costs £0.60

substitute £0.60 into t + c = £1.10

£0.60 + c = £1.10

rearrange to get c = £1.10 - £0.60 = £0.50

so one piece of cake costs £0.50

Answer:

200 kilometers and 150 kilometers

Answer:

Undefined

Step-by-step explanation:

Slope formula = [tex]\frac{y_{2}-y_{1}}{y_{2}-y_{1}}[/tex]

[tex]\frac{4-(-6)}{4-4}[/tex]

[tex]\frac{10}{0}[/tex]

A number can not have a denominator of 0, therefore making the slope undefined.

Answer:

Undefined.

Step-by-step explanation:

Use the slope formula: [tex]\frac{y_1-y_2}{x_1-x_2}[/tex]

[tex]m=\frac{-6-4}{4-4}=\frac{-10}{0}=[/tex] Undefined

Step-by-step explanation:

Rounding number are important in world-problem. They help us in many ways like counting class, food, etc. It's the same thing as estimating.

Tens Place:

50-99: round to 100

100th place:

150-101: round to 100

There is still a lot I'm missing out on, but you could say does are the lowest group that can be round to 100. I'm not a expert, but I hope I could help! You can also ask for the other numbers, but it just depends on where you place or how you use the 100.

Answer: D

Step-by-step explanation:

[tex](4x+y)^3\\\\=(4x)^3+3*(4x)^2*y+3*(4x)*y^2+y^3\\\\=64x^3+48x^2y+12xy^2+y^3\\\\Answer\ D[/tex]

Answer:

D

Step-by-step explanation:

Answer:

5/8

Step-by-step explanation:

Add the two fractions

3/8 + 1/4

Get a common denominator

3/8 + 1/4 *2/2

3/8 + 2/8

5/8

Answer:

because this figure does not have two parallel sides

I'm Sorry for by bad English but I am italian

Answer:

Two numbers differ by 9 and the sum of their square is 653. What are the numbers?

Well,that's a mathematical question from algebra and it's quite difficult to answer such questions by writing through the circumstances offered by apps like quora.

However,I have tried to answer your question in an understandable way.Hope you may not find it difficult to analyze.

Let the numbers be x and (9+x)

Therefore,according to given,

x^2 + (9+x)^2 =653

=>x^2 + (9)^2 + x^2 + 2×(9)×(x)=653 (Applying the formula of (a+b)^2)

=>x^2 + 81 + x^2 + 18x =653

=>2x^2 + 18x + (81-653)=0

=>2x^2 + 18x - 572=0

=>2x^2 + (44x - 26x) - 572=0

=>2x^2 + 44x - 26x - 572=0

=>2x(x + 22) - 26(x + 22)=0

=>(x + 22)(2x - 26)=0

But since the number can't be negative

Therefore, x=13

Hence,the required numbers are 13 and 22.

Step-by-step explanation:

in first hope you like it

Answer:

r = 7 cm

Step-by-step explanation:

The radius is 1/2 of the diameter

r = d/2

r =14/2

r = 7 cm

Step-by-step explanation:

An atom is a chemical unit. It is the smallest particle of a chemical element. A cell is a biological unit. It is the smallest unit of any living beings. A cell is composed of molecules, and molecules are composed of atoms

Answer:

C. 44.98

Step-by-step explanation:

Hi there!

We are given the right triangle ABC, m<B=12°, and CB =44

We want to find the length of AB

We can use trigonometry to do it

Let's find the ratio in reference to angle B, as that angle is given.

In reference to angle B the opposite angle is AC, the adjacent side is CB, and the hypotenuse is AB

Now let's recall the 3 most commonly used functions:

[tex]sine=\frac{opposite}{hypoptenuse}[/tex]

[tex]cosine=\frac{adjacent}{hypotenuse}[/tex]

[tex]tangent=\frac{opposite}{adjacent}[/tex]

Let's find the cosine of angle B, as it uses CB and AB, which are the given side and the side we need to find

In that case,

cos(12)=[tex]\frac{CB}{AB}[/tex]

cos(12)=[tex]\frac{44}{AB}[/tex]

Multiply both sides by AB

[tex]AB[/tex]*cos(12)=44

Divide both sides by cos(12)

AB=[tex]\frac{44}{cos(12)}[/tex]

Now plug [tex]\frac{44}{cos(12)}[/tex] into your calculator. Make sure your calculator is on degree mode

AB≈44.98

So the answer is C

Hope this helps!

Answer:

3 girls and 4 boys

Step-by-step explanation:

Writing the number of girls in the family as g and the number of boys in the family as b,

we know that each girl has twice as many brothers as sisters. Therefore, the amount of boys in the family (b, or how many brothers each girl has) is twice the number of the amount of girls in the family (g) minus 1 (g-1) (subtract 1 because each girl's number of sisters does not include the girl herself). We can write this as

b = 2(g-1)

Next,

we know that each boy has the same amount of brothers as sisters. Therefore, the amount of boys in the family minus 1 (b-1, subtracting 1 because we don't include the boy that has the brothers) is equal to the amount of girls in the family (g). we can write this as

b-1 = g

Therefore, we have

b = 2(g-1)

b-1 = g

Plugging b-1 = g into the first equation, we get

b = 2 (g-1)

2(g-1) = 2((b-1) - 1) = b

= 2(b-1-1)

= 2(b-2)

= 2b-4

b = 2b-4

subtract 2b from both sides to make it so that only b values and their coefficients are on one side

-b = -4

multiply both sides by -1 to solve for b

b=4

Therefore, there are 4 boys in the family and b-1 = 4-1 = 3 girls in the family.

Answer:

2775

Step-by-step explanation:

Well of course since the problem is not restricted, the smallest number is 3. I'm almost sure that's not what you mean. The next smallest number is 2775. I found that using a  programing language. I'm sure as well that does not satisfy the question, either.

I think you are intended to do this by finding the lowest common multiple and adding 3.

21: 3 * 7

28: 2 * 2 * 7

36: 2 * 2 * 3 * 3

44: 2 * 2 * 11

LCM = 2 * 2 * 3 * 3 * 7 * 11 = 2772

Now add 3 and the number you want is 2775

Answer:

Bro it will be +1200

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

Answer:

Step-by-step explanation:

a) 5 cm(25000)(1 m/100 cm)(1 km/1000 m) = 1.25 km

b) 2.2 km (1000 m/km)(100 cm/m) / 25000 = 8.8 cm

Answer:

-1

Step-by-step explanation:

let,x=-1

f(x)= 12/4x + 2

f(-1)= 12/4x(-1) + 2

=12/(-4) +2

= -3+2

= -1

Q(x)=x^2+3x+2

[tex]\\ \sf\longmapsto Q(-4)[/tex]

[tex]\\ \sf\longmapsto (-4)^2+3(-4)+2[/tex]

[tex]\\ \sf\longmapsto 16+(-12)+2[/tex]

[tex]\\ \sf\longmapsto 16-12+2[/tex]

[tex]\\ \sf\longmapsto 4+2[/tex]

[tex]\\ \sf\longmapsto 6[/tex]

The value of the function at x = - 4 will be 6. Then the correct option is D.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The function is given below.

Q(x) = x² + 3x + 2

The value of the function at x = - 4, then we have

Q(-4) = (-4)² + 3(-4) + 2

Simplify the equation, then we have

Q(-4) = (-4)² + 3(-4) + 2

Q(-4) = 16 - 12 + 2

Q(-4) = 18 - 12

Q(-4) = 6

The value of the function at x = - 4 will be 6. Then the correct option is D.

More about the function link is given below.

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9514 1404 393

Answer:

  61.5°

Step-by-step explanation:

The tangent relation is useful here. The angle is opposite the vertical side and adjacent to the horizontal side of the right triangle.

  Tan = Opposite/Adjacent

  tan(α) = 35/19

  α = arctan(35/19) ≈ 61.5°

The angle made by v and the positive x-axis is 61.5°.

Answer:

1/2x + 3/2(x+1) - 1/4 = 5

1/2x + 3/2(x) + 3/2 - 1/4 = 5

1/2x + 3/2(x) + 6/4 - 1/4 = 5

4/2(x) + 5/4 = 5

2x + 5/4 = 5

2x = 15/4

x = 15/8

Let me know if this helps!

Answer:

x = 15/8

Step-by-step explanation:

1/2x + 3/2(x+1) - 1/4=5 ​

1/2x + 3/2x + 3/2 - 1/4 = 5

2x + 5/4 = 5

2x = 15/4

x = 15/8

Answer:

Step-by-step explanation:

Answer:

27,000,200

Step-by-step explanation:

Going by basic math you know a million has six 0's.

So; one million is represented as 1,000,000.

Hence twenty-seven million as 27,000,000.

Using you tens, hundreds and thousands you'll know 200 will fall into the last area.

The telescope shape and the characteristic equations of the telescope parameters are the same as parabolic equations

The distance between the focus and the vertex, of the parabola is 3.375 meters

The process for obtain the above values is as follows:

The known parameters of the parabola are;

The location of the vertex of the parabola= The origin = (0, 0)

The height of the parabola = 9 meters

The width of the parabola = 12 meters

The unknown parameter;

The distance between the focus and the vertex

Method:

Finding the coordinate of the focus from the general equations of the the parameters of a parabola

The equation of the parabola in standard form is y = a·(x - h)² + k

From which we have;

(x - h)² = 4·p·(y - k)

The coordinates of the focus, f = (h, k + p)

Where;

(h, k) = The coordinates of the vertex of the parabola = (0, 0)

∴ a = 1/(4·p)

From the question, we have the following two points on the parabola,

given that the parabola is 12 meters wide at 9 meters above the origin and

it is symmetric about the y-axis;

Points on the parabola = (9, 6), and (9, -6)

Plugging in the values of the vertex, (h, k) and the two known points, in the equation, y = a·(x - h)² + k, we get;

6 = a·(9 - 0)² + 0 = 81·a

a = 6/81 = 2/27

p = 1/(4·a)

∴ p = 1/(4 × 2/27) = 27/8

The coordinate of the focus, f =  (h, k + p)

∴ f = (0, 0 + 27/8) = (0, 27/8)

The coordinate of the focus f = (0, 27/8)

Given the vertex and the focus of the parabola have the same x-values of 0, we have;

The distance between the focus and the vertex, d = the difference in their y-values;

∴ d = 27/8 - 0 = 27/8 = 3.375

The distance between the focus and the vertex, d = 3.375 meters

Learn more about parabola here;

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9514 1404 393

Answer:

  A.  T<-4, -8>

Step-by-step explanation:

To get the second equation, we had to replace x with x+4 (a translation left 4) and we had to add -8 to the function value (a translation down 8).

Left 4 and down 8 is the translation ...

  T<-4, -8>