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3 years ago

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What is the center and radius of the circle with the given equation?

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1 answer:

Mamont248 [21]3 years ago

5 0

Answer:

(- 1, - 4 ) and r = 5

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

To obtain this form from the given equation use the method of completing the square.

Given

x² + y² + 2x + 8y = 8 ( rearrange by collecting x and y terms )

x² + 2x + y² + 8y = 8

To complete the square

add ( half the coefficients of the x/ y terms )² to both sides

x² + 2(1)x + 1 + y² + 2(4)x + 16 = 8 + 1 + 16

(x + 1)² + (y + 4)² = 25 ← in standard form

with centre (h, k ) = (- 1, - 4 ) and r = $\sqrt{25}$ = 5

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Each leg of a 45°-45°-90° triangle measures<br> 14 cm. What is the length of the hypotenuse?

4vir4ik [10]

For a 45-45-90 angle the hypotenuse is s * square root of 2

so the hypotenuse is 14 * square root of 2 or 19.8

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3 years ago

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Serena paid $194.99 for a game system and then bought two equally-priced games. If she spent a total of $284.97, what is the pri

Nataly_w [17]

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3 years ago

The equation of the graphed line in point-slope form is _______, and its equation in slope-intercept form is .

Ivenika [448]

Answer:

Point-slope form equation line

$(y-3)=(-0.6)\times (x+2)$

Slope-intercept form is:

$y=-0.6x+1.8$

Step-by-step explanation:

Point-slope form equation line passing through points $(x_1,y_1)(x_2,y_2)$

Slope = m = $\frac{y-2-y_1}{x_2-x_1}$

slope-intercept form is:

y = mx +c

where : c = intercept of on axis

$(y-y_1)=m\times (x-x_1)$

Equation of line passing through (-2,3) and (3,0).

$m=\frac{0-3}{3-(-2)}=-0.6$

$(y-3)=-0.6\times (x-(-2))$

Point-slope form equation line

$(y-3)=(-0.6)\times (x+2)$

For slope-intercept form open the brackets of Point-slope form equation l:

$y-3=-0.6x-1.2$

So, the slope-intercept form is:

$y=-0.6x+1.8$

7 0

3 years ago

Is anyone able to give a step by step process to this?

Thepotemich [5.8K]

Answer:

The value of y is 3 cm.

Step-by-step explanation:

Given,

Perimeter of triangle = $29\ cm$

Solution,

Lets redraw the triangle with nomenclature ABC, given in the attachment.

∴P(ΔABC) = 29 cm (P stands for perimeter)

Length of AB = $y+9$

Length of BC = $2y$

Length of CA = $4y-1$

Now, we all know that the perimeter of a triangle is sum of all the three sides of triangle.

P(ΔABC) = Length of AB+Length of BC+Length of CA

On substituting the values, we get;

$(y+9)+2y+(4y-1)=29\\y+2y+4y+9-1=29\\7y+8=29\\7y=29-8\\7y=21\\y=\frac{21}{7} =3\ cm$

Length of AB = $y+9=3+9=12\ cm$

Length of BC = $2y=2\times3=6\ cm$

Length of CA = $4y-1=4\times3-1=12-1=11\ cm$

Hence the value of y is 3 cm.

8 0

4 years ago

Find x<br>and<br>each of the<br>interior angles.

Kay [80]

Answer:

Part 1) $x=27$

Part 2) The measure of the interior angles are 64°-67°-49°

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the value of x

we know that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

In this problem

$(3x-17)^o+(x+40)^o+(2x-5)^o=180^o$

Solve for x

Combine like terms

$(6x+18)^o=180^o$

Subtract 18 both sides

$6x=180-18$

$6x=162$

Divide by 6 both sides

$x=27$

step 2

Find the measure of each interior angle

substitute the value of x in each measure

$(3(27)-17)=64^o$

$(27+40)=67^o$

$(2(27)-5)=49^o$

5 0

3 years ago