What is the 6th term in the geometric sequence described by this explicit formula? an= 3•4^(n-1)​

Answer:

The second one

Step-by-step explanation:

470 kids went on the trip, and 120 students returned home, the total of kids staying is 350.

One cabin= 8 students

The equation i came up with is 350/8 = 43.75

They need 44 cabins to fit all the kids

Answer: The number is 974

Step-by-step explanation:

First, any 3 digit number can be written as:

N = a*100 + b*10 + c

Where a, b, and c are single-digit numbers.

a is the hundreds digit

b is the tens digit

c is the unit digit

We can write the clues as:

#1: a + b + c = 20

#2: b = a - 2

#3: c = a + b - 12

Then we have a system of equations:

a + b + c = 20

b = a - 2

c = a + b - 12

To solve this, we need to isolate one of the variables in one equation and then replace this in the other equations, we can see that b is already isolated in the second equation, then we can replace that in the first and third equations:

a + (a - 2) + c = 20

c = a + (a - 2) - 12

Now we can see that c is isolated in the second equation, then we can replace that in the first one to get:

a + (a - 2) + (a + (a - 2) - 12) = 20

Now we can solve this for a:

a + a - 2 + a + a -2 - 12 = 20

4*a - 16 = 20

4*a = 20 + 16

4*a = 36

a = 36/4 = 9

With this, we can find the values of b and c.

b = a - 2 = 9 - 2 = 7

c = a + b - 12 = 9 + 7 - 12 = 4

Then the 3-digit number is:

N = a*100 + b*10 + c = 9*100 + 7*10 + 4 = 974

N = 974

Answer:

B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

I hope this helps you out!

Answer:

yes it is b

Step-by-step explanation:

Answer:

H

Step-by-step explanation:

Step 1 of 2: Subtract, sub-step b: Convert mixed number to improper fraction.

Convert mixed number to improper fraction

2 and 1 over 32

1

3

= ( 2 × 3 ) over 3

2 × 3

3

+ 1 over 3

1

3

= ( 6 + 1 ) over 3

6 + 1

3

= 7 over 3

7

3

Step 1 of 2: Subtract, sub-step c: Find common denominator.

Find common denominator

32 over 9

32

9

− 7 over 3

7

3

= ( 32 × 1 ) over ( 9 × 1 )

32 × 1

9 × 1

− ( 7 × 3 ) over ( 3 × 3 )

7 × 3

3 × 3

= 32 over 9

32

9

− 21 over 9

21

9

9 is the least common multiple of denominators 9 and 3. Use it to convert to equivalent fractions with this common denominator.

Step 1 of 2: Subtract, sub-step d: Subtract.

Subtract

32 over 9

32

9

− 21 over 9

21

9

= ( 32 − 21 ) over 9

32 − 21

9

= 11 over 9

11

9

Step 1 of 2: Subtract.

Step 2 of 2: Simplify.

Simplify

11 over 9

11

9

= 1 and 2 over 91

2

9

Answer:

Length=8 Width=5

Step-by-step explanation:

Set this up as a system of equations with l standing for length and w standing for width.

w+3=l

l×w=40

Substitute rhe first equation into the 2nd one.

w(w+3)=40 --------> w^2+3w=40

Move all the terms to the left side

w^2+3w-40=0

Factor

(w+8) (w-5)

Set both factors equal to 0.

w+8=0 -----> w=-8

w-5=0 ------> w=5

Since distance cannot be negative we can eliminate -8. So w=5

Plug it back into any one of the equations and solve for l.

5+3=l -----> 8=l

So the answer is the length is 8 and the width is 5.

The dimensions of the rectangle are:

Length = 8 meters.

width = 5meters.

We are given that the length of a rectangle is 3 meters longer than its width and the area of a rectangle is 40 square meters.

We need to find the length and width of the rectangle.

A rectangle is a closed 2-dimensional shape that has two dimensions, the length, and the width. Length is the longer side and width is the shorter side of the rectangle.

