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3 years ago

Find the value of a2 + b when a = -2 and b = 5

Mathematics

1 answer:

REY [17]3 years ago

4 0

Answer: 9

Step-by-step explanation: In this problem, we're going to evaluate a² + b knowing that a = -2 and b = 5.

So the first thing we want to do is substitute these numbers into our problem.

Since a = -2, we will replace a with a -2 and as we do that, we will put that -2 in parentheses and square it since we have a². Squaring a number just means multiplying a number by itself so (-2)² is equal to 4 since a negative multiplied by a negative gives us a positive.

Now we will replace b with 5 and now we have the following.

4 + 5 simplifies to 9.

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Natalie has $5000 and decides to put her money in the bank in an account that has a 10% interest rate that is compounded continu

kakasveta [241]

Step-by-step explanation:

Natalie has $5000

She decides to put her money in the bank in an account that has a 10% interest rate that is compounded continuously.

Part a) What type of exponential model is Natalie’s situation?

Answer:

As Natalie's situation implies

continuous compounding. So, instead of computing interest on a finite number of time periods, for instance monthly or yearly, continuous compounding computes interest assuming constant compounding over an infinite number of periods.

So, it requires the more generalized version of the principal calculation formula such as:

$P\left(t\right)=P_0\times \left[1+\left(i\:/\:n\right)\right]^{\left(n\:\times \:\:t\right)}$

$P\left(t\right)=P_0\times \left[1+\left(\frac{i}{n}\:\right)\right]^{\left(n\:\times \:\:t\right)}$

Here,

$i$ = interest rate

= number of compounding periods

$t$ = time period in years

Part b) Write the model equation for Natalie’s situation?

For continuous compounding the number of compounding periods, $n$ , becomes infinitely large.

Therefore, the formula as we discussed above would become:

$P\left(t\right)=P_0\times e^{\left(i\:\times \:t\right)}$

Part c) How much money will Natalie have after 2 years?

Using the formula

$P\left(t\right)=P_0\times e^{\left(i\:\times \:t\right)}$

$₂ $=\:6107.02$ $

So, Natalie will have $\:6107.02$ $ after 2 years.

Part d) How much money will Natalie have after 2 years?

Using the formula

$P\left(t\right)=P_0\times e^{\left(i\:\times \:t\right)}$

$₁₀ $=13.597.50$ $

So, Natalie will have $13.597.50$ $ after 10 years.

Keywords: word problem, interest

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5 0

3 years ago

Factor. 10x^5 − 16x^4 + 4x^2

Licemer1 [7]

We have to find the GCD between 10, 16 and 4 and between x^5, x^4 and x^2

GCD (10,16,4) = 2
GCD (x^5,x^4,x^2) = x^2

So we divide all terms for 2x^2

Final result: 2x^2(5x^3-8x^2+2)

4 0

3 years ago

At the Science Museum, there is an exhibition with 150 displays about energy.

tatuchka [14]

1/5

This is a matter of elimination. So let's figure out how many of each display there is. 30% of 150 = 0.30 * 150 = 45 displays about electricity. 2/5 * 150 = 0.40 * 150 = 60 displays about renewable energy 1/10 * 150 = 150/10 = 15 displays about gas. The rest of the displays are about nuclear power. So 150 - 45 - 60 - 15 = 30 displays about nuclear power. Since we want a fraction, we get 30/150 But 30/150 isn't in it's simplest form. The largest number that will evenly divide both 30 and 150 is 30. So divide both the numerator and denominator by 30 (30/30)/(150/30) = 1/5 So 1/5 of the displays are about nuclear power.

8 0

3 years ago

Brainliest and 60 points ;) 8 * 65 * 7 * 321 * 0 * 1=??

puteri [66]

Answer:

The answer is zero. Any number times zero will always be zero.

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Colin and Brian were playing darts. Colin scored 139 Brian scored 53 more than Colin. What was their combined score?

Inga [223]

Answer

Their combined score is 331 points

Explanation

Determine each person's score

Collin score: 139

Brian: 139 + 53 = 192

Add the scores together

139 + 192 = 331

5 0

3 years ago