1,Find the eighth term of the geometric sequence whose 1st term is 5 and whose 4th term is

1/25.​

Answer:

The answer is A.

Step-by-step explanation:

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

√[tex]80k^3[/tex] expressed in simplest radical form is 4√[tex](5k^2)[/tex].

To simplify the expression √[tex]80k^3[/tex] (square root of [tex]80k^3[/tex]) in its simplest radical form, you can break down [tex]80k^3[/tex] into its prime factors:

[tex]80k^3 = 2^4 * 5 * k^3[/tex]

Now, take the square root of each factor:

√[tex]80k^3[/tex] = √[tex](2^4 * 5 * k^3)[/tex]

Since square roots of perfect squares simplify to whole numbers, and the square root of [tex]k^3[/tex] is [tex]k^{3/2}[/tex], the simplified radical form is:

√[tex]80k^3[/tex] = [tex]2^2[/tex] * √[tex](5k^2)[/tex] = 4√[tex](5k^2)[/tex]

Therefore, √[tex]80k^3[/tex] expressed in its simplest radical form is 4√[tex](5k^2)[/tex].

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Answer:

the lowest common multiple is 60

Step-by-step explanation:

The multiples of 12 are : 12, 24, 36, 48, 60, 72, 84,

The multiples of 15 are : 15, 30, 45, 60, 75, 90, ....

60 is a common multiple (a multiple of both 12 and 15), and there are no lower common multiples.

Therefore, the lowest common multiple of 12 and 15 is 60.

Answer:

[tex]60[/tex]

Step-by-step explanation:

Least Common Multiplier (LCM)

The LCM of [tex]a,b[/tex] is the smallest positive number that is divisible by both [tex]a[/tex] and [tex]b[/tex]

Prime factorization of [tex]12[/tex]

[tex]12[/tex]

[tex]12[/tex] divides by [tex]2[/tex]     [tex]12=6*2[/tex]

[tex]=2*6[/tex]

[tex]6[/tex] divides by [tex]2[/tex]     [tex]6=3*2[/tex]

[tex]2,3[/tex] are both prime numbers, therefore no further factorization is possible

[tex]=2*2*3[/tex]

Prime factorization of [tex]15[/tex]

[tex]15[/tex]

[tex]15[/tex] divides by [tex]3[/tex]    [tex]15=5*3[/tex]

[tex]3,5[/tex] are both prime numbers, therefore no further factorization is possible

Multiply each factor the greatest number of times it occurred in either [tex]12[/tex] or [tex]15[/tex]

[tex]=2*2*3*5[/tex]

Multiply the numbers: [tex]2*2*3*5=60[/tex]

[tex]=60[/tex]

9514 1404 393

Answer:

  -3y +7x = 14

Step-by-step explanation:

The inverse relation is found by swapping the x- and y-variables. The relation that is the inverse of ...

  -3x +7y = 14 . . . . given relation

is

  -3y +7x = 14 . . . . inverse relation

Answer:

40

Step-by-step explanation:

Answer:

[tex]\dfrac{-8^3}{6}[/tex]

Step-by-step explanation:

According to the divergence theorem;

The flux through the surface S is given by the formula:

[tex]\iint _S F.dS = \iiint_E \ div (F) \ dV[/tex]

where the vector field is:

F = [tex]\langle y,z-y,x \rangle[/tex]

Then the divergence of the vector field is:

[tex]div (F) = \bigtriangledown.F = \Bigg [ \dfrac{\partial (y)}{\partial x} + \dfrac{\partial (z-y)}{\partial (y)}+ \dfrac{\partial (x)}{\partial (z)} \Bigg ][/tex]

= 0 - 1 + 0

= -1

Thus, the flux through the surface of the tetrahedron is:

[tex]\iint_S . FdS = \iiint _E(-1) \ dV \\ \\ = - \iiint_E \ dV[/tex]

To determine the  volume of the tetrahedron with vertices O(0,0,0), A(8,0,0), B (0,8,0) & C(0,0,6)

The equation of the plane P moving through the vertices A, B and C is:

[tex]P = \dfrac{x}{8}+ \dfrac{y}{8}+ \dfrac{z}{8} = 1[/tex]

x + y + z = 8

Range:

For z: 0 ≤ z ≤ 8 - x - y

For y: 0 ≤ y ≤ 8 - x

For x; 0 ≤ x ≤ 8

Thus;

[tex]\iiint_E \ dV = \int ^8_0 \int ^{8-x}_{0} \int ^{8-x-y}_{0}[/tex]

[tex]\int ^8_0 \int ^{8-x}_{0} [z] ^{8-x-y}_{0} \ dydx = \int ^8_0 \int ^{8-x}_{0} \ (8 -x-y) \ dy dx[/tex]

[tex]\int ^8_0 [ (8-x)^2 - \dfrac{(8-x)^2}{2} ] dx = \dfrac{1}{2} \int ^8_0 (8-x)^2 \ dx[/tex]

i.e.

