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Temka [501]
3 years ago
5

Someone please help me and thanks in advance

Mathematics
1 answer:
BARSIC [14]3 years ago
3 0
There is no way to drag these around so I made a copy of your graphic and copied and pasted the boxes.  (see attached).


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Complete the square to write the quadratic expression in vertex form.
Anvisha [2.4K]

Answer:

1. (x - 3)² = 8

2. (x + 2)² = 3

3. (x + 6)² = $ \frac{101}{2} $

4. (x + 3)² = 27

5. (x + 4)² = 13

6.  $ \bigg( x - \frac{15}{9} \bigg) ^2 = \frac{261}{81} = \frac{29}{9} $

Step-by-step explanation:

Completion of Square: $ (x - a) ^2 = x^2 - 2ax + a^2 $

In the following problems the terms in the RHS of the above equation may be missing. We balance the equation. Simplify it and re write it in terms of LHS.

1. x² - 6x + 1 = 0

Taking the constant term to the other side, we get:

x² - 6x = - 1

⇒ x² - 2(3)x = -1

⇒ x² -2(3)x + 9 = - 1 + 9  [Adding 9 to both the sides]

⇒ x² -2(3)x + 3² = 8

⇒ (x - 3)² = 8 is the answer.

2. 3x² + 12x + 3 = 0

Note that the co-effecient of x² is not 1. We make it 1, by dividing the whole equation by 3. And then proceed like the previous problem.

3x² + 12x = -3

Dividing by 3 through out, x² + 4x = - 1

⇒ x² + 2(2) + 4 = -1 + 4

⇒ x² +2(2) + 2² = 3

⇒ (x + 2)² = 3 is the answer.

3. 2x² + 24x = 29

x² + 12x = $ \frac{29}{2} $

⇒ x² + 2(6)x + 36 = $ \frac{29}{2} $ + 36

⇒ x² + 2(6)x + 6² = $ \frac{29 + 72}{2} $

⇒ (x + 6)² = $ \frac{101}{2} $ is the answer.

4. x² + 6x - 18 = 0

x² + 6x = 18

⇒ x² + 2(3)x = 18

⇒ x² + 2(3)x + 9 = 18 + 9

⇒ x² + 2(3)x + 3² = 27

⇒ (x + 3)² = 27 is the answer.

5. x² + 8x + 3 = 0

x² + 8x = -3

⇒ x² + 2(4)x = -3

⇒ x² + 2(4)x + 16 = - 3 + 16

⇒ x² + 2(4)x + 16 = 13

⇒ (x + 4)² = 13 is the answer.

6. 9x² - 30x + 6 = 0

9x² - 30x = - 6

⇒ x² $ - \frac{30}{9} $ x = - 6

$ \implies x^2 -2 \bigg( \frac{15}{9} \bigg )x + \frac{225}{81} = - 6 + \frac{225}{81} $

$ \implies x^2 - 2\bigg( \frac{15}{9} \bigg ) x + \bigg ( \frac{15}{9} \bigg ) ^2 = \frac{261}{81} $

$ \bigg( x - \frac{15}{9} \bigg) ^2 = \frac{261}{81} = \frac{29}{9} $ is the answer.

6 0
4 years ago
A class is made up of 10 boys and 4 girls. Half of the girls wear glasses. A student is selected at random from the class. What
Andreas93 [3]

Hi!

Add the student together to get the number of students

10+4 = 14

Divide the girls by half

4/2 = 2

2/14 is the answer for this question.

<em>Hope this helps! Have an amazing day <3</em>

<em />

4 0
4 years ago
Zapisz w jak najprostszej postaci:<br> a) -x-4(1-x)<br> b) 3(5x-2)-5(3-4x)<br> c) √2(3-x)-2(1-x√2)
Sonja [21]

Answer:

Step-by-step explanation:

a) -x-4(1-x)  =

− 2 x −4 ( 1 − x ) .

2 x − 4

b) 3(5x-2)-5(3-4x)  =

3 ⋅ (5 x − 2 ) − 5 ⋅ ( 5 − 4 x )

35 x  −  31

c) √2(3-x)-2(1-x√2) =

√ 2 x ⋅ ( 3 −x ) − 2 ⋅( 1 − x √ 2 ) .

2 x √ 2 + 3 √ 2 x -√ 2 x x − 2

4 0
3 years ago
Find the values of x y and z
andrey2020 [161]

9514 1404 393

Answer:

  • x = 18√2
  • y = 18√3
  • z = 36

Step-by-step explanation:

These "special" right triangles have side length ratios that it is useful to remember.

<u>45°-45°-90° triangle</u>

Sides have the ratios 1 : 1 : √2. That is, x is √2 times as long as the side length shown as 18.

  x = 18√2

<u>30°-60°-90° triangle</u>

Shortest to longest, sides have the ratios ...

  1 : √3 : 2

That is, y is √3 times the length of the side marked 18, and z is 2 times the length of the side marked 18.

  y = 18√3

  z = 2·18 = 36

4 0
3 years ago
A babysitter earns the same amount per hour. She earned $36 for 3 hours of babysitting. Which equation describes the relationshi
Brilliant_brown [7]

Answer:

y= 12x

Step-by-step explanation:

36/3=12

12× x =y

________________________

6 0
3 years ago
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