All categories

3 years ago

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

Mathematics

1 answer:

Ede4ka [16]3 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

You might be interested in

Pls help branliest if right

Bezzdna [24]

Answer:

sorry I donot know

I wish I could help

7 0

3 years ago

A pole that is 3.1m tall casts a shadow that is 1.46m long. At the same time, a nearby building casts a shadow that is 36.75m lo

Mademuasel [1]

You have to find the angle of sunlight and the pole , which then cast a shadow
length of the pole is equal to 3.1m
creating a hypotenuse of 4.52m
the angle will be
[email protected] = opposite side / hypotenuse
= 1.46/4.52
= 0.32 that's 18.66 °
now for the building sin18.66° = opposite/hypotenuse
0.32 = 36.75/ hypotenuse
hypotenuse = 114.84 m
thus using Pythagoras theorem
114.84*114.84 = 36.75*36.75 + x^2
which comes around = 108.8 roughly 109 metres long

4 0

3 years ago

Solve the equation. show all work.<br><br> 3x - 10 = 5x + 22

inysia [295]

<span>Simplifying 3x + 10 = 5x + 22 Reorder the terms: 10 + 3x = 5x + 22 Reorder the terms: 10 + 3x = 22 + 5x Solving 10 + 3x = 22 + 5x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5x' to each side of the equation. 10 + 3x + -5x = 22 + 5x + -5x Combine like terms: 3x + -5x = -2x 10 + -2x = 22 + 5x + -5x Combine like terms: 5x + -5x = 0 10 + -2x = 22 + 0 10 + -2x = 22 Add '-10' to each side of the equation. 10 + -10 + -2x = 22 + -10 Combine like terms: 10 + -10 = 0 0 + -2x = 22 + -10 -2x = 22 + -10 Combine like terms: 22 + -10 = 12 -2x = 12 Divide each side by '-2'. x = -6 Simplifying x = -6</span>

5 0

4 years ago

Determine the number of solutions for the quadratic function f(x) = -x^2 + 3x - 9.

Setler79 [48]

Answer:

Step-by-step explanation:

Rewrite the equation as x^2-3x+9=0

find the determinant.

D = b^2-4ac = (-3)^2-4*1*9 <0

no solution

7 0

3 years ago

The equation for the ellipse given is 4x^2+9y^2-16x+18y-11

natita [175]

Answer:

a. a = 3, b = 2

b. The coordinate of the center is (2, -1)

c. The eccentricity of the ellipse is √5/3

d. Please see attached graph of the ellipse created with MS Excel

Step-by-step explanation:

7. a. The given equation of the ellipse is presented as follows;

4·x² + 9·y² - 16·x + 18·y - 11

The general equation of an ellipse

$\dfrac{(x - h)^2}{a^2} + \dfrac{(y - k)^2}{b^2} = 1$

We can write;

4·x² - 16·x + 9·y² + 18·y - 11

4·(x² - 4·x + 4) + 9·(y² + 2·y + 1) - 25 - 11

4·(x² - 4·x + 4) + 9·(y² + 2·y + 1) = 25 + 11 = 36

4·(x - 2)² + 9·(y + 1)² = 36

$\dfrac{4\cdot (x - 2)^2}{36} + \dfrac{9 \cdot (y + 1)^2}{36} = \dfrac{36}{36}$

$\therefore \dfrac{ (x - 2)^2}{9} + \dfrac{ (y + 1)^2}{4} = \dfrac{ (x - 2)^2}{3^2} + \dfrac{ (y + 1)^2}{2^2} = 1$

By comparison, a = 3, b = 2, h = 2, k = -1

b. The coordinate of the center, (h, k) = (2, -1)

c. The eccentricity of the ellipse = c/a

c² = a² - b²

∴ c² = 3² - 2² = 5

c = √5

Eccentricity = √5/3

d. Please find attached the graph of the ellipse created with MS Excel

8 0

3 years ago