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Nataliya [291]
3 years ago
9

Find the center, vertices, and foci of the ellipse with equation 2x2 + 8y2 = 16.

Mathematics
1 answer:
Pavlova-9 [17]3 years ago
4 0

{2}x^{2}  + 8 {y}^{2}  = 16 \\  \\ 1. \:  {2x}^{2}  =  - 8 {y}^{2}  + 16 \\ 2. \:  {x}^{2}  =  - 4y^{2}  + 8 \\ 3. \: x =  \sqrt{ - 4y^{2}  + 8}  \\ x =  -  \sqrt{ - 4y^{2} + 8 }  \\  \\ answer \\ x =  \sqrt{ - 4y^{2} + 8 }  \\ x =  -  \sqrt{ - 4y^{2}  + 8}

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A country is planning to decrease government spending in order to reduce the national debt. If the outlined changes are put into
SOVA2 [1]

<u>Answer</u>

Graph D represents the national debt of the country over the next years.

<u>Solution-</u>

The country's debt will decrease exponentially by one-third each year.

Current debt is $60 billion.

This problem can be treated as an exponential decay problem.

The general exponential decay function is,

y=a(r)^{-x}

Where,

a = initial value,

r = rate of change,

-ve sign of x represents the decrease in value of y as x increases.

Here, the rate of change is 3 as each year the debt becomes on third, and initial value of debt is $60, so

y=60(3)^{-x}

Plotting a graph taking number of year on x-axis and debt on y-axis, we can generate a graph for this function.

Putting different values of x, we can get the values of y. So the graph must have (0, 60), (1, 20), (2, 6.66), (3, 2.22), (4, 0.74), (5, 0.24) points on it.

Option B and C are incorrect, as they do not start from 60. (they don't have (0,60) on their curve)

Between option A and D, curve in D has all the points on it. So D is the correct graph.

5 0
3 years ago
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What is the absolute value of 2
Anna71 [15]

Answer:The Absolute Value of a number tells us how far the number is from zero, on a Number Line. 2 is 2 units away from zero. Hence |2|=2.hope it helps

Step-by-step explanation:

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What is 15 to the third power
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Answer:

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Step-by-step explanation:

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Write 3x^2-18x-6 in vertex form
Vedmedyk [2.9K]
The standard form of a quadratic equation is \displaystyle{ y=ax^2+bx+c, while the vertex form is:

                      y=a(x-h)^2+k, where (h, k) is the vertex of the parabola.

What we want is to write \displaystyle{ y=3x^2-18x-6 as y=a(x-h)^2+k

First, we note that all the three terms have a factor of 3, so we factorize it and write:

\displaystyle{ y=3(x^2-6x-2).


Second, we notice that x^2-6x are the terms produced by (x-3)^2=x^2-6x+9, without the 9. So we can write:

x^2-6x=(x-3)^2-9, and substituting in \displaystyle{ y=3(x^2-6x-2) we have:

\displaystyle{ y=3(x^2-6x-2)=3[(x-3)^2-9-2]=3[(x-3)^2-11].

Finally, distributing 3 over the two terms in the brackets we have:

y=3[x-3]^2-33.


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6 0
3 years ago
What is the equation of the line passing through the points (3,6) and (2,10)
andrezito [222]

Answer: y= - 4x+18

Step-by-step explanation:

Equation: y=mx+b

***remember: b is the y-intercept and m is the slope.

m=\frac{y2-y1}{x2-x1}

3= x1

2= x2

6= y1

10=y2

m=\frac{10-6}{2-3}= \frac{4}{1}= -4

m=-4

Now we have y=-4x+b , so let's find b.

You can use either (x,y) such as (3,6) or (2,10) point you want..the answer will be the same:

   (3,6). y=mx+b or 6=-4 × 3+b, or solving for b: b=6-(-4)(3). b=18.

   (2,10). y=mx+b or 10=-4 × 2+b, or solving for b: b=10-(-4)(2). b=18.

Equation of the line: y=-4x+18

3 0
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