[tex]= \dfrac{1}{2} [ \dfrac{(8-x)^3}{(-1)^3}]^8_0[/tex]

[tex]= \dfrac{-1}{6}[(8-8)^3-(0-8)^3][/tex]

[tex]= \dfrac{-8^3}{6}[/tex]

This question is based on the Gauss Divergence theorem. Therefore, the surface integral  [tex]\int\limits {F.dS}[/tex] is  -85.33.

Given:

F(x, y, z) = y i + (z − y) j + x k S in outward orientation.

Tetrahedron with vertices (0, 0, 0), (8, 0, 0), (0, 8, 0), and (0, 0, 8).

We have to evaluate the surface integral  [tex]\int\limits {F.dS}[/tex] .

According to the Gauss divergence theorem ,

The flux through the surface S is given by the formula:

[tex]\int\int _s F.dS = \int \int \int_e div (F)\; dV[/tex]

Where the vector field is:

F  = ( y, z-y, x )

Therefore,  the divergence of the vector field is:

[tex]div(F) = \bigtriangledown .F = ( \dfrac{\partial( y)}{\partial (x)} + \dfrac{\partial(z-y)}{\partial(y)} + \dfrac{\partial(x)}{\partial(z)} )\\\\div(F) = \bigtriangledown .F = 0-1+0=-1[/tex]

Thus, the flux through the surface of the tetrahedron is:

[tex]\int\int _s F.dS = \int \int \int_e (-1)\; dV = -\int \int \int_e \; dV[/tex]

Now, determine the  volume of the tetrahedron with vertices O(0,0,0), A(8,0,0), B (0,8,0) & C(0,0,6).

The equation of the plane P moving through the vertices A, B and C is:

[tex]P = \dfrac{x}{8} +\dfrac{y}{8} +\dfrac{z}{8} = 1[/tex]

x + y + z = 8

Range:

For z: 0 ≤ z ≤ 8 - x - y

For y: 0 ≤ y ≤ 8 - x

For x; 0 ≤ x ≤ 8

Thus,

[tex]\int\int\int_e dV = \int\limits^8_0\int\limits^{8-x} _ 0 \int\limits^{8-x-y}_0 \; dzdxdy\\= \int\limits^8_0\int\limits^{8-x} _ 0 [z]\limits^{8-x-y}_0 dx \\= \int\limits^8_0\int\limits^{8-x} _ 0 (8-x-y) dy dx\\= \int\limits^8_0 [ 8y-xy-\dfrac{y^{2} }{2} ]\limits^{8-x}_ 0 dx\\= \int\limits^8_0 ([ 8-x]^{2} - \dfrac{ [ 8-x]^{2}}{2} ) dx\\= \dfrac{1}{2} [\dfrac{(8-x)^{3} }{(-1)^{3} } ] \limits^8_0\\=\dfrac{-8^{3} }{6} \\\\= -85.33[/tex]

Therefore, the surface integral  [tex]\int\limits {F.dS}[/tex] is  -85.33.

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Answer:

8.5 cm

Step-by-step explanation:

We know that the square has side lengths of 6cm. To calculate the distance from one corner of the square to the opposite corner, we are calculating the diagonal of the square.

Along the diagonal is where the square gets split in half into two right triangles. The Pythagorean theorem states that [tex]a^2+b^2=c^2[/tex] where c is the longest side of a right triangle and a and b are the other two sides.

To find the length of the square's diagonal, we essentially need to calculate c, the longest side of the triangles. We can do this by plugging 6 into the equation as a and b.

[tex]a^2+b^2=c^2\\6^2+6^2=c^2\\36+36=c^2\\72=c^2\\\sqrt{72} =c[/tex]

[tex]8.5[/tex] ≈ [tex]c[/tex]

Therefore, it will be approximately 8.5cm from one corner of the square to the opposite corner.

