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Damm [24]
3 years ago
8

A substance has a half-life of 6 years. If 20 pounds are present initially, how much will remain after 2 years?

Mathematics
1 answer:
Vladimir [108]3 years ago
8 0

Answer:

16.66pound

Step-by-step explanation:

roughly 16.66 pound

if in 6 years it become half which is =10

then 10÷6= 1.67

then 1.67 pound is decayed every year.

in 2 years it decay 1.67×2= 3.34

so , the remaining is 20-3.34=16.66pound

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makkiz [27]
Answer:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
x-(3*x^3+8*x^2+5*x-7)=0
Step by step solution :Step 1 :Equation at the end of step 1 : x-((((3•(x3))+23x2)+5x)-7) = 0 Step 2 :Equation at the end of step 2 : x - (((3x3 + 23x2) + 5x) - 7) = 0 Step 3 :Step 4 :Pulling out like terms :
4.1 Pull out like factors :
-3x3 - 8x2 - 4x + 7 =
-1 • (3x3 + 8x2 + 4x - 7)
Checking for a perfect cube :
4.2 3x3 + 8x2 + 4x - 7 is not a perfect cube
Trying to factor by pulling out :
4.3 Factoring: 3x3 + 8x2 + 4x - 7
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 3x3 - 7
Group 2: 8x2 + 4x
Pull out from each group separately :
Group 1: (3x3 - 7) • (1)
Group 2: (2x + 1) • (4x)

Please 5 star and like. Appreciated
8 0
3 years ago
HELP PLEASE <br><br>must show work ​
matrenka [14]

Answer:

1. 4n^3

2. 4k^7

3. 3

4. -30x

5. -6

Step-by-step explanation:

1. The prime factorization of 12 is 2 x 2 x 3 and the prime factorization of 16 is 2 x 2 x 2 x 2. When you look at these two expressions you can see the common factors of these two numbers are 2 x 2, which is 4. Next, we look at the GCF of the N's which would be n^3 since n^5 has three N's in it. Therefore, we get 4n^3 when we multiply the two together.

2. The factors of 8 are 1, 2, 4, and 8. Out of these, 1, 2, and 4 are the only factors that 20 shares with it and 4 is the greatest. Then, we look at the K's and the GCF of the K's is k^7 since k^8 has seven K's. We multiply the two and we get 4k^7.

3. Since one of the numbers of the three given here does not include the variable n, there will not be any N's in the GCF of the three, so we don't have to worry about that. Now, we just find the GCF of 18, -24, and -21. The factors of 18 are 1, 2, 3, 6, 9, and 18, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24, and lastly, the factors of 21 are 1, 3, 7, and 21. From these, 3 is the biggest common divisor, therefore the GCF is 3.

4. Between the two X's, X^1 is the biggest amount of X's this GCF has, so the final GCF will be some constant multiplies with X. Since we are dealing with bigger numbers on this problem, we should use prime factorization. The prime factorization of 90 is 2 x 3 x 3 x 5, and the prime factorization of 120 is 2 x 2 x 2 x 3 x 5. From these expressions, we take the biggest amount of each common factor as we can. Since these expressions both have 2, we take the smaller amount of 2's which is one two. Then we get one three from both expressions, and one five as well. 2 times 3 times 5 equals 30, therefore, we get -30x, and not 30x, because both of these numbers are negatives.

5. All of these numbers do not have an x, so there won't be an x in our GCF. Another method of quickly finding the GCF of numbers is to look at the smallest number's factors first to see what factors it shares with the other numbers. The factors of 12 are 1, 2, 3, 4, 6, and 12. 42 and 30 do not have the factor 12, so we can go down the list and see if 42 and 30 share the factor 6, which they do since 6 times 7 is 42 and 6 times 5 is 30. Since all of these numbers share the negative sign, the GCF of these three numbers is -6.  

5 0
3 years ago
Please answer this please
cluponka [151]

Step-by-step explanation:

<h3>1. x² + 4 = (x+2)² </h3>

<h3> : x² + 4 = x² + 4 (Yes)</h3>

<h3>2. (2x+6)²= 4(x+3)²</h3>

<h3> : 4x²+36 = 4x² + 36 ( Yes)</h3>

<h3>3. (x-3)(x-3)= (x-9)² (NO)</h3>

<h3>beacause , True statement is</h3><h3> (x+3)(x-3)= (x-9)²</h3>

<h3>4. x²-10x+25 = (x-5)(x+5) (No)</h3>

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4 0
3 years ago
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KonstantinChe [14]

Answer:

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Woof watchers

y = 9 + 5x

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Step-by-step explanation:

Let

Number of hours = x

Total cost = y

Total cost = fixed cost + variable cost

The equations are:

Happy paws

y = 20 + 4x

Woof watchers

y = 9 + 5x

solve the equation to find for how many hours the total cost of the services is equal.

Equate total cost of both services

20 + 4x = 9 + 5x

Collect like terms

20 - 9 = 5x - 4x

11 = x

x = 11 hours

Check:

Happy paws

y = 20 + 4x

= 20 + 4(11)

= 20 + 44

= 64

Woof watchers

y = 9 + 5x

= 9 + 5(11)

= 9 + 55

= 64

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3 years ago
Use inductive and deductive reasoning to solve the problem. Draw a diagram and solve the problem Freddie the frog is a at the bo
Wewaii [24]

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Step-by-step explanation:

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