Find the vertex of the function h(x) = x2 – 4x – 21

Answer:

Let a(n) denote the n-th term in the GP. We're given

a(6) = 8a(10)

a(7) + a(8) = 192

In a geometric progression, consecutive terms are scaled up or down by a fixed ratio r such that

a(n) = r a(n - 1)

By substitution, we get

a(n) = r (r a(n - 2)) = r ² a(n - 2)

and we can continue the pattern down to the first term,

a(n) = r a(n - 1) = r ² a(n - 2) = r ³ a(n - 3) = … = rⁿ ⁻¹ a(1)

So we can rewrite the first two equations in terms of the first term of the GP a(1) and the common ratio r :

r ⁵ a(1) = 8r ⁹ a(1)

r ⁶ a(1) + r ⁷ a(1) = 192

Solve the first equation for r :

r ⁵ a(1) = 8r ⁹ a(1)   →   1 = 8r ⁴   →   r = 1/∜8 ≈ 0.5946

Solve the second equation for a(1) :

r ⁶ a(1) + r ⁷ a(1) = r ⁶ a(1) (1 + r ) = 1/(16√2) a(1) (1 + 1/∜8) = 192

→   a(1) = 6144 ∜2 / (1 + ∜8) ≈ 2724.48

Answer:

27

Step-by-step explanation:

first we can simplify by dividing by r

[tex] \frac{9 {r}^{2} }{r} = \frac{9 \times r \times r}{r} = 9 \times r \times 1 = 9r[/tex]

the r on the bottom of the fraction will cancel out one of the r's on top, this happens because anything divided by itself is 1, thus r divided by r is 1

finally we can evaluate when r =3,

9r = 9(3) = 27

Answer:

CP = Rs 500

Step-by-step explanation:

Given that,

Selling price of a book, SP = Rs 550

Profit percent = 10%

We need to find the cost price of the book. The formula for profit percent is given by :

[tex]P\%=\dfrac{SP-CP}{CP}\times 100\\\\\dfrac{10}{100}=\dfrac{550-CP}{CP}\times 100\\\\\dfrac{1}{10}=\dfrac{550-CP}{CP}\\\\CP=5500-10CP\\\\CP+10CP=5500\\\\11CP=5500\\\\CP=500[/tex]

So, the cost price of the book is Rs 500.

Answer:

1.+25

2 -6

3 +6

4.

5. 0

Step-by-step explanation:

Sana Makatulong

Answer:

A  -4a(3 + 2a)

Step-by-step explanation:

-12a - 8a^2) factor out a -4

-4(3a + 2a^2) factor out an a

-4a(3 + 2a)

Answer:

-55

Step-by-step explanation:

7+x/5=-4

Subtract 7 from both sides

x/5 = -11

multiply both sides by 5

x = -55

Answer: 0.06

Step-by-step explanation:

2/(3+25+2)=0.06

Answer:

12 and 12

Step-by-step explanation:

12lcm +12lcm=24lcm

Answer:

F = 15

Good luck! Have a wonderful day!

Answer:

15

Step-by-step explanation:

Yw

Answer:

5

Step-by-step explanation:

Hi there!

Finding the equivalen ratio means to find a equivalent numbers that’s equivalent to 6 and 7 which also means a number that 6 and 7 all goes into...

6,12,18,24,30,36,42

7,14,21,28,35,42

Final Result: 42

Answer:

200 tulips

Step-by-step explanation:

The computation of the number of tulips are shown below:

Given that

Ratio of number of tulips to number of ratios is 2:3 we can write 8:12

And, the peonies to roses are 1:4 we can write as 3:12

So,

Tulips : Roses : Peonies

8:12:3

Now

Total units of flowers + 8 + 12 + 3

= 23

For tulips it would be

= 575 × 8 ÷ 23 units  

= 200 tulips

Answer:

WHat does that mean?/

Step-by-step explanation:

Answer:

the last set: {1, 1, 1, 1, 2, 2, 2, 2}

Step-by-step explanation:

Notice the smallest standard deviation will come from the addition of the differences between the average value and each individual number in the set.

We notice that there is one set where all values are very close to the average . This is the set:

{1, 1, 1, 1, 2, 2, 2, 2} whose clear average is 1.5 , and therefore the deviations from the mean will produce contributions of 0.5 for each of the elements.

Answer:

c

Step-by-step explanation:

Answer:

$2216.02

Step-by-step explanation:

Compound interest formula:

[tex]FV=PV(1+\frac{i}{n})^{nt}\\\\FV=500(1+\frac{.06}{4})^{25*4}\\\\500(1.015)^{100}\\=2216.02[/tex]

Answer:

Part A:

c = 4 + 1.50h

c = 1 + 3h

Part B:

2 hours

$7

Step-by-step explanation:

Part A:

Number of hours = h

Cost = c

Cost for Ice Dream:

c = 4 + 1.50h

Cost for Skating Paradise:

c = 1 + 3h

Part B:

Set the equation equal to each other and solve for h:

4 + 1.50h = 1 + 3h

Collect like terms

4 - 1 = -1.50h + 3h

3 = 1.50h

Divide both sides by 1.50

3/1.5 = h

2 = h

h = 2

The cost for both locations would be equivalent at 2 hours

✔️The cost is:

4 + 1.50h = 1 + 3h

4 + 1.50(2) = 1 + 3(2)

4 + 3 = 1 + 6

7 = 7

The cost is $7

Answer:

b=53 degrees

Step-by-step explanation:

90 degrees - 37 degrees = 53 degrees

Answer:

-o.91

Step-by-step explanation:

first u - 10.75 by 11.66 and then u get the answer

Step-by-step explanation:

Hjqjzjzj is a complete* of the following elements has the largest atomic size in the world is the difference between human rights

Answer:

We know:

A+2B=777

2A+B=789

Let's rearrange the first equation to solve for A:

A=777-2B

Now let's plug 777-2B in for A in the second equation, and solve for B:

2(777-2B)+B=789

1554-4B+B=789

1554-789=3B

765=3B

B=255

Now we can substitute 255 in for B in the first rearranged equation, and solve for A:

A=777-2(255)

A=777-510

A=267

So candy bar A has 267 calories, and candy bar B has 255

I Hope it helps

Answer:

221 books

Step-by-step explanation:

Answer:

About 14.14

Step-by-step explanation:

V = 4/3pi x r^3

To find the radius, divide the diameter by 2 (1.5)

Substitute 1.5 in place of r and solve the equation.

Answer:

14 in^3

Step-by-step explanation: had the question too and got it right

Answer:

43 degrees

Step-by-step explanation:

Using SOHCAHTOA, you are given the opposite and adjacent, the opp being 15 and the adj being 16.

Tan B = [tex]\frac{opp}{adj}[/tex]

Tan B = [tex]\frac{15}{16}[/tex]

      B = [tex]tan^{-1}[/tex]([tex]\frac{15}{16}[/tex])

      B = 43.15238973 degrees

Therefore, the answer is 43 degrees since you're looking for it to the nearest degree.

Answer:

43 degrees

Step-by-step explanation:

i did the work

Replace x with 1 nd solve, then replace x with 3 and solve:

x^3 - 2x^2 +3x

When x = 1:  1^3 -2(1)^2 +3(1) = 3 -3 +3 = 3

When x = 3: 3^3 -2(3)^2 + 3(3) = 27 -18 +9 = 18

The difference between the two solutions is 18-3 = 15

The difference between the two x values = 3-1 = 2

The rate of change is 15/2  or 7.5 as a decimal.

Answer:

4.9%

Step-by-step explanation: