Line jm intersects line gk at point n. which statements are true about the figure? check all that apply. gnj is complementary to jnk. mnl is complementary to knl. mng is complementary to gnj. knj is supplementary to mnl. gnm is supplementary to jnk.

Second and fifth statement is correct.

Step-by-step explanation:

Given Line JM intersects line GK at point N. we have to check for the following statements.

Complementary angles are the either of two angles whose sum is equal to 90° and supplementary angles are those whose sum is 180°

First statement: GNJ is complementary to JNK.

Both angles ∠GNJ and ∠JNK are of 90° which gives the sum of 180°. Hence, above statement is not correct.

Second statement: MNL is complementary to KNL.

∠MNL+∠KNL=∠MNK=180°-∠JNK=180°-90°=90°

Hence, the sum of above two angles ∠MNL and ∠KNL is 90° ∴ complementary gives this statement is correct.

Third statement: MNG is complementary to GNJ.

Both angles ∠MNG and ∠GNJ are of 90° which gives the sum of 180°. Hence, above statement is not correct.

Fourth statement: KNJ is supplementary to MNL.

The sum of above two angles is not 180° hence incorrect statement.

Fifth statement: GNM is supplementary to JNK.

Both angles ∠GNM and ∠JNK are of 90° which gives the sum of 180°. Hence, above statement is correct.

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)