put the following unit fractions in order from smallest to largest. 1/16 1/24 1/8 1/10 1/4 1/12 1/3 1/6 1/2


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S = √2+√8+√18+√32+……………… n terms.

or, S = √2 + 2√2 +3√2 +4√2.+………………….+ n terms.

This is an A.P. in which a = √2. , d = √2.

Sn = n/2.[2.a +(n-1).d].

or, Sn = n/2.[ 2√2 +(n-1).√2].

or, Sn = (n/2).√2.[ 2 +n-1].

or, Sn = n.(n+1)/√2. Answer.

Given AP :√2,√8,√18,√32,...

First term = √2

Common difference = √8-√2

⇛ √(2×2×2)-√2

⇛ 2√2-√2

⇛√2

We know that

Sum of first n terms of an AP

⇛ Sn = (n/2)[2a+(n-1)d]

⇛ Sn = (n/2)[2√2+(n-1)(√2)]

⇛ Sn = (n/2)[2√2+√2 n -√2]

⇛ Sn = (n/2)[√2 n +√2)

⇛ Sn = (n/2)×(√2)(n+1)

⇛Sn = (n/√2)(n+1)

⇛ Sn = n(n+1)/√2

Additional comment:

nth term of an AP = a+(n-1)d

Sum of first n terms of an AP

Sn = (n/2)[2a+(n-1)d]

Sum of the first n terms = Sn =

(n/2)(a+an)

If a,b,c are the three consecutive terms in an AP then b = (a+c)/2

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The sum of the 8th & 4th of an Ap is 24 and sum of and sum of 6th & 10th term is 44 Find the Ap

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Answer:

Step-by-step explanation:

It's the third choice. Since the triangles are given as similar and they are right triangles, points A, B, and D are all on the hypotenuses of those 2 triangles and are co-linear. The slope between all points on a single line is constant.

The first equation is separable:

dy/dx = x/y   ⇒   y dy = x dx

(provided that y ≠ 0)

Integrating both sides yields

1/2 y² = 1/2 x² + C

Given that y(0) = -8, we find

1/2 • (-8)² = 1/2 • 0² + C   ⇒   C = 32

so that the particular solution is

1/2 y² = 1/2 x² + 32

Solving for y explicitly, we have

y² = x² + 64

y = ± √(x² + 64)

but since y(0) is negative, we take the negative solution:

y = - √(x² + 64)

The second equation is also separable:

du/dt = (2t + sec²(t)) / (2u)   ⇒   2u du = (2t + sec²(t)) dt

Integrate both sides:

u² = t² + tan(t) + C

Given u(0) = -6, we have

(-6)² = 0² + tan(0) + C   ⇒   C = 36

and so

u² = t² + tan(t) + 36

u = ± √(t² + tan(t) + 36)

but again we take the negative root here to agree with the initial condition, so

u = - √(t² + tan(t) + 36)

Answer:

25%

Step-by-step explanation:

8-6=2

2/8=0.25

0.25×100=25%

Answer:

Y is cookies x is cupcakes

for the first birthday party: 20x + 40y = 61

For the second party 30x + 30y = 64.50

There aren't any other constraints

20x + 40y = 61

30x + 30y = 64.50

Step-by-step explanation:

Answer:

0 and -81

Step-by-step explanation:

So, we know anything times zero is zero, and anything added or subtracted to zero would give you that number, meaning one of these numbers is zero.

Zero plus -81 will give you the same number, -81, and zero times -81 will give you zero since anything added to or subtracted to zero is that number.

Answer:

27

Step-by-step explanation:

Use synthetic division:

8 | 1 -5 3

   __8_24

    1  3 | 27

Therefore, (x²-5x+3)/(x-8) = x+3 R27

Answer: 219

Step-by-step explanation:

Answer:

its C

1.convert the mixed number to an improper fraction

([tex]\frac{-20}{6\\}[/tex] x [tex]\frac{2}{3}[/tex] )

2. reduce the numbers with the greatest common factor (2)

[tex]\frac{-20}{3}[/tex] x [tex]\frac{1}{3}[/tex]

3. then multiply and get

[tex]\frac{-20}{9}[/tex]

4. then reduce to get

-2[tex]\frac{2}{9}[/tex]

Step-by-step explanation:

Answer:

And x=12 are the two numbers.

