What is the explicit formula for this sequence?
2,6, 18, 54, 162, ...

Answer:

We need to solve the each side as though it is the hypotenuse:

AB: 6^2 + 5^2 = 61 => 7.81

BC: 8^2 + 5^2 = 89 => 9.43

CD: 4^2 + 3^2 = 25 => 5

DE: 4^2 + 2^2 = 20 => 4.47

EA: 2^2 + 5^2 = 29 => 5.39

Total 32.10 Units

Step-by-step explanation:

Please mark brainliest and have a great day!

ANSWER

C. (0,4)

EXPLANATION

The given graph has equation:

[tex]y = 4( {3}^{x} )[/tex]

The y-intercept is where the graph touches the y-axis.

At this point the value of x is zero.

We substitute x=0 into the equation to obtain:

[tex]y = 4( {3}^{0} )[/tex]

Recall that any non-zero number exponent zero is 1.

This implies that,

[tex]y = 4( 1 ) = 4[/tex]

Hence the y-intercept is (0,4)

The correct answer is C.

Answer:

8 Gauss

Step-by-step explanation:

Since your moving the magnet from 10 to 20cm you're essentially multpliying the distance by 2.

K = 2

Therefore k ^ 3 = 2^3

64/2^3

=8

Answer:

8 Guass

Step-by-step explanation:

We multiply the distance by a factor of $2$, and thus divide the magnetic field strength by a factor of $2^3 = 2 \cdot 2 \cdot 2 = 8$. We get a magnetic field strength of 64/8 = 8

Answer:

B.)7√5

Step-by-step explanation:

2√5+ 5√5 = 7√5

we simply let √5  = x

therefore;

2√5+ 5√5 = 2x + 5x

2x + 5x = 7x

but x = √5

2√5+ 5√5 = 7√5

Answer:

3 TERMS

Step-by-step explanation:

There are total 3 terms in the polynomial  [tex]x^{2} + xy - y^{2}[/tex] .

The given polynomial expression is  [tex]x^{2} + xy - y^{2}[/tex] .  

The number of terms of any expression is the total number of independent variables present in the given polynomial expression.

We can see that there are total 3 independent variables present in the polynomial expression and therefore the number of terms present is also three.    

Thus, there are total 3 terms in the polynomial  [tex]x^{2} + xy - y^{2}[/tex] .

To learn more about terms in the polynomial, refer -

https://brainly.com/question/24290590

#SPJ2

Answer:

53 miles

Step-by-step explanation:

I'm going to assume "$0.25 for each time" is "$0.25 per mile."

$1.75 is the flat fee. It costs 25 cents for each mile. We can represent this as:

1.75 + 0.25m

The sum of this equation has to be less than or equal to $15. We can display this as:

1.75 + 0.25m ≤ 15.

To solve, we must first isolate 0.25m. To do this, we subtract 1.75 from each side.

0.25m ≤ 15 - 1.75

0.25m ≤ 13.25.

Now, we must isolate the variable 'm' to determine how many miles Eddie can travel. To do this, we divide 0.25 from each side.

m ≤ 13.25 / 0.25

m ≤ 53.

Therefore, Eddie can travel 53 miles if he has $15 to spend.

Answer:

3

Step-by-step explanation:

Answer:

The correct answer is (3,2)

Answer:

2,-1

Step-by-step explanation:

2x^2 -2x -4 =0

Factor out a 2

2(x^2 -x-2) =0

What 2 number multiply to -2 and add to -1

-2*1 = -2

-2 +1 = -1

2(x-2) (x+1) =0

Using the zero product property

x-2 = 0               x+1 = 0

x-2+2=0+2       x+1-1=0-1

x=2                   x=-1

Answer:

see explanation

Step-by-step explanation:

Given

2x² + 9x + 10 = 0

To factor the quadratic

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 2 × 10 = 20 and sum = + 9

The factors are + 4 and + 5

Use these factors to split the x- term

2x² + 4x + 5x + 10 = 0 ( factor the first/second and third/fourth terms )

2x(x + 2) + 5(x + 2) = 0 ← factor out (x + 2) from each term

(x + 2)(2x + 5) = 0

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

2x + 5 = 0 ⇒ 2x = - 5 ⇒ x = - [tex]\frac{5}{2}[/tex]

Answer:

1. x = 2

2. x = - 5/2

Step-by-step explanation:  First put parenthesis around the equation

( 2x^2 + 4x ) + ( 5x + 10) = 0

2x ( x+ 2) 5 (x + 2),

when you have the same answer inside the parenthesis you know your right.

