HELP WILL MARK BRAINLIEST IF GOTTEN RIGHT

Answer:

[tex]\alpha + \beta = -\frac{b}{a}[/tex]

[tex]\alpha \beta = \frac{c}{a}[/tex]

Step-by-step explanation:

Given

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

[tex]Roots: \alpha \& \beta[/tex]

Required

Show that:

[tex]\alpha + \beta = -\frac{b}{a}[/tex]

[tex]\alpha \beta = \frac{c}{a}[/tex]

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

Divide through by a

[tex]\frac{a}{a}x^2 + \frac{b}{a}x + \frac{c}{a} = \frac{0}{a}[/tex]

[tex]x^2 + \frac{b}{a}x + \frac{c}{a} = 0[/tex]

The general form of a quadratic equation is:

[tex]x^2 - (Sum)x + (Product) = 0[/tex]

By comparison, we have:

[tex]-(Sum)x = \frac{b}{a}x[/tex]

[tex]-(Sum) = \frac{b}{a}[/tex]

Sum is calculated as:

[tex]Sum = \alpha + \beta[/tex]

So, we have:

[tex]-(\alpha + \beta) = \frac{b}{a}[/tex]

Divide both sides by -1

[tex]\alpha + \beta = -\frac{b}{a}[/tex]

Similarly;

[tex]Product = \frac{c}{a}[/tex]

Product is calculated as:

[tex]Product = \alpha * \beta[/tex]

So, we have:

[tex]\alpha * \beta = \frac{c}{a}[/tex]

[tex]\alpha \beta = \frac{c}{a}[/tex]

Answer:

216

Step-by-step explanation:

18 which is the base will be multiplied by the height which is 12 giving you

18 x 12 = 216

Answer:

246 physics books

186 biology books

Step-by-step explanation:

1) there are 432 total books

2) there are 60 more physics books than biology books

3) 432 - 60 = 372

4) 372 divided by 2 = 186

5) 432 - 186 = 246

Check:

246 + 186 = 432

246 - 186 = 60

hope this helped :)

Answer:

33.49 mm³

Step-by-step explanation:

The formula of volume of sphere

[tex] = \frac{4}{3} \pi {r}^{3} [/tex]

The volume of the sphere

[tex] = \frac{4}{3} \times 3.14 \times {2}^{3} [/tex]

[tex] = \frac{100.48}{3} [/tex]

[tex] = 33.4933333...[/tex]

= 33.49 mm³ (rounded to the nearest hundredth)

Answer:

2x+1

Step-by-step explanation:

the second answer

Answer:

(3, 8)

Step-by-step explanation:

x² - 6x - y + 17 = 0

x² - 6x = y - 17

x² - 6x + 9 = y - 17 + 9

(x - 3)² = y - 8

The vertex is (3, 8)

The vertex of the parabola given by the equation x² - 6x - y + 17 = 0 is (3, 8).

To complete the square and find the vertex of the parabola given by the equation x² - 6x - y + 17 = 0, we can follow these steps:

1. Rearrange the equation: Move the constant term (17) to the other side of the equation by subtracting it from both sides. This gives us x² - 6x - y = -17.

2. Group the x-terms together: Rearrange the equation so that the x-terms are next to each other. This gives us x² - 6x = y - 17.

3. Complete the square: Take half of the coefficient of x (-6) and square it. Add this value to both sides of the equation. Half of -6 is -3, and (-3)² is 9. So we add 9 to both sides: x² - 6x + 9 = y - 17 + 9.

4. Simplify the equation: On the left side, the expression x² - 6x + 9 can be factored as (x - 3)². On the right side, -17 + 9 simplifies to -8. So the equation becomes (x - 3)² = y - 8.

5. Rewrite the equation in vertex form: The vertex form of a parabola is (x - h)² = 4p(y - k), where (h, k) represents the vertex of the parabola. Comparing this with our equation, we have (x - 3)² = y - 8, which matches the vertex form.

6. Identify the vertex: By comparing the equations, we can see that the vertex of the parabola is at the point (h, k) = (3, 8).

Therefore, by completing the square, we have found that the vertex of the parabola given by the equation x² - 6x - y + 17 = 0 is (3, 8).

To learn more about parabolas;

https://brainly.com/question/21685473

#SPJ4

its 3 1/4 you will thank me later :)

Answer:

the third one

3 1/4

Step-by-step explanation:

Answer:

just use the calculator

The answer is 0 because the equation has something being multiplied by zero, and anything multiplied by 0 is 0, and the same applies to any subsequent multiplications..

