Creating an Exponential Model
In this activity, you will formulate and solve an exponential equation that models a real-world situation.
Emma doesn't have experience using credit cards. In fact, she just got her first one. She is also about to start her first year
of college. She uses her new credit card to purchase textbooks for her classes. The total comes to $300. These are the
terms of her credit card:
• It has a 15% annual interest rate.
• The interest is compounded monthly
• The card has $0 minimum payments for the first four years it is active.
The expression that models this situation is P(1 + r/n)^nt, where (1 + r/n) represents the growth factor of the interest rate.

Answer:

Step-by-step explanation:

A: -1/3x+1

B: 1/4x -2

Answer:

Given Below.

question (a)

coordinates:

(0,1), (3,0)

slope:

[tex]\frac{0-1}{3-0}[/tex]

[tex]-\frac{1}{3}[/tex]

equation:

[tex]y - y1 = m(x - x1)[/tex]

[tex]y - 1 = -\frac{1}{3} (x-0)[/tex]

[tex]y = -\frac{1}{3}x+1[/tex]

question (b)

coordinates:

(0,-2) , (4, -1 )

slope:

[tex]\frac{-1--2}{4-0}[/tex]

[tex]\frac{1}{4}[/tex]

equation:

[tex]y - y1 = m(x - x1)[/tex]

[tex]y + 1 = \frac{1}{4} (x - 4)[/tex]

[tex]y=\frac{1}{4} x -1-1[/tex]

[tex]y=\frac{1}{4} x -2[/tex]

Answer:

Domain: All real numbers
Range: f(x) ≥ - 10

Step-by-step explanation:

I had the same test. Completed it and got it right.
Sorry for the lack of explanation, I can't put it into words at the moment.

Answer:

D of course:

Step-by-step explanation:

Think about it,

50.54 is 50 estimated to the roundest digit, and 20.10 is 20 estimated. So we'll just do 50-20 which is 30

I hope this answers your concern :) Mark me brainliest if you want to (:

Answer:

-30

Step-by-step explanation:

50.54 - 20.10 = 30.44

Answer:

A) 9. B) 16

Step-by-step explanation:

Range is

12, 14, 15, 16, 17, 17, 21

so 21-12= 9

add all them up 12+14+15+16+17+17+21 = 112/7 = 16

Answer:

d

Step-by-step explanation:

d

Answer:

Step-by-step explanation:

The ordinates of the  linear system  is mathematically given as

C=(4,-6)

Question Parameters:

The equations

x - 4y = 28

2x + y = 2

Generally the equation for the linear system is mathematically given as

x - 4y = 28

2x + y = 2

Resolving the equations

x=4 and y=-6

Therefore

co ordinates are

C=(4,-6)

For more information on Graph

https://brainly.com/question/14375099

Answer:

1. 5

2. 3 adult tickets; 2 child tickets

3. See below

Step-by-step explanation:

1.

2 adult tickets cost 2 × $12 = $24

Subtract $24 from $64:

$64 - $24 = $40

Divide $40 by $8:

$40 ÷ $8 = 5

Answer: 5 child tickets

2.

x = number of adult tickets

y = number of child tickets

The total number of tickets is 5, so the first equation is:

x + y = 5

The cost of x adult tickets is 12x. The cost of y child tickets is 8y. The total cost is 12x + 8y. We are told the total cost is $52. The second equation is:

12x + 8y = 52

The system of equation is:

x + y = 5

12x + 8y = 52

Let's solve it by substitution.

Solve the first equation for x.

x = 5 - y

Now we substitute x in the second equation by 5 - y.

12(5 - y) + 8y = 52

Distribute:

60 - 12y + 8y = 52

Combine like terms on the left side:

-4y + 60 = 52

Subtract 60 from both sides:

-4y = -8

Divide both sides by 4.

y = 2

Substitute y = 2 in the first original equation and solve for x.

x + y = 5

x + 2 = 5

x = 3

Answer: 3 adult tickets; 2 child tickets

3.

The customer's claim is incorrect. His sum is $71. 71 is an odd number. Since all ticket prices are even numbers, it is impossible to add only even numbers and get an odd sum. A sum of several amounts of 12 and several amounts of 8 can never equal 71.

We can also show his claim is false using a system of equations.

x + y = 7

12x + 8y = 71

Use substitution.

x = 7 - y

12(7 - y) + 8y = 71

84 - 12y + 8y = 71

84 - 4y = 71

-4y = -13

y = 3.25

This means 3.25 child tickets. The problem states that tickets can be purchased only in whole numbers, so 3.25 tickets cannot be purchased, so the customer's claim is false.

Answer:

can be written as  without exponent.

Given:

To find:

Write the given expression without exponent.

Solution:

Formula to be used:

Step 1:

Write the expanded form of given expression.

Step 2:

simplify

or

125×y×y×y without exponent.

Answer:

5 × y × y × y

Step-by-step explanation:

5y³ ( only y is being cubed with 5 a multiplier ) , so

= 5 × y × y × y

Answer:

1: x = 19 y = 16 ; 2. x = 5 y = -4

Step-by-step explanation:

To check your work plug the numbers back into one of the equations and see if it's true.

For example:
10(19)-9(16)=46

46=46

1. I distributed 3 to all the numbers so that 9y and -9y would cancel then you add like terms.

2. I distributed -4 to all the numbers so that 4x and -4x would cancel. Then add all like terms.

Once you get x or y plug it back into one problem to get the other variable.

Hope this helps!

#1

(2)×3

[tex]\\ \tt\hookrightarrow -6x+9y=30[/tex]--(3)

Subtracting eq(1) from (3)

[tex]\\ \tt\hookrightarrow -16x=-16[/tex]

[tex]\\ \tt\hookrightarrow x=1[/tex]

Put in eq(2)

[tex]\\ \tt\hookrightarrow -2+3y=10[/tex]

[tex]\\ \tt\hookrightarrow y=4[/tex]

#2

(2) ×4

[tex]\\ \tt\hookrightarrow 4x-8y=52--(3[/tex]

Subtracting eq(1) from (3)

[tex]\\ \tt\hookrightarrow -11y=44[/tex]

[tex]\\ \tt\hookrightarrow y=-4[/tex]

Put in eq(2)

[tex]\\ \tt\hookrightarrow x+8=13[/tex]

[tex]\\ \tt\hookrightarrow x=5[/tex]

Answer:

each of the four blocks weighs 12 ounces

Step-by-step explanation:

3 lbs = 3(16) or 48 ounces

48/4 = 12

each of the four blocks weighs 12 ounces

Step-by-step explanation:

-21=0.6k

divide both side by0.6=

-21\0.6=35

Hi!

I can help you with joy!

The first step in solving this equation is dividing both sides by -0.6:

-21:(-0.6)=-0.6k:(-0.6k)

35=k

k=35 (Answer)

_______________

Additional comment

* Whatever we do to one side, we do to the other.

** A negative number divided by a negative number is a positive.

______________

Hope it helps! Enjoy your day!

Ask me if you have any questions.

~Misty~

(x - 7)(x + 12)

Answer:

[tex] {x}^{2} + 5x - 84 \\ {x}^{2} + 12x - 7x - 84 \\ x(x + 12) - 7(x + 12) \\ (x - 7)(x + 12)[/tex]

Answer: Option 2

The line starts at an x of -4, so the domain is from -4 to infinity since the arrow goes off the graph, meaning it keeps going. The line starts on a y of 2, and the line continues up with the arrow pointing slightly up, so the range is from 2 to infinity.

The domain is from left to right, and the range is down to up

Answer:

2.  {x | x ≥ −4}; {y | y ≥ 2}

Step-by-step explanation:

Let's try to determine the domain first. Look at the x values. The function begins at -4, so our possible domain values also begin at -4, and the values continue positively after -4.

Therefore, our domain is: Domain: {x ≥ -4}.

Or, we could assign our domain using interval notation: [-4,infinity).

Our range, or y values, begin at 2 and continue positively after 2.

Therefore, our range is: Range: {y ≥ 2}.

Again, we could use interval notation to assign our range: [2,infinity)

Therefore, the answer would be

2. {x | x ≥ −4}; {y | y ≥ 2}

Look at the picture to help you better understand

Answer:

the other person is wrong

Step-by-step explanation:

I looked it up and its HEXAHEDRON

Tetrahedron is a pyramid

Answer:

The answer is B.

w + m > 224.

11w + 15m ≤ 2,876

Step-by-step explanation:

w + m > 224. There were more than (>) 224 who donated.

11w + 15m ≤ 2,876 No more than (≤) $2,876 was donated.

Hope that helps!

Answer:

You would expect to win the game 16 times.

Step-by-step explanation:

I set up a proportion for this :

2/7 = x/56

2(56) = 7x (cross multiply)

112 = 7x (multiply 2 and 56)

x = 16 (divide 7 from both sides)

:)

Answer:

(8.2 x 10^9) x (4.5 x 10^-5) = (8.2 x 4.5) x 10 ^(9 - 5) = 36.9 x 10^4 = 3.69 x 10^5

Step-by-step explanation:

Answer:

Let the denominator be x

x-18/x=2/5

5(x-18)=2x

5x-90=2x

3x=90

x=30

The fraction is 12/30

Hope it helps you!

Step-by-step explanation:

Function defines relationship between variables. The value of the f[g(x)] when the value of f(x)=6x+11 and g(x)=x²+6 is f[g(x)]= 36x²+47.

A function assigns the value of each element of one set to the other specific element of another set.

Given to us

f(x) = 6x + 11

g(x) = x² +  6

As we know the two functions, given to us f(x) = 6x + 11, therefore substitute the value of x as g(x) in order to find the value of f[g(x)] ,

[tex]f(x) = 6x + 11\\\\f[g(x)] = 6(x^2 + 6) + 11\\\\f[g(x)] = 6x^2 + 36 + 11\\\\f[g(x)] = 6x^2 + 47[/tex]

Hence, the value of the f[g(x)] when the value of f(x)=6x+11 and

g(x)=x²+6 is f[g(x)]= 36x²+47.

Learn more about Function:

https://brainly.com/question/5245372

Answer:

y = -3x + 5

Step-by-step explanation:

Step-by-step explanation:

Let use have a interger,n

Thus three consectice intergers can be represented by

[tex]n[/tex]

[tex]n + 1[/tex]

[tex]n + 2[/tex]

Multiply, and we get

[tex]n(n + 1)(n + 2)[/tex]

[tex]n( {n}^{2} + 3n + 2)[/tex]

[tex]n {}^{3} + 3 {n}^{2} + 2n[/tex]

Then add the middle number, n+1.

[tex] {n}^{3} + 3n {}^{2} + 3n + 1[/tex]

We must prove that the middle number cubed = the equation.

Using the binomial theroem,

[tex](n + 1) {}^{3} = {n}^{3} + 3( {n}^{2} 1 {}^{1} ) + 3n( {1}^{2} ) + 1 {}^{3} [/tex]

[tex](n + 1 ){}^{3} = {n}^{3} + 3 {n}^{2} + 3n + 1[/tex]

So this is indeed true.

You can do the subsitue variables for n to prove it.

Answer:

22,100 for range

Step-by-step explanation:

To find range you subtract the lowest number from the highest number

Answer:

All the provided answers are incorrect

Step-by-step explanation:

Cross multiply and get

4(x + 5) = (-3)*11

4x + 20 = -33

4x = -33 - 20 = -53

x = -53/4 = -13 1/4

It’s -13 1/4

Step-by-step explanation:

Answer:

.22 chance next customer pays with credit card

Step-by-step explanation:

This is because there was in all 139 customers during that week, and 30/ 139 0.21582733812. This rounded to hundredth would be .22

Answer:

4π/7 radians is 102.86°

Step-by-step explanation:

changing radian to degrees: 1 radian → [tex]\frac{180}{\pi }[/tex]

changing radians to degrees:

[tex]\dfrac{4\pi }{7} *\frac{180}{\pi }[/tex]

[tex]\dfrac{4*180}{7}[/tex]

[tex]\dboxed{102.86}[/tex]

[tex]\\ \rm\longmapsto \dfrac{4\pi}{7}\times \dfrac{180)(\pi}[/tex]

[tex]\\ \rm\longmapsto \dfrac{180(4)}{7}[/tex]

[tex]\\ \rm\longmapsto 720/7[/tex]

[tex]\\ \rm\longmapsto 102.8°[/tex]

Answer:

there are 2 swans to 1 monkey

Step-by-step explanation: