To solve a system of inequalities, you just need to graph each inequality and see which points are in the overlap of the graphs

Max has $2000: $1000 decreased in value exponentially at a rate of 0.5% annually

Sergio039 [100]

Answer:

$2147.36

Step-by-step explanation:

The first value can be modeled by ...

b1 = 1000·(1 -0.005)^t

After 10 years, that balance is ...

b1 = 1000·0.995^10 = 951.11

__

The second value can be modeled by ...

b2 = 1000·(1 +0.018/2)^(2t)

After 10 years, that balance is ...

b2 = 1000·1.009^20 = 1196.25

__

The total of the two investments after 10 years is ...

$951.11 +1196.25 = $2147.36

6 0

3 years ago

John, Sally, and Natalie would all like to save some money. John decides that it would be best to save money in a jar in his clo

Radda [10]

Answer:

Part 1) John’s situation is modeled by a linear equation (see the explanation)

Part 2) $y=100x+300$

Part 3) $\$12,300$

Part 4) Is a exponential growth function

Part 5) $A=6,000(1.07)^{t}$

Part 6) $\$11,802.91$

Part 7) Is a exponential growth function

Part 8) $A=5,000(e)^{0.10t}$ or $A=5,000(1.1052)^{t}$

Part 9) $\$13,591.41$

Part 10) Natalie has the most money after 10 years

Step-by-step explanation:

Part 1) What type of equation models John’s situation?

Let

y ----> the total money saved in a jar

x ---> the time in months

The linear equation in slope intercept form

$y=mx+b$

The slope is equal to

$m=\$100\ per\ month$

The y-intercept or initial value is

$b=\$300$

so

$y=100x+300$

therefore

John’s situation is modeled by a linear equation

Part 2) Write the model equation for John’s situation

$y=100x+300$

see part 1)

Part 3) How much money will John have after 10 years?

Remember that

1 year is equal to 12 months

so

10 years=10(12)=120 months

For x=120 months

substitute in the linear equation

$y=100(120)+300=\$12,300$

Part 4) What type of exponential model is Sally’s situation?

we know that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$P=\$6,000\\ r=7\%=0.07\\n=1$

substitute in the formula above

$A=6,000(1+\frac{0.07}{1})^{1*t}$

$A=6,000(1.07)^{t}$

therefore

Is a exponential growth function

Part 5) Write the model equation for Sally’s situation

$A=6,000(1.07)^{t}$

see the Part 4)

Part 6) How much money will Sally have after 10 years?

For t=10 years

substitute the value of t in the exponential growth function

$A=6,000(1.07)^{10}=\$11,802.91$

Part 7) What type of exponential model is Natalie’s situation?

we know that

The formula to calculate continuously compounded interest is equal to

$A=P(e)^{rt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

$P=\$5,000\\r=10\%=0.10$

substitute in the formula above

$A=5,000(e)^{0.10t}$

Applying property of exponents

$A=5,000(1.1052)^{t}$

therefore

Is a exponential growth function

Part 8) Write the model equation for Natalie’s situation

$A=5,000(e)^{0.10t}$ or $A=5,000(1.1052)^{t}$

see Part 7)

Part 9) How much money will Natalie have after 10 years?

For t=10 years

substitute

$A=5,000(e)^{0.10*10}=\$13,591.41$

Part 10) Who will have the most money after 10 years?

Compare the final investment after 10 years of John, Sally, and Natalie

Natalie has the most money after 10 years

4 0

4 years ago

Read 2 more answers

Dora bought a bottle of nail polish that was marked down by 20 percent from its original price of $4.50. Including a 9 percent s

igomit [66]

Answer:

3.92$

Step-by-step explanation:

The first step is to deduct 20% of 4.50 from 4.50.

20% of 4.50 is 0.2 x 4.50 = .90

4.50 - 0.90 = 3.60

That's the new price without the sales tax.

Now we need to add 9% of 3.60 to 3.60 to get the final cost.

9% of 3.60 is .09 x 3.60 = 0.32

3.60 + .32 = $3.92

Hope it helps.. If yes mark me BRAINLIEST

Tysm!

8 0

3 years ago

Read 2 more answers

Find the value of x

Alexxandr [17]

Answer:

Step-by-step explanation:

This is an Isosceles triangle, two of the angles are equal

A triangle has how many degrees in it? 180°

A two angles that form a line also has 180°

Think of two right angles 90° + 90° = 180° (I wish i could draw on this)

|

90°|90°_

angle SRT = angle STR = 20°

angle STR + angle STU = 180°

20° + angle STU = 180° subtract 20° from both sides

angle STU = 160°

angle STU = 4x subs in 160°

160° = 4x divideboth sides by 4

40° = x <---------------- FINAL ANSWER D

8 0

3 years ago

Divide (16x6 − 12x4 + 4x2) by 4x2.

Degger [83]

We know that
(16x6 − 12x4 + 4x2) / 4x2
is equal to
[16x6/4x2]+[-12x4/4x2]+[4x2/4x2]
=[4x4]+[-3x2]+[1]
=4x4-3x2+1

the answer is
4x4-3x2+1

6 0

4 years ago