The equation for the area of a triangle is A= b*h /2. So, plug in your known variables, and you get 270in^2= b*30 /2. First you multiply by 2 to cancel out the division for 2, which gets you 540= b* 30. To get "b" by itself, divide both sides by 30, giving you <u>18=b</u>.
To check this, plug in your new known variable, as 270= 18* 30 /2. This will equal as 270=270, confirming 18in as the correct measurement.
4, 7 and 9 are mutually coprime, so you can use the Chinese remainder theorem.
Start with
Taken mod 4, the last two terms vanish and we're left with
We have 
, so we can multiply the first term by 3 to guarantee that we end up with 1 mod 4.
Taken mod 7, the first and last terms vanish and we're left with
which is what we want, so no adjustments needed here.
Taken mod 9, the first two terms vanish and we're left with
so we don't need to make any adjustments here, and we end up with 
.
By the Chinese remainder theorem, we find that any 
such that
is a solution to this system, i.e. 
for any integer 
, the smallest and positive of which is 149.
Answer:
x= -3
Step-by-step explanation:
Distribute 4(2-4x) which leaves you with 8-16x-3x=65
combine the like terms which leaves you with 8-19x=65
subtract 8 from both sides 8-19x-8=65-8 which leaves you with -19x=57
lastly divide -19 from both sides which leaves you with x= -3
1. The formula for calculate the perimeter of a rectangle, is:
P=2L+2W
P is the perimeter of the rectangle (P=320 feet).
L is the lenght of the rectangle.
W is the width of the rectangle.
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2. The problem says that the length of the rectangle is three times the width, so you have:
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L=3W
3. When you substitute L=3W and P=320, into P=2L+2W, you obtain:
P=2L+2W
320=2(3W)+2W
320=6W+2W
8W=320
W=320/8
W=40 feet
4. The barn forms one end of the rectangle. Therefore the linear feet of fence (x) is:
x=P-W
x=320 feet-40 feet
x=280 feet
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How many linear feet of fence must he buy?
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The answer is: 280 feet
Answer:
Step-by-step explanation:
n 1
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f( – 2)
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How do we work this? I cannot figure out the path to solve. Th 4x2 + 3x + 1, evaluate f( - 2)
f( – 2)
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How do we work this? I cannot figure out the path to solve. Th
