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3 years ago

Use complete sentences to explain how the quadratic formula is related to the process of completing the square.

Mathematics

1 answer:

ohaa [14]3 years ago

5 0

SOS

Answer:

Completing the square is a method that will solve all quadratic equations. By completing the square on the general quadratic equation, we obtain a formula that is worth learning and that will solve all quadratic equations.

The quadratic formula does the same thing as completing the square. The formula reads: $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

The a, b and c terms are the coefficients of a polynomial where a is the coefficient of the squared term, b the linear term and c the constant when the equation is set equal to zero [ax squared plus bx plus c = 0].

Solving quadratics with this formula is then just as simple as substituting the numbers from an equation into these placeholder variables. Then, you need to simplify the expression to get the two solutions, one where you use the plus sign and the other the minus sign.

Hope this helps!!

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What is the volume of the following rectangular prism? 3 1/3 units^2 1 2/5 units

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The Answer : 23.6 units

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3 years ago

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n social studies class, Cole is making a scale drawing of a flag. The flag measures 24 inches high by 36 inches wide, having thr

Ray Of Light [21]

The complete question in the attached figures

we know that

1 ft---------------> 0.083333 in

so
24 inches high--------------> 24*0.083333=2 ft
36 inches wide--------------> 36*0.083333=3 ft

we will analyze each drawing

drawing a) scale 1/4 in/ 1 ft ----------> (1/4)/1=1/4
for a high of 2 ft-------------> 2*(1/4)=0.5 in
for a wide of 3 ft-------------> 3*(1/4)=0.75 in
drawing a) is not solution

drawing b) scale 1/2 in/ 1 ft ----------> (1/2)/1=1/2
for a high of 2 ft-------------> 2*(1/2)=1 in
for a wide of 3 ft-------------> 3*(1/2)=1.5 in
drawing b) is not solution

drawing c) scale 1/2 in/ 1 ft ----------> (1/2)/1=1/2
for a high of 2 ft-------------> 2*(1/2)=1 in
for a wide of 3 ft-------------> 3*(1/2)=1.5 in
drawing c) is not solution

drawing d) scale 1 in/ 1 ft ----------> (1)/1=1
for a high of 2 ft-------------> 2*(1)=2 in
for a wide of 3 ft-------------> 3*(1)=3 in
drawing d) is a solution

the answer is
The correct model of the flag is the drawing D

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3 years ago

If the length of a rectangle is decreased by 6 cm and the width is increased by 3 cm, the result will be a square, the area of w

Serhud [2]

Answer:

252 centimeters squared is the answer.

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3 years ago

Simplify the complex fraction

Irina-Kira [14]

Answer:

2 4/9

Step-by-step explanation:

You need to divide the two fractions.

You need to multiply 11/4 by the reciprocal of 9/8.

11/4 times 8/9

You can simplify first.

11 times 2/9

22/9

Simplify to

2 4/9

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3 years ago

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You are creating an open top box with a piece of cardboard that is 16 x 30“. What size of square should be cut out of each corne

Arada [10]

Answer:

$\frac{10}{3} \ inches$ of square should be cut out of each corner to create a box with the largest volume.

Step-by-step explanation:

Given: Dimension of cardboard= 16 x 30“.

As per the dimension given, we know Lenght is 30 inches and width is 16 inches. Also the cardboard has 4 corners which should be cut out.

Lets assume the cut out size of each corner be "x".

∴ Size of cardboard after 4 corner will be cut out is:

Length (l)= $30-2x$

Width (w)= $16-2x$

Height (h)= $x$

Now, finding the volume of box after 4 corner been cut out.

Formula; Volume (v)= $l\times w\times h$

Volume(v)= $(30-2x)\times (16-2x)\times x$

Using distributive property of multiplication

⇒ Volume(v)= $4x^{3} -92x^{2} +480x$

Next using differentiative method to find box largest volume, we will have $\frac{dv}{dx}= 0$

$\frac{d (4x^{3} -92x^{2} +480x)}{dx} = \frac{dv}{dx}$

Differentiating the value

⇒ $\frac{dv}{dx} = 12x^{2} -184x+480$

taking out 12 as common in the equation and subtituting the value.

⇒ $0= 12(x^{2} -\frac{46x}{3} +40)$

solving quadratic equation inside the parenthesis.

⇒ $12(x^{2} -12x-\frac{10x}{x} +40)$ =0

Dividing 12 on both side

⇒ $[x(x-12)-\frac{10}{3} (x-12)]$ = 0

We can again take common as (x-12).

⇒ $x(x-12)[x-\frac{10}{3} ]$ =0

∴ $(x-\frac{10}{3} ) (x-12)= 0$

We have two value for x, which is $12 and \frac{10}{3}$

12 is invalid as, w= $(16-2x)= 16-2\times 12$

∴ 24 inches can not be cut out of 16 inches width.

Hence, the cut out size from cardboard is $\frac{10}{3}\ inches$

Now, subtituting the value of x to find volume of the box.

Volume(v)= $(30-2x)\times (16-2x)\times x$

⇒ Volume(v)= $(30-2\times \frac{10}{3} )\times (16-2\times \frac{10}{3})\times \frac{10}{3}$

⇒ Volume(v)= $(30-\frac{20}{3} ) (16-\frac{20}{3}) (\frac{10}{3} )$

∴ Volume(v)= 725.93 inches³

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3 years ago