I hope this helps!

Answer: (4,12) or (1/3) simplified

Answer:

2/6

Step-by-step explanation:

so do rise of run but you would move down on the rising. So you go down 2 and run 6

Answer:

The equation which determined the rule for the function is:

Thus, option B is true.

Step-by-step explanation:

We know the slope-intercept form of line function is

y = mx+b

where m is the slope and b is the y-intercept

Given the table

x     -2       -1        0       1       2

y      -4       -1        2      5       8

Finding the slope between the points (-2, -4) and (-1, -1)

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\left(x_1,\:y_1\right)=\left(-2,\:-4\right),\:\left(x_2,\:y_2\right)=\left(-1,\:-1\right)[/tex]

[tex]m=\frac{-1-\left(-4\right)}{-1-\left(-2\right)}[/tex]

[tex]m=3[/tex]

Thus, the slope of the function = m = 3

We know that the y-intercept can be determined by setting x = 0 and determining the corresponding y-value.

It is clear,

at x=0, y = 2

Thus, the y-intercept 'b' = 2

now substituting m = 3 and b =2 in the slope-intercept form

y = mx+b

y = 3x + 2

Therefore, the equation which determined the rule for the function is:

Thus, option B is true.

Step-by-step explanation:

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

= 10x + 8 + 6x + 3

= 16x + 11.

Answer:

0.4708413 is the answer

Answer:

K1. 25   K2. 25  K3. 22.5  K4.  22

Step-by-step explanation:

im kinda confused what its asking

Answer:

m=0

Step-by-step explanation:

We simplify the equation to the form, which is simple to understand  

93+12m=3(4m-1)+96

Reorder the terms in parentheses

93+12m=+(+12m-3)+96

Remove unnecessary parentheses

+93+12m=+12m-3+96

We move all terms containing m to the left and all other terms to the right.  

+12m-12m=-3+96-93

We simplify left and right side of the equation.  

m=0

Hope this helps!

Brain-List?

Answer:

infinite solutions

Step-by-step explanation:

First, you do the property of distribution

93+12m=3(4m-1) +96

93+12m=12m-3+96

then you combine like terms

93+12m=12m+93

0=0 is the answer if you were to continue.

Answer:

Step-by-step explanation:

1/24

Answer:

0

Step-by-step explanation:

(2m)/(2m+3)-(2m)/(2m-3)=1

Simplifying the left hand first

(2m)/(2m+3)-(2m)/(2m-3) = {2m(2m-3) - 2m(2m+3)}/(4m²-9)

(4m²-6m-4m²-6m)/(4m²-9) = (-12m) / (4m²-9)

Now this equates to 1

(-12m) / (4m²-9) = 1

-12m =  4m²-9

4m²+ 12m -9 =0 ⇒⇒⇒ This is a quadratic equation that has 2 real solutions.

4m²+ 12m -9 =0

m² + 3m + (3/2)²= 9/4 + 9/4

(m + 3/2)² = 18/4

m = √18/2 - 3/2 or m = -√18/2 - 3/ = 0.621 = -3.621

So we can say that the equation has NO extraneous solutions.

Answer = 0

(I'm pretty sure it's correct)

Answer:

70°

Step-by-step explanation:

1. the rule is: m(∠1)+m(∠2)+m(∠3)=180°.

2. the substitution according to the rule above:

b+2b-90+b-10=180;

4b=280;

b=70°

Answer:

There are no like terms.

Step-by-step explanation:

Answer:

-9-9x=27+9

-9x=36÷(-9)

x=-4

Step-by-step explanation:

prove me wrong

Answer:

Rotate 90 clockwise wxyz

Step-by-step explanation:

Answer:

y = 8

Step-by-step explanation:

Two triangles are said to be congruent if all the three sides and three angles of both triangles are equal.

The distance between two points on the coordinate plane is given as:

[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\[/tex]

In triangle ABC:

[tex]|AB|=\sqrt{(2-8)^2+(6-4^2)}=\sqrt{40} =2\sqrt{10}\\\\|AC|=\sqrt{(5-8)^2+(0-4)^2}=5\\\\|BC|=\sqrt{(5-2)^2+(0-6)^2 }=\sqrt{45}[/tex]

In triangle MNO:

[tex]|MN|=\sqrt{(1-7)^2+(2-4^2)}=\sqrt{40} =2\sqrt{10}\\\\|MO|=\sqrt{(4-7)^2+(y-4)^2}\\\\|NO|=\sqrt{(4-1)^2+(y-2)^2 }[/tex]

Since triangle ABC and triangle MNO are congruent, hence:

|AB| = |MN| = 2√10, |AC| = |MO| = 5, |BC| = |NO| = √45

[tex]|AC|=|MO|=5\\\\\sqrt{(4-7)^2+(y-4)^2}=5\\\\(4-7)^2+(y-4)^2=25\\\\9 +(y-4)^2=25\\\\(y-4)^2=16\\\\square\ root\ of\ both\ sides:\\\\y-4=4\\\\y=4+4\\\\y=8[/tex]

Hence O = (4, 8)

Answer:

4(x-3)(x+6)

Step-by-step explanation:

Answer:

Have a great rest of your day :)

Step-by-step explanation:

Answer:

Week 1 =3.03

Week 2 =2.99

Week 3=2.9

Week 4=2.83

Step-by-step explanation:

Computation for the multifactor productivity measure for each of the weeks shown for production of chocolate bars.

Using this formula

Week Multifactor productivity measure = (Output / Total Cost)

Where:

Output represent Quantity produced

Total cost represent Labor cost + Material cost + Overhead

Let plug in the formula

Week 1= 30,000/(40*12*6)+[(40*12*6)1.5]+(450*6)

Week 1 =30,000/(2,880)+(2,880*1.5)+2,700

Week 1 =30,000/(2,880+4,320+2,700)

Week 1=30,000/9,900

Week 1 =3.03

Week 2= 33,600/(40*12*7)+[(40*12*7)1.5]+(470*6)

Week 2 =33,600/(3,360)+(3,360*1.5)+2,820

Week 2=33,600/(3,360+5,040+2,820)

Week 2=33,600/11,220

Week 2 =2.99

Week 3= 32,200/(40*12*7)+[(40*12*7)1.5]+(460*6)

Week 3 =32,200/(3,360)+(3,360*1.5)+2,760

Week 3=32,200/(3,360+5,040+2,760)

Week 3=32,200/11,160

Week 3=2.9

Week 4= 35,400/(40*12*8)+[(40*12*8)1.5]+(480*6)

Week 4 =35,400/(3,840)+(3,840*1.5)+2,880

Week 4=35,400/(3,840+5,760+2,880)

Week 4=35,400/12,480

Week 4=2.83

Therefore the multifactor productivity measure for each of the weeks shown for production of chocolate bars is :

Week 1 =3.03

Week 2 =2.99

Week 3=2.9

Week 4=2.83

Answer:

a = 3

Step-by-step explanation:

The vertex form of a quadratic is

y = a(x-h) ^2 +k  where ( h,k) is the vertex

the vertex is (-2,2)

y = a(x- -2) ^2 +2

y = a(x+2) ^2 +2

Pick another point on the graph to determine a

(-1,5) and substitute into the equation

5 = a( -1+2) ^2 +2

5 = a(1)^2 +2

5 = a(1) +2

Subtract 2 from each side

5-2 = a+2-2

3 = a

Answer:

A=3

Step-by-step explanation:

I got it right on the test

Answer:

8(w+6)=9

You must add parentheses to show the order in which you will complete the problem. Because it says “eight times the sum of a number and 6” you have to find the sum first, then multiply 8.

Answer:

B $129.04

Step-by-step explanation:

Just took the exam on edgu

Answer:

B

Step-by-step explanation:

Answer:

Should be 9 feet.

Step-by-step explanation:

Well I just set up the equation 2x + 2(x-3) = 42 Then solved x and subtracted x by 9.

Answer:

Step-by-step explanation:

Let width be w and length be l

Then we have equations below:

Substitute l = w + 3 in the second equation and solve for w:

Answer:

5,7,9,11

Step-by-step explanation:

Answer:

D. a pencil can not have thoughts like a person, so it is personification.

Answer:

The answer is D.

Answer:

Angle EFG= 90

Angle EHF= 130

Angle HFG=56

Angle G =74

Answer:

angle EFD = 90

angle HFG=56

angle EHF= 29

angle G=73

Step-by-step explanation:

angle EHF=180-51=29

In triangle FGH :

angle FHG = 51 (given)

angle HFG= 90-34= 56( angle EFG given 90)

angle HGF= 180-(51+56) (anglesome prop)

angle G=180-107=73