The sum of the first n terms of an arithmetic sequence is n/2(4n + 20).
a) Write down the expression for the sum of the first (n − 1) terms.
b) Find the first term and common difference of the above sequence.
​

Answer:

x^3 - y^3

Step-by-step explanation:

9514 1404 393

Answer:

  m = 3.97

Step-by-step explanation:

Your equation is written as a "one-step" linear equation.

  m -2 = 1.97

It is solved by adding 2 to both sides of the equation. (This is the "one step.")

  m -2 +2 = 1.97 +2

Simplifying gives ...

  m = 3.97

_____

If this is supposed to be an equation where -2 is a exponent, then the rules related to exponents apply. In plain text, this would be written m^-2 = 1.97.

  [tex]m^{-2}=1.97\\\\\dfrac{1}{m^2}=1.97\qquad\text{write using a positive exponent}\\\\\dfrac{1}{1.97}=m^2\qquad\text{multiply by $m^2/1.97$}\\\\\sqrt{\dfrac{1}{1.97}}=m\approx0.71247050\qquad\text{take the square root}[/tex]

Angle ∠COD and angle ∠HOG are vertically opposite angles. Then the correct option is C.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Vertically opposite angle - When two lines intersect, then their opposite angles are equal.

The diagram is given below.

Angle ∠COD and angle ∠HOG are vertically opposite angles.

Hence, Angle ∠COD and angle ∠HOG are congruent.

Then the correct option is C.

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Answer:

Hey mate.....

Step-by-step explanation:

This is ur answer....

(Diagram attached)

Hope it helps!

Brainliest pls!

Follow me! :)

the full segment of half of the circle is diameter and half segment us called radius

Answer:

(-0.5, 1)- the midpoint, the distance is sqrt157

Step-by-step explanation:

The midpont is O

x0= (-6+5)/2= -0.5

yo= (4-2)/2=1

(-0.5, 1)

The distance is sqrt ((5-(-6))^2+(-2-4)^2)=sqrt 157

Answer:

Order of Operations was aught at a younger age for those just grasping the idea of multiplication and division. Exposing PEMDAS at a young age would confuse them too much, hence the order of operation groups, addition/subtraction and multiplication/division. So for the second example problem, PEMDAS would be correct because it does involve you to use parentheses as well as exponents to solve for. Very easy to mix up between order of operations and PEMDAS, but just look at it as if Order of operations is a beginner level of PEMDAS.

Step-by-step explanation:

Answer:

x = -5 and x = -9.

Step-by-step explanation:

To factor this, we need to find two numbers that add to 14 and multiply to 45.  These are 5 and 9.  Therefore, this equation factors to (x + 5)(x + 9) = 0.  The two x values that would make this true are -5 and -9 because they would make (x + 5) and (x + 9) equal to 0 respectively.  

Answer:

Step-by-step explanation:

[tex]\begin{array}{|c|c|c|c|c}day&1&2&3&4\\----&-----&-----&-----&-----\\Mary&\frac{1}{8} &\frac{2}{8} &\frac{3}{8} &\frac{4}{8} \\Assis&\frac{1}{12} &\frac{2}{12} &\frac{3}{12} &\frac{4}{12} \\Sum&\frac{1}{8}+\frac{1}{12}&\frac{2}{8}+\frac{2}{12}&\frac{3}{8}+\frac{3}{12}&\frac{4}{8}+\frac{4}{12}\\part&\frac{5}{24}&\frac{10}{24}&\frac{15}{24}&\frac{20}{24}=\boxed{\frac{5}{6}}\\----&-----&-----&-----&-----\\\end{array}[/tex]

The fraction of the catalog that is checked after 4 days is 5/6

If Mary takes 8 days to do a full check and her assistant takes 12 days then if they work together then the fraction of the catalog that is checked after 4 days is 1000/12.

Fraction is a combination of numerator and denominator. The number above division sign is known as numerator and the number below the division sign is known as denominator. It is in p/q form in which q cannot be equal to 0.

let the catalog contains 100 things.So in this way ,

In 1 day Mary does 100/8 things completed and her assistant does 100/12 things completed in 1 day.

So in four days they will complete =100*4/8+100*4/12

=400/8+400/12

=(4800+3200)/96

=8000/96

=1000/12

Hence if Mary takes 8 days to do a full check and her assistant takes 12 days then if they work together then the fraction of the catalog that is checked after 4 days is 1000/12.

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Step-by-step explanation:

I have attached pictures. Hopefully they are visible.

:)

Answer:

[tex]\displaystyle QR = 12[/tex]

Step-by-step explanation:

First, it's never a bad idea to draw the line and see what it looks like! This is shown below (not to scale).

We are given that PS = 18 and PR = 15, and we want to determine QR.

PS is the sum of PR and RS:

[tex]\displaystyle PS = PR + RS[/tex]

Substitute:

[tex]\displaystyle (18) = (15) + RS[/tex]

Solve for RS

[tex]\displaystyle RS = 3[/tex]

Since RS ≅ PQ:

[tex]\displaystyle RS = PQ = 3[/tex]

PS is also the sum of PQ, QR, and RS. Hence:

[tex]PS = PQ + QR + RS[/tex]

Since PS = 18 and RS = PQ = 3:

[tex](18) = (3) + QR + (3)[/tex]

Solve for QR:

[tex]QR = 12[/tex]

In conclusion, QR measures 12 units.

Answer:

Ice can exist at 32°F and at -34°C since they freeze at those temperature points.

Answer:

Step-by-step explanation:

It could exist at -4oC degrees and - 8oC degrees. It could exist anywhere between 0 and - 100 . All numbers are randomly chosen. The point is that they are minus.

Horse = x = 1 head and 4 feet

Chicken =y = 1 head and 2 feet

Horse + chicken = x + y = 43 ( total heads)

Horse = 43 - y

4x + 2y = 122

4(43-y) + 2y = 122

Simplify:

172-4y + 2y = 122

Combine like terms

172-2y = 122

Subtract 172 from both sides

-2y = -50

Divide both sides by-2

Y = 25

X + y = 43

X + 25 = 43

X = 18

There are 18 horses and 25 chickens.

Answer:

mistaken,

incorrect,

wrong,

bad,

untruthful

Answer:

Extraneous solution

Step-by-step explanation:

Extraneous solutions are solutions that come from solving a problem but are ultimately not a valid solution.

Answer:

240m^3

Step-by-step explanation:

Volume = length x width x height.

5x12x4= 240

Answer:

45820

Step-by-step explanation:

the "10" means adding 1 zero to "4582" in place value

Hundred Thousand= 4

Thousand= 5

Hundred= 8

Tens= 2      

Units= 0

Answer:

19

Step-by-step explanation:

There are 38 points total, each field goal is 2 points.

If we do 38/2 we get 19.

Image has work...

[tex]\frac{38}{2}[/tex]

Answer:

On the pic

Step-by-step explanation:

Sorry if my handwriting is bad

This distance would be written as a whole number as 93,000,000.

Answer:

Van: 36 mph.

Plane: 102 mph.

Step-by-step explanation:

x = speed of van

y = common time value

(3x - 6) * y = 204 // plane

x * y = 72 // van

3xy - 6y = 204 // plane simplified

We can now substitute 72 for xy in the equation above.

3*72 - 6y = 204 --> 216 - 6y = 204

We now subtract 216 from both sides.

-6y = -12

We now divide both sides by -1 to get rid of the negative sign & then divide both sides by 6 to simplify.

y = 2

If x*y = 72, then x = 72/y = 72/2 = 36.

Thus, the speed of the van is 36 mph.

We can find the speed of the plane by using the equation from earlier, 3x - 6.

3x - 6 = 3*36 - 6 = 108 - 6 = 102.

Answer:

5 walnuts = 4 cups of pecans

8 walnuts = 9 cups of pecans

Answer:

10 cups of pecans.

Step-by-step explanation:

The ratio between pecans and walnuts are:   [tex]\frac{4}{5}[/tex]×8

So if we make a smaller batch with 1 cup of walnuts, we will need [tex]\frac{4}{5}[/tex] cup of pecans.

So for 8 cups of walnuts, we will need [tex]\frac{4}{5}[/tex] x 8 = 6,4 cups or [tex]6 \frac{2}{5}[/tex] cups of pecans.

I'm vietanh and good luck studying!

Answer:

the sum of the number is 16 and it is al least 20 points

Let X be the random variable representing the weight of a hamster. Transform X to Z, which follows the standard normal distribution. We have

P(X < 4.4) = P((X - 4.3)/0.25 < (4.4 - 4.3)/0.25) = P(Z < 0.4) ≈ 0.6554

By the divergence theorem, the flux of [tex]\vec F[/tex] across S is equal to the volume integral of [tex]\mathrm{div}(\vec F)[/tex] over the interior of S.

We have

[tex]\vec F(x,y,z) = (x^3+y^3)\,\vec\imath + (y^3+z^3)\,\vec\jmath + (z^3+x^3)\,\vec k \\\\ \implies \mathrm{div}(\vec F) = \dfrac{\partial(x^3+y^3)}{\partial x} + \dfrac{\partial(y^3+z^3)}{\partial y} + \dfrac{\partial(z^3+x^3)}{\partial z} = 3(x^2+y^2+z^2)[/tex]

so that

[tex]\displaystyle \iint_S \vec F(x,y,z)\cdot\mathrm d\vec s = \iiint_T \mathrm{div}(\vec F)\,\mathrm dV = 3 \iiint\limits_{x^2+y^2+z^2\le3} (x^2+y^2+z^2)\,\mathrm dx\,\mathrm dy\,\mathrm dz[/tex]

To compute the volume integral, convert to spherical coordinates with

x = ρ cos(θ) sin(ϕ)

y = ρ sin(θ) sin(ϕ)

z = ρ cos(ϕ)

so that

ρ ² = x ² + y ² + z ²

dx dy dz = ρ ² sin(ϕ) dρ dϕ dθ

The region T is the interior of the sphere S, given by the set

[tex]T = \left\{(\rho,\theta,\phi) \mid 0\le\rho\le3 \text{ and } 0\le\phi\le\pi \text{ and }0\le \theta\le2\pi\right\}[/tex]

So we have

[tex]\displaystyle 3 \int_0^{2\pi} \int_0^\pi \int_0^3 \rho^4 \sin(\phi) \,\mathrm d\rho \,\mathrm d\phi \,\mathrm d\theta \\\\ = 6\pi \left(\int_0^\pi \sin(\phi)\,\mathrm d\phi\right) \left(\int_0^3 \rho^4 \,\mathrm d\rho\right) = \boxed{\frac{2916\pi}5}[/tex]

The required surface integral S, and flux across F·dS; that is [tex]\dfrac{2916\pi }{5}[/tex]

Given that,

Function;[tex]F(x, y, z) = (x^3 + y^3)\vec{i} + (y^3 + z^3)\vec{j} + (z^3 + x^3)\vec{k},[/tex]

S is the sphere with center the origin and radius 3.

We have to determine,

Use the Divergence Theorem to calculate the surface integral S, F.dS that is, calculate the flux of F across S.

According to the question,

By the divergence theorem, the flux of [tex]\vec{F}[/tex]across S is equal to the volume integral of  [tex]div(\vec{f})[/tex] over the interior of S.

S is the sphere with center the origin and radius 3.