The area of a rectangle is given by :

A = Length x Width.

Let the area, length, and width of the rectangle be A, L, and W.

The length of a rectangle is 3 meters longer than its width.

We can write it as,

L = 3 + W

The area of a rectangle is 40 square meters.

We can write it as,

A = 40 square meters

We can write it as,

L x W = 40

Substituting  L = 3 + W.

(3 + W) W = 40

[tex]3W + W^2 = 40\\W^2 + 3W = 40 \\W^2 + 3W - 40 = 0[/tex]

This is a quadratic equation and we will apply middle-term factorization.

[tex]W^2 + 3W - 40=0\\W^2 + (8-5)W - 40=0\\W^2 + 8W - 5W - 40=0\\W(W + 8) - 5 ( W + 8)=0\\(W+8)(W - 5)=0\\W+8 = 0~~and~~W-5=0\\W = -8~~and~~W=5[/tex]

The distance can not be negative so W = -8 is eliminated.

We have, W = 5

Substituting W = 5 in L = 3 + W.

We get,

L = 3 + 5 = 8

L = 8.

The dimensions of the given rectangle are:

Length = L = 8 meters.

Width = W = 5 meters.

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The value of x from the quadratic equation is x = { 2 , -12 }

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

x² + 10x = 24   be equation (1)

Adding 5² on both sides of the equation , we get

x² + 10x + 25 = 24 + 25

( x + 5 )² = 49

Taking square roots on both sides , we get

x + 5 = ±7

Subtracting 5 on both sides , we get

x = 2

And , x = -12

Hence , the quadratic equation is solved and value of x is x = -12 or x = 2

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9514 1404 393

Answer:

  C.  3x² +24

Step-by-step explanation:

Use the given function definitions and simplify.

  [tex]g(f(x))=g\left(\dfrac{1}{3}x^2+4\right)\\\\=9\left(\dfrac{1}{3}x^2+4\right)-12\\\\=3x^2+36-12\\\\\boxed{g(f(x))=3x^2+24}\qquad\textbf{matches C}[/tex]

Answer:

157

Step-by-step explanation:

Answer:

can you explain what two number you added to get that number "157"

Step-by-step explanation:

Answer:

26.6

Step-by-step explanation:

(12*5)-(8.35*4)

60-33.4

26.6

Answer: A: no, because each vertex is not multiplied by the same scale factor.

Step-by-step explanation: got it right on Edge 2020!

(B) [tex]\frac{78-87}{8-2}[/tex]

Therefore, (B) [tex]\frac{78-87}{8-2}[/tex] can be simplified to find the slope of the trend line in the scatter plot.

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Answer:

[tex](-1.5, 1)[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Endpoint A (-2, 1)

Endpoint B (-1, 1)

Step 2: Find Midpoint

Simply plug in your coordinates into the midpoint formula to find midpoint

Answer:0.52, 0.545, 0.55, 0.6, 0.65

Source:trust me bro

Answer:

O.52 m, 0.545 m, 0.55 m, 0.6 m, 0.65m. :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step one:

given

monthly allowance= $21

from January to June= 6 months

total savings = 21*6= $126

cost of gift = $110

Step two:

Ian will have enough money to buy the gift

since he saved $126 which is greater than the cost of the gift of $110

he would have a balance of $16

Answer:

1) Between 0 and 1 minute the rate of change is 25 ft./min

2) Between 1 and 2 minute the rate of change is 0 ft./min

3) Between 2 and 4 minute the rate of change is -12.5 ft./min

Step-by-step explanation:

1) Between 0, and 1 feet, we have;

The rate of change = (Final height - Initial height)/(Final time - Initial time)

The rate of change = (40 - 15)/(1 - 0) = 25 ft/min

Between 0 and 1 minute the rate of change = 25 ft./min

2) Between 1, and 2 feet, we have;

The rate of change = (40 - 40)/(2 - 1) = 0 ft/min

Between 1 and 2 minute the rate of change = 0 ft./min

3) Between 2, and 4 feet, we have;

