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2 years ago

Which equation is y = 9x^2 + 9x – 1 rewritten in vertex form

2 answers:

6 0

Vertex form equation
y = a(x - h)² + k

We need to solve it by completing quadratic form
To complete the quadratic form, multiply the equation by 4. We multiply it by 4 so the coefficient of x² is in complete quadratic form and the coefficient of x is an even number.
y = 9x² + 9x - 1
--------------------- (multiply 4)
4y = 36x² + 36x - 4

Change the quadratic expression into complete quadratic form
Add +9 to the both side
4y = 36x² + 36x - 4
4y + 9 = 36x² + 36x + 9 - 4
4y + 9 = (6x + 3)² - 4
4y = (6x + 3)² - 4 - 9
4y = (6x + 3)² - 13
------------------------------ divide by 4
$y = \frac{1}{4} (6x+3)^{2}- \frac{13}{4}$

user100 [1]2 years ago

3 0

You have to solve for 9x first

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Andre ran 2 kilometers in 15 minutes, and Jada ran 3 kilometers in 20 minutes. Both ran at a constant speed. Did they run at the

Goshia [24]

Answer:

speed of Jada = 6km per hour which is not equal to

speed of Andre = 8km per hour

They did not run at same speed

Step-by-step explanation:

formula of speed = distance covered/ time taken

For Andre

Distance = 2 KM

time = 15 mins

60 mins = 1 hour

15 mins = 1/60 * 15 hour = 0.25 hours

thus,

speed = 2km/0.25 hour = 8 km per hour

Similarly for Jada

Distance = 3 KM

time = 20 mins

60 mins = 1 hour

20 mins = 1/60 * 20 hour = 1/3 hours

thus,

speed = 2km/(1/3)hour = 6 km per hour

Now we have

speed of Jada = 6km per hour which is not equal to

speed of Andre = 8km per hour

6 0

2 years ago

The number 8/7 = 1.14285714285714 ... obviously has no exact representation in any decimal floating point system (beta = 10) wit

arlik [135]

Answer:

The answer to this question can be defined as follows:

Step-by-step explanation:

In the first point:

Yes, the Finite Floating Point Structures are considered Where $\beta = 7$

$\to \frac{8}{7}= (1.1)_7$

$\bold{= 1 \times 7^0 + 1 \times 7^{-1}}\\\\$

In the second point:

There is no device with a finite floating-point since the right side is

This equality never happens, then, with the rational numbers ( $\alpha_i$ and $\beta$ is rational).

5 0

2 years ago

The following histogram presents the amounts of silver (in parts per million) found in a sample of rocks. One rectangle from the

gladu [14]

Answer:

The height of the missing rectangle is 0.15

Explanation:

The image attached has the mentioned histogram.

Such histogram presents the relative frequencies for the clases [0,1], [1,2],[2,3], [4,5], and [5,6] Silver in ppm.

Only the rectangle for the class [3,4] is missing.

The height of each rectangle is the relative frequency of the corresponding class.

The relative frequencies must add 1, because each relative frequency is calculated dividing the absolute class frequency by the total number in the sample; hence, the sum of all the relative frequencies is equal to the total absolute class frequencies divided by the same number, yielding 1.

In consequence, you can sum all the known relative frequencies and subtract from 1 to get the missing relative frequency, which is the height of the missing rectangle.

1. Sum of the known relative frequencies:

0.2 + 0.3 + 0.15 + 0.1 + 0.1 = 0.85

2. Missing frequency:

1 - 0.85 = 0.15

3. Conclusion:

The height of the missing rectangle is 0.15

4 0

2 years ago

A cereal company is putting 1 11 of 3 33 prizes in each box of cereal. The prizes are evenly distributed so the probability of w

Black_prince [1.1K]

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

A cereal company is putting 1 of 3 prizes in each box of cereal. The prizes are evenly distributed so the probability of winning any given prize is always 1/3. Adam wonders how many boxes he should expect to buy to get all 3 prizes. He carried out 32 trials of a simulation and his results are shown below.

3 12

4 4

5 5

6 5

7 0

8 0

9 2

10 2

11 0

12 2

Use his results to estimate the probability that it takes 9 or more boxes to get all 3 prizes. Give your answer as either a fraction or a decimal. P ( 9 or more boxes ) =

Answer:

P(x ≥ 9) = 18.75%

Step-by-step explanation:

A cereal company is putting 1 of 3 prizes in each box of cereal.

Adam is trying to find out how many boxes he should buy to get all 3 prizes.

He carried out 32 trials and got the following results.

We want to estimate the probability that it takes 9 or more boxes to get all 3 prizes.

No. of Boxes | frequency

3 | 12

4 | 4

5 | 5

6 | 5

7 | 0

8 | 0

9 | 2

10 | 2

11 | 0

12 | 2

9 or more boxes means equal to 9 boxes or greater than 9 boxes.

P(x ≥ 9) = No. of boxes equal or greater than 9/total no. of boxes

The total no. of boxes is 32

From the above data, count the number of boxes equal to or greater than 9. (6 times)

P(x ≥ 9) = 6/32

P(x ≥ 9) = 3/16

P(x ≥ 9) = 0.1875

P(x ≥ 9) = 18.75%

Therefore, there is 18.75% probability that it takes 9 or more boxes to get all 3 prizes.

3 0

2 years ago

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A costumer pays $18 for a DVD that originally cost $20. What is the percent decrease in the cost of the DVD? A.2% B.10% C.11% D.

jonny [76]

Answer:11%

Step-by-step explanation:

Percentage decrease is gotten with thus formula.

Actual price - Old Price= New price

New price/Old Price * 100/1

From the above question.. $18= Old price , $20= New price

So 20-18 = 2(New Price)

2/18 *100 = 0.11 * 100 = 11%

3 0

2 years ago

Read 2 more answers