14÷976= /32÷1857 show your work please help
1 answer:
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Answer:
or
Step-by-step explanation:
We use casework on when and when
.
For the first case, , we add 9 to both sides to get
.
Dividing both sides by 3 gives
For the second case, , we add 9 to both sides to get
.
Dividing both sides by 3 gives
.
Checking both cases, we plug in and
.
For the first case, we have , which satisfies the equation.
For the second case, we have , which also satisfies the equation.
This gives us two solutions to the equation; and
.
Answers & Step-by-step explanation:
<h2>PEMDAS (Parenthesis, exponents, multiplication, division, addition, subtraction)</h2>Now let's solve your problems!
<h2>___________________________________________________</h2><h2>16.</h2>First, we see if there are any parentheses. Since there are no parentheses, we will evaluate the exponent 3² first.
After this, our problem now looks like this:
<h2>Next, since multiplication (not subtraction) is next on the list, we will evaluate 6 × 3, which equals 18.
After that, we will subtract:
41 - 9 = 32
18 - 26 = -8
We now have 32/-8 or 4/-1 or simply -4.
<h2>The answer is: -4</h2><h2>___________________________________________________</h2><h2>17.</h2>With this, one, note the parentheses. This means that we will do these operations first.
(21 - 4²) = 5
(3 + 1) = 4
The problem now looks like this:
Next, we do the exponents:
8² = 64
After that, we do the multiplication of 5 x 4, which equals 20.
We now have 20/64 - 44, which simplifies to 20/20 or 1/1 or 1.
<h2>The answer is: 1</h2><h2>___________________________________________________</h2><h2>18.</h2>Again, we see parentheses, so that means we need to do these operations first.
(6² - 20) = 16
We now have:
48 ÷ 16 + 5
48/16 = 3 and 3 + 5 = 8
<h2>The answer is: 8</h2><h2>___________________________________________________</h2><h2>19.</h2>Here, we see an exponent 3³, so we'll need to evaluate this first.
3³ = 27
We now have:
4 × 27 ÷ 18 + 14
4 × 27 = 108
108/18 = 6
And finally:
6 + 14 = 20
<h2>The answer is: 20</h2><h2>___________________________________________________</h2><h2>20.</h2>Here we again see the parentheses, which means we need to evaluate the subtraction first.
3 - 8 = -5
We now have:
11 + 2 (-5)
2 × -5 = -10
11 + -10 (same as 11 - 10) = 1
<h2>The answer is: 1</h2><h2>___________________________________________________</h2><h2><em>I AM ALWAYS HAPPY TO HELP :)</em></h2>Answer:
The compounded annually account will earn more interest over 10 years
Step-by-step explanation:
The rule of the simple interest is I = Prt, where
- P is the original value
- r is the rate in decimal
- t is the time
The rule of the compounded interest is A = P, where
- A is the new value
- P is the original value
- r is the rate in decimal
- n is the number of periods
- t is the time
The interest I = A - P
∵ Each account start with $200
∴ P = 200
∵ They have an interest rate of 5%
∴ r = 5% = 5 ÷ 100 = 0.05
∵ One account earns simple interest and the other is compounded
annually
∴ n = 1 ⇒ compounded annually
∵ The time is 10 years
∴ t = 10
→ Substitute these values in the two rules above
∵ I = 200(0.05)(10)
∴ I = 100
∴ The simple interest = $100
∵ I = A - P
∵ A = 200
∴ A = 325.7789254
∵ I = 325.7789254 - 200
∴ I = 125.7789254
∴ The compounded interest = $125.7789254
∵ The simple interest is $100
∵ The compounded interest is $125.7789254
∵ $125.7789254 > $100
∴ The compounded annually account will earn more interest
over 10 years