Please help me answer this question ASAP

Complete the square to put he equation in convenient form for graphing. Then graph the conic section

Maslowich

First off, I think the equation should have a negative 9 in it originally and then you move it to the other side and it becomes positive.

You'll basically complete the square for two equations at the same time. Set it up like this:

(16x^2 + 96x) + (9y^2 - 18y) = 9

Divide everything by 16 to get the x^2 by itself, then divide everything by 9 to get y^2 by itself. You should end up with this.

(x^2 + 6x) + (y^2 - 2y) = 9/144

then complete the square by taking the second term of each polynomial, dividing by two, and squaring it.

For instance the first one will be 6/2 = 3^2 = 9

The next one will be 2/2 =1^2 = 1

Add these to numbers to the polynomials as well as to the other side of the equation to keep it equal. You should end up with this.

(x^2 + 6x+9) + (y^2 - 2y+1) = (9/144)+9+1

Then find a common denominator on the right side of the equals sign and add them all together to get:

(x^2 + 6x+9) + (y^2 - 2y+1) = 1449/144

Factor out the two polynomials

(x+3)^2 + (y-1)^2 = 1449/144

the center of the circle is (-3,1) according to the factored out polynomials and the radius will be the square root of the number on the right side of the equals sign = sqrt(1449/144) = 3.17

8 0

3 years ago

Elsa invested $500 in a fund for 4 years and was paid simple interest. The total interest that she received on the investment wa

dezoksy [38]

The annual interest rate of her investment would be = 4%

<h3>Calculation of annual interest rate</h3>

The principal amount invested= $500

The period of investment= 4years

The interest received= $80

The interest rate= ?

To calculate the interest rate use the formula,

SI = P×T×R/100

80 = 500 × 4 ×R/100

Make R the subject of formula,

R= 80 ×100/500×4

R= 8000/2000

R= 4%

Therefore, the annual interest rate of her investment would be = 4%.

Learn more about simple interest here:

brainly.com/question/20690803

#SPJ1

8 0

2 years ago

2. The prices, in dollars per unit, of the three commodities X, Y and Z are x, y and z,

34kurt

Answer:

Price of X is $24.81

Price of Y is $3.66

Price of Z is $11.36

Step-by-step explanation:

for person A, we know that earns $40, then we can write the equation:

-4*z + 3*x + 3*y = $40

For person B, we know that earns $50, then:

1*z + 2*x - 3*y = $50

For person C, we know that earns $130, then:

6*z - 1*x + 4*y = $130

Then we have a system of equations:

-4*z + 3*x + 3*y = $40

1*z + 2*x - 3*y = $50

6*z - 1*x + 4*y = $130

To solve the system, we need to isolate one of the variables in one of the equations.

Let's isolate z in the second equation:

z = $50 - 2*x + 3*y

now we can replace this in the other two equations:

-4*z + 3*x + 3*y = $40

6*z - 1*x + 4*y = $130

So we get:

-4*($50 - 2*x + 3*y) + 3*x + 3*y = $40

6*($50 - 2*x + 3*y) - 1*x + 4*y = $130

Now we need to simplify both of these, so we get:

-$200 + 11x - 9y = $40

$350 - 13*x + 28*y = $130

Now again, we need to isolate one of the variables in one of the equations.

Let's isolate x in the first one:

-$200 + 11x - 9y = $40

11x - 9y = $40 + $200 = $240

11x = $240 + 9y

x = ($240 + 9y)/11

Now we can replace this in the other equation:

$350 - 13*x + 28*y = $130

$350 - 13*($240 + 9y)/11 + 28*y = $130

Now we can solve this for y.

- 13*($240 + 9y)/11 + 28*y = $130 - $350 = -$220

-13*$240 - (13/11)*9y + 28y = - $220

y*(28 - (9*13/1) ) = -$220 + (13/11)*$240

y = ( (13/11)*$240 - $220)/(28 - (9*13/1) ) = $3.66

We know that:

x = ($240 + 9y)/11

Replacing the value of y, we get:

x = ($240 + 9*$3.66)/11 = $24.81

And the equation of z is:

z = $50 - 2*x + 3*y = $50 - 2* $24.81 + 3*$3.66 = $11.36

Then:

Price of X is $24.81

Price of Y is $3.66

Price of Z is $11.36

4 0

3 years ago

What is the rate of change for f(x)=-2cos4x-3 on the interval from x=0 to x=pi over 4

Anestetic [448]

Answer:

$\frac{16}{\pi}$

Step-by-step explanation:

The average rate of a function $f$ on interval $x=a$ to $x=b$ is:

$\frac{f(b)-f(a)}{b-a}$ .

$a=0$ and $b=\frac{\pi}{4}$ here for this problem where $f(x)=-2\cos(4x)-3$ .

So we will need to evaluate $f$ for $x=0 \text{ and } b=\frac{\pi}{4}$ .

To find $f(0)$ we will replace $x$ in $f(x)=-2\cos(4x)-3$ with $0$ :

$f(0)=-2\cos(4(0))-3$

$f(0)=-2\cos(0)-3$

$f(0)=-2(1)-3$

$f(0)=-2-3$

$f(0)=-5$

To find $f(\frac{\pi}{4})$ we will replace $x$ in $f(x)=-2\cos(4x)-3$ with $\frac{\pi}{4}$ :

$f(\frac{\pi}{4})=-2\cos(4(\frac{\pi}{4}))-3$

$f(\frac{\pi}{4})=-2\cos(\pi)-3$

$f(\frac{\pi}{4})=-2(-1)-3$

$f(\frac{\pi}{4})=2-3$

$f(\frac{\pi}{4})=-1$

So now we need to compute the change in $f$ over the change in $x$ :

$\frac{-1-(-5)}{\frac{\pi}{4}-0}$

$\frac{-1+5}{\frac{\pi}{4}}$

Dividing by $\frac{\pi}{4}$ is the same as multiplying by $\frac{4}{\pi}$ :

$(-1+5)\cdot \frac{4}{\pi}$

$4 \cdot \frac{4}{\pi}$

$\frac{16}{\pi}$

8 0

3 years ago

Which of the following shows the equation after both sides have been distributed

jolli1 [7]

A. 4x-8=15x-40 is the right answer (though I think the 4 should be negative)

7 0

3 years ago