Write the Quadratic Formula for the quadratic equation.

Write The Quadratic Formula For The Quadratic Equation.

Answers

Answer 1

Answer:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

Step-by-step explanation:

Hello!

Let's start with the given equation and work our way towards x.

Solve for x[tex]ax^2 + bx + c = 0[/tex]

Divide both sides by a

[tex]a(x^2 + \frac bax + \frac ca) = 0[/tex]        [tex]x^2 + \frac bax + \frac ca = 0[/tex]

Move c/a to the other side

[tex]x^2 + \frac bax = -\frac ca[/tex]

At the step, we have to use the Completing the Square method.

[tex]x^2 + \frac bax + (\frac{b}{2a})^2 = -\frac ca + (\frac b{2a})^2[/tex][tex]x^2 + \frac bax + \frac{b^2}{4a^2} = -\frac ca + \frac {b^2}{4a^2}[/tex][tex](x + \frac b{2a})^2= -\frac ca + \frac{b^2}{4a^2}[/tex]

Multiply -c/a by 4a and add the two fractions

[tex](x + \frac b{2a})^2= \frac{b^2 - 4ac}{4a^2}[/tex]

Square Root both sides

[tex]\sqrt{(x + \frac b{2a})^2}= \sqrt{\frac{b^2 - 4ac}{4a^2}}[/tex][tex]x + \frac b{2a} = \pm\frac{\sqrt{b^2 - 4ac}}{2a}}[/tex]

Subtract b/2a

[tex]x = \pm \frac{ \sqrt{b^2 - 4ac}}{2a} - \frac b{2a}[/tex][tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

And that's the derivation of the Quadratic Formula.


Related Questions

Find the value of x. Round to the nearest degree as needed.

Answers

9514 1404 393

Answer:

  x° = 59°

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the trig relations. The one applicable here is ...

  Tan = Opposite/Adjacent

  tan(x°) = 5/3

  x° = arctan(5/3) ≈ 59.04°

The value of x is about 59.

Can someone please answer?

Answers

Answer:

Volume = 803.84 cubic inches

Step-by-step explanation:

Volume = πr²h

= 3.14 x 8 x 8 x 4

= 3.14 x 256

= 803.84 cubic inches

can you help me out ..please and thank you

Answers

You’re going to want to distribute the number directly before the parenthesis. So for number 1 you’re going to want to distribute the -11 to x+9 so the equation would look like: x-8=43-11x-99. Then combine like terms: x-8=-56-11x then add 11x to move the x’s to one side: 12x-8=-56 then add 8 to move it away so the x’s are alone. 12x=-48 then divide the -48 by 12 to get the x fully alone so you’d get x=-4

how to solve this problem 8(x + 5)

Answers

8(x+5)
=8x+40
boom :)

Answer:

8x + 40

Step-by-step explanation:

Step 1: Expand by distributing terms.

8x+8x5

Step 2: Simplify 8x5 to 40 = 8x + 40

Monica deposits ​$300 into a savings account that pays a simple interest rate of ​%3.3. Paul deposits ​$400 into a savings account that pays a simple interest rate of ​%2.8. Monica says that she will earn more interest in 1 year because her interest rate is higher. Is she​ correct? Justify your response.

Answers

Answer: The formula for calculating simple interest is given by :

S.I =

For Monica

S.I = 300 x 3.4 x 1 / 100

S.I = $10.2

For Paul

S.1 = 400 x 2.4 x 1 / 100

S.I = $9.6

Therefore : Monica earned more interest

Step-by-step explanation:

Write an equation for when slope =-3 and y-intercept = 36

Answers

y=mx+b

m= slope

b=y-intercept

Therefore Y=-3x+36

find the area of the figure will give brain illest if correct! ​

Answers

I’m sure that the area is 80. If you do 10 times 5, that will be 50.Then if you do 6 times 5, for the upper remaining part of the figure it would be 30. So 30 plus 50 is 50. Hope this helps!

Twenty-seven is % of 60.

Help tysm

Answers

Answer:

Step-by-step explanation:

So it’s 10

the answer is 45
bc 27 is 45% of 60

Is it true or false?

Answers

Answer:

false (this is what I believe)

Step-by-step explanation:

because participant 1 has 7 squares and he almost does the same as participant 2 and he only has 5 squares which means participant 2 I'd faster

Answer:

false (i think im not really good with math)

Step-by-step explanation:

BEST ANSWER GETS BRAINLIEST, THANKS ON ANSWER, AND THANKS ON YOUR PROFILE!

Answers

Answer:

I thinks it's the third one

Write down the inequality for x that is shown on this line.
0
1
2
3
4
5
6
7
8

Answers

Answer:

x > 3

Step-by-step explanation:

Here, we want to write the inequality represented

We start by looking at the value on which we have the circle

It is on the value 3

we can also see that the circle is unshaded and also that, the graph faces the right direction

As the circle

is unshaded, we have it that we only use the inequality without the equal to

So we have the representation as;

x > 3

What is the sum of the 12th square number and the 10th square number?

Answers

Answer:

12^2 is 144 and 10^2 is 100 :)

Step-by-step explanation:

12 * 12 = 144

10 * 10 = 100

The sum of the 12th square number and the 10th square number is 244. This problem is based on the principle of addition.

The principle of addition states that when two numbers are added together, their sum is a unique number which is not necessarily be divisible by either the numbers or their factors. The addition is inverse operation of the subtraction.

The square of 12th number is 12² = 12 × 12 = 144.

The square of 10th number is 10² = 10 × 10 = 100.

The sum of both numbers = 144 + 100 = 244.

Hence, the answer to the given problem is 244.

Learn more about Addition here:

https://brainly.com/question/29464370

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PLS HELP ASAP 4 BRAINLIEST

Answers

Answer:

The answer is A

Step-by-step explanation:

105+90=5x-70

195+70=5x-70+70

[tex] \frac{265}{5} = \frac{5x}{5} [/tex]

53=x and then when you insert to in the formula 5(53)-70 you get 195

and 105+90 is also equal to 195

Youre welcome!

a. What is the minimum value taken by the
expression (x – 4)2 + 6?

Answers

Answer:

2x-2

Step-by-step explanation:

Answer:

Minimum value = 6

Step-by-step explanation:

Choose yes or no to tell whether each expression is equivelent to this expression -3(0.15-0.2+0.25p)

Answers

Answer:

See Explanation

Step-by-step explanation:

No options were given. So, I will just solve the question (step by step) in order to get numerous equivalent expressions.

The result of each step is an equivalent expression

We have:

[tex]-3(0.15-0.2+0.25p)[/tex]

Simplify the bracket

[tex]-3(-0.05+0.25p)[/tex]

Open bracket

[tex]-3*-0.05-3*0.25p[/tex]

Simplify each term

[tex]0.15-0.75p[/tex]

5x-y<-6 and 3x-y>/4

Due tonight!!!

Answers

Answer:

1.

x<1/5y + -6/5

2.

x>1/3y + 4/3

What’s 10-8+434+87+64

Answers

it is 587
i trust my calculator
587 is the answer because of Order of operations addition from left to right

Help me, not sure how to solve this, my teacher didn't teach us yet, and I want a solid understanding of it, so the answer will be great! Also will give the most brainliest!

Answers

x = 15°--------------------------

Step-by-step explanation:

10 + 5x = 10 + 5(15)

= 10 + 75

= 85°

4x - 10 = 4(15) - 10

= 60 - 10

= 50°

6x - 5 = 6(15) - 5

= 90 - 5

= 85°

-------------------------FOLLOW ME

Mean
Vasquez read 5 books in January, 8 books in February,
4books in March, and 7 books in April. What is the
average number of books Vasquez reads per month?

