After 9 years in an account with a 3.9% annual interest rate compounded continuously, an investment is worth a total of $17,757.16. What is the value of the principal investment? Around the answer to the nearest penny.

Answer: The two numbers are $x = 5$ and $y = 7.5$.

Step-by-step explanation:

Let the two numbers be $x$ and $y$, where $x < y$. We can write the two given statements as the following two equations:

$$2y = 3x + 15$$

$$\frac{1}{5}x + \frac{1}{9}y = 10$$

We can solve this system of equations using elimination. Multiplying the first equation by 5 and the second equation by 9, we get

$$10y = 15x + 75$$

$$9x + y = 90$$

Subtracting these equations, we get

$$8y - 9x = 15$$

Multiplying this equation by 8, we get

$$64y - 72x = 120$$

Adding this equation to 5 times the first equation, we get

$$69y - 72x = 120 + 75$$

$$69y - 72x = 195$$

Dividing both sides by 3, we get

$$23y - 24x = 65$$

Subtracting this equation from 4 times the second equation, we get

$$96y - 36x = 360 - 260$$

$$96y - 36x = 100$$

Dividing both sides by 60, we get

$$\frac{16}{3}y - \frac{6}{5}x = \frac{5}{3}$$

Substituting the expression for $y$ from the first equation, we get

$$\frac{16}{3}(3x + 15) - \frac{6}{5}x = \frac{5}{3}$$

This simplifies to

$$\frac{16}{5}x + \frac{64}{5} = \frac{5}{3}$$

Solving for $x$, we find that $x = 5$. Substituting this value into the first equation, we find that $y = 15/2 = 7.5$. Therefore, the two numbers are $x = 5$ and $y = 7.5$.

Both of you are correct because using either way can solve the equation for the value of x.

In the case of solving for x in  2/5 x = 14, the goal is to get rid of the fraction that is multiplying x on the left side. This can be done by either multiplying both sides of the equation by the inverse of 2 / 5 ( which is 5 / 2 ) or by dividing both sides by 2 / 5.

Doing either of these things would get rid of the 2 / 5 and give an answer to x as shown below :

Multiplying :

2/5 x = 14

5 / 2 x 2 / 5 x = 14 x 5 / 2

x = 35

Dividing :

2/5 x = 14

2 / 5 x / 2 / 5 = 14 / 2 / 5

x = 35

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Step-by-step explanation:

think of it as a ruler the small dashes represents the 16ths and the big dashes represents the 4ths. They are on the same line therefore they are equal.

Using PEMDAS to resolve the trigonometric identity which involves trigonometric function, the value of tan A + tan B is 416 / 87

A trigonometric identity is an equation that is true for any value of the variables involved. These identities are useful in solving problems involving trigonometric functions. Examples include the Pythagorean identity, the sine and cosine addition formulas, and the double angle formulas.

In the given problem, we have a compound angle problem and we can solve it as;

tan A + tan B = [(tan A + tan B)] / [1 - tan A * tan B]

Substituting the values into the expression and solve;

tan A + tan B = [(7/24 + 15/8)] /[1 - (7/24)(15/8)]

Applying the rules of PEMDAS;

tan A + tan B = (13 / 6) / (29 / 64)

tan A + tan B = 416/87

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Graph A is defined by the function y=(x + 2)(x+7) as the graph at y=0 where the function crosses those two points .

The study of mathematics comprises the study of quantities and their variations, equations and associated structures, shapes and their positions, and locations where they can be found. A combination of inputs and corresponding outputs are referred to as a "function," which describes the relationship between them. The term "function" refers to an association between inputs and outputs where each input produces a single, unique result. There are two domains, or scopes, assigned to each function. Usually, the symbol f is used to signify functions (x). input is an x. There are four basic categories of functions that are available: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

given

The function's zeros are

0=x+2 x=-2

and

0=x+7 x=-7

Consequently, the graph at y=0 where the function crosses those two points .

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Answer:

it's equal to = 242 =484. I think so that's the right answer please

The rate of change of the end points of the line is 32/10

What is slope?

Slope is defined as the rate of change of y with respect to x.  Also it is defined as increase in y over increase in x or decrease in y over decrease in x

slope is denoted by the formula = Δy/Δx

Where Δy = change in y

Δx= change in x

The given points are (-9, -2) and (5, 119/5)

The slope of the end points   (119/5 + 21)/(5+9)

The slope is (119+105)/5

M= 44.8/14

The slope is 3.2 = 32/10

Therefore the rate of change is given as 32/10

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UV is a segment Bisector.

