All categories

3 years ago

Solve 2x2 + 12x - 14 = 0 by completing the square

Mathematics

1 answer:

vovangra [49]3 years ago

5 0

Answer:

Step-by-step explanation:

$(a+b)^2=a^2+2ab+b^2\qquad(*)\\\\\\2x^2+12x-14=0\qquad\text{divide both sides by 2}\\\\x^2+6x-7=0\qquad\text{add 7 to both sides}\\\\x^2+2(x)(3)=7\qquad\text{add}\ 3^2=9\ \text{to both sides}\\\\\underbrace{x^2+2(x)(3)+3^2}_{(*)}=7+9\\\\(x+3)^2=16\Rightarrow x+3=\pm\sqrt{16}\\\\x+3=-4\ or\ x+3=4\qquad\text{subtract 3 from both sides}\\\\x=-7\ or\ x=1$

You might be interested in

In a game of luck, a turn consists of a player rolling 7 six-sided dice and counting how many of the dice

harkovskaia [24]

Answer: Binomial

Step-by-step explanation:

1 / 3

A binomial setting has a set number of trials, and the variable in question is the number of

successes that occur in those trials.

A geometric setting does not have a set number of trials, and the variable in question is the

number of trials it takes to get the first success.

In both settings, the trials are independent and the probability of success remains the same on

each trial.

2/3

In this game, the player rolls 7 dice, and F is the number of dice that show a 5. So the variable is

counting the number of successes

The rolls are independent, and the probability of getting a 5 is the same on each roll,

3/3

F is a binomial variable

4 0

2 years ago

Given that f ( x ) = 5 x − 5 and g ( x ) = 4 x , evaluate g ( g ( − 2 ) )

Stels [109]

Answer:

g(g(-2))

g(-8)

-32

This is the correct solution

8 0

3 years ago

N divided Into 8 is what

Goryan [66]

Answer:

$\frac{N}{8}$

Dividing is the same as putting numbers into a fraction. This is N/8. We don't get the answer until we figure out what N is equal to.

7 0

3 years ago

If gas prices are now $3.75 and they were up 10% from 6 months ago, how much were gas prices 6 months ago?

Hatshy [7]

Given

gas prices are now $3.75 and it up 10% from 6 months ago.

Find out how much were gas prices 6 months ago.

To proof

gas prices now = $3.75

let the gas price 6 month ago = x

gas price now is rise up 10% from 6 months ago

First write 10% in simpler form

$= \frac{10}{100}$

= 0.1

Now the equation becomes

0.1x + x = 3.75

1.1x = 3.75

$x =\frac{3.75}{1.1}$

x = 3.41 (approx)

Thus gas prices 6 months ago be $ 3.41 (approx )

Hence proved

7 0

3 years ago

Prism M and pyramid N have the same base area and the same height. Cylinder P and prism Q have the same height and the same base

m_a_m_a [10]

Answer:

Answer Cone Z and Cylinder Y.

Step-by-step explanation:

The relationship between the volume of the cone and the volume of the cylinder with the same height and same base is the volume of the cone is 1/3 of the volume of the cylinder.

The formula for the volume of the cone is :

V = 1/3π $r^{2}$ h

The formula for the volume of the cylinder is :

V = π $r^{2}$ h

Let be the height of the cylinder Y. Therefore the height of the cone Z is 3h, when we put it into the formula we get :

V = 1/3π $r^{2}$ (3h) = π $r^{2}$ h

Therefore Cone Z and Cylinder Y have same volume.

8 0

3 years ago

Read 2 more answers