Complete the square to re-write the quadratic function in vertex form: y = x ^ 2 - 2x - 8

Answer:

solution in attachment

hope it helps

Answer: multiplying the number by 2.5

Your answer

Step-by-step explanation:

Jay took a number n and increased it by 25%. This will be:

= n + (25% × n)

= n + (0.25 × n)

= n + 0.25n

= 1.25n

Then, he doubled the resulting product. This will now be:

= 2 × 1.25n

= 2.50n

Therefore, the equivalent will be option D "multiplying the number by 2.5".

Completing the square method rearranges the equation to have the

square of linear equation and constant on both sides of the equation.

Responses:

The given equation is; x² - 10·x - 11 = 0

Line 1: p² - 10·p - 11 = 0

Which gives;

p² - 10·p = 11

Adding 25 to both sides gives;

Line 2: p² - 10·p + 25 = 11 + 25

11 + 25 = 36

Factorizing p² - 10·p + 25 = (p - 5)·(p - 5)  = (p - 5)²

Line 3: (p - 5)² = 36

Which gives;

p - 5 = ±√36

Line 4: p - 5 = √36 = 6 or p - 5 = -√36 = -6 (Line that has a mistake)

Line 5: p = 6 + 5 = 11, or p = -6 + 5 = -1

Line 6: p = 11 or p = -1

The constant on the left and side is then subtracted from the positive

and negative value of the square root of the right hand side to give two

results.

Learn more about completing the square here:

https://brainly.com/question/3939104

Answer:

-9

Step-by-step explanation:

why not

Answer:

5x4x9=180  then 4 divided by 2 is 2 then 2x180 you get the answer

Step-by-step explanation:

Answer:

Rectangle 11.59 sqft

Rectangle 36 sqft

Polygon 47.59 sqft

Step-by-step explanation:

Answer:

729 square yards

Step-by-step explanation:

Area = l x w

Area = 27 x 27

Area = 729 square yards

Hope that helps! :)

-Aphrodite

Answer:

It’s 729

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

2 ÷ 1/2 = 4

Answer:

In statistics, the three most common measures of central tendency are the mean, median, and mode. Each of these measures calculates the location of the central point using a different method.

example: Two polygons are congruent if they are the same size and shape - that is, if their corresponding angles and sides are equal.

Answer:

Two polygons are congruent if they are the same size and shape - that is, if their corresponding angles and sides are equal. Move your mouse cursor over the parts of each figure on the left to see the corresponding parts of the congruent figure on the right.

Step-by-step explanation:

Here is the complete question.

Members of the Alachua district choir were asked when given the choice between romanticism gothic style singing, which style they preferred to sing for state competition. The data was broken down by gender:

48 males preferred Romanticism

63 males preferred Gothic

59 females preferred Romanticism

62 females preferred Gothic

Part A: Fill in and complete the following contingency table. Circle the largest joint frequency and put a box around the smallest marginal frequency.

Romanticism Gothic Total

Males

Females

Total

Part B: Which style was preferred as the state competition piece and by what percentage?

Part C: Which subject was preferred the most by Males?

Part D: What frequency does 125/232 represent?

Answer:

The answer is below

Step-by-step explanation:

Part A:

Romanticism, Gothic, Total

Males 48, 63, 111

Females 59, 62, 121

Total 107, 125, 232

Part B: The preferred style is Gothic by a percentage of

P = 125 ÷ 232

Hence, we have P = 54%

Part C: Based on the table provided, the subject aspired the most by males was Gothic since 63 males chose it over 48 chose Romanticism.

Part D: The frequency 125/232 depicts the total of people that preferred Gothic over the total of people in both categories.

Answer:

320 marks = 40 percent therefore the total marks for the exam= 320+320+160=800 marks.

Step-by-step explanation:

let the full marks be " x "

Rajani has scored 295 marks , if she would had scored 25 more marks then she would had passed the examination,

So, passing marks :

=》295 + 25

=》320

passing percentage ( P% ) :

=》

[tex]40 = \dfrac{passing \: \: marks}{total \: \: marks} \times 100[/tex]

=》

[tex]40 = \dfrac{320}{x} \times 100[/tex]

=》

[tex]x = \dfrac{320 \times 100}{40} [/tex]

=》

[tex]x = 8 \times 100[/tex]

=》

[tex]x = 800[/tex]

So, passing marks = 800 marks

Answer:

Step-by-step explanation:

Answer:

35 multiplied by 12

Step-by-step explanation:

Because either you multiply it or you do sohcahtoa

Answer:

467

Step-by-step explanation:

Determine the percentage of those sampled whose favourite season is fall

(18/70) x 100 = 25.7%

the sample is representative of the population of students. So, 25.7% of the students would like fall

number of students at Franklin High School whose favourite season is fall = 25.7% x 1816 = 466.7 students

rounding off to the nearest whole number gives 467

Answer:

467

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

j - 4 ≤ 0 ( add 4 to both sides )

j ≤ 4

The graph has a closed circle at 4 on the number line with the arrow pointing left

Answer:

bvcnfghnh

Step-by-step explanation:

gfhtfv

Answer:

get a ruler and meshure out 72 millimeters.

Step-by-step explanation:

did exam

Answer:

No

Step-by-step explanation:

Since the hypotenuse is 13, the 2 legs' sum HAVE to be GREATER than the hypotenuse or else it is not a triangle.

"A triangle is valid if sum of its two sides is greater than the third side."

Answer:

e

Step-by-step explanation:

Answer:

2100

Step-by-step explanation:

60%=0.6

35%=0.35

0.6*0.35=0.21

0.21*10000=2100

Answer:

I Believe it's D

Step-by-step explanation:

Answer:

[tex]4 \frac{1}{9}x[/tex] + [tex]12\frac{1}{3}[/tex] = 0

Step-by-step explanation:

Based on 2x - 9y - 12 = 0

-9y = 12 - 2x

9y = -12 + 2x

y = [tex]-1\frac{1}{3} + \frac{2}{9} x[/tex]

Therefore...

5x - 4y + 7 = 0

5x - 4([tex]-1\frac{1}{3} + \frac{2}{9} x[/tex]) + 7 = 0

5x + [tex]5\frac{1}{3}[/tex]  - [tex]\frac{8}{9} x[/tex] + 7 = 0

[tex]4 \frac{1}{9}x[/tex] + [tex]12\frac{1}{3}[/tex] = 0

Answer:

Step-by-step explanation:

CAN YOU CHOOSE ME BRAİNLİEST PLS?

Answer:

a) hundreds

b) tens

c) hundreds

d) hundreds

Answer:

This is easy!!

Step-by-step explanation:

1. hundreds

2. tens

3. hundreds

4. hundreds

Hope this Helps!!

Answer:

56.52 cm^2

Step-by-step explanation:

curved surface area = 2πrh

the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.

A radius is half of the diameter

10 / 2 = 5

2 x 3.14 x5 x 18 = 56.52 cm^2

Answer:

(c)

Step-by-step explanation:

Given

See attachment for A and B

Required

Compare A and B

First, we get the initial population of A and B.

The initial population is at when [tex]t =0[/tex]

From the table of bacteria A, we have:

[tex]Initial = 100[/tex] when [tex]t = 0[/tex]

From the graph of bacteria B, we have:

[tex]Initial = 75[/tex] when [tex]t = 0[/tex]

Since the initial of bacteria B is less than that of bacteria A, then (a) is incorrect.

Next, calculate the slope of A and B i.e. the rate

Slope (m) is calculated as:

[tex]m = \frac{y_2 - y_1}{t_2 - t_1}[/tex]

Where

y = Number of bacteria

t = time

For bacteria A:

[tex](t_1,y_1) = (0,100)[/tex]

[tex](t_2,y_2) = (2,140)[/tex]

So, the slope is:

[tex]m_A = \frac{140 - 100}{2 - 0}[/tex]

[tex]m_A = \frac{40}{2}[/tex]

[tex]m_A = 20[/tex]

For bacteria B:

[tex](t_1,y_1) = (0,75)[/tex]

[tex](t_2,y_2) = (1,100)[/tex]

So, the slope is:

[tex]m_B = \frac{100- 75}{1 - 0}[/tex]

[tex]m_B = \frac{25}{1 }[/tex]

[tex]m_B = 25[/tex]

Since [tex]m_B > m_A[/tex], then the rate of bacteria B is greater than that of bacteria A.

Hence, (d) cannot be true

Next, we determine the equation of both bacteria

This is calculated using:

[tex]y = m(t - t_1) + y_1[/tex]

For bacteria A, we have:

[tex]y = m_A(t - t_1) + y_1[/tex]

Where:

[tex](t_1,y_1) = (0,100)[/tex]

[tex]m_A = 20[/tex]

So:

[tex]y = 20(t - 0) +100[/tex]

[tex]y = 20(t) +100[/tex]

[tex]y = 20t +100[/tex]

For bacteria B, we have:

[tex]y = m_B(t - t_1) + y_1[/tex]

Where:

[tex](t_1,y_1) = (0,75)[/tex]

[tex]m_B = 25[/tex]

So:

[tex]y = 25(t - 0) + 75[/tex]

[tex]y = 25(t) + 75[/tex]

[tex]y = 25t + 75[/tex]

At 3 hours, the population of bacteria A is:

[tex]y = 20t +100[/tex]

[tex]y = 20* 3 + 100[/tex]

[tex]y = 60 + 100[/tex]

[tex]y = 160[/tex]

At 3 hours, the population of bacteria B is:

[tex]y = 25t + 75[/tex]

[tex]y=25 * 3 + 75[/tex]

[tex]y=75 + 75[/tex]

[tex]y=150[/tex]

After 3 hours, bacteria B is 150 while A is 160.

This implies that (c) is correct because the population of B is less than that of A, at 3 hour

Lastly, to check if they will ever have equal population or not, we simply equate both equations.

So, we have:

[tex]y = y[/tex]

[tex]25t + 75 =20t + 100[/tex]

Collect like terms

[tex]25t - 20t = 100 - 75[/tex]

[tex]5t = 25[/tex]

Solve for t

[tex]t = 25/5[/tex]

[tex]t = 5[/tex]

They will have equal population at 5 hours.

Hence, b is incorrect

From the above computation, only (c) is correct