Answer:
Step-by-step explanation:
f(x) = ax+b
passing through the point (6,-1) : when x = 6 f(x) = -1
means : -1 = a (6)+b
passing through the point (-3,-2) : when x = -3 f(x) = -2
means : --2 = a (-3)+b
you have the system :: 6a +b = - 1......(1)
-3a +b = -2........(2)
by (1) : b = -1 - 6a
by (2) : b = -2+3a
so : -2+3a = -1 - 6a
3a+6a =2 -1
9a =1 a =1/9 put the value of a in (1) or (2) : -3(1/9)+b = - 2
-1/3 +b = - 2
b = -2+1/3
b = -5/3
f(x) = 1/9 x - 5/3
Marisol bought three pairs of shoes that cost $38 each if the tax rate was 8% how much did marisol pay ?
Answer:
See Below
Step-by-step explanation:
To Clarify a rational number is just a number that can be made into a mixed fraction. Or another way of doing this would be to say a number like 1.50. So currency is a form of rational numbers.
EX: You decided to go to college but as a broke college student you couldn't pay for college (because it is expensive) so you decide to take out a student loan. For simplicity's sake let's say that you only need a $15,236.75 loan to add to the money you had saved up for college. However, the loan agency adds a 0.05 per month interest rate as soon as your 4 years of college are over. Knowing that interest adds up fast you decide to try to pay off as much loan debt as you can while still in college with your part-time job. You end up paying off $746.98 leaving you with only $14,489.77 left of the loan. The first month out of college you wind up with only $15,214.26 of college debt. Before the next month however you marry your college sweetheart and as a couple, you take on each other's debts making your grand sum for college debts $32,416.51. After five blissful years of marriage you wind up getting a divorce but because finances have been jumbled (real-world ish) you decide just to divide the $12,758.36 debt from college evenly between the two of you.
Subtraction:
Multiplication:
Addition:
Division:
1. The first step to answering this question is to find the volume of a single spherical lead shot and then multiply this by 5000 to find the total volume of 5000 lead shots.
So, given that the lead shots are spherical, we must use the formula for the volume of a sphere:
V = (4/3)πr^3
Given that the diameter is 3mm, we can find the radius by dividing this by 2:
r = 3/2 = 1.5 mm
From here, there are two ways to proceed; we can either covert the radius into cm, or we can continue with the mm value and then convert the resulting volume in cubic mm into cubic cm (since we are given that 1 cm cubed of lead weighs 11.4g, we can already tell that we will have to finish with a volume in cubic cm). I will show both these methods as a) and b), respectively.
a) If there are 10 mm in 1 cm, and we have a radius of 1.5 mm, then to convert this into cm we need to simply divide by 10:
1.5 mm = 1.5/10 = 0.15 cm
Now that we have our radius in cm form, we can substitute this into the formula for the volume of a sphere that we specified at the very beginning:
V = (4/3)πr^3
V = (4/3)π(0.15)^3
V = (9/2000)π cm cubed, or
0.0045π cm cubed (in decimal form)
Now that we have the volume of one lead shot, all we need to do is multiply this by 5000 to find the volume of 5000 lead shots:
0.0045π*5000 = 22.5π cm cubed
Since we already have the total volume in cm cubed, there is no need to do any more conversions.
b) In this method, we will use radius = 1.5 mm and substitute this into the general formula for the volume of a sphere again:
V = (4/3)πr^3
V = (4/3)π(1.5)^3
V = (9/2)π mm cubed, or
4.5π mm cubed (in decimal form)
Thus, to calculate the volume of 5000 lead shots, we must multiply this value by 5000:
4.5π*5000 = 22500π mm cubed
Now comes the part where we must convert this into cubic cm; to do this we simply take the value in cubic mm and divide it by 10^3 (ie. 1000). Thus:
22500π/1000 = 22.5π cm cubed
As you can see, we end up with the same answer as in a). The key here is to remember that you need to convert, so maybe write a note to yourself at the start of the question and pay close attention to the different units in both the question and your working.
2. Now that we know that the volume of 5000 spherical lead shots is 22.5π cm cubed, we need to calculate their mass.
We are given that 1 cm cubed of lead weighs 11.4 g, thus to calculate the mass of 22.5π cm cubed of lead, we need to multiply this value by 11.4. Thus:
Mass = 22.5π*11.4
= 256.5π g
Note that this is the answer in exact form. I wasn't entirely sure about the rounding required or the value of π that you were specified to use (eg. exact, 22/7, 3.14), so if you wanted me to edit the answer to reflect that or had any questions, feel free to comment below.
A. -12
B. -6
c. -4
D.4
E 4 2/3
Answer:
Use a calculator
Step-by-step explanation: