Answer:
- greater area: A
- no, B has the greater volume
Step-by-step explanation:
The relevant area and volume formulas are ...
A = 2(LW +H(L +W))
V = LWH
When there are multiple instances of the calculations to be done, it is convenient to let a spreadsheet do them. The results are attached.
Figure A has the larger area.
Figure B has the larger volume.
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<em>Additional comment</em>
The more "cube-like" the prism is, the less area it will have for the same volume. Here, package B is more "cube-like" than package A. (The ratio of largest-to-smallest dimensions is smaller for package B.)
a.
Sally has $28.00 in her bank account and starts saving $18.25 every week.
Let x represent the number of weeks from when he have $28.00 in her account.
and y represent the amount in her account at week x;
We can write the function of the case as;
where m is the amount she saves every week, and b the initial amount in her account.
So, the function will be;
b.
Her friend Suzy has $161.00 in her bank account and is withdrawing $15 every week.
Using the same rule as in a above;
The function will be;
c.
The graph of the two functions is shown below;
d.
The point where the two lines intersect is shown in the graph above.
The point is at;
Which is at week 4 and balance $101.
e.
The point at which they intersect is the point where they both have the same values.
It is the week when both Sally and Suzy have the same amount in there account.
So, at the fourth week (week 4) Sally and Suzy both have $101 in their account
Answer:
150 degrees
Step-by-step explanation:
Let's start off by looking at what we are working with in this specific problem:
We can see that we are looking at 2 angles, angle L and angle M, that add up to a total of 180 degrees (aka a straight line)
Now that we know that, we also have to keep is mind that angle L + angle M = 180 degrees.
Now that we've got all of that out of the way, let's set up a simple algebraic equation:
angle L + angle M = 180
We also know that angle L is 30 degrees so let's add it into the equation we have just created:
30 + angle M = 180
We now know that 30 plus angle M (whatever it might be) is equal to 180 so in order to solve this problem we have to do some simple subtraction.
180 - 30 = angle M
Now we are left with:
150 degrees = angle M
Answer:the number of children that swam in the public pool that day is 222
the number of adult that swam in the public pool that day is 259
Step-by-step explanation:
Let x represent the number of children that swam in the public pool that day.
Let y represent the number of adult that swam in the public pool that day.
On a certain hot summer day, 481 people used the public swimming pool. This means that
x + y = 481
The daily prices are 1.25 for children and 2.25 for adults. The receipts for admission totaled to 86.25. This means that
1.25x + 2.25y = 860.25 - - - - - - - -1
Substituting x = 481 - y into equation 1, it becomes
1.25(481 - y) + 2.25y = 860.25
601.25 - 1.25y + 2.25y = 860.25
- 1.25y + 2.25y = 860.25 - 601.25
y = 259
Substituting y = 259 into x = 481 - y, it becomes
x = 481 - 259
x = 222
Answer:
see explanation
Step-by-step explanation:
(a)
x² + 2x + 1 = 2x² - 2 ( subtract x² + 2x + 1 from both sides
0 = x² - 2x - 3 ← in standard form
0 = (x - 3)(x + 1) ← in factored form
Equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
x - 3 = 0 ⇒ x = 3
-----------------------------------
(b)
- 
= 
( multiply through by 15 to clear the fractions )
5(x + 2) - 2 = 3(x - 2) ← distribute parenthesis on both sides
5x + 10 - 2 = 3x - 6
5x + 8 = 3x - 6 ( subtract 3x from both sides )
2x + 8 = - 6 ( subtract 8 from both sides )
2x = - 14 ( divide both sides by 2 )
x = - 7
--------------------------------------------
(c) Assuming lg means log then using the rules of logarithms
log 
⇔ nlogx
log x = log y ⇒ x = y
Given
log(2x + 3) = 2logx
log(2x + 3) = log x² , so
x² = 2x + 3 ( subtract 2x + 3 from both sides )
x² - 2x - 3 = 0
(x - 3)(x + 1) = 0
x = 3 , x = - 1
x > 0 then x = 3
