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4 years ago

11

Which shape is always a rectangle?

1 answer:

meriva4 years ago

8 0

Answer:

D. A square because it has 4 right angles.

Step-by-step explanation:

A square is a rectangle but a rectangle is not a square.

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The center of an ellipse is (-9,3). one focus is (-7,3). The major axis is 24 units long. What is the equation of the ellipse in

CaHeK987 [17]

Answer:

$\frac{(x+9)^2}{144}+\frac{(y-3)^2}{140}=1$

Step-by-step explanation:

The standard equation of the ellipse is

$\frac{(x-\alpha)^2}{a^2}+\frac{(y-\beta)^2}{b^2}=1\;\cdots(i)$

where, $(\alpha, \beta)$ is the center and a,b are semi axes of the ellipse along x-axis and y-axis respectively.

Given that, $(\alpha, \beta)=(-9,3)$ and major axis, $2a=24$ .

So, semi major axis, $a=24/2=12$ .

Now, focus of the ellipse is (-7,3).

Let $e$ be the eccentricity of the ellipse,

So, $e=\frac c a$

where $c$ is the distance between the center and focus of the ellipse.

By using the distance formula,

$c=\sqrt{(-9-(-7))^2+(3-3)^2}=2$

$\Rightarrow e=\frac {2}{12}=\frac{1}{6}\;\cdots(ii)$

Again, the relationship among $a,b$ and $e$ is

$e=\sqrt{1-\frac{b^2}{a^2}$

$\Rightarrow \frac{1}{6}=\sqrt{1-\frac{b^2}{(12)^2}$ [from equation (ii)]

$\Rightarrow \frac{1}{36}=\sqrt{1-\frac{b^2}{144}$ [squaring on both the sides]

$\Rightarrow \frac{b^2}{144}=1-\frac{1}{36}$

$\Rightarrow b^2=\frac{35}{36}\times144=140$

So, the value of square of semi-minir axis, $b^2=140$ .

Hence, from equation (i), the equation of required ellipse is standard form is

$\frac{(x-(-9))^2}{144}+\frac{(y-3)^2}{140}=1$

$\Rightarrow \frac{(x+9)^2}{144}+\frac{(y-3)^2}{140}=1$

8 0

3 years ago

Simplify Please <br> -2a +a + 7 - 5

Eduardwww [97]

Answer:

-a+2

Step-by-step explanation:

-2a+a+7-5

=-a+2

6 0

3 years ago

Read 2 more answers

What number is 7 units to the left of -1?

expeople1 [14]

7 unit to the left, means it is 7 less than -1.
-1-7 = -8

Ans: -8

7 0

3 years ago

Through (-1, 3), slope =-1

Allushta [10]

Linear slope is formed through

3 0

4 years ago

What is the slope of a line perpendicular to the line with equation y = 5x – 2?

LekaFEV [45]

Answer:

- $\frac{1}{5}$

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 5x - 2 ← is in slope- intercept form

with slope m = 5

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{5}$

4 0

3 years ago