Answer:

2: 176.8mm

4: ?

Step-by-step explanation:

2: 56 times 3.14 = 175.84 --> Nearest tenth: 176.8

4: I can't see the problem, sorry :(

Answer:

2. 2461.8

4. 86.6

Explanation:

your formula for area is pi×radius^2

you are using 3.14 for pi

and your radius is half way across the circle or half the diameter.

2. 3.14×(28)^2

3.14×784

=2461.8

4.This one shows the diameter so you have to divide it by 2 first.

10.5/2=5.25

radius=5.25

3.14×(5.25)^2

3.14x27.5625

=86.6

I ROUNDED BOTH ANSWERS AT THE END

Answer:

7.4

Step-by-step explanation:

10% of 74 is 7.4 by moving the decimal over one place. This will save them $7.40

Answer:I need help with the same thing.

Step-by-step explanation:

Answer:

I want to say it is b but yeah not sure.

hope I am right

Answer:

I think it is option B

Step-by-step explanation:

I dont know if I am right

if I am your welcome

Answer:

16.33 inches

Step-by-step explanation:

circumference = πd = (3.14)(5.2) = 16.33 inches

Answer:

the answer is 3

Step-by-step explanation:

3x4 equals twelve and twelve minus two is ten so the answer is a: 3

also next time be truthful because you said 10 points But this question is only 5.

YOURE VERY LUCKY I DECIDED TO HELP U.

Step-by-step explanation:

120=2/5t

120×5/2=t

t=600/2

t=300

hope it helps u

Answer:

fish stick :DDDD  funny

Step-by-step explanation:

4z +6v = 12z + 6v = 12   :? there is something fishy going on here   :/ what did you mean to ask in the question??

Answer:

20:23?

Step-by-step explanation:

Answer:

square root of 36 is 6

Step-by-step explanation:

because 6 x 6 =36

Answer:

the square root is of 36 is 6

Answer:1,250

Step-by-step explanation:

Answer:

4.6666(repeating)

Step-by-step explanation:

Answer: C.

Step-by-step explanation:

You notice how the number goes from

3.50 to 3.62 to 3.49 to 3.88

hThe 3.49 is out of place. Thus ruining the order of least to greatest.

Answer: Hewo, there your Answer is Below

My answer would Be C

Step-by-step explanation:

I chose this Answer Because, It starts with 3.5 and then 3.62 and then 3.498

Hope this helps you!!

Have a great day!!!

Answer:

true

hope it is helpful to you

Answer:

The Answer is gonna be True

Answer:

7.5

Step-by-step explanation:

90 divided by 12

Answer:C

Step-by-step explanation: goobaldy gock

Answer:

the answer is B not C you're welcome

Answer: + 8 degrees

Step-by-step explanation: average (-8+24)/2= 16/2 degrees

Answer:

x = 4

Step-by-step explanation:

If you do not want to read the explanation go the the next part in bold

Ok so the shorter leg of the triangle is a radius of the circle. ( This is indicated by the point in the middle of the circle.) for the hypotenuse we are given one part of the length (2) The other part also happens to be a radius ( remember that a radius is a line that starts from the center of the triangle to any point of the circumference. ) Also remember that the radius is equal to 3. That being said the hypotenuse = 2+3 which equals 5.  

This triangle then happens to be a right triangle. ( A triangle formed by a tangent line and a radius is a right triangle.) This means that we can use the Pythagorean theorem to solve for x.

Below here is where the work is shown

a² + b² = c². where a and b = legs and c = hypotenuse. We are given the hypotenuse (5) and a leg (3) So we plug in what we are given and solve for the missing information. 5² = 3² + b²  

5² = 25

3² = 9

we would then have 25 = 9 + b²

Next we subtract 9 from each side

25 - 9 = 16

9 - 9 cancels out

Now we have 16 = b²

finally we want to get rid of the ²

To do so we take the square root of each side

[tex]\sqrt{16}=4\\\sqrt{b^2}=b\\b = 4[/tex]

we're left with b = 4 which means that x = 4

Answer:

A=108in^2

Step-by-step explanation:

The area of a triangle is given by:

[tex]a = \frac{b \times h}{2} [/tex]

So,

[tex]a = \frac{12 \times 18}{2} = 108 \: {in}^{2} [/tex]