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3 years ago

The equation (x-6)^2/16 + (y+7)^2/4 = 1 represents an ellipse. What are the vertices of the ellipse?

Mathematics

2 answers:

pentagon [3]3 years ago

6 0

Answer:

C is the correct answer

Step-by-step explanation:

topjm [15]3 years ago

5 0

Answer:

The correct option is C.

Step-by-step explanation:

The given equation is

$\frac{(x-6)^2}{16}+\frac{(y+7)^2}{4}= 1$

It can be rewritten as

$\frac{(x-6)^2}{4^2}+\frac{(y+7)^2}{2^2}= 1$ .....(1)

The standard form of an ellipse is

$\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}= 1$ ....(2)

Where (h,k) is center of the ellipse.

If a>b, then the vertices of the ellipse are $(h\pm a, k)$ .

From (1) and (2) we get

$h=6,k=-7,a=4,b=2$

Since a>b, therefore the vertices of the ellipse are

$(h+a, k)=(6+4,-7)\Rightarrow (10,-7)$

$(h-a, k)=(6-4,-7)\Rightarrow (2,-7)$

The vertices of the given ellipse are (10, –7) and (2, –7). Therefore the correct option is C.

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Graph by using the slope and the y intercept.

Mashutka [201]

1. a) equation of the line :

$y = \dfrac{2}{5}x - 7$

y - intercept = -7

so, it will pass through point (0, -7)

and if we plug the value of x as 5, we get

$y = (\dfrac{2}{5} \times 5) - 7$

$y = 2 - 7$

$= - 5$

so, it will pass through point (5, -5) too

now, just plot the points (0 , -7) and (5 , -5) and join them.

2. b) equation of line is :

$y = - 3x + 5$

here, y - intercept = 5

so the line passes through point (0 , 5)

now, Plugging the value of x = 1 we get :

$y =( - 3 \times 1) + 5$

$y = - 3 + 5$

$y = 2$

so, the given line passes through point (1 , 2)

plotting the points, we can get our required line.

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3 years ago

Classify the figure in as many ways as possible.

Dima020 [189]

The answer is D.

This figure has 4 sides which makes it a quadrilateral.

This figure has 2 sets of parallel sides which makes it a parallelogram.

This figure has 4 equal sides which makes it a rhombus.

This figure has 4 right angles which makes it a rectangle.

And this figure has both 4 equal sides and 4 equal angles which makes it a square.

To make it easier, all squares are: quadrilaterals, parallelograms, rhombuses, rectangles and of course squares.

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3 years ago

how to make a 89 inch snow man with a three balls of snow at the top piece 3 pieces 8 inches 3 inches and 7.09 inches now with a

oksano4ka [1.4K]

The answer is 112.09 i added 89+3+3+8+2=105+7.09=112.09

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3 years ago

What is the pattern in the values as the exponents increase?

nirvana33 [79]

Answer:

"Multiply the previous value by 2"

Step-by-step explanation:

Let's check the first 2 terms for all the answer choices.

1. Add $\frac{1}{16}$ to the previous value:

$\frac{1}{32}+\frac{1}{16}=\frac{3}{32}$

Doesn't match.

2. Subtract $\frac{1}{16}$ from the previous value:

$\frac{1}{32}-\frac{1}{16}=-\frac{1}{32}$

Doesn't match.

3. Divide the previous value by 2:

$\frac{\frac{1}{32}}{2}\\=\frac{1}{32}*\frac{1}{2}=\frac{1}{64}$

Doesn't match.

4. Multiply the previous value by 2:

$\frac{1}{32}*2=\frac{2}{32}=\frac{1}{16}$

DOES WORK!

Also, doing the same thing with all the other values would give us matching answer. So this choice is right.

7 0

3 years ago

Read 2 more answers

In 2000, the population of Big Springs was 13 thousand. Use the given doubling

trasher [3.6K]

Answer:

The answer is "26179.4".

Step-by-step explanation:

Assume year 2000 as t, that is t =0.

Formula:

$A= A_0e^{rt}$

Where,

$A_0 = \ initial \ pop \\\\r= \ rate \ in \ decimal \\\\t= \ time \ in \ year$

for doubling time,

$r = \frac{log (2)}{t} \\$

$r = \frac{\log (2)}{ 40} \\\\r= \frac{0.301}{40}\\\\r= 0.007$

Given value:

$A = A_0e^{rt} \\\\$

$A_0 = 13000$

$t= 40 \ years$

when year is 2000, t=0 so, year is 2100 year as t = 100.

$A = 13000 \times e^{et}\\\\A = 13000 \times e^{e \times t}\\\\A = 13000 \times e^{0.007 \times 100}\\\\A = 13000 \times e^{0.7}\\\\A= 13000\times 2.0138\\\\A = 26179.4$

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3 years ago