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3 years ago

Please help!!!!!

Mathematics

2 answers:

vampirchik [111]3 years ago

8 0

Answer:

Step-by-step explanation:

Consider the quadratic equation, we have

$ax^2+bx+c=0$

Dividing the equation by a, we get

$x^2+\frac{b}{a}x+\frac{c}{a}=0$

Put $\frac{c}{a}$ on the other side,

$x^2+\frac{b}{a}x=\frac{-c}{a}$

Add $(\frac{b}{2a})^2$ on both the sides,

$x^2+\frac{b}{a}x+(\frac{b}{2a})^2=\frac{-c}{a}+(\frac{b}{2a})^2$

completing the square, we have

$(x+\frac{b}{2a})^2=\frac{-c}{a}+(\frac{b}{2a})^2$

Now, solving for x,

$x+\frac{b}{2a}={\pm}\sqrt{\frac{-c}{a}+(\frac{b}{2a})^2}$

$x=\frac{-b}{2a}{\pm}\sqrt{\frac{-c}{a}+(\frac{b}{2a})^2}$

Multiply right side by $\frac{2a}{2a}$ ,

$x=\frac{-b{\pm}\sqrt{b^2-4ac}}{2a}$

which is the required quadratic formula.

astraxan [27]3 years ago

8 0

Finish square of ax2 + bx + c = 0 to get the Quadratic Formula. Then youDivide both sides of the equation by A, so the coefficient of x2 is 1. Write again so the left side is in form x2 + bx.

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Find a second-degree polynomial (that is, an equation of the form y =a + bx + cx2 d that goes through the three points (0, 1), (

Lostsunrise [7]

Answer:

$y = 1 - x^2$

Step-by-step explanation:

we're given three points (0,1),(1,0) and (-1,0). and and equation of a parabola

$y = a + bx + cx^2$

we can plug in each of the coordinates, and 3 equations

(x,y) = (0,1)

$1 = a + b(0) + c(0)^2$

$a=1\quad\quad\Rightarrow A$

(x,y) = (1,0)

$0 = a + b(1) + c(1)^2$

$a + b + c=0\quad\quad\Rightarrow B$

(x,y) = (-1,0)

$0 = a + b(-1) + c(-1)^2$

$a - b + c=0\quad\quad\Rightarrow C$

These are are three equations, well we can simultaneously solve them to find the values of a, b and c.

we already found that, a = 1. so we plug this value in the rest of the equations. we'll use equation B.

$a + b + c=0$

$1 + b + c=0$

$b=-1-c$

we can substitute this value of b and a = 1, equation C

$a - b + c=0$

$1 -(-1-c) + c=0$

$1 +1+c + c=0$

$2+2c=0$

$c=-1$

we can use this value of c back in b

$b=-1-(-1)$

$b=0$

hence our equation of the 2-degree polynomial will be:

$y = a + bx + cx^2$

$y = 1 + (0)x + (-1)x^2$

$y = 1 - x^2$

and this polynomial indeed passes through all the points (0, 1), (1, 0), and (-1, 0).

And since these are the only solutions to the simultaneous equation we solved (i.e. we have single values of a,b and c). there's no other possibility.

8 0

3 years ago

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kondaur [170]

Answer:

B. 1 8/21

Step-by-step explanation:

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5 0

3 years ago

Read 2 more answers

Triangle P Q R is shown. The length of P Q is 17, the length of Q R is 15, and the length of P R is 14. Law of cosines: a2 = b2

Maksim231197 [3]

Answer:

P = 57°

Step-by-step explanation:

Given the following :

PQ = 17

QR = 15

PR = 14

Using the cosine formula since the length of the three sides are given:

a2 = b2 + c2 – 2bccos(A)

To find P:

QR^2 = PQ^2 + PR^2 – 2(PQ)(PR)cos(P)

15^2 = 17^2 + 14^2 – 2(17)(14)cos(P)

225 = 289 + 196 - 476 cosP

476*CosP = 485 - 225

476*CosP = 260

CosP = 260/476

CosP = 0.5462184

P = Cos^-1(0.5462184)

P = 56.892029

P = 57°

8 0

3 years ago

Which inequality statement describes the two numbers on a number line? "−5 and a number 4 units to the right of −5" A) 4 < −5

Marina CMI [18]

Answer: D

Step-by-step explanation:be cause you have to add 4 to negetive 5 and and that negetive 1 which is greater than -5

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3 years ago

Which property or properties of arithmetic do you use when you calculate 3×70 by first calculating 3×7 = 21 and then putting a z

ANEK [815]

The property used is the Associative property

3 × 70 = 3(70) = 3 (7×10) = (3×7) ×10

The formula is

a × bc = a (bc) = a (b×c) = (a×b) ×c

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4 years ago