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3 years ago

3x²-9x+1+0 Find the discriminant

Mathematics

1 answer:

Sindrei [870]3 years ago

3 0

Answer:

$\boxed{D = 69}$

Step-by-step explanation:

The given quadratic equation is:

$3x^2-9x+1 = 0$

Comparing it with the standard form of Quadratic Equation $ax^2+bx+c = 0$ , we get:

a = 3, b = -9 and c = 1

Discriminant = b² - 4ac

D = (-9)²-4(3)(1)

D = 81 - 12

D = 69

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Line JM intersects line GK at point N Which statements are true about the figure? Check all that apply.

Likurg_2 [28]

we know that

Complementary angles are two angles whose sum is equal to $90$ °, while supplementary angles are two angles whose sum is equal to $180$ °.

Statements

case 1) GNJ is complementary to JNK

Is False

Angle GNJ is $90$ degrees and angle JNK is $90$ degrees. The sum of the angles GNJ and JNK is $180$ degrees. Therefore, GNJ is not complemetary to JNK.

$angle\ GNJ+angle\ JNK=180\ degrees$

GNJ is supplementary to JNK, not complementary

case 2) MNL is complementary to KNL

Is True

The sum of angles MNL and KNL is MNK which is $90$ degrees. Therefore, MNL is complementary to GNJ.

$angle\ MNL+angle\ KNL=90\ degrees$

MNL is complementary to KNL

case 3) MNG is complementary to GNJ

Is False

Angle MNG is $90$ degrees and angle GNJ is $90$ degrees. The sum of the angles MNG and GNJ is $180$ degrees. Therefore, MNG is not complemetary to GNJ.

$angle\ MNG+angle\ GNJ=180\ degrees$

MNG is supplementary to GNJ, not complementary

case 4) KNJ is supplementary to MNL

Is False

Angle KNJ is $90$ degrees and angle MNL is less than $90$ degrees. The sum of the angles KNJ and MNL is less than $180$ degrees. Therefore, KNJ is not supplementary to MNL

$angle\ KNJ+angle\ MNL < 180\ degrees$

case 5) GNM is supplementary to JNK

Is True

Angle GNM is $90$ degrees and angle JNK is $90$ degrees. The sum of the angles GNM and JNK is $180$ degrees. Therefore, GNM is supplementary to JNK.

$angle\ GNM+angle\ JNK = 180\ degrees$

GNM is supplementary to JNK

therefore

the answer is

MNL is complementary to KNL

GNM is supplementary to JNK

4 0

3 years ago

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yulyashka [42]

The equation for a circle is as followed:

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

where the center of the circle is at (h,k) and the radius of the circle is r.

We are given (h,k) and need to find the radius. To do so, we can use the distance formula to find the distance from the center to the point on the circle:

$d= \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

Plug in the two points:

$d= \sqrt{(3-(-6))^2+(2-(-4))^2}$

$d= \sqrt{(9)^2+(6)^2}$

$d= \sqrt{117}$

If the distance from the center to the edge of the circle is the square root of 117, then r^2 = 117.

The answer is:

$(x-3)^2+(y-2)^2=117$

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Step 2: Flip the equation.

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