The rate of change = (15 - 40)/(4 - 2) = -12.5 ft/min

Between 2 and 4 minute the rate of change = -12.5 ft./min

Answer:

∠A=∠W

∠Z=∠D

AB=WX

ZY=DC

AD=WZ

Step-by-step explanation:

Answer: 91

Step-by-step explanation:

Angle between the two vectors u and v is option (a) 0 degree

Vector, in mathematics, a quantity that has both magnitude and direction

Given,

u=(-2,3)

v=(-6,9)

Angle between the two vectors θ =[tex]cos^{-1} \frac{u.v}{|u| |v|}[/tex]

[tex]u.v=(-2)(-6)+(3)(9)\\u.v=12+27\\u.v=39[/tex]

[tex]|u|=\sqrt{-2^{2}+3^{2} } \\|u|=\sqrt{13}[/tex]

[tex]|v|=\sqrt{-6^{2}+9^{2} } \\|v|=\sqrt{117}[/tex]

Angle between two vectors θ =[tex]cos^{-1} \frac{u.v}{|u| |v|}[/tex]

θ=[tex]cos^{-1} \frac{39}{\sqrt{13}.\sqrt{117} } \\cos^{-1}\frac{39}{39}\\ cos^{-1}1=0[/tex]

Hence, the angle between the vectors u and v is 0 degree

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Answer:

Y=3 is a horizontal line. So, a line perpendicular to y=3 must be vertical. The only vertical line among the choices is x=-3, so C must be the answer.

Step-by-step explanation:

Answer:

Total gas used = 3/2 of a tank of gas

Step-by-step explanation:

Visit to friend = 6/8 of a tank of gas

Commute to work = 1/2 of a tank of gas

Weekend trip = 1/4 of a tank of gas

Total gas used = Visit to friend + Commute to work + Weekend trip

= 6/8 + 1/2 + 1/4

= 6+4+2/8

= 12/8

= 3/2

Total gas used = 3/2 of a tank of gas

Answer: Here we answer "What is the square root of 674 (√674) in simplest radical form?"

The square root of 674 in its simplest form means to get the number 674 inside the radical √ as low as possible.

The square root of 674 is already in the simplest radical form. Therefore, the answer is:

√674

hope this helps.. Stay safe and have a great day/night!!! :D

The square root of 674 is expressed as √674 in the radical form.

A square root of a number is a value that, when multiplied by itself, gives the number.

Given that, what is the square root of 674 in the simplest radical form,

The square root of 674 is expressed as √674 in the radical form,

The square root of 674 rounded up to 7 decimal places is 25.9615100. It is the positive solution of the equation x² = 674.

Hence, the square root of 674 is expressed as √674 in the radical form.

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Answer:

0.00039

Step-by-step explanation:

Answer:

As you can see, these are all set up in slope intercept form (with a y-intercept of 0). These equations are called "direct variation" because y varies directly with x. If x increases, then y increases as well. If x decreases, then y decreases.

Step-by-step explanation:

As you can see, these are all set up in slope intercept form (with a y-intercept of 0). These equations are called "direct variation" because y varies directly with x. If x increases, then y increases as well. If x decreases, then y decreases.

Answer:

dude i can't even see that sorry

Step-by-step explanation:

I like your cut G

Answer: The shirt's price after reduction = $ 84.15

Step-by-step explanation:

Given: Price of shirt= $ 85

Marked up percent = 10%

Reduced percent = 10%

Price after mark up = (Price of shirt) + 10% of (Price of shirt)

= $ (85+10% x 85)

= $ (85+(0.1) x (85))

= $ (85+8.5)

= $ 93.5

Price after 10% reduction = (Price after mark up)- 10% of (Price after mark up)

= $ (93.5-0.1 x 93.5)

= $ (93.5-9.35)

= $ 84.15

Hence, the shirt's price after reduction = $ 84.15