Step-by-step explanation: need to find a basis for the solutions to the equation Ax = 0. To do this ... 0 0 0 1 −3. ⎤. ⎦. From this we can read the general solution, x = ⎡. ⎢. ⎢. ⎢. ⎢. ⎣ ... two vectors are clearly not multiples of one another, they also give a basis. So a basis ... 4.4.14 The set B = {1 − t2,t − t2,2 − 2t + t2} is a basis for P2.
Ok so we can see for every 2 cups of medium coffee, the balance goes down 5.30$. So that means that for every coffee, her balance goes down 2.65$. Solving for the x-intercept means how many medium coffees can I get until my balance is 0. First, we have to find the y-int so it's easy. The slope is -2.65 because for every medium coffee, her balance goes down 2.65$. So we have y=-2.65x+b. Plugging in any point, I choose (4,14.40), we get 14.4 = -2.65 × 4 +b. Solving for b we get 25 for the y intercept, meaning the equation is y = -2.65x + 25 . To find the x intercept, we set y=0. So we have 0 = -2.65x+25. Solving for x we get approx. 9.4. We can't have decimals so we round down to 9. So the x int is ≈ 9.4 meaning we can only buy 9 coffee and have a little extra. But, if the problem said how many more coffees can she get, then here is how we do it. Since she already got 4 coffees, and the max is 9, we do 9-4 and we get 5, so she can buy 5 coffeed more.
Answer: Exponential function
Step-by-step explanation:
A linear function is the form
, where m is the constant rate of change of y with respect to x and c is the y-intercept.
An exponential growth function is in the form 
, where r is the rate of growth (generally in percent) and A is initial value.
If the population of a certain type of seahorse grew by 13% from year to year, then the rate of growth is 13% .
Hence it is an exponential equation.
Answer:
1800
Step-by-step explanation:
Labor quantity variance= Actual quantity ×standard price - standard quantity ×standard price
Standard quantity=2×2600=5200
Labor quantity variance
5050×12-5200×12=1800
Answer:
At approximately x = 0.08 and x = 3.92.
Step-by-step explanation:
The height of the ball is modeled by the function:
Where f(x) is the height after x seconds.
We want to determine the time(s) when the ball is 10 feet in the air.
Therefore, we will set the function equal to 10 and solve for x:
Subtracting 10 from both sides:
For simplicity, divide both sides by -1:
We will use the quadratic formula. In this case a = 16, b = -64, and c = 5. Therefore:
Substitute:
Evaluate:
Simplify the square root:
Therefore:
Simplify:
Approximate:
Therefore, the ball will reach a height of 10 feet at approximately x = 0.08 and x = 3.92.
