help please i been stuck for 2 hours........... the triangle above is a right-angled isosceles triangle. what would the measurem
ent of x have to be, given that the hypotenuse is 8cm and legs a and b have the same length? please explain your answer
1 answer:
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Answer:
40 mL of vinegar,
280 mL of dressing
Step-by-step explanation:
Let v = the milliliters ( mL ) of 100% vinegar,
Then it should be that 320 - v = mL of dressing.
v + .12( 320 - v ) = .23( 320 ) - So in this case the mL of vinegar is associated with the percent of vinegar composed. 100 percent is, in other words, 1, and is multiplied by " v " the mL of 100% vinegar. 1 v is also v, and so is written as such in our equation. 0.12 is the decimal form of the 12% vinegar, associated with the mL of dressing - as the italian dressing is composed of 12% vinegar. 23% is 0.23 in decimal form, multiplied by the mL of of vinegar in the mixture, 320 mL.
Let's solve for the mL of 100% vinegar, subtracting from 320 to receive the mL of dressing,
v + .12( 320 - v ) = .23( 320 ) - Distribute " .12 "
v + 38.4 - 0.12v = .23( 320 ) - Multiply " 0.32 " by " 320 "
v + 38.4 - 0.12v = 73.6 - Combine like terms and add / subtract
0.88v = 35.2 - Divide 0.88 on either side
v = 40 mL of vinegar,
320 - v = 320 - 40 = 280 mL of dressing
Answer:
a) decay
b) 2,950,000
c) 0.025
d)
e) 2,409,123
Step-by-step explanation:
<u>Part (a)</u>
Exponential DECAY, since the population was decreasing annually.
<u>Part (b)</u>
Initial amount = 2,950,000 people (in the year 2000)
<u>Part (c)</u>
Decay factor = 2.5% = 0.025 (in decimal form)
<u>Part (d)</u>
General form of exponential decay function:
where:
- a = initial amount
- r = rate of decay (in decimal form)
- x = time (in years)
Given:
- a = 2950000
- r = 0.025
<u>Part (e)</u>
To determine the city's population in 2008: