Answer:
21) 12 cm
22) 5.9 cm
Step-by-step explanation:
21) The base is 10, and if the other two sides are congruent and the perimeter is 36, we can figure out with simple algebra that the sides are 13 cm long.
Half of 10 is 5, so we can use the pythagorean theorem.
5^2+x^2=13^2
Rearranging the variables we have 169-25=x^2
144=x^2
x can be plus or minus 12, but since negative length is impossible we find that x is positive 12 cm.
22) We want to use sine, because we have opposite and hypotenuse. A simple and easy way to memorize this is the SohCahToa method. If we have opposite (O) and hypotenuse (H) we have OH. Soh has the letters O and H, and the S means we should use sine.
sine 36=a/10
Plug this into a calculator or desmos scientific calculator to get a=5.9
<span>Cost of maple syrup = $6.00 a Gallon
Cost of corn syrup = 0.80 cents a Gallon
Cost of the syrup mixture = $2.36 a Gallon
There is mixture of 50 Gallons
Lets maple syrup be x gallons, so corn syrup be 50-x gallons
Hence,
6*x + 0.80(50-x) = 2.36*50
6x + 40 - 0.8x = 118
5.2x = 78
=> x = 78/5.2 => x = 15
So Maple will be syrup be 15 gallons.
Corn syrup will be 35 gallons.</span>
1) Let's write out both expressions subtracting 4m²+2mn+8n² from 2m²+6mn+2n²
2) Note that when we subtract 4m^2 + 2mn + 8n^2 from 2m^2 + 6mn + 2n^2 we need to swap the sign by placing -1 outside the parentheses and then combine like terms adding those terms algebraically.
Answer:
x = e^2/2 + 3
Step-by-step explanation:
Solve for x:
log(2 x - 6) = 2
Hint: | Eliminate the logarithm from the left hand side.
Cancel logarithms by taking exp of both sides:
2 x - 6 = e^2
Hint: | Isolate terms with x to the left hand side.
Add 6 to both sides:
2 x = e^2 + 6
Hint: | Solve for x.
Divide both sides by 2:
Answer: x = e^2/2 + 3
Answer:
Lindsey, who is delivering her speech in a large auditorium
Step-by-step explanation:
Jin, who is delivering her speech to a small group sitting around a table
Lindsey, who is delivering her speech in a large auditorium
Luke, who is delivering his speech in a typical classroom
Jordan, who is delivering his speech in a small meeting room
