Answer:
x =
Step-by-step explanation:
Given that y varies directly with x then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = - 6 when x = 2, then
- 6 = 2k ( divide both sides by 2 )
- 3 = k
y = - 3x ← equation of variation
When y = - 22, then
- 22 = - 3x ( divide both sides by - 3 )
x = =
Answer:
.
Step-by-step explanation:
Let m represent meters and h represent hours.
We have been given that Captain Brain and Mr. Pinky start 1500 meters below the surface of the water and ascend at 37 meters per hour.
Since the submarine ascends at a rate of 37 meters per hour, so elevation of submarine after h hours would be .
Since the elevation under water surface is negative, so 1500 meters below the surface of water would be .
The final elevation in meters of submarine after h hours would be initial elevation plus change in elevation after h hours that is .
Therefore, the equation . represents the given scenario.
Answer:
3. f(x) = 5^x
4. f(x) = 3 (8)^x
Step-by-step explanation:
3. Which function represents the data 2=>25, 3=>125, 4 =>625
You just have to plug the values of x in the equations provided and see which one fit, you stop testing for a given equation when it doesn't match the data table.
f(x) = x^4 + 9 - NO
for x = 2, 2^4 + 9 = 16 + 9 = 25 YES
for x = 3, 3^4 + 9 = 81 + 9 = 90 NO, should be 125
f(x) = 4^x + 9 - NO
for x = 2, 4^2 + 9 = 16 + 9 = 25 YES
for x = 3, 4^3 + 9 = 64 + 9 = 73 NO, should be 125
f(x) = x^5 - NO
for x = 2, 2^5 = 32 NO, should be 25
f(x) = 5^x YES
for x = 2, 5^2 = 25 YES
for x = 3, 5^3 = 125 YES
for x = 4, 5^4 = 625 YES
4. Which of the options is equivalent to f(x) = 3(2)^(3x)
By property of the powers you can easily break down the 3x exponent into a much simpler way.
From (2)^(3x) we got to 8^x, so the equation can now be written:
f(x) = 3 (8)^x, which is the first choice.
You could easily verify it with x = 2 in each equation.