Therefore,

[tex]F(x, y, z) = (x^3 + y^3)\vec{i} + (y^3 + z^3)\vec{j} + (z^3 + x^3)\vec{k},\\\\= div\vec({F}) = \dfrac{d(x^3+y^3)}{dx} + \dfrac{d(y^3+z^3)}{dx} + \dfrac{d(z^3+x^3)}{dx} = 3(x^{2} + y^{2} + z^{2} )\\\\Then,\\\\\int \int_S \vec{F}(x, y, z) . \vec{ds} = \int \int \int _T div\vec{F}dV= 3 \int \int\int (x^{2} + y^{2} + z^{2} )dx.dy.dz[/tex]

To compute the volume integral, convert to spherical co-ordinate,

[tex]x = p\ cos\theta\ sin\phi\\\\y = p \ sin\theta \ sin\phi\\\\z = p\ cos\phi\\\\[/tex]

Therefore,

[tex]p^2 = x^{2} + y^{2} +z^{2} \\\\dx.dy.dz = x^{2} \ sin\phi \ dp\ d\phi \ d\theta[/tex]

The region T is the interior of the sphere S is given by the set,

[tex]T = {[ p,\theta,\phi}] | \ (0\leq p\leq 3 \ and \ \ 0\leq \phi \leq \pi \ and \ 0\leq 0\leq 2\pi )[/tex]

Then,

[tex]= 3 \int^2_0 \int^\pi _0 \int^3_0 p^4. sin(\phi). dp.d\phi .d\theta\\\\= 6\pi ( \int^\pi _0 sin(\phi).d\phi) (\int^3_0 p^4dp\\\\= \dfrac{2916\pi }{5}[/tex]

Hence, The required surface integral S, F·dS; that is [tex]\dfrac{2916\pi }{5}[/tex]

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Answer:

292

Step-by-step explanation:

73 students in 1 group

4 groups all together

73 Students times 4 groups = amount of students all together

so 73x4=292

Answer:

Step-by-step explanation:

No because the sum of the two shorter legs does not equal the square of the hypotenuse.

3^2 =  9

6^2 =36

8^2 =64

9 and 36 do not equal 64

Answer:

Hence, total surface area of the pyramid is 360 cm².

Step-by-step explanation:

We first calculate slant height L of the pyramid with base s=10 cm and height 12 cm:

L²=H²+(s/2)²=122+(10/2)²=122+5²

=144+25=169⇒

L=(169)^1/2=13

The perimeter of the base is P=4s, since it is a square, therefore, 

P=4×10=40 cm

The general formula for the lateral surface area of a regular pyramid is LSA=1/2Pl where P represents the perimeter of the base and l is the slant height.

Since the perimeter of the pyramid is P=40 cm and the slant height is l=13 cm, therefore, the lateral surface area is:

LSA=1/2Pl=1/2×40×13=260 cm²

Now, the area of the base B=s² with s=10 cm is:

B=s²=10²=100 cm²

The general formula for the total surface area of a regular pyramid is TSA=1/2Pl+B where P represents the perimeter of the base, l is the slant height and B is the area of the base.

Since LSA=1/2Pl=260 cm² and area of the base is B=100 cm², therefore, the total surface area is:

TSA=1/2Pl+B=260+100=360 cm²

Hence, total surface area of the pyramid is 360 cm².

Answer:

Step-by-step explanation:

The next step is the result of calculating the square roots:

and

This will make the step:

Correct choice is B

eksponent

—

[tex] = 4^{ \frac{1}{2} } .3 ^{ \frac{1}{2} } + \sqrt{36} \times 3^ \frac{1}{2} [/tex]

[tex] = \sqrt{4} \times 3 {}^{ \frac{1}{2} } + 6 \times 3 {}^{ \frac{1}{2} } [/tex]

[tex] = 2 \times 2 + 6 \times 3 {}^{ \frac{1}{2} } [/tex]

[tex] = 4 + 6 \times \sqrt{3} [/tex]

[tex] = 4 + 6 \sqrt{3} [/tex]

9514 1404 393

Answer:

  (a)  10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10

Step-by-step explanation:

You may recall that we use a multiplier to signify repeated addition:

  x + x + x = 3x

In a similar way, we use an exponent to signify repeated multiplication:

  10 × 10 × 10 = 10³

__

The exponent 9 in 10⁹ means the factor 10 appears 9 times in the product:

  10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 = 10⁹

Answer:

a  10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10

Step-by-step explanation: