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Rus_ich [418]
3 years ago
7

A wire is first bent into the shape of a triangle. Each side of the triangle is 12 cm long. Then the wire is unbent and reshaped

into a square. What is the length of
a side of the square?
Mathematics
2 answers:
Alinara [238K]3 years ago
6 0
Answer: The lengths of the square side lengths is 9 cm.

Explanation:
storchak [24]3 years ago
3 0
Multiply the 12 by three and get 36. Then divide that by four and get 9
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You have 2000 grams of substance A which has decay constant 0.03, and you have 3000 grams of substance B, which has decay consta
joja [24]

Answer:

If you have a quantity X of a substance, with a decay constant r, then the equation that tells you the amount of substance that you have, at a time t, is:

C(t) = X*e^(-r*t)

Now, we know that:

We have 2000g of substance A, and it has a decay constant of 0.03 (i assume that is in 1/year because the question asks in years)

And we have 3000 grams of substance B, with a decay constant of 0.05.

Then the equations for both of them will be:

Ca = 2000g*e^(-0.03*t)

Cb = 3000g*e^(-0.05*t)

Where t is in years.

We want to find the value of t such that Ca = Cb.

So we need to solve:

2000g*e^(-0.03*t) = 3000g*e^(-0.05*t)

e^(-0.03*t) = (3/2)e^(-0.05*t)

e^(-0.03*t)/e^(-0.05*t) = 3/2

e^(t*(0.05 - 0.03))  = 3/2

e^(t*0.02) = 3/2

Now we can apply Ln(x) to both sides, and get:

Ln(e^(t*0.02)) = Ln(3/2)

t*0.02 = Ln(3/2)

t = Ln(3/2)/0.02 = 20.3

Then after 20.3 years, both substances will have the same mass.

6 0
3 years ago
What is the measure of an exterior angle in a regular polygon with 15 sides?
vlabodo [156]
First, find the measure of an interior angle:
the sum of the interior angles of a polygon is (n-2)*180, n is the number of sides
for a 15-sided polygon, the sum is 13*180
each interior angle is then 13*180/15=156
the measure of each exterior angle=180-156=24
4 0
3 years ago
Read 2 more answers
The expression √93 is in between two whole numbers. Write the two numbers with a comma and a space in between
nalin [4]

Answer:

9, 10

Step-by-step explanation:

square root of √93 is 9.64.

Thus, we see that the number 9.64 is greater than  but less than 10.

On number line it can be represented as

-∞ _____________7___8___9__9.64___10___11_______+∞

Thus, we see that  the two whole numbers between which √93 lies is 9, 10

5 0
2 years ago
Solve the equation using the distributive property and properties of equality. -5(a+3)=-55 What is the value of a? A.)-14 B.) -8
Colt1911 [192]

Answer:

C) 8

Step-by-step explanation:

-5(a+3)=-55

a+3=-55/-5

a+3=11

a=11-3

a=8

4 0
3 years ago
Write the quadratic equation whose roots are 3 and -1, and whose leading coefficient is 5.
Assoli18 [71]

Answer:

5x² - 10x - 15 = 0

Step-by-step explanation:

Given that the roots are x = 3 and x = - 1, then the factors are

(x - 3) and (x + 1) and the quadratic is the product of the factors, that is

f(x) = a(x - 3)(x + 1) ← a is a multiplier

Here a = 5, thus

f(x) = 5(x - 3)(x + 1) ← expand factors using FOIL

     = 5(x² - 2x - 3) ← distribute parenthesis by 5

     = 5x² - 10x - 15

Thus equation is

5x² - 10x - 15 = 0

6 0
3 years ago
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