Four times a number -5 is the same as twice the number +3

Find the vertices and foci of the hyperbola with equation quantity x minus five squared divided by eighty one minus the quantity

Papessa [141]

If you notice, the positive fraction, is the one with the "x" variable in it, that simply means, the hyperbola is opening over the x-axis, so is a horizontal one, therefore

$\bf \textit{hyperbolas, horizontal traverse axis }
\\\\
\cfrac{(x- h)^2}{ a^2}-\cfrac{(y- k)^2}{ b^2}=1
\qquad 
\begin{cases}
center\ ( h, k)\\
vertices\ ( h\pm a, k)\\
c=\textit{distance from}\\
\qquad \textit{center to foci}\\
\qquad \sqrt{ a ^2 + b ^2}
\end{cases}\\\\
-------------------------------$

$\bf \cfrac{(x-5)^2}{81}-\cfrac{(y-1)^2}{144}=1\implies \cfrac{(x-5)^2}{9^2}-\cfrac{(y-1)^2}{12^2}=1~~
\begin{cases}
a=9\\
b=12
\end{cases}
\\\\\\
c=\sqrt{9^2+12^2}\implies c=15\\\\
-------------------------------\\\\
vertices~~(5\pm 9,1)\implies 
\begin{cases}
(14,1)\\
(-4,1)
\end{cases}~~foci~~(5\pm 15,1)\implies 
\begin{cases}
(20,1)\\
(-10,1)
\end{cases}$

3 0

3 years ago

What is 2^5<br> 1. 32<br> 2. 10<br> 3. 12

shtirl [24]

$\huge\text{Hey there!}$

$\mathsf{2^5}$

$\mathsf{2\times 2\times2 \times 2 \times2}$

$\mathsf{2\times2 = 4}$

$\mathsf{4\times4\times2}$

$\mathsf{4\times 4 = 16}$

$\mathsf{16\times2 = 32}$

$\boxed{\boxed{\large\text{Answer: \huge \bf 32 }}}\huge\checkmark$

$\text{Good luck on your assignment and enjoy your day!}$

~ $\frak{Amphitrite1040:)}$

4 0

3 years ago

Which of the following are continuous variables, and which are discrete? (a) number of traffic fatalities per year in the state

sukhopar [10]

Answer:

a) Discrete

b) Continuous

c) Continuous

d) Discrete

e) Continous

Step-by-step explanation:

Continuous:

Real numbers, can be integer, decimal, etc.

Discrete:

Only integer(countable values). So can be 0,1,2...

(a) number of traffic fatalities per year in the state of Florida

You cannot have half of a traffic fatality, for example. So this is discrete

(b) distance a golf ball travels after being hit with a driver

The ball can travel 10.25m, for example, which is a decimal number. So this is continuous.

(c) time required to drive from home to college on any given day

You can take 10.5 minutes, for example, which is a decimal value. So this is continuous.

(d) number of ships in Pearl Harbor on any given day

There is no half ship, for example. So this is discrete.

(e) your weight before breakfast each morning continuous discrete

You can weigh 80.4kg, for example, which is a decimal number. So this is continuous.

7 0

3 years ago

A plane flying at a certain altitude is observed from two points that are 2.2 meters apart. The angles of elevation made by the

lana [24]

$tan(72)= \frac{y}{x} ; tan(55)= \frac{y}{2.2 + x}$
$y=xtan(72);y=(2.2+x)tan(55)$
So we are to merge the two equations into one, since both of the equations are equal to y. a = b, b = c therefore, a = c.
$xtan(72)=2.2tan(55)+xtan(55)$
We are to isolate x.
$x[tan(72)-tan(55)]=2.2tan(55)$
$x=\frac{2.2tan(55)}{tan(72)-tan(55)}$
The value of x is approximately, 1.9047m
Then, substitute the value of x from $y=xtan(72)$
$y=1.9047tan(72)$
y = 5.862m
Round up, then the answer would be D.

7 0

3 years ago

Find the measure of this angle in the triangle.

bixtya [17]

Answer:

the angle measures 85 degrees

4 0

3 years ago