How do you know which variable goes with axis when you graph

What is the value of b2-4ac for the following equation? 5x2+7x=6

poizon [28]

Answer:

169

Step-by-step explanation:

Given data

The function is

5x^2+7x=6

rearrange

5x2+7x-6=0

From the above expression, we can see that

a=5

b=7

c=-6

Substitute into the expression b^2-4ac

=7^2-4*5*-6

= 49-(-120)

=49+120

=169

Hence the answer is 169

8 0

3 years ago

Write an exponential function for graph that passes through the following points (-3,80);(-1,20)

padilas [110]

Answer:

y

=

4

(

1

2

)

x

Explanation:

An exponential function is in the general form

y

=

a

(

b

)

x

We know the points

(

−

1

,

8

)

and

(

1

,

2

)

, so the following are true:

8

=

a

(

b

−

1

)

=

a

b

2

=

a

(

b

1

)

=

a

b

Multiply both sides of the first equation by

b

to find that

8

b

=

a

Plug this into the second equation and solve for

b

:

2

=

(

8

b

)

b

2

=

8

b

2

b

2

=

1

4

b

=

±

1

2

Two equations seem to be possible here. Plug both values of

b

into the either equation to find

a

. I'll use the second equation for simpler algebra.

If

b

=

1

2

:

2

=

a

(

1

2

)

a

=

4

Giving us the equation:

y

=

4

(

1

2

)

x

If

b

=

−

1

2

:

2

=

a

(

−

1

2

)

a

=

−

4

Giving us the equation:

y

=

−

4

(

−

1

2

)

x

However! In an exponential function,

b

>

0

, otherwise many issues arise when trying to graph the function.

The only valid function is

y

=

4

(

1

2

)

x

7 0

3 years ago

PLEASE HELP log (5x – 10) = log (6 – 5x)

Bond [772]

Answer: look at the picture

Step-by-step explanation: Hope this help :D, Can I have a Brainliest I really needed it please

7 0

3 years ago

The plane x + y + z = 12 intersects paraboloid z = x^2 + y^2 in an ellipse.(a) Find the highest and the lowest points on the ell

emmasim [6.3K]

Answer:

a)

Highest (-3,-3)

Lowest (2,2)

b)

Farthest (-3,-3)

Closest (2,2)

Step-by-step explanation:

To solve this problem we will be using Lagrange multipliers.

a)

Let us find out first the restriction, which is the projection of the intersection on the XY-plane.

From x+y+z=12 we get z=12-x-y and replace this in the equation of the paraboloid:

$\bf 12-x-y=x^2+y^2\Rightarrow x^2+y^2+x+y=12$

completing the squares:

$\bf x^2+y^2+x+y=12\Rightarrow (x+1/2)^2-1/4+(y+1/2)^2-1/4=12\Rightarrow\\\\\Rightarrow (x+1/2)^2+(y+1/2)^2=12+1/2\Rightarrow (x+1/2)^2+(y+1/2)^2=25/2$

and we want the maximum and minimum of the paraboloid when (x,y) varies on the circumference we just found. That is, we want the maximum and minimum of

$\bf f(x,y)=x^2+y^2$

subject to the constraint

$\bf g(x,y)=(x+1/2)^2+(y+1/2)^2-25/2=0$

Now we have

$\bf \nabla f=(\displaystyle\frac{\partial f}{\partial x},\displaystyle\frac{\partial f}{\partial y})=(2x,2y)\\\\\nabla g=(\displaystyle\frac{\partial g}{\partial x},\displaystyle\frac{\partial g}{\partial y})=(2x+1,2y+1)$

Let $\bf \lambda$ be the Lagrange multiplier.

The maximum and minimum must occur at points where

$\bf \nabla f=\lambda\nabla g$

that is,

$\bf (2x,2y)=\lambda(2x+1,2y+1)\Rightarrow 2x=\lambda (2x+1)\;,2y=\lambda (2y+1)$

we can assume (x,y)≠ (-1/2, -1/2) since that point is not in the restriction, so

$\bf \lambda=\displaystyle\frac{2x}{(2x+1)} \;,\lambda=\displaystyle\frac{2y}{(2y+1)}\Rightarrow \displaystyle\frac{2x}{(2x+1)}=\displaystyle\frac{2y}{(2y+1)}\Rightarrow\\\\\Rightarrow 2x(2y+1)=2y(2x+1)\Rightarrow 4xy+2x=4xy+2y\Rightarrow\\\\\Rightarrow x=y$

Replacing in the constraint

$\bf (x+1/2)^2+(x+1/2)^2-25/2=0\Rightarrow (x+1/2)^2=25/4\Rightarrow\\\\\Rightarrow |x+1/2|=5/2$

from this we get

x=-1/2 + 5/2 = 2 or x = -1/2 - 5/2 = -3

and the candidates for maximum and minimum are (2,2) and (-3,-3).

Replacing these values in f, we see that

f(-3,-3) = 9+9 = 18 is the maximum and

f(2,2) = 4+4 = 8 is the minimum

b)

Since the square of the distance from any given point (x,y) on the paraboloid to (0,0) is f(x,y) itself, the maximum and minimum of the distance are reached at the points we just found.

We have then,

(-3,-3) is the farthest from the origin

(2,2) is the closest to the origin.

3 0

3 years ago

Simplify 4( x - 6) ^2 / ( x - 6)

Leno4ka [110]

Answer:

4x - 24

Step-by-step explanation:

$\frac{4(x - 6 {)}^{2} }{(x - 6)}$