Step-by-step explanation:

x+y=20-----(1)

Let x be the larger number of the two.

x=2y-4

Hence 4=2y-x------(2)

Adding (1) and (2) we get 3y=24 so y=8

And x=12 are the two numbers.

Answer: x has to be less than 5 i can’t read it but it is starting from positive 5 with the arrow going to the left

Step-by-step explanation:

[tex]6(31)+6(4)-6(15)=6(31+4-15)=6(20)=120[/tex]

ok done. Thank to me :>

Answer:

HOPE ITS HELP

Answer:

[tex]y=\frac{1}{3}x+\frac{5}{3}[/tex]

Step-by-step explanation:

The point-slope form of an equation for a line is  y = mx + b  (m is the slope; b is the y-intercept).

First, find the slope using the two given points.

[tex]m=\frac{y_2 - y_1}{x_2-x_1}=\frac{3-0}{4-(-5)}=\frac{3}{9}=\frac{1}{3}[/tex]

At this stage, you know the slope and need to find the y-intercept.  Plug in one of the points (either one) into the equation.  Let's use (-5, 0).

[tex]y=\frac{1}{3}x+b\\0=\frac{1}{3}(-5)+b\\0=-\frac{5}{3}+b\\\frac{5}{3}=b[/tex]

The equation for the line is [tex]y=\frac{1}{3}x+\frac{5}{3}[/tex].

You can check for errors by putting in the point you didn't use...

Check to make sure the point (4, 3) satisfies the equation.

[tex]3=\frac{1}{3}(4)+\frac{5}{3}\\3=\frac{4}{3}+\frac{5}{3}\\3=\frac{9}{3}[/tex]   True!

Answer:

936

Step-by-step explanation:

Therefore you multiply 6 by 18 = 6×18= 108

1,044 - 108 = 936

So therefore the total is 936

From the power rules, the power [tex]3^{-2}[/tex] is equal to the fraction [tex](\frac{1}{3})^{-2}[/tex].

There are different power rules one of them is the negative exponent. For this rule when you have a negative exponent, you need to invert the number, i.e, the power base is converted to the denominator. After that, you should solve the power with a positive exponent.  See the  examples:

[tex]5^{-3}=(\frac{1}{5})^3=\frac{1}{125} \\ \\ \\ {\frac{4}{6} }^{-2}={\frac{6}{4} }^2=\frac{36}{16}[/tex]

Then, the question gives:

[tex]3^{-2}=({\frac{1}{3}})^2[/tex]

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Answer:It’s money so use the $ symbol. You got this

Step-by-step explanation:

[tex](a+b)^2 =a^2 +b^2 + 2ab = 54~~~.....(i)\\\\(a-b)^2 = a^2 +b^2 -2ab = 46~~~.....(i)\\\\\\(i)+(ii):\\\\(a+b)^2 +(a-b)^2 = 54+46\\\\\implies a^2 +b^2 + 2ab + a^2 +b^2 - 2ab =100\\\\\implies 2a^2 +2b^2 =100\\\\ \\\implies 2(a^2 +b^2) =100\\\\\implies a^2 +b^2 = \dfrac{100}2 = 50[/tex]

Answer:

110

Step-by-step explanation:

Know the angle for BCD which is 130.

Subtract 180 from 130 and you get angle c for the triangle which is 50

Already knowing B and C, add them both which comes up to 70

All triangle angles equal 180 so subtract 70 for 180 and you get 110

Answer:

none

Step-by-step explanation:

a-114=35 ⇒ a= 149

a+358=434⇒ a=76

416+a=523⇒ a=107

ax38=214⇒ a=5.63

The equation that has 112 as it's solution is not existing in the options.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given are four linear equations.

Check the solution of each equation.

a - 114 = 35

Adding both sides of the equation with 114,

⇒ a = 35 + 114 = 149

a + 358 = 434

Subtracting both sides of the equation with 358,

⇒ a = 434 - 358 = 76

416 + a = 523

Subtracting both sides of the equation with 416,

a = 523 - 416 = 107

a × 38 = 214

Dividing both sides of the equation with 38,

a = 214/38 = 5.63

Hence none of the equations have 112 as it's solution.

