If the 5th term in a geometric sequence is 162, and the common ratio is 3. What is the first term in the sequence?

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].

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:

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:

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

Answer:

0,-4

-2.65,2.62

2.65,2.62

Step-by-step explanation:

[tex]0^2 = 0\\-2.65^2 =7.0225\\ 2.65^2 =7.0225[/tex]

[tex]y = x^2 - 4[/tex]

-4, 3.0225

[tex]-4^2 = 16\\3.0225^2=9.1355[/tex]

Answer:

Rupees 39,000 are

378.63 Pound sterling

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:

Step-by-step explanation:

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

or,3x - x = 6 + 12

or,2x = 18

or,x = 18/2

•: x=9#

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.

Step-by-step explanation:

i think minerals and vitamins since they are micro nutrients

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

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: 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]

Answer:

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

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

-2x = -6

or, x = -6 / -2

or, x = 3

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:

[tex]y=3x-17[/tex]

Step-by-step explanation:

Parallel equations always share a slope.

So since we know the slope and a point the equation needs to pass through we can plug in the values and replace -8 with [tex]b[/tex]

[tex]-5=3(4)+b[/tex]

simplify both sides

[tex]-5=12+b[/tex]

isolate the variable

[tex]-17=b[/tex]

plug [tex]b[/tex] back into the equation and you get

[tex]y=3x-17[/tex]

Answer:

y = 3 x + 11

 Explanation:

Parallel lines have the same slopes.

The slope of the new line will have the same slope as the given line:

y = 3 x − 4

⇒ m = 3

One point on the line is given,  

( − 2  5 ) .

This is  ( x 1  y 1 )

The formula for slope is  

m = ( change in y values/ change in x-values ) =  y 2  −  y 1/ x 2 − x 1

If you have the slope and one point , substitute them into a formula which is based on the formula for slope given above.

y  −  y 1 =  m  ( x  −  x 1 )  

y  −  5  =  3 ( x  −  ( − 2 ) )

y  −  5  =  3 ( x + 2 )

Simplify to get the required equation of the line.

y  =  3 x  +  6  +  5

y  =  3 x  +  11

Step-by-step explanation:

Answer:

QP ≈ HG

Common side between those angles are QP and HG

so, they should be congruent to prove AAS

Answered by GAUTHMATH

Answer:

C y=x^2+2x+1

Step-by-step explanation:

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:

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:

b) y=sqrt(x) shifted 3 units left

Step-by-step explanation:

3rd line in the attached table:

f(x+3) = sqrt(x+3) horizontal translation left 3 units

Answer:

AC is greater than BC

Step-by-step explanation:

First, we know that the angle of a straight line is 180°, so angle B as a whole is equal to 180 degrees. Therefore, angle YBC + angle ABC = 180 degrees. As angle YBC is a right angle, signified by the small square on the angle, it is 90 degrees. Therefore,

90 degrees + angle ABC = 180 degrees

subtract 90 degrees from both sides to isolate angle ABC

angle ABC = 90 degrees

Therefore, as angle ABC is equal to 90 degrees, and a right angle is 90 degrees, triangle ABC has a right angle, making it a right triangle.

In a right triangle, using the Pythagorean Theorem, the square of the side opposite the right angle is equal to the sum of the squares of the other side. Since side AC is opposite the right angle, we can say that

AC² = AB² + BC²

As the length of a side has to be greater than 0, we can say that

AC² = AB² + BC²

AB² > 0

AC² > BC²

square root both sides

AC > BC

Therefore, AC is greater than BC

Step-by-step explanation:

(3^5 - 3^4) (3^3 + 3^2)

= (243 - 81) (27 + 9)

= (162) (36)

= 5832

24 = 8*3

since 832 is divisible by 8 and 5+8+3+2 = 18 is divisible by 3

5832 is therefore divisible by 24

check:

5832/24 = 243

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:

e = -1/2

Step-by-step explanation:

To solve this problem, our first step is to add 5/3 to both sides of the equation.  This gives us:

4/3 + 5/3 = -6e - 5/3 + 5/3

9/3 = -6e

We can simplify the left side of the equation by performing the division.

3 = -6e

Next, we can solve for e by dividing both sides of the equation by -6.

e = -1/2

Therefore, the correct answer is e = -1/2.

Hope this helps!

Answer:

The value of e is -1/2

Step-by-step explanation:

4/3 = - 6e - 5/3

Now, add 6e both side we get,

4/3 + 6e = + 6e - 6e - 5/3

4/3 + 6e = - 5/3

Now, subtract 4/3 from both side we get,

4/3 - 4/3 + 6e = -4/3 - 5/3

6e = -4/3 - 5/3

6e = -4 - 5/3

6e = -9/3

6e = -3

Now, divide 6 from both side we get,

6e/6 = -3/6

e = -1/2

Thus, The value of e is -1/2

-TheUnknownScientist

Answer:

836.8

Step-by-step explanation: