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.

The first school sends 3 times as many German students as French students, so if they send 21 German students, they must also be sending 21/3 = 7 French students. The first school then sends a total of 21 + 7 = 28 students.

The other 3 schools send the same number of students. There are 4 schools, so the total number of students is 4 × 28 = 112.

Answer:

i guess the answer is 64x^5

Step-by-step explanation:

(4x^2)^3

=64x^5

The domain of a function is the set of input values the function can take

The domain is all set of real numbers

The expression is given as:

[tex]\frac{x^2 - x - 12}{x - 4}[/tex]

Factorize the numerator of the expression

[tex]\frac{(x - 4)(x + 3)}{x - 4}[/tex]

Simplify: Cancel out the common terms

[tex]x + 3[/tex]

The above expression can take any value of x.

Hence, the domain is all set of real numbers

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You use the formula

3000*.09*3=810

She will have to pay back the amount of $3,810.

Simple interest is defined as interest paid on the original principal and calculated with the following formula:

S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100.

We have been given data as:

Principal (P) = $3,000

Rate of Interest (R) = 9% = 9/100 = 0.09

Time (T) = three years

⇒ Simple interest  = P × R × T

Substitute the value of P, R, and T in the above formula,

⇒ Simple interest  = 3,000× 9% × 3

⇒ Simple interest  = 3,000× 9/100 × 3

⇒ Simple interest  = 3,000× 0.09 × 3

Apply the multiplication operation, and we get

⇒ Simple interest  = $810

The total payback amount = $3,000 + $810 = $3,810

Therefore, she will have to pay back the amount of $3,810.

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Answer:

yellow box

Step-by-step explanation:

if you follow the graph. it is a difference of 6 between each 2 points

so you don't have to solve with the formula

6/2 = 3 so 3 is your X

and you get larger as you go towards 0 so it is positive

and so add 6 to 10 because (-2,10) and you follow the 6 y for every 2 you go

so (0,16)

y = 3x + 16

Answer:

75%

Step-by-step explanation:

457.7/610

divide it out

.75

make it a percentage

.75 × 100 = 75%

Hey guys! Person above me is correct, I made a mistke in my calculations!

Answer:

RHS

Step-by-step explanation: the hypotenuse and one side of the triangle is respectively equal to the hypotenuse and one side of the other triangle

so, its rhs

Answer:

b

Step-by-step explanation:

Answer:

11m^3+16m+16

Step-by-step explanation:

First, you have to subtract the m^3, then the m, and the 11 and -5.

Answer:

11m^3-21m^2+20m+16

Step-by-step explanation:

In the carnival the number of games number of rides Wyatt went on is 3 and 6 respectively.

A system of equation is the set of equation in which the finite set of equation is present for which the common solution is sought.

The number of unknown objects can be find using the system of solution.

Given information-

The cost of each game is $1.25.

The cost of each ride is $2.75.

Total amount of money spent by the Wyatt is $20.25.

The number of rides he went on is twice the number of games he played.

Suppose the number of games Wyatt played is x and the number of rides he went in the carnival is y.

As, the number of rides he went on is twice the number of games he played. Thus,

[tex]y=2x[/tex]

Let the above equation as equation one.

As total amount of money spent by the Wyatt is $20.25 and The cost of each game is $1.25 and the cost of each ride is $2.75. Thus,

[tex]1.25x+2.75y=20.25\\[/tex]

Put the value of y in the above equation from the equation one as,

[tex]1.25x+2.75(2x)=20.25\\1.25x+5.5x=20.25\\6.75x=20.25\\x=3[/tex]

Thus the number of games he played is 3.

Put this value of x in the equation one as,

[tex]y=2\times3\\y=6[/tex]

Thus the number rides Wyatt went on is 6.

Hence, In the carnival the number of games number of rides, Wyatt went on is 3 and 6 respectively.

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Answer:

14

Step-by-step explanation:

[tex](3 + 4)2 \\ add \: 3 \: to \: 4 = 7 \\ (7)2 \\ 7 \times 2 \\ 14[/tex]

Answer:

4 hours

Step-by-step explanation:

the cost of movie is $48

means they have $32 left with them

parking charge is $8 (32/8= 4)

means they can spend 4 hours in Emeryville

we know that θ is in the I Quadrant, namely that cosine as well as sine are both positive, well, we know that

[tex]cos(\theta )=\cfrac{\stackrel{adjacent}{2}}{\underset{hypotenuse}{\sqrt{19}}}\qquad\qquad \textit{let's get the \underline{opposite side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{(\sqrt{19})^2-2^2}=b\implies \pm\sqrt{19-4}=b\implies \pm\sqrt{15}=b\implies \stackrel{I~Quadrant}{+\sqrt{15}=b} \\\\[-0.35em] ~\dotfill[/tex]

[tex]tan(\theta)=\cfrac{\stackrel{opposite}{\sqrt{15}}}{\underset{adjacent}{2}}~\hspace{10em} tan(2\theta)=\cfrac{2tan(\theta)}{1-tan^2(\theta)} \\\\[-0.35em] ~\dotfill\\\\ tan(2\theta)=\cfrac{2\cdot \frac{\sqrt{15}}{2}}{1-\left( \frac{\sqrt{15}}{2} \right)^2}\implies tan(2\theta)=\cfrac{\sqrt{15}}{1-\frac{15}{4}}\implies tan(2\theta)=\cfrac{\sqrt{15}}{~~\frac{4-15}{4}~~} \\\\\\ tan(2\theta)=\cfrac{\sqrt{15}}{~~ \frac{-11}{4}~~}\implies tan(2\theta)=-\cfrac{4\sqrt{15}}{11}[/tex]

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{2}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{4}}}\implies \cfrac{-7}{-4}\implies \cfrac{7}{4}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{\cfrac{7}{4}}(x-\stackrel{x_1}{4}) \\\\\\ y-2=\cfrac{7}{4}x-7\implies y=\cfrac{7}{4}x-5[/tex]

Answer:

B: 84%

Step-by-step explanation:

Answer:

24 min

Step-by-step explanation:

14-8 is 6 so you need to shrink it 6 feet until it has a daimiter of 8.

6 divided by .25 is 24 so you have your answer

14-.25x=8

The equation is 14 - 0.25x = 8.

It will take 24 minutes for the balloon to shrink.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Given:

A hot-air balloon has a 14-foot diameter.

Rate of 0.25 feet per minute.

Now, equation to represent the situation is

14 - 0.25x = 8

On further solving

6= 0.25x

x= 6/0.25

x= 24

Hence, it will take 24 minutes for the balloon to shrink.

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Answer: 0 = 0 and/or Infinitely Many Solutions

Step-by-step explanation:

When solving this equation we want to find x then substitute the answer we find for x to see if both sides are equal to the same number.

So once we find x replace x with that number: x = 8

Rewrite equation: [tex]-24+3(8)=16-2(8)[/tex]

So we solve          [tex]-24+24=16-16\\0=0[/tex]      

Since both sides are equal the answer would be Infinitely Many Solutions

Answer:

the answer is graph 1

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

House number:

1. has 3 people

2. has 2 people

3. has 3 people

4. has 2 people

5. has 3 people

6. has 2 people

7. has 3 people

looking at each rule, it all fits.

so now add it all up so its 18

Answer:

[tex]\sqrt[15]{m^2n^4}[/tex]

Step-by-step explanation:

[tex](\sqrt[5]{m^2n^4} )^{\frac{1}{3}}\\\\\implies( (m^2n^4)^{\frac{1}{5}})^{\frac{1}{3}}\\\\\implies (m^2n^4)^{\frac{1}{5}\times \frac{1}{3}}\\\\\implies (m^2n^4)^{\frac{1}{15}}\\\\\implies (m^2)^{\frac{1}{15}} (n^4)^{\frac{1}{15}}\\\\\implies m^{\frac{2}{15}} n^{\frac{4}{15}}[/tex]

[tex]\sqrt[15]{m^2n^4}[/tex]

it's was helpful to you

# be careful#

In a right-angled triangle, the Pythagoras theorem is used to find the hypotenuse. Then the hypotenuse is 32.2 inches.

It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.

Given

A right triangle has legs measuring 16 inches And 28 inches.

We know the Pythagoras theorem

[tex]\rm Hypotenuse ^2 = Base ^2 + Perpendicular^2[/tex]

Then the hypotenuse will be.

[tex]\rm Hypotenuse ^2 = Base ^2 + Perpendicular^2\\\\\rm Hypotenuse ^2 = 16^2 + 28^2\\\\ \rm Hypotenuse ^2 = 256 + 784\\\\\rm Hypotenuse ^2 = 1040\\\\\rm Hypotenuse \ = 32.2[/tex]

Thus, the hypotenuse is 32.2 inches.

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Answer:

i dont know Ecactly but i think mybe its 10 or 15

The equation of the parabola whose focus is at (3, 0) and the directrix is at x = –3 is y=6x²+6x.

y = a(x-h)² + k

where,

(h, k) are the coordinates of the vertex of the parabola in form (x, y);

a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.

As it is given that the focus of the parabola is at F(3,0) and its directrix is the line x=−3, therefore, we can write that

x=-3

x+3=0

Now, Let A(x,y) be any point in the plane of the directrix and focus, and MA be the perpendicular distance from A to the directrix, therefore, A lies on parabola if FA=MA,

[tex]FA=MA\\\\\sqrt{(x-3)^2 +(y-0)^2}=\dfrac{|x+3|}{1}\\\\{(x-3)^2 +(y-0)^2}={(x+3)^2}\\\\-6x^2+y=6x\\\\y=6x^2+6x[/tex]

Hence, the equation of the parabola whose focus is at (3, 0) and the directrix is at x = –3 is y=6x²+6x.

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Answer:

Explained below

Step-by-step explanation:

4(x + 2) = - 4

Let's solve:

4(x + 2) = - 4

4(x) + 4(2) = - 4

4x + 8 = - 4

    - 8     - 8

4x = -12

/4     /4

x = -3

Hope this helps!

Answer:

Step-by-step explanation:

For the given data the height of the tree will be 12.86.

A triangle is a three-sided polygon having three edges and three vertices in terms of geometry. The sum of the inner angles of the triangle is 180°.

Given that, Andrés is 1.65 meters tall, this is obvious. He determines the length of a tree's shadow at 2 p.m. to be 40.15 meters. The tip of his shadow touches the tip of the tree's shadow while he stands 35 meters away from the tree.

Since the triangle ABC and ADF are similar, their ratio will be the same.

Suppose the height of the tree to the nearest hundredth of a meter will be x.

5.15/40.15=1.65/x

5.15x=1.65× 40.15

5.15x=66.2475

x=66.24/5.15

x=12.86

Thus, the height of the tree will be 12.86.

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The inflow rate of water is given by the function of the volume of the

tank derived from the shape of the tank.

Response:

The given parameter are;

Shape of the tank = Conical

Rate at which water is leaking out of the tank = 7,000 cm³/min

Height of the tank = 6 m

Diameter of the tank = 4 m

Solution:

We have;

[tex]\dfrac{D}{h} = \mathbf{\dfrac{2 \cdot r}{h}}[/tex]

[tex]r = \mathbf{\dfrac{D}{2 \cdot h}}[/tex]

Which gives;

[tex]r= \mathbf{\dfrac{h}{3}}[/tex]

[tex]V = \dfrac{1}{3} \cdot \pi \cdot r^2 \cdot h = \dfrac{1}{3} \cdot \pi \cdot \left(\dfrac{h}{3} \right)^2 \cdot h = \mathbf{ \pi \cdot \dfrac{h}{27} ^3}[/tex]

Which gives;

[tex]\dfrac{dV}{dh} = \mathbf{\pi \cdot \dfrac{h}{9} ^2}[/tex]

By using chain rule of differentiation, we have;

[tex]\dfrac{dV}{dt} = \mathbf{\dfrac{dV}{dh} \times \dfrac{dh}{dt}}[/tex]

Which gives;

[tex]\dfrac{dV}{dt} = \mathbf{\pi \cdot \dfrac{h}{9} ^2\times 20}[/tex]

[tex]\dfrac{dV}{dt} = \pi \cdot \dfrac{200}{9} ^2\times 20 \approx 279,252.68[/tex]

[tex]\dfrac{dV}{dt} = \mathbf{Inflow \ rate - Outflow \ rate}[/tex]

Therefore;

[tex]Inflow \ rate = \mathbf{\dfrac{dV}{dt} + Outflow \ rate}[/tex]

Which gives;

Inflow rate ≈ 279,252.68 + 7000 = 286,252.68 ≈ 286,253

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