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3 years ago

Find the equation of the parabola with a vertex of (5, -2) and a focus of (5, -3)

1 answer:

6 0

Use the form $\left(x-h\right)^2=\frac{1}{4p}\left(y-k \right)$
Then we have the vertex is $(h,k)$ and the distance from the vertex to the focus is p. Therefore we have $\left(x-5\right)^2=-\frac{1}{4}\left(y+2\right)$ . It is negative because the parabola is pointing downwards.

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How do you solve the equation F = 9/5(K - 273.15) + 32 when you're solving for K?

Mumz [18]

$\displaystyle\\Answer:\ K=\frac{5}{9}(F-32^0)+273.15^0$

Step-by-step explanation:

$\displaystyle\\F=\frac{9}{5} (K-273.15)+32\\F-32=\frac{9}{5} (K-273.15)+32-32\\F-32=\frac{9}{5} (k-273.15)\\Multiply\ both\ parts\ of\ the\ equation\ by\ \frac{5}{9} \\(\frac{5}{9})(F-32)=\frac{9}{5} (K-273.15)(\frac{5}{9} )\\\\\frac{5}{9} (F-32)=K-273.15\\\\\frac{5}{9} (F-32)+273.15=K-273.15+273.15\\\\\frac{5}{9} (F-32)+273.15=K$

7 0

2 years ago

-4.75 + (-2.75) + 1

Ket [755]

Answer:

-6.5

Step-by-step explanation:

4 0

4 years ago

Read 2 more answers

?4x y=10 rewrite in slope intercept form

aleksandrvk [35]

Wait, do you mean that y=10 is what you want in slope intercept form? Oh btw I'm not answering this just for the points. I'll actually answer the question

6 0

3 years ago

|1/2b-8|=|1/4b-1|<br> b=____ and ____

Deffense [45]

Answer:

b = 12 and 28

Step-by-step explanation:

The absolute value equation |1/2b-8| = |1/4b-1| resolves to a piecewise linear function with three pieces. There are two solutions.

<h3>Domains</h3>

The absolute value function on the left has a turning point where its value is zero:

1/2b -8 = 0

b -16 = 0

b = 16

The absolute value function on the right has a turning point where its value is zero:

1/4b -1 = 0

b -4 = 0

b = 4

For b > 16, both absolute value functions are identity functions. In this domain, the equation is ...

1/2b -8 = 1/4b -1

For 4 < b < 16, the function on the left negates its argument, so the equation in this domain is ...

-(1/2b -8) = 1/4b -1

For b < 4, both functions negate their arguments, so the equation in this domain is ...

-(1/2b -8) = -(1/4b -1)

For the purpose of finding the value of b, this is effectively identical to the equation for b > 16. (The value of b does not change if we multiply both sides of the equation by -1.)

<h3>Solutions</h3>

<u>Domain b < 4 ∪ 16 < b</u>

1/2b -8 = 1/4b -1

2b -32 = b -4 . . . . . . . . multiply by 4

b = 28 . . . . . . . . . . . . add 32-b to both sides

This solution is in the domain of the equation, so is one of the solutions to the original equation.

<u>Domain 4 < b < 16</u>

-(1/2b -8) = 1/4b -1 . . . . equation in this domain

-2b +32 = b -4 . . . . . . multiply by 4

36 = 3b . . . . . . . . . . . add 2b+4 to both sides

12 = b . . . . . . . . . . . . divide by 3

This solution is in the domain of the equation, so is the other solution to the original equation.

<h3>Graph</h3>

For the purposes of the graph, we have define the function g(b) to be the difference of the two absolute value functions. The solutions are found where g(x) = 0, the x-intercepts. The graph shows those to be ...

b = 12 and b = 28

<em>Additional comment</em>

Defining g(b) = |1/2b-8| -|1/4b-1|, we can rewrite it as ...

$g(b)=\begin{cases}7-\dfrac{1}{4}b&\text{for }b < 4\\-\dfrac{3}{4}b+9&\text{for }4\le b < 16\\\dfrac{1}{4}b-7&\text{for }16\le b\end{cases}$

Then the solutions are the values of b that make g(b) = 0.

4 0

2 years ago

A store is offering a 30% discount off the regular price of a jacket them amount off the discount was $21 what was the regular p

SSSSS [86.1K]

Answer:

(21/30)*100 = $70

Step-by-step explanation:

4 0

3 years ago