Use the initial term and the recursive formula to find an explicit formula for the sequence an. Write your answer in simplest form.

Answer: 7 hr

Step-by-step explanation:

Given

Distance between Emily and Kylie is [tex]140\ \text{miles}[/tex]

Speed of Emily [tex]v_e=12\ mph[/tex]

Speed of Kylie [tex]v_k=8\ mph[/tex]

Distance traveled by Emily [tex]\Rightarrow d_e=12t[/tex]

Distance traveled by Kylie [tex]\Rightarrow d_k=8t[/tex]

[tex]\Rightarrow 12t+8t=140\\\Rightarrow 20t=140\\\Rightarrow t=7\ hr[/tex]

They will meet after 7 hour.

Answer:

836.8

Step-by-step explanation:

Step-by-step explanation:

hope it is helpful to you ☺️

Answer: 80 feet

Step-by-step explanation:

We can write these as fractions and do cross multiplication with the numerator being the height of the object while the denominator being the length of the shadow:

5 * 128 = 8x

640 = 8x

80 = x

Thus, the height of the lighthouse is 80 feet tall.

Answer:

Total amount of ticket free = £64.89

Step-by-step explanation:

Given:

Cost of theater ticket = £63 plus

Booking fee of theater ticket = 3%

Find:

Total amount of ticket free

Comutation:

Total amount of ticket free = Cost of theater ticket + Booking fee of theater ticket

Total amount of ticket free = 63 + 3%

Total amount of ticket free = 63 + 1.89

Total amount of ticket free = 64.89

Total amount of ticket free = £64.89

Answer:

None of the options is true

Step-by-step explanation:

Given

[tex]y < 3x - 1[/tex]

[tex]y > -x + 4[/tex]

Required

Which makes the above inequality true

The missing options are:

[tex](4,0)\ (1,2)\ (0,4)\ (2,1)[/tex]

[tex](a)\ (x,y) = (4,0)[/tex]

Substitute values for x and y in the inequalities

[tex]y < 3x - 1[/tex]

[tex]0<3*4 - 1[/tex]

[tex]0<12 - 1[/tex]

[tex]0<11[/tex] ---- This is true

[tex]y &gt; -x + 4[/tex]

[tex]0 > -4 + 4[/tex]

[tex]0 > 0[/tex] --- This is false

[tex](b)\ (x,y) = (1,2)[/tex]

Substitute values for x and y in the inequalities

[tex]y &lt; 3x - 1[/tex]

[tex]2<3 * 1 - 1[/tex]

[tex]2<3 - 1[/tex]

[tex]2<2[/tex] --- This is false (no need to check the second inequality)

[tex](c)\ (x,y) = (0,4)[/tex]

Substitute values for x and y in the inequalities

[tex]y &lt; 3x - 1[/tex]

[tex]4< 3*0-1[/tex]

[tex]4< 0-1[/tex]

[tex]4<-1[/tex] --- This is false (no need to check the second inequality)

[tex](d)\ (x,y) = (2,1)[/tex]

Substitute values for x and y in the inequalities

[tex]y &lt; 3x - 1[/tex]

[tex]1<3*2-1[/tex]

[tex]1<6-1[/tex]

[tex]1<5[/tex] --- This is true

[tex]y &gt; -x + 4[/tex]

[tex]1 > -2+4[/tex]

[tex]1 > 2[/tex] -- This is false

Hence, none of the options is true

Answer:

what are the answer choice?

Step-by-step explanation:

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 (●'◡'●)

X -Y =44 will represent the number of glasses of ice tea .

Answer:6

Step-by-step explanation:

sorry if im wrong

Step-by-step explanation:

i think minerals and vitamins since they are micro nutrients

Answer:

The vertex is located at (-2,-1)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Acres of corn harvested : time taken = 8 3/4 : 5/6

How much corn can she collect in a hour. ?

Let

x = Acres of corn harvested

Acres of corn harvested : time taken = x : 1

8 3/4 : 5/6 = x : 1

35/4 : 5/6 = x : 1

35/4 ÷ 5/6 = x/1

35/4 × 6/5 = x/1

35*6/4*5 = x/1

210/20 = x/1

210 * 1 = 20 * x

210 = 20x

x = 210/20

= 10 1/2 acres

x = Acres of corn harvested = 10 1/2 acres

Answer:

11.2

Step-by-step explanation:

[tex]p =\frac{160.16}{14.3}=\frac{160.16*10}{14.3*10}\\\\p = \frac{1601.6}{143}\\\\[/tex]

p = 11.2

Answer:

The person above me is correct I just did the work and I got the same answer as them :)

Step-by-step explanation:

The y-coordinate of the red point is -3.

Answer:

The answer is 32.

Step-by-step explanation:

Just multiply the height by the base length. 4*8=32

Answer:

(-1,-1)

Step-by-step explanation:

Step 1 identify coordinates of A

A is located at ( -3 , -3 )

Step 2 apply dilation by multiplying the x and y values of coordinate A by the scale factor

Given:

scale factor = 1/3

Coordinates of A: ( -3 , -3 )

* Multiply the x and y values by 1/3 *

( -3 * 1/3 , -3 * 1/3 ) -------> ( -1 , -1 )

The new coordinates would be (-1,-1)

multiply the coordinates of A by the scale factor given

Answer:

20.6 m

Step-by-step explanation:

Hi there!

Assuming that the utility pole makes a 90-degree angle with the ground, this scenario creates a right triangle.

The 45 m-long cable is the hypotenuse and the 40 m between the base of the pole and the cable is one of the legs.

We must solve for the height of the utility pole, which is essentially the other leg of the right triangle.

We can use the Pythagorean theorem: [tex]a^2+b^2=c^2[/tex] where a and b are the legs and c is the hypotenuse

Plug in the known information (leg=40, hyp=45)

[tex]40^2+b^2=45^2\\1600+b^2=2025\\b^2=2025-1600\\b^2=425\\b=20.6[/tex]

Therefore, when rounded to the nearest tenth, the height of the utility pole is 20.6 m.

I hope this helps!

Answer:

Point A, C and D

Point B

Step-by-step explanation:

[tex]{hope it helps[/tex]

Answer:

[tex]90^{\circ}[/tex]. In other words, these two angles are both right angles, and this parallelogram would be a rectangle.

Step-by-step explanation:

Two angles that congruent have the same size.

At the same time, those two adjacent angles of this parallelogram would be a pair of consecutive interior angles. Because the two sides of a parallelogram are parallel to one another, the sum of these two consecutive interior angles would be [tex]180^{\circ}[/tex]- they are supplementary to one another.

Let the two angles be [tex]\angle1[/tex] and [tex]\angle 2[/tex].

[tex]\angle 1 = \angle 2[/tex] because the two angles are congruent.

[tex]\angle 1 + \angle 2 = 180^{\circ}[/tex] because these two angles are adjacent angles of a parallelogram.

Hence, [tex]\displaystyle \angle 1 = \angle 2 = \frac{1}{2} \times 180{^\circ} = 90^{\circ}[/tex].

Answer:

The probability that they each will catch 3 fish is 0.000063956

Step-by-step explanation:

The hyper geometric distribution is used to solve this as it has a population, a sample , number of successes  for both the population and sample.

Here

Population size= N =200

Sample size= n =9= (3*3)

Number of successes in population = k = 3 hours

Number of successes in sample = x= 3

Applying the hyper geometric distribution

P (x=3) = kCx *(N-k) C (n-x)/ N Cn

   = 3 C 3 * 197 C 6/ 200 C 9

    =0.000063956

The probability that they each will catch 3 fish is 0.000063956

Answer:

(1,-3) and (4,-6)

Step-by-step explanation:

The solutions are where the linear line intersects the graphed parabola.

Answer:

Graph B

Step-by-step explanation:

The vertical intercept I am getting is (0,-1) and B is the only one with that point. Therefore, it should be B.

Given:

The focus of the parabola is at (6,-4).

Directrix at y=-7.

To find:

The equation of the parabola.

Solution:

The general equation of a parabola is:

[tex]y=\dfrac{1}{4p}(x-h)^2+k[/tex]                  ...(i)

Where, (h,k) is vertex, (h,k+p) is the focus and y=k-p is the directrix.

The focus of the parabola is at (6,-4).

[tex](h,k+p)=(6,-4)[/tex]

On comparing both sides, we get

[tex]h=6[/tex]

[tex]k+p=-4[/tex]                            ...(ii)

Directrix at y=-7. So,

[tex]k-p=-7[/tex]                            ...(iii)

Adding (ii) and (iii), we get

[tex]2k=-11[/tex]

[tex]k=\dfrac{-11}{2}[/tex]

[tex]k=-5.5[/tex]

Putting [tex]k=-5.5[/tex] in (ii), we get

[tex]-5.5+p=-4[/tex]

[tex]p=-4+5.5[/tex]

[tex]p=1.5[/tex]

Putting [tex]h=6, k=-5.5,p=1.5[/tex] in (i), we get

[tex]y=\dfrac{1}{4(1.5)}(x-6)^2+(-5.5)[/tex]

[tex]y=\dfrac{1}{6}(x-6)^2-5.5[/tex]

Therefore, the equation of the parabola is [tex]y=\dfrac{1}{6}(x-6)^2-5.5[/tex].

Step-by-step explanation:

=> (3x-12) =(x+6)

or,3x - x = 6 + 12

or,2x = 18

or,x = 18/2

•: x=9#

Answer:

7

Step-by-step explanation:

evaluate the function means substitute x=-1 and calculate

f(x) = 3x²-4x

f(-1) =f(x=-1) = 3(-1)²-4(-1) =3+4 =7, because (-1)²=1 and -4(-1) =4

Answer: 19/3

Step-by-step explanation:

[tex]4x+3-x-5=30-3x\\\\3x-8=30-3x\\\\6x-8=30\\\\6x=38\\\\x=\frac{19}{3}[/tex]

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

Explanation:

1/2 is the probability of flipping tails because we have one side labeled tails out of 2 sides total.

1/6 is the probability of rolling a 5, because there's one side we want out of 6 total.

The two events (flipping the coin and rolling the die) are independent, allowing us to multiply those previously mentioned fractions:

(1/2)*(1/6) = (1*1)/(2*6) = 1/12

Step-by-step explanation:

given the geometric sequence 2, -4, 8, -16, ...

a1 = 2

r = -4/2 = -2

find : a9 and a15

solutions:

an = a1. r^(n-1)

=> a9 = 2. (-2)^(9-1)

= 2. (-2)^8

= 2. 2^8

= 2^9

= 512.

=> a15 = 2. (-2)^(15-1)

= 2. (-2)^14

= 2. 2^14

= 2^15

= 32,768

Step-by-step explanation:

Hey there!

The given geometric sequence is: 2, -4, 8, -16.

The;

a1 = 2

Common ratio (r) = T2/T1

= -4/2

= -2

Now;

Use general formula of geometric sequence;

[tex]tn = {a1.r}^{n - 1} [/tex]

Where, "a1" is first term, "n" is no.of terms and "r" is common ratio.

Then;

[tex]t9 = 2 \times { (- 2)}^{9 - 1} [/tex]

or, t9 = 2*256

Therefore, t9 = 512.

Again;

[tex]t15 = 2. { (- 2)}^{15 - 1} [/tex]

or, t15= 2*16384

Therefore, t15 = 32768.

Hope it helps!