Ask question

Ask question

All categories

3 years ago

12

Given: triangle LNK, m of angle NLK =72 degrees. m of angle N=58 degrees. MP is perpendicular bisector of side LK and intersects

it at point M and side NK at point P. if Pk=12 in the following image, find the measure of angle LKN.

1 answer:

sweet-ann [11.9K]3 years ago

4 0

Answer:

50°

Step-by-step explanation:

<u>Given triangle LNK </u>

m∠NLK = 72°
m∠LNK = 58°
m∠LKN = ?

<u>Interior angles sum to 180°</u>

m∠NLK + m∠LNK + m∠LKN = 180°
72° + 58° + m∠LKN = 180°
m∠LKN = 180° - 130°
m∠LKN = 50°

You might be interested in

there are 98515 trees at Washington Park. if there are 85 aceres of land and the trees are spread out evenly how many trees are

Vlada [557]

There are 1159 trees per acre because 98515/85 = 1159

6 0

3 years ago

If CE and FH are parallel lines and m<HGI are parallel lines and m<HGI = 126º, what is m<FGI? HELP ASAP

lisov135 [29]

Answer: <FGI = 54

Step-by-step explanation:

180-126=54

u go to agora cyber charter school?

whos ur math teacher is it Mrs. P?

6 0

2 years ago

Find an equation of the sphere containing all surface points P = (x, y, z) such that the distance from P to A(−3, 6, 3) is "twic

Marina86 [1]

Answer:

Equation of Sphere = $x^{2}$ + $y^{2}$ + $z^{2}$ - 18x - 4/3y +10z + 142/3 = 0

Step-by-step explanation:

Data Given:

P = (x,y,z)

Distance from P to A (-3,6,3) = Twice the distance from P to B(6,2,-3)

Solution:

Find the equation of the sphere:

It is given that:

PA = 2PB

Squaring both sides:

$(PA)^{2} = (2PB)^{2}$

$(PA)^{2} = 4 (PB)^{2}$

$(x - (-3))^{2}$ + $(y - 6)^{2}$ + $(z-3)^{2}$ = 4 x $(x-6)^{2}$ + $(y-2)^{2}$ + $(z-(-3))^{2}$

Solving the above equation:

$(x + 3))^{2}$ + $(y - 6)^{2}$ + $(z-3)^{2}$ = 4 x { $(x-6)^{2}$ + $(y-2)^{2}$ + $(z + 3))^{2}$ }

$x^{2}$ + 9 + 6x + $y^{2}$ + 36 - 12y + $z^{2}$ + 9 - 6z = 4 { $x^{2}$ + 36 - 12x + $y^{2}$ + 4 - 4y + $z^{2}$ + 9 + 6z}

$x^{2}$ + 9 + 6x + $y^{2}$ + 36 - 12y + $z^{2}$ + 9 - 6z = 4 $x^{2}$ + 144 - 48x +4 $y^{2}$ + 16 - 16y + 4 $z^{2}$ + 36 + 24z

Putting the right hand side = 0 and solving the equation:

$x^{2}$ - 4 $x^{2}$ + $y^{2}$ - 4 $y^{2}$ + $z^{2}$ - 4 $z^{2}$ + 6x + 48x - 12y +16y -6z - 24z + 9 + 36 + 9 -144 - 16 - 36 = 0

-3 $x^{2}$ - 3 $y^{2}$ -3 $z^{2}$ + 54x + 4y -30z -142 = 0

Taking (-) common

- ( 3 $x^{2}$ + 3 $y^{2}$ + 3 $z^{2}$ - 54x - 4y +30z + 142) = 0

3 $x^{2}$ + 3 $y^{2}$ + 3 $z^{2}$ - 54x - 4y +30z + 142 = 0

dividing the whole equation by 3

$x^{2}$ + $y^{2}$ + $z^{2}$ - 54/3x - 4/3y +30/3z + 142/3 = 0

$x^{2}$ + $y^{2}$ + $z^{2}$ - 54/3x - 4/3y +30/3z + 142/3 = 0

$x^{2}$ + $y^{2}$ + $z^{2}$ - 18x - 4/3y +10z + 142/3 = 0

7 0

3 years ago

7. CHALLENGE: Use the digits 0 to 9 to make the equation true. You don't need to use all thedigits you can only use each digit o

labwork [276]

9514 1404 393

Answer:

20 = 2 + (7 -4) × 6

Step-by-step explanation:

The Order of Operations requires the parentheses be evaluated first, then the multiplication performed. Finally, the addition is performed.

If each of the blanks is filled with a single digit, the result of the multiplication must be a composite number greater than 10. Those are 12, 14, 15, 16, 18, 20. For the expression shown above, we have chosen to make the product be 18. That means the first blank is filled with 2 and the remaining blanks must evaluate to one of the products 2×9 or 3×6.

We have chosen 6 for the last blank, so the two blanks in parentheses must have a difference of 3. The digits 2 and 6 cannot be used, leaving possible choices as (3-0), (4-1), (7-4), (8-5).

Our final expression is chosen to be ...

20 = 2 +(7 -4)×6

3 0

2 years ago

Help please I beg if you can

MAVERICK [17]

Answer:

24.30 Difference, sale price 56.70

Step-by-step explanation:

30% off 81.00 is 56.70

The difference is 24.30

7 0

2 years ago