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3 years ago

Identify the hyperbolas (represented by equations) whose centers are at (2, 1)

1 answer:

5 0

When the transverse axis is horizontal, a hyperbola centered at (h,k) has formula (x-h)^2/a^2-(y-k)^2/b^2=1. Plug in h=2, k=1, the formula is (x-2)^2/a^2-(y-1)^2/b^2=1 for some a,b. If the transverse axis is vertical, the formula is (y-h)^2/a^2-(x-k)^2/b^2=1, and (y-2)^2/a^2-(x-1)^2/b^2=1 in our case.

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Given an integer, how do you find it's opposite?

Alenkasestr [34]

I hope you can see it just try to zoom in

4 0

3 years ago

Jacob decided to ride his bicycle across the country during his 2-month summer vacation. the route he took from washington, dc t

Artist 52 [7]

Step 1: Assign variable for the unknown that we need to find.

Let ' x ' be the number of miles traveled by Jacob so far (His distance from starting point)

Step 2: Use the sentence given to set up an equation

Sentence 1: "His distance from his starting point was exactly 100 miles more than three times the distance remaining until the finishing point"

Total distance is 2800 miles, if his distance from the starting point is 'x', then remaining distance can be represented by 2800 - x.

Using the sentence we can write the below equation...

$x = 100 + 3(2800 - x)$

Distributing 3 in the right side of the equation, we get...

$x = 100 + 8400 - 3x$

Adding 3x on both sides of the equation, we get...

$x+3x = 8500$

Combine like terms in the left side of the equation, we get...

$4x=8500$

Dividing 4 on both sides of the equation, we get...

$\frac{4x}{4} =\frac{8500}{4}$

Simplifying the fraction on either side of the equation, we get...

$x=2125miles$

Conclusion:

Out of the 2800 miles, Jacob travelled a distance of 2125 miles and remaining miles that he need to cover will be <u>675 miles</u>.

3 0

3 years ago

Thea has a key on her calculator marked $\textcolor{blue}{\bf\circledast}$. If an integer is displayed, pressing the $\textcolor

mel-nik [20]

Answer:

$9$

Step-by-step explanation:

Given: Thea enters a positive integer into her calculator, then squares it, then presses the $\textcolor{blue}{\bf\circledast}$ key, then squares the result, then presses the $\textcolor{blue}{\bf\circledast}$ key again such that the calculator displays final number as $243$.

To find: number that Thea originally entered

Solution:

The final number is $243$.

As previously the $\textcolor{blue}{\bf\circledast}$ key was pressed,

the number before $243$ must be $324$.

As previously the number was squared, so the number before $324$ must be $18$.

As previously the $\textcolor{blue}{\bf\circledast}$ key was pressed,

the number before $18$ must be $81$

As previously the number was squared, so the number before $81$ must be $9$.

6 0

3 years ago

I'm honestly conflicted between C and D. Help.

hichkok12 [17]

It’s B. because 6•6=36 and B shows a little over six so B would be your answer.

3 0

3 years ago

Read 2 more answers

What is the first step in writing f(x) = 6x2 + 5 – 42x in vertex form?

Marat540 [252]

F(x) = 6x² + 5 - 42x

first step in writing the f(x) in vertex form? WRITE THE FUNCTION IN STANDARD FORM.

f(x) = 6x² - 42x + 5

Exponents must be in decreasing order.

7 0

3 years ago

Read 2 more answers