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Answer:

44⁰.

Step-by-step explanation:

Its supplement = 180 - 136

= 44 degrees.

Answer:

125 cm3

Step-by-step explanation:

V = l * w * h

V = 5 * 5 * 5

V = 125 cm3

Answer:

125 cm^3

Step-by-step explanation:

To calculate the area of a cube, just do the side length to the power of 3.

5^3=125

Answer:

Distance is 100 m

Step-by-step explanation:

From second equation of motion;

[tex]{ \rm{s = ut + \frac{1}{2} {at}^{2} }} \\ [/tex]

[tex]{ \rm{s = (0 \times 10) + ( \frac{1}{2} \times 2 \times {10}^{2}) }} \\ \\ { \rm{s = {10}^{2} }} \\ \\ { \rm{s = 100 \: {m} }}[/tex]

The distance covered is 200m

Data;

To find the distance covered by the object, we have to use the formula

of velocity. But we are not given the velocity or speed of the object here.

[tex]v = s/t[/tex]

where s and t are the distance and time respectively.

But from acceleration,

[tex]a = v/t\\v = a*t\\v = 2 * 10 \\v = 20m/s[/tex]

The velocity of the object is 20m/s

let's use this to find the distance covered.

[tex]v = s/t\\20 = s/10\\s = 20*10\\s= 200m\\[/tex]

The distance covered is 200m

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Answer:

Future value, $63,398.79; Interest, $16,798.79

Step-by-step explanation:

The perimeter of a rectangle is 2L + 2W, where L and W are the length and width, respectively. The dimensions of the garden are given, 6 x 12 ft.

The amount of fencing needed is 2(6) + 2(12) = 12 + 24 = 36 ft of fencing

Problem 1

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Explanation:

a1 = 1.7 = amount of concrete for the first step

a4 = x = amount of concrete for the fourth step

Sn = sum of the first n terms of an arithmetic sequence

Sn = (n/2)*(a1 + an)

S4 = (4/2)*(a1 + a4)

S4 = 2(1.7+x)

S4 = 2x+3.4

S4 = 17

2x+3.4 = 17

2x = 17-3.4

2x = 13.6

x = (13.6)/2

x = 6.8

We need 6.8 cubic feet of concrete for the fourth step. We'll use this value to help us find the common difference d

an = nth term of an arithmetic sequence

an = a1 + d(n-1)

a4 = a1 + d(4-1)

a4 = a1 + 3d

6.8 = 1.7 + 3d

6.8-1.7 = 3d

5.1 = 3d

(5.1)/3 = d

1.7 = d

d = 1.7

Coincidentally, the common difference is the same as the first term. This won't always happen.

Now we can compute the 12th term

an = a1 + d(n-1)

a12 = 1.7 + 1.7(12-1)

a12 = 20.4

which is then used to find the sum of the first 12 terms

Sn = (n/2)*(a1 + an)

S12 = (12/2)*(a1 + a12)

S12 = 6(1.7 + 20.4)

S12 = 132.6

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Problem 2

--------------------

Explanation:

The center is (h,k) = (0,10) which is where the nozzle is located.

The distance from (0,10) to (0,25) is 15 units, so r = 15.

Also, the distance from (0,10) to (0,-5) is also 15 units.

Plug those values into the equation below.

[tex](x-h)^2 + (y-k)^2 = r^2\\\\(x-0)^2 + (y-10)^2 = 15^2\\\\x^2 + (y-10)^2 = 225\\\\[/tex]

That equation represents the boundary of the circle, which is where the water can reach.

=============================================================

Problem 3

--------------------

Explanation:

Or note that,

a3 = 0.81*(a2) = 0.81*(0.81a1) = a1*(0.81)^2 = 6.7*(0.81)^2 =  4.39587

which must mean,

This is based off the idea that [tex]a_n = a(r)^{n-1}[/tex]

So,

a6 = a1*(0.81)^5

a6 = 6.7*(0.81)^5

a6 = 2.33614554867

a6 = 2.336

Step-by-step explanation:

$.07

$.7

The answer was first one.

Answer:

19 tennis rackets

Step-by-step explanation: