Given
\qquad \overline{OL}\perp\overline{ON}
OL
⊥
ON
start overline, O, L, end overline, \perp, start overline, O, N, end overline
\qquad m \angle LOM = 3x - 15^\circm∠LOM=3x−15
∘
m, angle, L, O, M, equals, 3, x, minus, 15, degrees
\qquad m \angle MON = 5x - 23^\circm∠MON=5x−23
∘
m, angle, M, O, N, equals, 5, x, minus, 23, degrees
Find m\angle MONm∠MONm, angle, M, O, N:

{}^{\circ}
∘
degrees

m∠MON=27

Step-by-step explanation:

From the diagram, we see that together m∠LOM and m∠MON form m∠LON, so

m∠LOM+ m∠MON=m∠LON

Since we are given that OL  ⊥  ON , we know m∠LON=90  

Substitute in the expressions that were given for each measure:

3x−15  + 5x−23  = 90  

Combine like terms:

8x - 38 = 90

Add 38 degrees to both sides:

8x = 128

Divide both sides by 8 to find x:

x = 16

Substitute 16 for x in the expression that was given for m∠MON:

m∠MON= 5(16) - 23

Simplify:

m∠MON  = 80 - 23

So m∠MON=57  

(took a while to decipher all the weird code from Khan Academy. Hope I was able to help)

n

step-by-step explanation:

the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

step-by-step explanation: