Elle’s family decided to save money for her to attend college after she graduates from high school. On the day she was born, Elle's grandparents made a deposit of $1,000 into a special savings account for her education. Elle's parents deposited $29 each month, beginning the day she was born, into the same special savings account.

Brandon’s family decided to save money for him to attend college after he graduates from high school Brandon’s parents decided to deposited $49 each month, beginning the day he was born, into the same special savings account.



A. Give the linear equation that represents Elle's savings account and the linear equation that represents Brandon's savings account.



B. Determine the point of intersection that simultaneously satisfies both linear equations



C. Describe the meaning of the point of intersection in the context of the situation

Can I have help on this please

Answer:

Step-by-step explanation:

Answer:

(29v)−(−13v+59)

29v + 13v - 59

42v -59

Answer:

42v-59

Step-by-step explanation:

(29v)+13v-59     In this step we first simplify

42v-59              Add like numbers (v)

Answer:

g(2) =7

Step-by-step explanation:

g (x)= 3/2x+4

Let x = 2

g (2)= 3/2 *2+4

      = 3 +4

      = 7

Answer: 3/8

Step-by-step explanation:

Put 2 as the x into the equation.

3/2(2)+4

Multiply 2•2

3/4+4

Add 4+4

3/8

Answer cannot be further simplified.

Answer:

20 seconds

Step-by-step explanation:

I assume you mean \(h(t)=8\cos(\frac{\pi}{10}t)\) for your function.

As the given function is in the form of \(f(t)=a\cos(bt+c)+d\) (some textbooks may write this formula differently), the period is equal to \(\frac{2\pi}{|b|}\). Hence, the period of the given function is \(\frac{2\pi}{|\frac{\pi}{10}|}=\frac{2\pi}{1}*\frac{10}{\pi}=\frac{20\pi}{\pi}=20\), or 20 seconds.

The period of the function that relates the sea level as the function of time is given by: Option D: 20 seconds.

Suppose that we've got: \(f(x) = a\cos\left(\dfrac{2\pi x}{b}\right)\)

Then, this function has:

For this case, we're given that:

\(h = 8\cos\left(\dfrac{\pi x}{10}\right)\)

We can rewrite it as:

\(h = 8\cos\left(\dfrac{2\pi x}{20}\right)\)

Thus, we get a = amplitude = 8 units(distance), and b = period = 20 units(time in seconds).

Thus, the period of the function that relates the sea level as the function of time is given by: Option D: 20 seconds.

Learn more about amplitude and period of a cosine function here:

https://brainly.com/question/4104379

The inequality relating −2\(e^{(-n/n^2)}\) to 121/\(n^2\) for n ≥ 1 is -2\(e^{(-n/n^2)}\) ≤ 121/\(n^2\).

To derive the inequality, we start by comparing the expressions −2\(e^{(-n/n^2)}\)  and 121/\(n^2\).

Since we want to express the numbers in exact form, we keep them as they are.

The inequality states that −2\(e^{(-n/n^2)}\)  is less than or equal to 121/\(n^2\).

This means that the left-hand side is either less than or equal to the right-hand side.

The exponential function e^x is always positive, so −2\(e^{(-n/n^2)}\)  is negative or zero.

On the other hand, 121/\(n^2\) is positive for n ≥ 1.

Therefore, the inequality −2\(e^{(-n/n^2)}\)  ≤ 121/\(n^2\) holds true for n ≥ 1.

The negative or zero value of −2\(e^{(-n/n^2)}\)  ensures that it will be less than or equal to the positive value of 121/\(n^2\).

In symbolic notation, the inequality can be written as −2\(e^{(-n/n^2)}\)  ≤ 121/\(n^2\) for n ≥ 1.

This representation captures the relationship between the two expressions and establishes the condition that must be satisfied for the inequality to hold.

Learn more about expressions here:

https://brainly.com/question/11701178

#SPJ11

Answer:

14 is C and 13 is also C

Step-by-step explanation:

so 14 and 13 a both C

mark brainliest or give 1 heart and 5 stars or maybe both

We have a value function of a machine at the end of the year t that is:

We know that C = 1038 and r = 0.28.

We have to calcula the value of the machine after 4 years (t = 4).

Then, we replace the parameters with their values and calculate V as:

Answer: the value is $278.95.

Step-by-step explanation:

plug in y

6=1/3x+11/15

multiply both sides by 15 to get rid of the fraction

90 = 5x +11

move terms to make them like terms

-5x =11- 90

-5x = -79

divide both sides by -5

evaluate for x

The required rate of return (or minimum acceptable rate of return) is 20 percent. If the net cash flows are $15,000 per year for ten years, the total cash flow is $150,000. The project's cost is $47,500. We can now apply the net present value formula to determine whether or not the project is feasible.

Net Present Value (NPV) = Cash flow / (1 + r)^n - Cost Where, r is the discount rate, n is the number of years, and Cost is the initial outlay.

Net Present Value = 150000 / (1 + 0.20)^10 - 47500

Net Present Value = $67,482.22

Since the NPV is positive, the project is feasible. When calculating net present value, it's important to remember that a positive NPV implies that the project is expected to generate a return that exceeds the cost of capital, whereas a negative NPV indicates that the project is expected to generate a return that is less than the cost of capital, and as a result, it should be avoided.

Know more about NPV here:

https://brainly.com/question/32720837

#SPJ11

Answer:

Step-by-step explanation:

To graph the equation 3y = -6x - 12, we can start by finding the x and y intercepts.

The x-intercept is the point where y = 0, so we can substitute 0 for y in the equation:

3y = -6x - 12

3 * 0 = -6x - 12

0 = -6x - 12

12 = -6x

x = -2

So the x-intercept is (-2, 0).

The y-intercept is the point where x = 0, so we can substitute 0 for x in the equation:

3y = -6x - 12

3y = -6 * 0 - 12

3y = -12

y = -4

So the y-intercept is (0, -4).

Now that we have the x and y intercepts, we can plot the points on the graph and draw a line that passes through both points. This line will be the graph of the equation.

In this case, the graph of the equation 3y = -6x - 12 is a downward sloping line that passes through the points (-2, 0) and (0, -4).

Answer:

The inequality that models the story is h < 16.

Step-by-step explanation:

The information provided states that Eduardo ONLY wants 16 hot dogs at most which means he doesn't want to cook anymore hot dogs than 16 of them. The line below the symbol means that it could also equal to that number which is what Eduardo also wants. Now that we know the inequality, we also need to graph it. All you need to do is plot the endpoint at 16 with an arrow pointing to the left. It also requires a closed circle because it doesn't mean just less than, don't forget, it means less than OR equal to. A closed circle just means to shade the dot by the way.

Answer: h < 16

Step-by-step explanation:

h (the number of hotdogs) has to be less or equal to 16

for the line do a closed circle on 16, and have the arrow go left

The recurrence relation for the coefficients of the power series is given by c_(n+1) = (2/n+1) * c_n for n ≥ 0.

To find a power series expansion about x = 0 for the given differential equation y' - 2xy = 0, we can assume that the solution is of the form:

y(x) = ∑(n=0 to ∞) c_n * x^n

where c_n are the coefficients of the power series. Taking the derivative of y(x), we get:

y'(x) = ∑(n=1 to ∞) n * c_n * x^(n-1)

Substituting these expressions into the differential equation, we get:

∑(n=1 to ∞) n * c_n * x^(n-1) - 2x * ∑(n=0 to ∞) c_n * x^n = 0

Simplifying and regrouping terms, we get:

c_1 - 2c_0 * x + ∑(n=2 to ∞) [n * c_n * x^(n-1) - 2c_(n-1) * x^n] = 0

Since this equation holds for all values of x, we can equate the coefficients of each power of x to zero. This gives us a recurrence relation for the coefficients:

(n+1) * c_(n+1) = 2c_n for n ≥ 1

The initial condition for the series is y(0) = c_0. Therefore, the general solution to the differential equation is:

y(x) = c_0 + ∑(n=1 to ∞) (2^(n-1)/n!) * x^n

where c_0 is an arbitrary constant.

To know more about recurrence relation refer here:

https://brainly.com/question/32773332#

#SPJ11

Answer:

210

Step-by-step explanation:

Round the 208. 8 is closer to 10. so, it would ultimately round up to 210

During the 75-minute class, Jonah will teach 5 tricks. This is a problem with comparison. The longer the class lasts, the more tricks Jonah will teach.

The problem with comparison can be solved by understanding the connection between two variables.

Given

How many tricks will Jonah teach during the 75-minute class?

We can list two variables.

Class time    Tricks

    30                2

    75                x

In this case, the longer the class lasts, the more tricks Jonah will teach.

\(\frac{30} {75} = \frac{2} {x}\)

\(x = \frac{75} {30} \times 2\)

\(x = \frac{75} {15}\)

\(x = 5\)

Hence, during the 75-minute class, Jonah will teach 5 tricks.

Learn more about a problem with comparison here:

brainly.com/question/6649455

#SPJ4

The transformations are applied in the following order: horizontal translation, horizontal scaling, vertical reflection, and vertical scaling.

The transformations are applied in the following order:

Horizontal translation: The function is shifted 9 units to the right by subtracting 9 from the input variable x.

f(x) → f(x - 9)

Horizontal scaling: The function is compressed horizontally by a factor of 1/3 by dividing the input variable x by 3.

f(x - 9) → f(1/3(x - 9))

Vertical reflection: The function is reflected about the x-axis by multiplying the output values of f by -1.

f(1/3(x - 9)) → -f(1/3(x - 9))

Vertical scaling: The function is stretched vertically by a factor of 8 by multiplying the output values by 8.

-f(1/3(x - 9)) → -8f(1/3(x - 9))

Therefore, the transformations are applied in the following order: horizontal translation, horizontal scaling, vertical reflection, and vertical scaling.

To learn more about transformations

https://brainly.com/question/10904859

#SPJ11

Given that mean= 6.56 and standard deviation(σ)= 1.19

a) P(X ≤ 5)= ( (X-µ)/ σ) < (5- 6.56)/ 1.19)

                = 0.094946

P(X ≤ 5)= 0.95

So 0.95 proportion of the survey would think $5 is too expensive for a sandwich.

b) P(X ≥ 6.75) = ( (X-µ)/ σ) < (6.75- 6.56)/ 1.19)

                      = 0.43656

0.43656 proportion of people surveyed would be willing to pay more than $6.75 for a sandwich.

c)  P(X ≤ x)= 0.35

                 = P((x- µ)/ σ ≤ (x- 6.65)/ 1.19)

                  0.35

x= (-0.3853) (1.19) + 6.56

 = 6.1015

6.1015  is the 35th percentile for how much people are willing to pay for a sandwich.

Learn more about percentile here brainly.com/question/1561673

#SPJ4

The numeric value of the expression 16 + 4(3q + p) when q = 6 and p = 2 is given by: 96.

To find the numeric value of a function, we replace each instance of the variable in the function by the desired value. This also works for multi-variable functions or expressions, as each instance of each variable will be replaced by their attributed values.

For this problem, the expression is given by:

16 + 4(3q + p)

The attributed values are given by:

q = 6, p = 2.

Hence the numeric value of the expression is found as follows:

16 + 4(3 x 6 + 2) = 16 + 4(18 + 2) = 16 + 4 x 20 = 16 + 80 = 96.

More can be learned about the numeric values of a function at brainly.com/question/28367050

#SPJ1

Interest be I

If interest is daily

If interest is monthly (30days)

Answer:

$ 1.20

Step-by-step explanation:

\(\sf Time = 10 \ days = \dfrac{10}{365}=\dfrac{2}{73}\)

\(Interest = Principal * time *rate\\\\\\=470*\dfrac{2}{73}*\dfrac{9}{100}\\\\= 1.20\)

= $ 1.20

The answer is 3

Step-by-step explanation:

I have the answer key pdf and, that is what the answer said, so I am pretty sure this is right.

Answer:

n=6

Step-by-step explanation:

The solution of the expression are,

⇒ n = 6

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ n + 5n + 7 = 43

Now, We can solve the expression for n as;

⇒ n + 5n + 7 = 43

⇒ 6n + 7 = 43

⇒ 6n + 7 - 7 = 43 - 7

⇒ 6n = 36

⇒ n = 6

Thus, The solution of the expression are,

⇒ n = 6

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ2

Answer:

6 matches

Step-by-step explanation:

Let’s call the teams A B C D

A will play B C D = 3 matches

B will play only C and D as it already played A, making 2 matches

C will play D, making 1 match

D has already played all

Total number of matches is thus 3 + 2 + 1 = 6 matches

The diameter d(c d) of the opening 20cm from the vertex is approximately 16.33cm.


To find the diameter of the opening 20cm from the vertex, we can use the fact that the cross-section of a cone is a circle. We can also use the formula for the slant height of a cone, which is given by the equation:
s = sqrt(r^2 + h^2)
where s is the slant height, r is the radius of the circular base, and h is the height of the cone.

In this case, we know that the height of the cone is 20cm from the vertex. We also know that the radius of the circular base is d/2, where d is the diameter we are trying to find.
So, using the formula for the slant height, we can write:
s = sqrt((d/2)^2 + 20^2)
We also know that the slant height of the cone is equal to the distance from the vertex to any point on the circumference of the base. Therefore, we can write:
s = r
where r is the radius of the circle formed by the cross-section of the cone at a height of 20cm from the vertex.
Now, equating the expressions for s and r, we get:
sqrt((d/2)^2 + 20^2) = d/2
Squaring both sides and simplifying, we get:
d^2 - 4d - 800 = 0
Using the quadratic formula, we can solve for d and get:
d = (4 + sqrt(4^2 + 4*800))/2
d = 4 + sqrt(3204))/2
d ≈ 16.33
Therefore, the long answer to your question is that the diameter of the opening 20cm from the vertex is approximately 16.33cm.

To know more about diameter  visit:
https://brainly.com/question/5501950

#SPJ11

According to the following table, the same constant of proportionality between yyy and xxx in the relation y=8x is.

The proportionality constant k is defined as k=y/x when y and x are two numbers that are directly proportional to one another. If you are aware of the proportionality constant, you can use the equation y=kx, where k is the proportionality constant you are interested in, to determine the direct link between x and y. As an example, we may write y = kx, where k is the proportionality constant, x is the quantity of gas in gallons, and y is the cost in dollars. In other words, the cost is directly related to the number of gallons pumped.

By calculating

32=4*8

56=7*8

64=8*8

Therefore, y=8x.

Learn more about constant of proportionality here

https://brainly.com/question/28413384

#SPJ4

Answer:

x = -6.667 y = 12.22

Step-by-step explanation:

You can easily figure out the vertex to a quadratic equation by inputting it into a graphing calculator and using the trace function to find the vertex. If you are stuck with these types of questions, I recommend investing in a TI-84 Plus CE.

Step-by-step explanation:

the easiest approach with a given point and the slope of the line is the point-slope form :

y - y1 = a(x - x1)

where "a" is the slope, and (x1, y1) is a point on the line.

so, we get

y - -8 = 4(x - -3)

y + 8 = 4(x + 3)

if we need the slope-intercept form

y = ax + b

we now simplify the point-slope form

y + 8 = 4x + 4×3 = 4x + 12

y = 4x + 4

The decorative mug at airport costs $10.99 and costs 70.99 Yuan. in China.

Let's choose the decorative mug with a cost of $10.99 and the country China with an exchange rate of 6.4651 Yuan per US dollar. To convert the cost of the decorative mug into Yuan, we need to multiply the cost by the exchange rate:

Cost in Yuan = $10.99 × 6.4651 Yuan/US dollar

Cost in Yuan = 70.986849 Yuan

Therefore, the cost of the decorative mug in China is 70.986849 Yuan. The exchange rate refers to the value of one currency for the purpose of conversion to another currency. It represents the amount of one currency that can be exchanged for a unit of another currency.

To learn more about exchange rate click here

brainly.com/question/28397345

#SPJ4

Complete Question

The cost of the five most popular items at an airport gift shop includes a $10.99 decorative mug, a $3.99 postcard, a $4.59 keychain, a $16.29 t-shirt, and a $7.89 teddy bear. Everleigh is interested in seeing the cost of the items in another currency. The most current currency conversion rates for 1 U.S. dollar are the following:

Country:

China

Denmark

Sweden

Name of currency:

Yuan(china)

Krone(Denmark)

Krona(Sweden)

Exchange rate:

6.4651(china)

6.3394(Denmark)

8.6964(Sweden)

Choose one airport gift shop souvenir and one country. Convert the cost of the chosen souvenir into the currency of that country. Show all necessary mathematical calculations.

Answer:

60×5= 0×5= 0= 6×5= 30

= 300

Answer:

60 x 5 = 300

and here's something cute

The fixed point x(t) = 0 is unstable and the fixed point x(t) = 3 / 4 is stable. We have also shown that the limit does not exist for x0 = 0.5 and the limit is lim x(t) = 3 / 4 for x0 = 2.

The given difference equation is x(t+1) = 4x(t)2 / 3x(t)2We have to find the equilibrium of the given differential equation. Equilibrium occurs when the value of x(t) is not changing from one time step to another time step.

Therefore, we can write the equation of equilibrium as x(t+1) = x(t)This is called a fixed point. To find the fixed point of the given difference equation, we replace x(t+1) with x(t) and simplify it as follows:

x(t+1) = x(t)4x(t)2 / 3x(t)2 = x(t)4 / 3x(t)

= x(t)3 / 4

Thus, the fixed point of the given differential equation is x(t) = 0 and x(t) = 3 / 4.

We can see that the fixed point x(t) = 0 is unstable, and the fixed point x(t) = 3 / 4 is stable.

Thus, we have found the equilibrium of the given differential equation and classified them as stable or unstable. We have also used cobwebbing to find the limit lim x(t) as t → ∞ for the given initial values (x0 = 0.5 and x0 = 2).

We have shown that the fixed point x(t) = 0 is unstable, and the fixed point x(t) = 3 / 4 is stable. We have also shown that the limit does not exist for x0 = 0.5, and the limit is lim x(t) = 3 / 4 for x0 = 2.

To know more about the equilbrium, visit:

brainly.com/question/32200875

#SPJ11