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3 years ago

Using the following equation, find the center and radius of the circle: x^2 + y^2 +2x − 4y − 20 = 0

1 answer:

6 0

You have to complete the squares on both the x terms and the y terms in order to solve this. Move the 20 over to the other side so it's negative. Group the x terms together and complete the square to get (x^2+2x+1) and then do the same with the y terms: (y^2-4y+4). You have to add 1 and 4 to other side with the 20 to get a 25. Then create 2 perfect square binomials within each x and y value to get the vertex coordinates: (x+1)^2 + (y-2)^2 = 25. This tells us that the vertex is located at (-1, 2) and the radius is the square root of 25 which is 5.So the answer is the first choice above.

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An object is propelled upward from the top of a 300 foot building. The path that the object takes as it falls to the ground can

serg [7]

Answer:

As per the statement:

The path that the object takes as it falls to the ground can be modeled by:

h =-16t^2 + 80t + 300

where

h is the height of the objects and

t is the time (in seconds)

At t = 0 , h = 300 ft

When the objects hit the ground, h = 0

then;

-16t^2+80t+300=0

For a quadratic equation: ax^2+bx+c=0 ......[1]

the solution for the equation is given by:

$x = \frac{-b\pm \sqrt{b^2-4ac}}{2a}$

On comparing the given equation with [1] we have;

a = -16 ,b = 80 and c = 300

then;

$t= \frac{-80\pm \sqrt{(80)^2-4(-16)(300)}}{2(-16)}$

$t= \frac{-80\pm \sqrt{6400+19200}}{-32}$

$t= \frac{-80\pm \sqrt{25600}}{-32}$

Simplify:

$t = -\frac{5}{2}$ = -2.5 sec and $t = \frac{15}{2}$ = 7.5 sec

Time can't be in negative;

therefore, the time it took the object to hit the ground is 7.5 sec

8 0

3 years ago

HELP DUE IN 5 MINUTES

Daniel [21]

$\huge \mathfrak \blue{Solution \: - }$

The formula for area of triangle is -

$\frac{1}{2} \times base \times height$

________________________________

So, the area of first triangle =

$\frac{1}{2} \times base \: \times height$

$\frac{1}{2} \times 4 \times 3$

$= \pink{6 \: units}$

________________________________

Area of second triangle =

$\frac{1}{2 } \times base \times height$

$\frac{1}{2} \times 4 \times 6$

$= \pink {12 \: units}$

________________________________

Area of second triangle - Area of first triangle

$= 12 - 6$

$= 6$

$\sf \underline\purple{The \: area \: increases \: by \: 6 \: square \: units.}$

3 0

3 years ago

Read 2 more answers

Classify the following triangle. Check all that apply.

Artist 52 [7]

Please which triangles

3 0

3 years ago

Having a hard time with this

raketka [301]

Answer:

the correct answer is D

Step-by-step explanation:

because the -9 5/8 is in absolute value marks.

6 0

3 years ago

Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = x2 + 2x +1?

raketka [301]

While the vertex of the function f(x) = x^2 is (0, 0), the vertex of the function g(x) = x^2 + 2x + 1 is (-1, 0).
Whereas both function has same y-cordinate, their x-coordinate are different which indicates that the function g(x) = x^2 + 2x + 1 is a horizontal translation of the function f(x) = x^2.

4 0

3 years ago

Read 2 more answers