Graph the ellipse with equation x squared divided by 4 plus y squared divided by 49 = 1

General equation is

Where (h,k) is the center

From the given equation h=0  and k=0

So center is (0,0)

compare the given equation with general equation

b^2 = 4  so b= 2

a^2 = 49 so a = 7

Vertices are (h, k+a) and (h, k-a)

We know h=0  , k=0  and a= 7

Vertices are (0,-7)  and (0,7)

Foci are (h, k+c)  and (h,k-c)

We know h=0  , k=0  and c=

Foci are (0,-)  and (0,)

Answer with Step-by-step explanation:

We have to graph the ellipse:

when x=0 ,

i.e. y²=49

i.e. y= ±7

ellipse passes through (0,7) and (0,-7)

when y=0,

i.e. x² = 4

i.e. x= ± 2

i.e. ellipse passes through (2,0) and (-2,0)

The ellipse is shown as below:

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

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x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

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x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

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x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

36 is the final answer! : )