2x + 5 = 0

x + 2 = 0

Next preform basic algebra

2x = -5  

[tex]\bf \begin{array}{rrlll} term&\stackrel{f(n+1)=-0.5f(n)}{~\hfill value~ }\\ \cline{1-2} f(1)&120\\ f(2)&-0.5(120)\\ &-60\\ f(3)&-0.5(-60)\\ &30\\ f(4)&-0.5(30)\\ &-15\\ f(5)&-0.5(-15)\\ &7.5 \end{array}[/tex]

Answer:

f(5) = 7.5

Step-by-step explanation:

The recursive formula allows a term in the sequence to be found from the previous term, thus

f(2) = - 0.5 f(1) = - 0.5 × 120 = - 60

f(3) = - 0.5f(2) = - 0.5 × - 60 = 30

f(4) = - 0.5f(3) = - 0.5 × 30 = - 15

f(5) = - 0.5f(4) = - 0.5 × - 15 = 7.5

Answer:

If x varies directly as y, then x=ky. y=5 and x=2.5 are substituted into x=ky to find k.

2.5=5k

k=2.5/5

k=5.

K =5 is substituted in x=ky to find y where x is 10.

x=5y

10=5y

y=10/2

y=2

Answer:  The required value of y is 20.

Step-by-step explanation:  Given that y is 5 when x is 2.5 and y varies directly with x.

We are to find the value of y when x is 10.

According to the given information, we can write

[tex]y\propto x\\\\\Rightarrow y=kx~~~~~~~~~~[\textup{where k is the constant of proportionality}][/tex]

When y = 5 and x = 2.5, then we have

[tex]5=k\times2.5\\\\\Rightarrow k=\dfrac{5}{2.5}\\\\\Rightarrow k=2.[/tex]

So, we get

[tex]y=2x.[/tex]

Therefore, when x = 10, then the value of y is

[tex]y=2\times10=20.[/tex]

Thus, the required value of y is 20.

Answer:

Never.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

By definition for a right triangle with sides a, b, c, where c is the hypotenuse,

the following must be true:

a² + b² = c²

By using this formula on all the choices, we find that only D satisfies this formula

i.e.

for

a = √35 --------> a² = 35

b = √14 --------->b² = 14

c = 7 ------> c² = 49

a² + b² = 35 + 14 = 49 which is equal to the value of c² above

The correct answer is √35 , √14 , 7

Pythagoras' theorem that the square of a right triangle's hypotenuse is equal to the sum of the squares of the other two sides.

p^2 + b^2 = h^2 ( In a right angled triangle)

p = perpendicular of the triangle

b = base of the triangle

h = hypotenuse of the triangle

According to the Pythagoras theorem:

p^2 + b^2 = h^2 (In a right angled triangle)

In Option D

(√35)^2 + (√14)^2 = 7^2

49 = 49

Pythagoras theorem is followed in this triangle, hence it is a right angled triangle.

