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3 years ago

Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.

Mathematics

2 answers:

Kryger [21]3 years ago

8 0

Answer:

The first, second, and fifth statements are correct.

Step-by-step explanation:

We are given a circle with the equation:

$x^2+y^2-2x-8=0$

And we want to select the statements that are true.

First, we can convert the equation into standard form. We can group each variable:

$(x^2-2x)+(y^2)=8$

And complete the square for the first term:

$(x^2-2x+1)+(y^2)=8+1$

Factor and simplify:

$(x-1)^2+y^2=9$

We can rewrite our equation as:

$(x-(1))^2+(y-(0))^2=(3)^2$

So, this tells us that we have a circle centered on (1, 0) with a radius of 3 units.

In this case, the first statement, second statement (the point (1,0) is on the x-axis), and fifth statements are correct (the square root of 9 is also 3).

Tcecarenko [31]3 years ago

5 0

Answer:

The first, second, and fifth statements are correct.

Step-by-step explanation:

i got it right on edg if right mark as brainliest

You might be interested in

A point is randomly chosen in the diagram shown below.

Anni [7]

Answer:

The likelihood that a point chosen inside the square will also be inside the circle: 78.54%

Step-by-step explanation:

Let x is the side of the suqare

=> the area of the square is: $x^{2}$

Let d is the diameter of the circle

=> the area of the circle : $\frac{1}{4} d^{2}$ π

However, d=x because of the square property

<=> the area of the circle : $\frac{1}{4} x^{2}$ π

The likelihood that a point chosen inside the square will also be inside the circle:

the area of the circle / the area of the square

= $\frac{1}{4} x^{2}$ π / $x^{2}$

= $\frac{1}{4}$ π *100%

= 0.7854 * 100%

= 78.54%

8 0

4 years ago

Read 2 more answers

A system of

jok3333 [9.3K]

Answer:

A system of

equations with infinitely many solutions would be represented on a graph

by parallel lines.

True

False

It would be True

Step-by-step explanation:

8 0

3 years ago

Help is very much needed

Nikitich [7]

Answer:

IT'S NEGATIVE 3. HOPE THIS HELPS...

8 0

3 years ago

"Find y". I got this wrong and want to understand why and how to do the problem. Can someone please help?

podryga [215]

Answer:

$y=\frac{15\sqrt{3} }{4}$

Step-by-step explanation:

Well what you have here are two right triangles within another right triangles created by an altitude. This results in 3 similar triangles (see attached for reference)

As a result , using the properties of similar triangles, and taking ratios of their sides of the medium triangle and the largest triangle, we can form the following relationship:

$\frac{b}{z}=\frac{y}{x} = \frac{z}{a+b}$ (we know that a+b = 15), hence the equation becomes:

$\frac{b}{z}=\frac{y}{x} = \frac{z}{15}$ ----------eq 1

If we consider the largest triangle, we will see that

cos 30° = z / 15

but from our special angles (see second attachment) we know that cos 30° = (√3)/2

hence

(√3)/2 = z / 15

z = (15√3) / 2 --------eq 2

from the same largest triangle, we will also see that

sin 30° = x / 15

similarly from our special angles, we know that sin 30° = 1/2

hence,

1/2 = x/15

x = 15/2 --------eq 3

now that we have values for x and z, we can neglect the first term of equation 1 and form an equality with x, y and z

$\frac{y}{x} = \frac{z}{15}$

$y = x\frac{z}{15}$ (substituting the values for x and z that we found above)

y = (15/2) · [ (15√3) / 2] / 15

y = (15√3) / 4

$y=\frac{15\sqrt{3} }{4}$

8 0

3 years ago

Supposed gasoline cost $2.54 per gallon how much would it cost to fill a 12 gallon tank

NemiM [27]

It will cost $30.48 to fill a 12 gallon tank.

Step-by-step explanation:

Given,

Cost of gasoline = $2.54 per gallon

Number of gallons in tank = 12 gallons

Cost of 12 gallons = Cost of gasoline per gallon * Number of gallons

Cost of 12 gallons = 2.54 * 12

Cost of 12 gallons = $30.48

It will cost $30.48 to fill a 12 gallon tank.

Keywords: multiplication

Learn more about multiplication at:

#LearnwithBrainly

5 0

3 years ago