12/15 is the answer in fraction form
80 % is the answer in percentage form
0.80 is the answer in decimal form
To find the product of (4x-5y)^2,
we can rewrite the problem as:
(4x-5y)(4x-5y) (two times because it is squared)
Now, time to use that old method we learned in middle school:
FOIL. (Firsts, Outers, Inners, and Lasts)
FOIL can help us greatly in this scenario.
Let's start by multiplying the 'Firsts' together:
4x * 4x = <em>16x^2</em>
Now, lets to the 'Outers':
4x * -5y = <em>-20xy</em>
Next, we can multiply the 'Inners':
-5y * 4x = <em>-20xy</em>
Finally, let's do the 'Lasts':
-5y * -5y = <em>25y</em>^2
Now, we can take the products of these equations from FOIL and combine like terms. We have: 16x^2, -20xy, -20xy, and 25y^2.
-20xy and -20xy make -40xy.
The final equation (product of (4x-5y)^2) is:
16x^2 - 40xy + 25y^2
Hope I helped! If any of my math is wrong, please report and let me know!
Have a good one.
74.6786 m² is the answer.
Step-by-step explanation:
<u>Step 1</u> :
we know that the diameter (D) of the cookie = 32 ft
Converting dimensions from feet (ft) to meter (m)
1 ft = 0.3048 m
32 ft = 32 × 0.3048
= 9.7536 m
<u>Step 2</u> :
To find the surface area of the cookie we have the formula,
<u> Area (A) = π . r²</u>
Diameter (D) = 32 ft
∴ d = 2r
d/2 = r (radius)
32 ÷ 2 = r
<u> r = 16</u> 16 feet = 4.8768 m
π . r² = 3.14 × (4.8768)² = 3.14 × 23.783
= 74.6786 m²
<u></u>
Answer:
Step-by-step explanation:
No idea what a gouilleul Sequence is, but hopefully it will help to show how I would find the answer.
A geometric sequence means a term is multiplied by something over and over So say we start with 100 and the common ratio is .5 then the sequence would go 100,50,25,12.5,6.25 and so on. Another way of writing it is:
100*.5^0 = 100
100*5^1 = 50
100*.5^2 = 100*.25 = 25
and so on.
ANyway, here we have the first and fourth term. so that's 3.5*x^0 and 3.5*x^3. Keep in mind the exponent will be n-1 when the term you want to find is the nth term. Anyway, we know 3.5*x^3 = 28, so we just use algebra to find x, which is the common ratio.
3.5*x^3 = 28
x^3 = 8
x = 2
So the common ratio is 2, or in other words it keeps doubling. You could try it real quick, keep doubling the starting term 3.5
3.5, 7, 14, 28 and 28 is the fourth term.
So we know the common ratio. you could just add the four terms listed then for part b, but there is an equation, for in case they ask you to find the sum of say the first 100 terms. that wouldn't be fun. Anyway, the formula is a((1-r^n)/(1-r)) where a is the starting term, r is the common ratio and n is the number term. In your case that's 3.5((1-2^4)/(1-2)) = 52.5. You can actually check since it's only 4 terms. 3.5 + 7 + 14 + 28 = 52.5.
If you want to know how that formula was gotten let em know and I can explain or give a link to a video or something to show.
Answer:
a) 10
b) The $40+5 dollars for every ticket
c) See below
Step-by-step explanation:
a)
1. Let t=number of tickets
2. Writing an equation
Breaking even means that you earn the same amount of money for both.
40 +5t=70+2t
3. Solving the equation
40 +5t=70+2t
5t-2t=70-40
3t=30
t=10
So the answer to a) is 10.
b)
1. Using an equation
We already know that there are 2 equations for this problem. (40+5t, 70+2t)
So, we will substitute 20 for t.
40+5*20=40+100=140
70+2t=70+2*20=110
2. Comparing equations
140>110, so the first offer is better
C)
The owner lets you choose how you get paid because one option will be better for you, as some days you might not sell many tickets (so you will go with the $70+2 tickets), or some days you might sell many tickets (you will choose the $40+5 dollars/ticket).
