Answer all the four q

X^2+y^2 +4x−6y+9=0<br> what is the center and the radius

mojhsa [17]

Answer: Center (-2,3), radius 2

Step-by-step explanation: Subtract 9 from both sides, then complete the square for the x and y variables & add to both sides: $x^2+4x+4+y^2-6y+9=-9+4+9$ $= (x+2)^2+(y-3)^2=4$ . The center of this circle in the form $(x-a)^2+(y-b)^2=r^2$ is (a,b) with radius r. a=-2, b=3, r= $\sqrt{4}$ =2

3 0

3 years ago

Use ΔABC shown below to answer the question that follows:

topjm [15]

Answer:

The correct options are a and b.

Step-by-step explanation:

It is given that triangle ABC with segment AD drawn from vertex A and intersecting side BC.

Two triangle are called similar triangle if their corresponding sides are proportional or the corresponding interior angle are same.

To prove ΔABC and ΔDBA are similar, we have to prove that corresponding interior angles of both triangle as same.

If segment AD is an altitude of ΔABC, then angle ADB is a right angle.

$\angle BDA=90^{\circ}$

The opposite angle of hypotenuse is right angle. If segment CB is a hypotenuse, then angle ABC is a right angle.

$\angle BAC=90^{\circ}$

In triangle ΔABC and ΔDBA

$\angle ABC\cong \angle DBA$ (Reflexive property)

$\angle BAC\cong \angle BDA$ (Right angles)

By AA rule of similarity ΔABC and ΔDBA are similar.

Therefore correct options are a and b.

3 0

3 years ago

Read 2 more answers

Julio spent $51 and now has no money left . He had blank before his purchase

tatiyna

Answer:

He had 51 before his purchases

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Consider the following information: Tony, Mike, and John belong to the Alpine Club. Every member of the Alpine club who is not a

zzz [600]

Answer:

ranslation into first order logic ,

Tony, Mike and John belong to Alpine club.

S1 Member (Tony)

S2 Member (mike)

S3 Member (john)

Every member of the Alpine club who is not a skier is a mountain climber

S4 \forallx(Member(x)\wedge~Skier(x)\supsetClimber(x))

Mountain climbers do not like rain

S5 \forallx(Climber(x) \supset ~Like(x,Rain))

Anyone who does not like snow is not a skier

S6 \forallx(~Like(x,snow) \supset ~ Skier(x))

Mike dislikes whatever Tony likes

S7 \forallx(Like(Tony,x) \supset ~ Like(mike,x))

And likes whatever Tony dislikes

S8 \forallx(~Like(Tony,x) \supset Like(Mike,x)

Tony likes rain and snow

S9 Like(Tony,rain)

S10 Like(Tony, snow)

From s10 we know that (I(tony),I(snow)) \in I(Like)

From s7 we know that for every assignment v

(D,I),v|= Like(tony,x)\supset ~Like(Mike,x)

(D,I),v|= Member(x) \wedge Climber(x) \wedge ~ Skier(x)

So

(D,I),v |= \existsx(Member(x)\wedgeClimber(x)\wedge~Skier(x))

Hence a member of Alpine club who is a mountain climber but not a skier

suppose we donot have S7 , we have only s1-s6 and s8-s10.

To prove , we have to produce interpretations as :

D ={ t,m,j,s,r }

Interpretations:

I(tony)=t, I(mike)=m, I(john)=j, I(snow)=s, I(rain)=r

I(member)= {t,m,j}

I(skier)= {t,m,j}

I(climber)= {}

I(Like)= {(t,s),(t,r),(m,s),(m,r),(m,m),(m,t),(m,j),(j,s)}

Hence a member of Alpine club who is a mountain climber but not a skier

4 0

4 years ago

Over what interval is the function decreasing? f(1) = x2 + 2x + 2

kotykmax [81]

Answer:

Step-by-step explanation:

$y=x^2+2x+2\\ \\ \frac{dy}{dx}=2x+2\\ \\ 2x+2$

7 0

3 years ago