Answer:
k = 7
Step-by-step explanation:
Step 1: Write equation
-18 = 5 - (6k - 19)
Step 2: Solve for <em>k</em>
<u>Distribute negative:</u> -18 = 5 - 6k + 19
<u>Combine like terms:</u> -18 = -6k + 24
<u>Subtract 24 on both sides:</u> -42 = -6k
<u>Divide both sides by -6:</u> k = 7
Step 3: Check
<em>Plug in k to verify it's a solution.</em>
-18 = 5 - (6(7) - 19)
-18 = 5 - (42 - 19)
-18 = 5 - 23
-18 = -18
Answer:
23 tables were used that day at lunch.
Step-by-step explanation:
203 - 19 = 184
184 ÷ 8 = 23
Answer:
The third side is around 58.043
Step-by-step explanation:
Use the law of cosines: 
Plug in the two sides we know (into a and b) and the angle we know (into angle C).
Thus:
Use a calculator:
(Note: Make sure you're in Degrees mode.)
Answer:
<em>a:b:c=8:12:15</em>
Step-by-step explanation:
<u>Combined Ratio</u>
We are given the ratios:
a:b=2:3
b:c=4:5
The combined ratio a:b:c will include all three variables in one single expression.
Before finding it, we must have a common number for the common variable (b). Since b is 3 in the first ratio and 4 in the second ratio, we must equate both by finding the LCM of 3 and 4=12, thus both ratios will be amplified as follows:
a:b=2:3=(2*4):(3*4)=8:12
b:c=4:5=(4*3):(5*3)=12:15
Now there is a common factor in both ratios, we can combine them removing the common factor:
a:b:c=8:12:15
Answer:
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Step-by-step explanation:
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