Answers

Answer: six per month

Answer:

6

Step By Step Solution:

[tex]5 + 8 + 4 + 7 = x\\ 13 + 4 + 7 = x \\ 17 + 7 = 24 \\ x = 24 \\ 24 \div 4 = 6[/tex]

A trapezoid is shown
What is the area of the trapezoid?
A)
21 m2
ing
B)
27 m2
O
34 m2
D)
42 m2

Answers

Answer:

what are the letters and numbers by the trapezoid i need them to solve it

Step-by-step explanation:

Answer:

answer 21 m2

Step-by-step explanation:

Area of a trapezoid

side a

5

parallel a,b

side b

9

height h

3

22 digit

area S

21    

Which measurement is the same length as 1 meter

Answers

Answer:

3 feet

Step-by-step explanation:

From the option available the measurement 1 meter is equal to 100 centimeters.

What is unit conversion?

The same attribute is expressed using a unit conversion but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometers, feet, or any other measurement unit instead of miles.

given the measurement is 1 meter

1 meter is equal to 100 centimeters

From unit conversion:

1 meter is also equal to 3.2808 feet

1 meter is also equal to 39.3701 inch

1 meter is also equal to 1000 millimeters

1 meter is also equal to 1.093 yards.

Learn more about unit conversion here:

https://brainly.com/question/19420601

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Complete question:

1
Note: Figure is not drawn to scale.
If h = 9 units and r = 6 units, then what is the volume of the cone shown above?
OA. 162 cubic units
ОВ.
1087 cubic units
C. 81 cubic units
OD. 324 cubic units
Reset
Submit
0 of 15 Answered
Session Timer: 0:25
Sessio
I
O Type here to search

Answers

Answer:

108π

Step-by-step explanation:

1/3 × 9 × π × (6²)

1/3 × 9π6²

(1 × 9π6²) / 3

(6² × 9π) / 3

6² × 3π

36 × 3π

108π

A 30-ft ladder is placed against a building. The bottom of the ladder is 18 feet from the base of a building. How tall is the building?

Answers

Answer: 24 ft tall

Step-by-step explanation:

a^2+b^2+c^2

18^2+b^2=30^2 where b in this case is the height of the building

Alex goes to the store to buy groceries . He has $20 to spend at the store.

Write an inequality to repesent the amount Alex can spend.

Answers

Answer:

20 ≥ x

Step-by-step explanation:

Alex has $20 or less to spend at the store

what is the side length of a square given the area to be 625m

Answers

Answer: 25 meters

Step-by-step explanation:

✓625 = 25

Answer:25

Step-by-step explanation:A square has equal length on all its sides, so the area of square is

Length x Length = 625

Which is

Length ^2 = 625

We want the number that when it times it’s self it’s 625

It can be done by square root of 625 which is 25. So the length of side is 25.

Or look at the prime factorization of 625 ( or just factors) and what number they can make up

Which is 5x5x5x5 = 625

They can make up

5^2 x 5^2 = 25 x 25 that is the “same” number

So the length is 25

if m< 3=3x+20 and m <6=x+50 , what is x?

Answers

Since you said they are supplementary, 3x+20+x+50=180

Since the definition of supplementary angles are they adds up to 180 degrees.

Now we just need to solve the equation

4x+70=180

4x=110

x=27.5

Reflect the point (2, -4) over y = x to become... a) (-4, 2) b) (-2, 4) c) (-2, -4) d) (2, 4)

Answers

CC.CC CC.CC CC.CC CC.CC

Question 1
x2+ 1 = 9
Question 1 options:

x = 16

x = 20

x = 4

x = 5

Answers

Answer:

16 es la respuestas y ahora es asi

Answer:

X=4

Step-by-step explanation:

2x + 1 = 9

2x=9-1

2x=8

X=4

if 35% of a number is 140 what is that number

Answers

Answer: The number is 47.6

Is it A B or C Help me

Answers

The answer is A. Hope this helpssssssss
A=314 in^2
A= π•r^2
314=3.14•r^2
r^2=314/3.14
r^2=100
r= √100
r=10
d=2•r
d=2•10
d=20in
Answer is B
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