All categories

2 years ago

What number must be added to the expression below to complete the square? x² - 18x

Mathematics

1 answer:

kiruha [24]2 years ago

5 0

Answer:

$\boxed {\boxed {\sf 81}}$

Step-by-step explanation:

The standard form of a quadratic is:

$ax^2+bx+c$

To complete the square, the a (leading coefficient) must be 1 and there can only be terms with variables on one side.

The expression given:

$x^2-18x$

follows these rules. Next, we divide the b (linear coefficient) by 2, then square it. Basically:

$(\frac{b}{2})^2$

The b in the expression is -18.

$(\frac{-18}{2})^2$

$(-9)^2= -9*-9= 81$

This is the number that is added.

You might be interested in

The midpoint of AB is M (2,0). If the coordinates of A are, (-3, 3), what are the coordinates of B?

gregori [183]

Given:

M is the midpoint of AB.

M(2,0) and A(-3, 3).

To find:

The coordinates of point B.

Solution:

Midpoint formula:

$Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

Let the coordinates of point B are (a,b). Then, using the midpoint formula, we get

$(2,0)=\left(\dfrac{-3+a}{2},\dfrac{3+b}{2}\right)$

On comparing both sides, we get

$\dfrac{-3+a}{2}=2$

$-3+a=2\times 2$

$a=4+3$

$a=7$

And,

$\dfrac{3+b}{2}=0$

$3+b=0$

$3+b-3=0-3$

$b=-3$

Therefore, the coordinates of point B are (7,-3).

5 0

2 years ago

Please help!!! Will give brainly!! 50 points

AleksAgata [21]

2. Angle Addition Postulate as they are adding both angles

3. 60 + 40 = m <ABC because it's a substitution

4. 100 = m <ABC as it is simplified already

5. Definition of obtuse angle

6 0

3 years ago

Read 2 more answers

Devon records 4 hours of reality shows on her DVR she records comedy shows for 3/8 of that amount of time. Devon watches all the

Alenkinab [10]

The number of half-hour sittings needed to watch all the shows by Devon is 11

Solution:

Given, Devon records 4 hours of reality shows on her DVR

she records comedy shows for 3/8 of that amount of time.

$\rightarrow \frac{3}{8} \text { of } 4 \text { hours } \rightarrow \frac{3}{8} \times 4 \rightarrow \frac{3}{2} \text { hours }$

Devon watches all the reality and comedy shows in half-hour sittings.

We have to find the number of half-hour sittings needed to watch all the shows

Now, number of half hour sittings is given as

$=\frac{\text { total time of videos }}{\text { time for hlaf hour sitting }}$

$\begin{array}{l}{=\frac{4 \text { hours for reality shows }+\frac{3}{2} \text { hours for comedy shows }}{\frac{1}{2} \text { hours for each sitting }}} \\\\ {=\frac{4+\frac{3}{2}}{\frac{1}{2}}=\frac{\frac{8+3}{2}}{\frac{1}{2}}=\frac{\frac{11}{2}}{\frac{1}{2}}=\frac{11}{2} \times \frac{2}{1}=11}\end{array}$

Hence Devon needs 11 sittings

3 0

2 years ago

What is 100 in pi form?

Tema [17]

That would be 314 because 100xpi

8 0

2 years ago

Read 2 more answers

What is the answer to this equation t+t+t=12

OLEGan [10]

Answer:

t = 4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS
Equality Properties

Algebra I

Combining Like Terms

Step-by-step explanation:

Step 1: Define equation

t + t + t = 12

Step 2: Solve for t

Combine like terms (t): 3t = 12
Divide 3 on both sides: t = 4

Step 3: Check

Plug in t into the original equation to verify it's a solution.

Substitute in t: 4 + 4 + 4 = 12
Add: 8 + 4 = 12
Add: 12 = 12

Here we see that 12 does indeed equal 12.

∴ t = 4 is a solution of the equation.

3 0

3 years ago