A segment bisector is a line, ray, or segment that splits another line segment in half evenly at its center. The midpoint of the line segment is always bisected by the line, which divides it into two equally sized parts.

The angle bisector theorem states that a triangle's opposite side is divided into two parts by an angle bisector that is proportional to the triangle's other two sides.

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Answer:

$26.19

Step-by-step explanation:

9% as a decimal is 0.09.

So, the fee is [tex](291)(0.09)=\$26.19[/tex].

Answer:

$26.19

Step-by-step explanation:

.09 x 291 = 26.19

Answer:18

Step-by-step explanation:15 + 6 u add the 15 and the 6 for it to be 18

The total cost of the 74 shirts will be;

⇒ $432

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 total cost in dollars, y, that a t-shirt company charges can be modeled by the toes per day by the equation is,

⇒ y = 5x + 62

Where, x represents the number of t-shirts sold.

Now,

Since, The equation is,

⇒ y = 5x + 62

Where, x represents the number of t-shirts sold.

Hence, For 74 shirts, the cost is fund by substitute x = 74 in above equation,

⇒ y = 5x + 62

⇒ y = 5 × 74 + 62

⇒ y = $432

Thus, The total cost of the 74 shirts = $432

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Answer:d. 120x+60=780

Step-by-step explanation:

120 cost per x hours

Flat Rental cost 60

120x+60=780

-60 as the flat rate which won’t change based on time.

120x=720

Divided by a rate of 120 per hour

x=6 hours

Answer:

See below

Step-by-step explanation:

Because it's an inequality, the upside-down parabola has dashed lines instead of a sold line. Additionally, only one side of that parabola will contain the solution set, which we can easily figure out by testing a point like (0,0):

[tex]0\stackrel{?}{ > }-3(0)^2-30(0)-48\\0\stackrel{?}{ > }-48\\\\0 > -48 \text{ is true}[/tex]

Hence, the side that contains (0,0) gets shaded. See the graph below.

Answer:

Step-by-step explanation:

34x60

60 minutes in a hour

34x60=204

204+204= 408

408 copies in 2 hours

Answer:

4080

Step-by-step explanation:

First you would multiply 34 by 120. After you multiply those numbers you should get 4080 as your answer.

The measure of ∠ 1 is 68.7°

Linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°.

Given is a figure of angles showing the pair of linear angles.

Therefore, by the definition of linear pair angles,

∠ 1 + 111.3° = 180°

∠ 1 = 180° - 111.3°

∠ 1 = 68.7°

Hence, the measure of ∠ 1 is  68.7°

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Answer: 15a – 12b – 5.

Step-by-step explanation: To solve this equation, we need to distribute the constants in front of the parentheses. Doing so, we get:

-3 + 4(a – 3b + 2) – 5(2 – a + 3b)

= -3 + 4a – 12b + 8 – 10 + 15a – 15b

= (15a – 12b) + (-10 + 8) – 3

= 15a – 12b + -2 – 3

= 15a – 12b – 5

Thus, the solution to the equation is 15a – 12b – 5.

Using the addition operation, the number of cups of flour Sasha needs to make both a batch of muffins and a loaf of bread is 2⁵/₁₂ cups.

We can use the addition operation to determine the quantity of flour that Sasha needs.

We add the cups of flour needed for both items to determine the total quantity.

The quantity of flour for making a batch of muffins = 3/4 cups

The quantity of flour for making a loaf of bread = 1²/₃ cups

The total quantity of flour needed for making a batch of muffins and a loaf of bread = 2⁵/₁₂ cups (³/₄ + 1²/₃)

(³/₄ + 1²/₃)

= ³/₄ + ⁵/₃

= (9 + 20)/12

= 29/12

= 2⁵/₁₂

Thus, to make a batch of muffins and a loaf of bread, Sasha needs 2⁵/₁₂ cups of flour.

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Answer: 2.403 × 10^3 atoms

Step-by-step explanation:

10^13 x 6.02 = 6.02^23 and 6.02^23 x 4 = 2,403 turned into 2.403 x 10^3 atoms.

Answer:

68 words

Step-by-step explanation:

If 34 words are typed in a minute what about two minutes hence take 34×2

Answer:

68

Step-by-step explanation:

A rate can be a quantity, or frequency, measured against a different quantity or amount.

If we know that Shaikha can type at a rate of 34 words per minute, and we need to figure out how many words she can type in 2 minutes, we can use an equation that looks like this:

Let m = minutes, w = words per minute and t = total words

m × w = t

Simply just insert your numbers into the equation.

2 × 34 = 68

Therefore, the number of words, or rate, that Shaikha types in 2 minutes is 68.

