Find the value of y A. 8√2 B. 4√2 C. 2√2 D. 4

What is the radius of a circle whose equation is X^2 plus Y^2 -10X +6 X +18=0?

frosja888 [35]

ANSWER

The radius is 4

EXPLANATION

The given equation is:

${x}^{2} + {y}^{2} - 10y + 6x + 18 = 0$

We complete the square to get the expression in standard form:

${x}^{2} + 6x + {y}^{2} - 10y + 18 = 0$

${x}^{2} + 6x + 9 + {y}^{2} - 10y + 25 = - 18 + 9 + 25$

We factor using perfect squares to get:

${(x + 3)}^{2} + {(y - 5)}^{2} = 16$

This implies that,

${(x + 3)}^{2} + {(y - 5)}^{2} = {4}^{2}$

Comparing to

${(x - h)}^{2} + {(y - k)}^{2} = {r}^{2}$

The radius is r=4

3 0

2 years ago

In triangle ΔABC, ∠C is a right angle and CD is the height to

Zina [86]

Answer:

$m\angle CDB=90\\m\angle CBD=90-\alpha\\m\angle BCD=\alpha\\\\m\angle CDA=90\\m\angle CAD=\alpha\\m\angle ACD=90-\alpha$

Step-by-step explanation:

The triangles are drawn below.

CD is perpendicular to AB as CD is height to AB.

Therefore, angles $m\angle CDB=m\angle CDA=90$ °

So, triangles ΔCBD and ΔCAD are right angled triangles.

Now, from the right angled triangle ΔABC,

$m\angle A+m\angle B =90\\\alpha+m\angle B=90\\m\angle B=90-\alpha$

From ΔCBD,

$m\angle CBD$ is same as $m\angle B$ .

So, $m\angle CBD=90-\alpha$

$m\angle BCD+m\angle BDC =90\\m\angle BCD+90-\alpha=90\\m\angle BCD=\alpha$

Now, from ΔCAD,

$m\angle CAD$ is same as $m\angle A$

So, $m\angle CAD=\alpha$

$m\angle CAD+m\angle ACD =90\\\alpha+m\angle ACD=90\\m\angle ACD=90-\alpha$

Hence, the unknown angles of both the triangles are:

$m\angle CDB=90\\m\angle CBD=90-\alpha\\m\angle BCD=\alpha\\\\m\angle CDA=90\\m\angle CAD=\alpha\\m\angle ACD=90-\alpha$

5 0

2 years ago

A street has parallel curbs 40 feet apart. A crosswalk bounded by two parallel stripes crosses the street at an angle. The lengt

andreev551 [17]

Answer:

The distance, in feet, between the strip = 12 feet.

Step-by-step explanation:

From the figure attached in relation with the question, we can deduce that crosswalk is a parallelogram where

CD/AB = CE/AE

CD = 40

CE = 50

AE = 15

Let AB = x

50x = 15 × 40

X = 12

The distance, in feet, between the strip is therefore 12 feet

6 0

2 years ago

Find the circumference and area of a circle with radius 3 yd. use the value 3.14 for pie

just olya [345]

Answer: circumference = 2Πr²

Where r= 3

Π=3.14

Therefore Circumference = 2×3.14× 3²

= 2×28.26

Circumference=56.52

Formula:

Subtitute in 3 for r.

Solve and the answer is 28.26

4 0

2 years ago

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Question 10 Complete 6 m/s = ? km/h

nadezda [96]

Answer:

21.6 km/hr

Step-by-step explanation:

multply the speed value by 3.6

8 0

2 years ago

Read 2 more answers