solve for the measure of x in the drawing shown below

Answer:

[tex]\displaystyle S_{8}=6560[/tex]

Step-by-step explanation:

We have the geometric sequence:

2, 6, 18, 54 ...

And we want to find S8, or the sum of the first eight terms.

The sum of a geometric series is given by:

[tex]\displaystyle S=\frac{a(r^n-1)}{r-1}[/tex]

Where n is the number of terms, a is the first term, and r is the common ratio.

From our sequence, we can see that the first term a is 2.

The common ratio is 3 as each subsequent term is thrice the previous term.

And the number of terms n is 8.

Substitute:

[tex]\displaystyle S_8=\frac{2((3)^{8}-1)}{(3)-1}[/tex]

And evaluate. Hence:

[tex]\displaystyle S_8=6560[/tex]

The sum of the first eight terms is 6560.

Answer:

S₈ = 6560

Step-by-step explanation:

The sum to n terms of a geometric sequence is

[tex]S_{n}[/tex] = [tex]\frac{a(r^{n}-1) }{r-1}[/tex]

where a is the first term and r the common ratio

Here a = 2 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{6}{2}[/tex] = 3 , then

S₈ = [tex]\frac{2(3^{8}-1) }{3-1}[/tex]

    = [tex]\frac{2(6561-1)}{2}[/tex]

    = 6561 - 1

    = 6560

Answer:

23.4 km

Step-by-step explanation:

We can use a ratio to solve

13 km         x km

--------   = ---------------

5 hours         9 hours

Using cross products

13*9 = 5x

117 = 5x

Divide each side by 5

117/5 = 5x/5

23.4 =x

Answer:

It travel 23.4 km in 9 hours.

Step-by-step explanation:

Given :-

A sea turtle can swim 13 km in 5 hours at this rate speed .

To find :-

How far can it travel in 9 hours.

Solution :-

Sea turtle swim 13 km in 5 hours Then find the how far it can travel in 9 hours.

Let us assume that In 9 hours turtle swim x km.

Now, We solve by using ratio for x.

In 5 hours it swim = 13 km

And, In 9 hours it swim = x km

Calculate for x

5 hours = 13 km

9 hours = x km

Use cross multiplication method , we get

5 × x = 9 × 13

5x = 117

Divide both side by 5

5x / 5 = 117 / 5

x = 23.4

Hence, It can travel 23.4 km in 9 hours.

We are given:

aᵇ = bᵃ

b = 2a

Finding (a+b):

Finding a:

replacing b by 2a in the first equation, we get:

(a²)ᵃ = (2a)ᵃ

(a²)ᵃ = 2ᵃ * aᵃ

a²ᵃ / aᵃ = 2ᵃ                  [dividing both sides by aᵃ]

aᵃ = 2ᵃ                          [because xᵃ / xᵇ = xᵃ⁻ᵇ]

a = 2                             [raising both sides to 1/a]

Finding b:

We are given that b = 2a

now that we know what a equals, we will plug that value here

b = 2(2)

b = 4

Finding a+b:

We found that a = 2, b = 4

a + b = 2 + 4 = 6

Answer:

h

Step-by-step explanation:

Double radius

Hello,

[tex]Formula:\ y=k*a^x+b\\\\ \lim_{x \to -\infty} y=-3 \Longrightarrow -3=k*a^{-\infty}+b=0+b \Longrightarrow b=-3\\\\if \ x=0\ then\ y=-2 \Longrightarrow -2=k*a^0-3 \Longrightarrow k=1\\\\if \ x=1\ then\ y=3 \Longrightarrow 3=a^1-3 \Longrightarrow a=6\\\\\boxed{y=6^x-3}\\[/tex]

Answer:

112

Step-by-step explanation:

add both bases the multiply by the height

Answer:

112

13 + 15

= 28 ÷ 2

= 14 × 8

= 112

Answer:

9. The area of rectangle S is four times bigger than rectangle R

10. (1, 3)

Step-by-step explanation:

To find the solution of the two linear equations:

y=x+2

y=-2x+5

x+2=y=-2x+5

3x=3

x=1

y=1+2

y=3

(1,3)

Step-by-step explanation:

went to a calculator

it said

Side a = 20.66803

Side b = 13

Side c = 17

Angle ∠A = 86°

Angle ∠B = 38.863°

Angle ∠C = 55.137°

Answer:

27 mi^2

Step-by-step explanation:

The area of a triangle is always 1/2 (base times height) so it is 1/2 (9×6) = 27

Answer:my uncle john told me D

Step-by-step explanation:Beacause john have a brain

Answer:

-6.895

Step-by-step explanation:

11.485

-18.38

______

-6.895

If these are number systems then it will turn out like this                                            [tex]\displaystyle\bf 523_7-65_7=\boxed{425_7}[/tex]

Answer:

-10x-4y

Step-by-step explanation:

Step-by-step explanation:

Explanation is in the attachment

your answer will be 10x(1+2y)

hope it is helpful to you ☺️

Answer:

v=fu/u-f

Step-by-step explanation:

the answer is explained in the diagram

(x-2)(x+2) is factorize is given eq

Answer:

71.4 degrees Celsius or 183.4 degrees Fahrenheit.

Step-by-step explanation:

The boiling point of water is 100 degrees Celsius.

I assume you mean the liquid's temperature is 28.60 degrees Celsius lower than the boiling point of water, so 100 - 28.6 = 71.4.

Therefore the liquid is 71.4 celsius.