4th option: parallelogram

1a) An equation that gives the width `y` of the book, if it has `x`-hundred pages printed on bond paper is; y = ¹/₂ + ¹/₄x

1b) Ledger paper has a thickness of 2/5 in. per `100` pages, the equation is; y = ¹/₂ + ²/₅x

2) The equation will be; y = ²/₃ +¹/₄x

1) We are told that the front cover and the back cover have a thickness of 1/4 inches and they also have a thickness of 1/4 inch. Thus;

The addition of both gives to the book thickness of;

1/4 + 1/4 = 1/2 inch, despite how many pages the book  has.

We are told that for every hundred pages, a thickness of 1/4 inch is added to the book, then the equation is:

y = ¹/₂ + ¹/₄x

where;

y is the width of the book in inches.

x is every hundred pages printed on bond paper.

1b) If ledger paper has a thickness of 2/5 in. per 100 pages, then the equation is now;

y = ¹/₂ + ²/₅x

2) If both front and back covers now, have a thickness of 1/3 inches instead of 1/4 inches each, then the equation will be;

y = 2(1/3) +¹/₄x

y = ²/₃ +¹/₄x

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The value of x is 20 and the value of y is 8 from the given quadrilaterals.

The definition of a congruent polygon is a polygon that is the same shape, has the same length of sides, and has the same interior angles as the polygon it is being compared to. Congruent shapes must all be the same type of shape in order to fulfill the requirement.

Given that, ABCD≅EFGH

We know that, corresponding parts of congruent polygon are equal.

Now, (4y-4)°=28°

4y=32

y=8

(10x-65)°=135°

10x=200

x=20

Therefore, the value of x is 20 and the value of y is 8 from the given quadrilaterals.

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Answer:

the quotient of g and 25 is g/15.

Answer: The matching jacket requires 1/6 yards less fabric than the dress, which is 3 1/4 - 1/6 = 3 1/4 - 2/12 = 3 1/4 - 1/6 = 3 1/4 - 1/6 = 3 1/4 - 1/6 = 3 3/12 yards of fabric.

To add these two amounts of fabric together, you need to add the yards and the inches separately.

For the dress: 3 1/4 yards = 3 + 1/4 = 3 + 0.25 = 3.25

For the jacket: 3 3/12 yards = 3 + 3/12 = 3 + 0.25 = 3.25

So, for both pieces, the required fabric is 3.25 + 3.25 = 6.5 yards

Step-by-step explanation:

The measure for θ is 25.747121°.

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

Hypotenuse = 14.5 meters

Opposite side = 6.3 meters

Now, using Trigonometry

sin θ = Opposite side / Hypotenuse

by putting the given values we get

sin θ = 6.3 / 14.5

sin θ = 63/145

sin θ = 0.4344

θ =25.747121°

Hence, the angle is 25.747121°.

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Answer:

- 7√10

Step-by-step explanation:

Step 1 : Take √10 common

2√10 - 5√10 - 4√10

= √10 ( 2 - 5 - 4 )

Step 2 : Subtract the numbers separately.

2 - 5 - 4

= 2 - 9

= - 7

Step 3 : Multiply √10 and - 7

√10 * - 7 = - 7√10

Therefore , the solution to the given problem is the equation of the midline is: y = M+m /2 .

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

Here,

The midline equation is y = M+m /2

when a function has: o a max M AND a min m or o (if it does not have extrema) a bound above M and a bound below m, where M is the minimum bound above and m is the maximum bound below.

When one of the following conditions is true for a function, even though it has a bound below, there is no midline (even if it has a bound above)

It is solely constrained from above (or below)

Any line is midline if a function has the values (-∞, +∞)

Therefore , the solution to the given problem is the equation of the midline is: y = M+m /2 .

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Answer:

Area= 46,000

Permiter= 4,600

Step-by-step explanation:

The formula to find the area of a rectangle is Length(L) times Width(W).

So 2,000(L) times 23 (W)= 46,000.

The formula for perimeter is 2(l+w).

So you're going to go 2,000 + 23 = 2,300 times 2 which equals 4,600.

Hope that helped, have a great day!!

Sean baked 372 cupcakes in total.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

Sean bakes 18 dozen chocolate cupcakes,

and 13 dozen vanilla cupcakes.

There are 12 cupcakes in one dozen.

To find the number of cupcakes:

Using multiplication operation,

18 x 12 = 216.

13 x 12 = 156.

The number of cupcakes = number of chocolate cupcakes + number of vanilla cupcakes.

The number of cupcakes = 216 + 156

The number of cupcakes = 372

Therefore, the number of cupcakes are 372.

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