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4 years ago

Identify this conic section. x 2 - 4x + y 2 - 4y + 4 = 12 line circle ellipse parabola hyperbola

Mathematics

2 answers:

ANTONII [103]4 years ago

7 0

Answer: The answer is (B) circle.

Step-by-step explanation: The given equation of the conic section is

$x^2-4x+y^2-4y+4=12.$

We are to select the correct type of the conic section from the given options.

Let us try to find the standard form of the given conic section as follows:

$x^2-4x+y^2-4y+4=12\\\\\Rightarrow (x^2-4x+4)+(y^2-4y+4)=12+4\\\\\Rightarrow (x-2)^2+(y-2)^2=16\\\\\Rightarrow (x-2)^2+(y-2)^2=4^2.$

Therefore, the given conic section is a circle with centre (2, 2) and radius 4 units.

The image of the circle is shown in the attached figure.

Thus, (b) Circle is the correct option.

Stells [14]4 years ago

4 0

The coefficients for the x² and the y² is the same, with the same sign, namely is +1 for both, and when that happens, what we have is a circle.

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What is the order of the quadratic functions f(x)=−0.5x2,f(x)=14x2, and f(x)=x2 from the widest graph to the narrowest graph?

Irina18 [472]

Answer:

$f(x) = - 0.5 {x}^{2} \to \: f(x) = {x}^{2} \to \: f(x) = 14 {x}^{2}$

Step-by-step explanation:

The given quadratic functions are:

$f(x) = - 0.5 {x}^{2}$

$f(x) = 14 {x}^{2}$

$f(x) = {x}^{2}$

We want to order these functions, from the widest to the narrowest.

How wide the graph will open depends on the absolute value of the coefficient of the function.

The smaller the absolute value of the coefficient, the wider the graph.

Since

$| - 0.5| \: < \: |1| \: < \: |4|$

Therefore from the widest graph to the narrowest graph, we have:

$f(x) = - 0.5 {x}^{2} \to \: f(x) = {x}^{2} \to \: f(x) = 14 {x}^{2}$

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3 years ago

Alex’s paycheck for the last two weeks totaled $239.64. He owes the cell phone company $45.87. How much money does he have left?

kolezko [41]

The answer is 193.77 because 239.64-45.87 is 193.77.

5 0

4 years ago

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Solve the following system x=3 y=3x-1

astraxan [27]

Answer:

x = 3

y = 8

Step-by-step explanation:

Since it gives you x, you need to plug in the number given for it into the equation:

y = 3x - 1

y = 3(3) - 1

y = 9 - 1

y = 8

So now you have, x = 3 and y = 8

5 0

3 years ago

Two thirds of a number decreased by six is two. what is the number?

Kisachek [45]

Answer: The number is: " 12 ".

____________________________________
Let "x" represent "the unknown number" (for which we wish to solve.

The expression:

$\frac{2}{3}$ x − 6 = 2 ; Solve for "x" ;
_______________________________________________
Method 1)

Add "6" to EACH SIDE of the equation;
_______________________________________________
→ $\frac{2}{3}$ x − 6 + 6 = 2 + 6 ;

to get:

→ $\frac{2}{3}$ x = 8 ;
______________________________________________
Multiply each side of the equation by " $\frac{3}{2}$ " ; to isolate "x" on one side of the equation ; and to solve for "x" ;
______________________________________________
→ $\frac{3}{2}$ * $\frac{2}{3}$ x = 8 * $\frac{3}{2}$ ;

→ x = 8 * $\frac{3}{2}$ ;

= $\frac{8}{1}$ * $\frac{3}{2}$ ;

= $\frac{8*3}{1*2}$ ;

= $\frac{24}{2}$ ;

= 12 .
______________________________________________
x = 12 .
______________________________________________
Method 2)
______________________________________________
$\frac{2}{3}$ x − 6 = 2 ; Solve for "x" ;

Add "6" to EACH SIDE of the equation;
_______________________________________________
→ $\frac{2}{3}$ x − 6 + 6 = 2 + 6 ;

to get:
→ $\frac{2}{3}$ x = 8 ;
______________________________________________
Multiply each side of the equation by "3" ; to get rid of the "fraction" ;
 → 3 * $\frac{2}{3}$ x = 8 * 3 ;
→ $\frac{3}{1}$ * $\frac{2}{3}$ x = 8 * 3 ;
→ $\frac{3*2}{1*3}$ x = 8 * 3
→ $\frac{6}{3}$ x = 24 ;

→ 2x = 24 ;

→ Divide each side of the equation by "2" ; to isolate "x" on one side of the equation; & to solve for "x" :

2x / 2 = 24 / 2 ;

x = 12 .
__________________________________________________
Method 3).
__________________________________________________
$\frac{2}{3}$ x − 6 = 2 ; Solve for "x" ;
_______________________________________________
Add "6" to EACH SIDE of the equation;
_______________________________________________
→ $\frac{2}{3}$ x − 6 + 6 = 2 + 6 ;

to get:

→ $\frac{2}{3}$ x = 8 ;
______________________________________________
Now, divide each side of the equation by " $\frac{2}{3}$ " ;
to isolate "x" on one side of the equation; & to solve for "x" ;
___________________________________________________
{ $\frac{2}{3}$ x } / { $\frac{2}{3}$ } = 8 / { $\frac{2}{3}$ } ;

to get: x = 8 / { $\frac{2}{3}$ } ;

= 8 * ( $\frac{3}{2}$ ;

= $\frac{8}{1}$ * $\frac{3}{2}$ ;

= $\frac{8*3}{1*2}$ ;

= $\frac{24}{2}$ ;

= 12 ;
___________________________________________
x = 12 .
___________________________________________
NOTE: Variant: (in "Methods 2 & 3") :
___________________________________________
At the point where:
___________________________________________
= 8 * ( $\frac{3}{2}$ ) ;

= $\frac{8}{1}$ * $\frac{3}{2}$ ;
__________________________________________
We can cancel out the "2" to a "1" ; and we can cancel out the "8" to a "4" ;
__________________________________________
{since: "8÷2 = 4" ; and since: "2÷2 =1" } ;
__________________________________________
and we can rewrite the expression:
__________________________________________
$\frac{8}{1}$ * $\frac{3}{2}$ ;
__________________________________________
as: $\frac{4}{1}$ * $\frac{3}{1}$ ;
__________________________________________
which equals:
__________________________________________
→ $\frac{4*3}{1*1}$ ;

= $\frac{12}{1}$ ;

= 12 .
__________________________________________
x = 12 .
__________________________________________
Answer: The number is: " 12 ".
__________________________________________

8 0

4 years ago

What is the answer???

timofeeve [1]

The answer is D. Most of the other answers are way to high to make sense

6 0

4 years ago

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