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2 years ago

8

Solve for completing the square x^2-12x+11=0

1 answer:

Ede4ka [16]2 years ago

4 0

Answer:

x = 6 ± 5

Step-by-step explanation:

x² - 12x + 11 =0

x² - 12x = -11 Now add this number to both sides of the equal sign (1/2 of the coefficient of x-term squared)

x² - 12x +36 = -11 + 36 1/2(-12)² = 36

(x - 6)(x - 6) = 25

(x - 6)² = 25

$\sqrt{(x-6)}$ ² = $\sqrt{25}$ square root of both side of the equation

x - 6 = ± 5 (5)² = 25 and (-5)² = 25

x = 6 ± 5

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PLEASE HELP SOON<br> Find the length of x.

DochEvi [55]

<h2>Hello!</h2>

The answer is:

The length of "x" is equal to 4 units.

<h2>Why?</h2>

To solve the problem and find the length of x, we need to remember the alternate angles rule. The alternate angles rule establish that alternate angles will be also equal.

So, for the triangles, we have:

The angle((α)) formed between the base (2.5) and the hypotenuse (5) of the big triangle is equal to the angle(α) formed between the base (2) and the hypotenuse (x) of the small triangle. It also means that the triangles are similar since they have congruent angles(α) and proportional sides (SAS).

We are given:

First triangle,

$AdjacentSide=2.5\\Hypotenuse=5\\$

Second triangle,

$AdjacentSide=2\\Hypotenuse=x\\$

So, using the cosine identity, we have:

$Cos(\alpha)=\frac{AdjacentSide}{Hypotenuse}$

$Cos(\alpha)=\frac{2.5}{5}=\frac{2}{x}$

$Cos(\alpha)=\frac{2.5}{5}=\frac{2}{x}\\\\\frac{2.5}{5}=\frac{2}{x}\\\\x=2*\frac{5}{2.5}=4$

Therefore, we have that the hypotenuse of the second triangle (x) is equal to 4 units.

Hence, the length of "x" is equal to 4 units.

Have a nice day!

3 0

2 years ago

Read 2 more answers

Can someone help me?

Sergio [31]

9514 1404 393

Answer:

tan B = 12/5
cos B = 5/13
sin B = 12/13

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the applicable ratios:

Tan = Opposite/Adjacent ⇒ tan B = CA/CB = 12/5

Cos = Adjacent/Hypotenuse ⇒ cos B = BC/BA = 5/13

Sin = Opposite/Hypotenuse ⇒ sin B = AC/AB = 12/13

3 0

2 years ago

Which expression is equivalent to x³ - x² - 14x + 24?

serg [7]

Answer:

<h3>A. ( x - 2 )( x - 3 )(x + 4 )</h3>

<h3>Step-by-step explanation:</h3>

<h3>x³ - x² - 14x + 24</h3>

<h3>1. Use the rational root theorem</h3>

$= (x - 2) \frac{x ^{3} -x^{2} - 14x + 24}{x - 2}$

<h3>2. $\frac{ {x}^{3} - {x}^{2} - 14x + 24 }{x - 2} = {x}^{2} + x - 12$ </h3><h3 />

= ( x - 2 )( x² + x - 12 )

<h3>3. Factor x² + x - 12 : ( x -3 )( x + 4)</h3>

= ( x - 2 )( x - 3 )(x + 4 )

<h3>Solution : </h3>

<h3>= ( x - 2 )( x - 3 )(x + 4 )</h3>

3 0

1 year ago

Cynthia is purchasing an electric heater for $181.25, including tax. She gives the sales clerk 2 fifty-dollar bills, 7 ten-dolla

Dafna1 [17]

The answer to the question is C.$0.75

5 0

2 years ago

Read 2 more answers

Wats 10 to the 2nd power divied by 5 to the 2nd power

Ilya [14]

Answer:

4

Step-by-step explanation:

10^2/5^2

Do the exponents first

10 to the 2nd power is 100

5 to the 2nd power is 25

100/25

100 divided by 25 is 4

So the answer is 4

Hope this helps!

6 0

2 years ago