If you wanted the temperature in Fahrenheit, the answer is 212 - 28.6 = 183.4 degrees Fahrenheit.

Answer:

C=25+5.50n

Step-by-step explanation:

C=25+5.50n where c is the total cost and n is the number of hours the clown entertains.

Step-by-step explanation:

Given that,

The positions of the first particle,[tex]s_1=4t-t^2[/tex]

Velocity,

[tex]v_1=\dfrac{ds_1}{dt}\\\\v_1=\dfrac{d(4t-t^2)}{dt}\\\\v_1=4-2t[/tex]

Position,

[tex]s_2=5t^2-t^3[/tex]

[tex]v_2=\dfrac{ds_2}{dt}\\\\v_2=\dfrac{d(5t^2-t^3)}{dt}\\\\v_2=10t-3t^2[/tex]

Hence, this is the required solution.

Answer:

A≈102.79

Step-by-step explanation:

The formula for area of a circle is πr² so we need to substitute the r by 5.72.

π×5.7² = 102.79 m²

Answer:

Approximately 102.79 meters squared

Step-by-step explanation:

pi times 5.72 meters squared

Hope this helps!

Answer:

B

Step-by-step explanation:

7x root2 + x root 2 =8x root 2 and you just add the -4 root 2 on

Answer= B

Answer:

sorry i cannot help you

Given:

For en exponential function f(a):

[tex]f(-3)=18[/tex]

[tex]f(1)=59[/tex]

To find:

The value of f(0).

Solution:

The general form of an exponential function is:

[tex]f(x)=ab^x[/tex]          ...(i)

Where, a is the initial value and b is the growth/ decay factor.

We have, [tex]f(-3)=18[/tex]. Substitute [tex]x=-3,f(x)=18[/tex] in (i).

[tex]18=ab^{-3}[/tex]            ...(ii)

We have, [tex]f(1)=59[/tex]. Substitute [tex]x=1,f(x)=59[/tex] in (i).

[tex]59=ab^{1}[/tex]            ...(iii)

On dividing (iii) by (ii), we get

[tex]\dfrac{59}{18}=\dfrac{ab^{1}}{ab^{-3}}[/tex]

[tex]3.278=b^{1-(-3)}[/tex]

[tex]3.278=b^{4}[/tex]

[tex](3.278)^{\frac{1}{4}}=b[/tex]

[tex]1.346=b[/tex]

Substituting the value of b in (iii).

[tex]59=a(1.346)^1[/tex]

[tex]\dfrac{59}{1.346}=a[/tex]

[tex]43.83358=a[/tex]

[tex]a\approx 43.83[/tex]

The initial value of the function is 43.83. It means, [tex]f(0)=43.83[/tex].

Therefore, the value of f(0) is 43.83.

Answer:

W'(4, -2), X'(3, -4), Y'(1, -4), Z'(0, -2)

Step-by-step explanation:

Its A Your Welcome :)

Answer:

A.

Step-by-step explanation:

Answer:

60ft

Step-by-step explanation:

DC is 50% longer than BD (given)

BD is 40ft (given)

DC is 50% longer than BD this means that DC= BD+50% of  BD

40ft +50/100 * 40

=40ft +20ft

=60ft

Another way to solve this could be DC is 150%of BD as BD =40ft=100% of it's length.

So, 150/100 *40

=60ft

Hope this helps.

Please mark me as brainliest.

Answer:

First dropbox: 7h + 43 = 64

Second dropbox: $3

Step-by-step explanation:

Here's what we know about the question so far:

$43 is the initial fee

The rototiller worked for 7 hours

$64 is the total cost (including initial fee)

h = hourly fee

The answer should be 7h + 43 = 64 because:

- It includes the initial fee of $43

- It sets the equation equal to $64, which is the total cost

- The hourly fee is being multiplied with 7 hours, which is correct since the h variable is hourly (not sure how to explain this part ;w; )

For the 2nd drop box, we will use basic algebra to solve for h:

7h + 43 = 64

(subtract both sides by 43)

7h = 21

(divide both sides by 7)

h = 3

There's your 2 answers!

Hope it helps (●'◡'●)

Answer:

a. -2

c. -1

Step-by-step explanation:

these are the only values for x, where the 2 equations deliver the same y value.

in case of a. y = -2×-2 - 1 = 4 - 1 = 3

and y = 3¹ = 3

c. y = -2×-1 - 1 = 2 - 1 = 1

y = 3⁰ = 1

Answer:

16.67% of your day is spent in math class.

Step-by-step explanation:

The total would be 100% and then since you have 6 periods we divide 100 by 6 to get 16.67%. So 16.67% of your day is spent in math class.

Answer:

34.9°

Step-by-step explanation:

SOH

CAH

TOA

SOH ... sin(x) = 8/14

arcsin(8/14) = 34.85°

Answer:

2.56 kgs

Step-by-step explanation:

76.8kg ÷ 30 days = 2.56 kgs

Amount of sugar used - 76.8 kg

No. Of Days in Month of April - 30 days

∴ Sugar used each day is = 76.8 ÷ 30

[tex]76.8 \div 30 \\ \\ = \frac{76.8}{30} \\ \\ = \frac{768}{30 \times 10} \\ \\ = \frac{ \cancel{768}}{ \cancel{30} \times 10} \fbox{cancelling by 3} \\ \\ = \frac{256}{10 \times 10} \\ \\ = \frac{256}{100} \\ \\ = 2.56 \: kg[/tex]