What’s the answer??(SOMEONE PLEASE HELP)

Write a quadratic equation with the given roots. Write the equation in the form of ax^2+bx+c=0 where a b and c are integers

Bas_tet [7]

You haven't provided the required roots, but I can tell you how to do this kind of exercises in general.

If the $x^2$ coefficient is 1, i.e. the equation is written like $x^2+bx+c=0$ , then you can say the following about the coefficients b and c:

$b$ is the opposite of the sum of the roots
$c$ is the multiplication of the roots.

So, for example, if we want an equation whose roots are 4 and -2, we have:

$4+(-2) = 4-2 = 2 \implies b = -2$
$4 \cdot (-2) = -8 \implies c = -8$

So, the equation is $x^2-2x-8=0$

If your roots are rational, you can work like this: suppose you want an equation with roots 3/4 and 1/2. You have:

$\dfrac{3}{4}+\dfrac{1}{2} = \dfrac{3}{4}+\dfrac{2}{4} = \dfrac{5}{4} \implies b = -\dfrac{5}{4}$
$\dfrac{3}{4} \cdot \dfrac{1}{2} = \dfrac{3}{8} \implies c = \dfrac{3}{8}$

And so the equation is

$x^2 - \dfrac{5}{4} + \dfrac{3}{8} = 0$

In order to have integer coefficients, you can multiply both sides of the equation by 8:

$8x^2 - 10 + 3 = 0$

5 0

2 years ago

Factor 3x^2y^2 − 2xy^2 − 8y^2. Show your work.

docker41 [41]

3x^2y^2 − 2xy^2 − 8y^2 =
y^2 (3x^2 - 2x - 8) =

factoring with leading coefficient:

for ax2+bx+c find two numbers n,m, that m*n = a*c and m+n = b

3x^2 - 2x - 8
a=3, b=-2, c=-8
a*c = 3*(-8) = -24
-24=(-6)*4 and -6+4=-2, so m=-6 and n=4

replace bx with mx + nx and factor by grouping

3x^2 - 2x - 8 = 3x^2 -6x + 4x -8 = 3x(x-2) + 4(x-2) = (3x+4)(x-2)

answer:
3x^2y^2 − 2xy^2 − 8y^2 = y^2(3x+4)(x-2)

7 0

3 years ago

Write an equation in slope-intercept form for the line passing through the pair of points.

Umnica [9.8K]

First find your slope! by doing
y2-y1/x2-x1
in this case it would be
2-(-3)/-1-(-6)
It would give you 5/5 which would reduce to 1 meaning your slope equals 1
with your slope now you should use the point slope formula y-y1=m(x-x1)

i’m going to use the point (-1,2) so the equation would be

y-2=1(x-(-1))

simplifying that you would get

y-2=1x+1

then put it in y=mx+b form and get

y=x+3

8 0

3 years ago

The product of 2x-3 and x+4 can be expressed as

erik [133]

6 is ur answer, good luck!

7 0

3 years ago

800 g pineapple

neonofarm [45]

Answer:

30 people

Step-by-step explanation:

The question is as following:

Here are the ingredients for pineapple sherbet for 6 people

800g pineapple 4 egg whites 1/2 lemon 100g caster sugar

Dan makes pineapple sherbet he uses 2 1/2 lemons

work out how many people he makes pineapple sherbet for?

=======================================================

1/2 lemon needed for pineapple sherbet for 6 people

2 1/2 lemons needed for pineapple sherbet for x people

1/2 : 6 = 2 1/2 : x

∴ x = ( 6 * 2 1/2 ) ÷ (1/2)

x = 6 * 5/2 * 2 = 30 people

So, he make the pineapple sherbet for 30 people

5 0

2 years ago