Learn more about Pythagoras theorem on:

https://brainly.com/question/343682

#SPJ2

Answer:

The set {10 , 24 , 26} formed a right triangle

Step-by-step explanation:

* Lets explain how to check the sides lengths which formed a  

 right triangle

- In triangle ABC

# If AC is the longest side in length

# If (AC)² = (AB)² + (BC)²

∴ AB , BC , AC formed a right angle triangle  

∴ m∠B = 90°  (The angle opposite to the longest side)

∴ AC is the hypotenuse

* Now lets solve the problem

- In set 8 , 12 , 15

∵ The longest side is 15 cm

∴ (15)² = 225

∵ (8)² + (12)² = 64 + 144 = 208

∵ (15)² ≠ (8)² + (12)²

∴ The set not formed a right triangle

- In set 10 , 24 , 26

∵ The longest side is 26 cm

∴ (26)² = 676

∵ (10)² + (24)² = 100 + 576 = 676

∵ (26)² = (10)² + (24)²

∴ The set formed a right triangle

- In set 12 , 20 , 25

∵ The longest side is 25 cm

∴ (25)² = 625

∵ (12)² + (20)² = 144 + 400 = 544

∵ (25)² ≠ (12)² + (20)²

∴ The set not formed a right triangle

- In set 15 , 18 , 20

∵ The longest side is 20 cm

∴ (20)² = 400

∵ (15)² + (18)² = 225 + 324 = 549

∵ (20)² ≠ (15)² + (18)²

∴ The set not formed a right triangle

* The set {10 , 24 , 26} formed a right triangle

Step-by-step explanation:

The ratio is the same each time (2/3), so this can be modeled as a geometric sequence.

an = a₁ (r)^(n-1)

where an is the nth term, a₁ is the first term, and r is the common ratio.

On the first rebound, the ball rises to 2/3 × 2 = 4/3, so a₁ = 4/3.

an = 4/3 (2/3)^(n-1)

On the sixth rebound, the ball rises to:

a₆ = 4/3 (2/3)^(6-1)

a₆ = 4/3 (32/243)

a₆ = 128/729

a₆ ≈ 0.176

Answer:

D) 50+31.5x

Step-by-step explanation:

10% of 35 is 3.5

35-3.5=31.5

Answer:

(5,-1)

Step-by-step explanation:

4x+3y=17

3x+2y=13

So elimination sounds fun but we will have to do manipulation:

Multiply top equation by 2 and bottom equation by 3. This will cause the second term in both by 6y which means we would be setup for elimination.

8x+6y=34

9x+6y=39

--------------------now subtract the equations

-x+0=-5

So x=5

Now plug it into either question (no matter which-pick and choose)

I will go with the second original 3x+2y=13

So if x=5 we have 15+2y=13

Subtract 15 on both sides:        2y=-2

Now divide both sides by 2:      y=-1

Answer (5,-1)

Final answer:

To solve the simultaneous linear equations 4x + 3y = 17 and 3x + 2y = 13, the elimination method shows that the solution is x = 5 and y = -1.

Explanation:

To solve the simultaneous linear equations 4x + 3y = 17 and 3x + 2y = 13, one could use either the substitution method, the elimination method, or matrix methods. However, as per the guidance, we will follow the elimination method which is efficient and easily understandable.'

Let's multiply the first equation by 2 and the second equation by 3, which will give us:

8x + 6y = 34 (equation 1 multiplied by 2)

9x + 6y = 39 (equation 2 multiplied by 3)

Now, subtract the first new equation from the second new equation to eliminate y:

9x - 8x + 6y - 6y = 39 - 34

x = 5

Substitute x = 5 into one of the original equations to find y. For example, put x = 5 in 4x + 3y = 17:

4(5) + 3y = 17

20 + 3y = 17

3y = -3

y = -1

Therefore, the solution to the system of equations is x = 5 and y = -1.

Answer:

60y = 30x - 12

y = 1/2x - 1/5

The slope is 1/2

Answer:

1/2

Step-by-step explanation:

30 over 60 is half

Answer:

[tex]\large\boxed{d)\ 12}[/tex]

Step-by-step explanation:

[tex]x-\dfrac{1}{2}y=-6\\\\\text{y-intercept is for x = 0. Substitute:}\\\\0-\dfrac{1}{2}y=-6\\\\-\dfrac{1}{2}y=-6\qquad\text{multiply both sides by (-2)}\\\\\left(-2\!\!\!\!\diagup^1\right)\left(-\dfrac{1}{2\!\!\!\!\diagup_1}y\right)=(-2)(-6)\\\\y=12[/tex]

Answer:

(

k

+

9

)

(

k

−

9

)

(k+9)(k-9)

Step-by-step explanation:

Answer:

It's C

Step-by-step explanation:

Answer:

See attachment.

If altitude = 45 then

side = 2 * height (or altitude) / square root of 3

side = 2 * 45 / 1.7320508076

side = 90 / 1.7320508076

side = 51.9615242271

Step-by-step explanation:

Follow below steps;

When dealing with an equilateral triangle, dividing it by an altitude creates two 30-60-90 right triangles. Since we know the length of the altitude (45), which corresponds to the shorter leg in the 30-60-90 triangle, we can find the length of the side of the equilateral triangle (which is the hypotenuse of the 30-60-90 triangle) using the properties of this special right triangle.

To begin, we recognize that the ratios of the sides of a 30-60-90 triangle are 1:\\(extbackslashsqrt{3}\\):2. Thus, if the shorter leg is 45, the hypotenuse will be twice that length, because the ratio of the shorter leg to the hypotenuse is 1:2. Therefore, the length of a side of the equilateral triangle is 45 * 2, which equals 90.

ANSWER

58°

EXPLANATION

The relationship between the measure of the bigger arc and the smaller arc and the angle created by the secant and the tangent is

[tex]51 \degree = \frac{1}{2} (160 - x)[/tex]

Multiply through by 2

This implies that

[tex]2 \times 51 \degree =2 \times \frac{1}{2} (160 - x)[/tex]

We simplify to get:

[tex]102 \degree =160 - x[/tex]

Solve for x.

[tex]102 \degree - 160 \degree =- x[/tex]

[tex] - 58 \degree =- x[/tex]

[tex]58 \degree =x[/tex]

3x +11 = K

To solve for X, we need to isolate x on one side.

Subtract 11 from both sides:

3x = K -11

Divide both sides by 3:

x = (k-11)/3

Answer:

3x +11 = K

x = (k-11)/3

Step-by-step explanation:

Answer:

32 students

Step-by-step explanation:

We are given that at the beginning of a class period, half of the students in a class go to the library and half of the remaining to the computer lab.

Given that there are 8 students remaining, we are to find the total number of students in the class initially.

At beginning = [tex]x[/tex] students

After half of them leave = [tex]\frac{x}{2}[/tex] students

After half of the remaining leave = [tex]\frac{x}{4}[/tex] students

So, [tex]\frac{x}{4} = 8[/tex]

[tex]x=8\times 4[/tex]

x = 32

Therefore, there were 32 students in the class originally.

there were 32 students in the class originally.

because in the computer lab before there were 16.  16 times 2 equals 32.

Answer:

The next number is 1321232112

Step-by-step explanation:

32 is read off as "one 3, one 2" = 1312

1312 is read off as "one 1, one 3, one 1, one 2" = 11131112

11131112 is read off as "three 1s, one 3, three 1s, one 2" = 31133112

31133112 is read off as "one 3, two 1s, two 3s, two 1s, one 2" = 1321232112

sin(θ) < 0 is another way to say sin(θ) is negative.

tan(θ) < 0 is another way to say tan(θ) is negative.

let's recall that, on the III Quadrant sine and cosine are both negative, and thus the tangent is positive, recall tan(θ)=sin(θ)/cos(θ).

on the IV Quadrant however, sine is negative and cosine is positive, thus tangent is negative.

Answer:

[tex]x-12[/tex]

Step-by-step explanation:

First open the brackets

[tex]=(4x-6)-(3x+6)\\\\\\=4x-6-3x-6[/tex]

Then collect the like terms

[tex]4x-3x-6-6[/tex]

Solve the like terms

[tex]4x-3x=x\\\\\\-6-6=-12\\\\\\=x-12[/tex]

The simplified form is

[tex]x-12[/tex]

Answer: -12

Step-by-step explanation:

Answer:

Hi there!

The answer to this question is negative 12.