Answer: The exponents in the prime factorization are 2, 1, and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1)(1 + 1) = 3 x 2 x 2 = 12. Therefore 315 has exactly 12 factors.
Step-by-step explanation: First, the exponents in the prime factorization are 2, 1, and 1. Then adding one to each and multiplying we get (2 + 1)(1 + 1)(1 + 1) = 3 x 2 x 2 = 12. Finally, 315 has exactly 12 factors.
In order to make this easier, let us convert the fraction into a mixed number. 2 2/3 would become 8/3. Now, let us divide 8 pints by 8/3 cups and we get 24/8 or 3 cups. Therefore, the amount of water that Cary has to use when she makes barbecue sauce with 1 pint of tomato is 3 cups.
Answer:
a = 0.25
Step-by-step explanation:
Our strategy to solve this problem will be to use the information given in the table to obtain first the value of c in the quadratic equation which has the form ax^2 + bx + c and then form a system of 2 linear equations and solve for the coefficients a and b as follow:
from x=0 and y=-3 a*0 + b* 0 + c = - 3
c = -3
from x=1 and y= -3.75
a*(1) + *(1) + (-3) = -3.75
a + b = -3.75 + 3 = -0.75
from x= 2 and y = -4
a* (2)^2 + b*(2) + (-3) = -4
4a + 2b = -4 +1
4a + 2b = -1
Now we can solve the system f equations by elimination:
a + b = -0.75
4a + 2b = -1
multiply first equation by -2 and add to the second and get
-2a - 2b = +1.50
4a + 2b = -1
2a = 0.50 and substituting into any of the equations get b = -1
so the quadratic equation has a= 0.25 b= -1 c= -3
we can even plug the any of the other values for x given in the table and check the answer.
Step-by-step explanation:
- Assume non-hypotenuse sides are 4 and 5, so tan =4/5=0.8 . Then hypotenuse is sqrt(16+25) = sqrt(41) So sides are 4,5,sqrt (41).
Connor has 16 nickels. If you have 9 dimes (90 cents) and you doubled it that would give you 18 quarters ($4.50). you have 7 more nickels than dimes, so you do 7+9 which equals 16 nickels (80 cents). 90+450+80=620.