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3 years ago

2. The two equal sides of an isosceles triangle each have a length of 4x + y - 5. The perimeter of the triangle is

Mathematics

1 answer:

Sever21 [200]3 years ago

5 0

9514 1404 393

Answer:

2x +2y -8

Step-by-step explanation:

If the equal sides are 'a' and the third side is 'b', then the perimeter is ...

P = a +a +b = 2a +b

The length of the third side is then ...

b = P -2a . . . . . . subtract 2a from both sides

Substituting the given expressions, we find ...

b = (10x +4y -18) -2(4x +y -5)

b = 10x +4y -18 -8x -2y +10

b = 2x +2y -8 . . . . the length of the third side

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3 years ago

5,000 lb equals how many tons

matrenka [14]

5000 pounds is equal to 2.5 tons because 1 ton is equal to 2000 pounds

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3 years ago

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iris [78.8K]

Answer:

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Step-by-step explanation:

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2 years ago

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A large tank is filled to capacity with 300 gallons of pure water. brine containing 5 pounds of salt per gallon is pumped into t

Licemer1 [7]

If $A(t)$ is the amount of salt in the tank at time $t$ , then the rate at which this amount changes over time is given by the ODE

$A'(t)=\dfrac{3\text{ gal}}{1\text{ min}}\cdot\dfrac{5\text{ lb}}{1\text{ gal}}-\dfrac{3\text{ gal}}{1\text{ min}}\cdot\dfrac{A(t)\text{ lb}}{300+(3-3)t\text{ gal}}$

$A'(t)+\dfrac1{100}A(t)=15$

We're told that the tank initially starts with no salt in the water, so $A(0)=0$ .

Multiply both sides by an integrating factor, $e^{t/100}$ :

$e^{t/100}A'(t)+\dfrac1{100}e^{t/100}A(t)=15e^{t/100}$
$\left(e^{t/100}A(t)\right)'=15e^{t/100}$
$e^{t/100}A(t)=1500e^{t/100}+C$
$A(t)=1500+Ce^{-t/100}$

Since $A(0)=0$ , we have

$0=1500+C\implies C=-1500$

so that the amount of salt in the tank over time is given by

$A(t)=1500(1-e^{-t/100})$

After 10 minutes, the amount of salt in the tank is

$A(10)=1500(1-e^{-1/10})\approx142.74\text{ lb}$

8 0

3 years ago

If 16 horses eat 5 stacks of hay in 35 days, how many horses can eat 4 stacks of hay in 8 days? Math question

Aleksandr [31]

Answer:

The number of horses that can eat 4 stacks of hay in 8 days = 56 horses

Step-by-step explanation:

The given parameters are;

The time it takes 16 horses to eat 5 stacks = 35 days

Therefore;

The time it takes 16 horses to eat 5/5 stacks (1 stack) = 35 days/5 = 7 days

The time it takes 16 horses to eat 1 stack of hay = 7 days

The time it takes 16 horses/16 to eat 1 stack of hay = 7 days × 16 = 112 days

Therefore;

The time it takes 1 horse to eat 1 stack of hay = 112 days

The time it takes 1 horse to eat 4 × 1 stack of hay = 112 days × 4 = 448 days

The time it takes 1 horse to eat 4 stacks of hay = 448 days

Therefore, given that (448 days)/(8 days/horse) = 56 horse, we have;

The number of horses that will eat 4 stacks of hay in 8 days = 56 horses.

7 0

2 years ago