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Free_Kalibri [48]
2 years ago
12

Consider the first five steps of the derivation of the Quadratic Formula.

Mathematics
1 answer:
lara31 [8.8K]2 years ago
6 0

Answer:

Full proof below

Step-by-step explanation:

\displaystyle ax^2+bx+c=0\\\\ax^2+bx=-c\\\\x^2+\biggr(\frac{b}{a}\biggr)x=-\frac{c}{a}\\\\x^2+\biggr(\frac{b}{a}\biggr)x+\biggr(\frac{b}{2a}\biggr)^2=-\frac{c}{a}+\biggr(\frac{b}{2a}\biggr)^2\\\\x^2+\biggr(\frac{b}{a}\biggr)x+\frac{b^2}{4a^2}=-\frac{c}{a}+\frac{b^2}{4a^2}\\ \\\biggr(x+\frac{b}{2a}\biggr)^2=-\frac{4ac}{4a^2}+\frac{b^2}{4a^2}\\ \\\biggr(x+\frac{b}{2a}\biggr)^2=\frac{b^2-4ac}{4a^2}\\ \\x+\frac{b}{2a}=\pm\frac{\sqrt{b^2-4ac}}{2a}\\ \\x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

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An eight-sided die, which may or may not be a fair die, has four colors on it; you have been tossing the die for an hour and hav
Romashka [77]

Answer:

Probability of an Orange on the next toss

= (23/60) = 0.3833

Step-by-step explanation:

Orange: 46

Brown: 23

Green: 32

Yellow: 19

Probability of an Orange on the next toss

= n(orange colours obtained in the tosses) ÷ n(number of tosses)

n(orange colours in the tosses) = 46

Total number of tosses = 46 + 23 + 32 + 19

= 120.

Probability of an Orange on the next toss

= (46/120) = (23/60) = 0.3833

Hope this Helps!!!!

4 0
3 years ago
PLEASE HELP!! :( <br> 6th grade math ( I suck at math)
agasfer [191]

Answer:

Width              Length

5                        8.7

7.9                    11.6

9                        12.7

11.3                     15.0

13                      16.7

Step-by-step explanation:

If they gave you the width, you add 3.7 to get the length.

If they gave  you the length, you subtract 3.7 to get the width.

4 0
3 years ago
Read 2 more answers
Find the missing lengths of the sides
Ket [755]

ANSWER

The correct answer is C

EXPLANATION

The given triangle is a right triangle. Since two angles are equal, it is a right isosceles triangle.

This implies that, x=8 units.

Using Pythagoras Theorem,

{y}^{2}  =  {8}^{2}  +  {8}^{2}

This implies that:

{y}^{2}  = 64  +  64

{y}^{2}  =128

Take positive square root,

{y}  =  \sqrt{128}

{y}  = 8 \sqrt{2}

The correct answer is C

5 0
3 years ago
Read 2 more answers
dale has a square garden. He adds a 2-foot-wide walkway around his garden. If the total area of the walkway and garden is 196 sq
dem82 [27]
Let the side of the garden alone (without walkway) be x.  
Then the area of the garden alone is x^2.  
The walkway is made up as follows:

1) four rectangles of width 2 feet and length x, and 
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The total walkway area is thus x^2 + 4(2^2) + 4(x*2).  

We want to find the dimensions of the garden.  To do this, we need to find the value of x.

Let's sum up the garden dimensions and the walkway dimensions:

x^2 + 4(2^2) + 4(x*2) = 196 sq ft

x^2 + 16 + 8x = 196 sq ft

x^2 + 8x - 180 = 0

(x-10(x+18) = 0

x=10 or x=-18.  We must discard x=-18, since the side length can't be negative.  We are left with x = 10 feet.

The garden dimensions are (10 feet)^2, or 100 square feet.


4 0
3 years ago
the area of a rectangle is 10 square units the length is 2 units and the width is y units 10 = 2y what is the value of y. y = 12
frutty [35]

Answer:

2(5+y)+2y=38 10+2y+2y=38 4y=28 y=7  i think

Step-by-step explanation:

4 0
3 years ago
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