Heather deposits $500 into an account that pays simple interest at a rate of 2% per year. How much interest will she be paid in the first years?

The goal of using similarity transformations is to make the evaluation of a matrix's eigenvalues less complicated. In fact, the computation of the eigenvalues would be instantaneous if a given matrix could be translated into a similar matrix in diagonal or triangular form.

A geometric similarity or a matrix transformation that produces a likeness are both covered by the term "similarity transformation."

A conformal mapping with a similarity transformation is one whose transformation matrix A' has the formula A'=BAB⁻¹, where A and A' are referred to as similar matrices.

Space-based items are converted to equivalent objects by similarity transformations. Fractals and iterated function systems have a lot to do with similarity transformations and the idea of self-similarity.

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The equation a²-4=0, which corresponds to the factorization of a²-4= (a+ 2)(a-2)

Factorization refers to the process of breaking down a mathematical expression into simpler parts that can be multiplied together to give the original expression. For example, factorizing the expression x² + 4x - 12 would give (x - 3)(x + 4) as the factors.

In algebra, factorization is used to simplify expressions and to find the solutions of equations. For example, in the quadratic equation ax² + bx + c = 0, the first step in solving the equation is to factorize the quadratic expression ax² + bx + c. Once this is done, it becomes easier to find the solutions of the equation by setting each factor equal to zero and solving for x.

Factorization can also be used to simplify expressions in other branches of mathematics, such as number theory. For example, the prime factorization of a composite number is the representation of that number as a product of prime numbers.

Given:

The equation a²-4= (a+ 2)(a-2) is a factorization of a quadratic expression. It states that the expression a²-4 can be represented as the product of two binomials, (a+ 2) and (a-2).

This can be visualized as the graph of a parabola, where the x-intercepts of the parabola are -2 and 2. These are the solutions of the equation a²-4=0, which corresponds to the factorization of a²-4= (a+ 2)(a-2)

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Answer:

x = 7

Step-by-step explanation:

Given 2 congruent arcs then the chords are congruent , that is

VW = XY , substitute values

9x - 34 = 4x + 1 ( subtract 4x from both sides )

5x - 34 = 1 ( add 34 to both sides )

5x = 35 ( divide both sides by 5 )

x = 7

Answer:

13.04m/s^2

Step-by-step explanation:

v=u+at

therefore

a=v-u÷t

300m/s-0÷23s

=13.04m/s^2

The equation of line passes through the point (2, 3) will be;

⇒ y = 1/2x + 2

And, Graph of this equation of line is shown in figure.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The point on the line are (2, 3).

And, The perpendicular line is,

⇒ y - 4 = - 2 (x + 3)

⇒ y -  4 = - 2x - 6

⇒ y = - 2x - 2

Now,

Since, The equation of line passes through the point (2, 3).

So, We need to find the slope of the line.

Since, The product of slope of the perpendicular line is - 1.

Hence, Slope of the given perpendicular line is,

⇒ y = - 2x - 2

m = dy/dx = - 2

m = - 2

So, The slope of line is,

⇒ m₂ = - 1/m

         = 1/2

Thus, The equation of line with slope 1/2 is,

⇒ y - 3 = 1/2 (x - 2)

⇒ y - 3 = 1/2 (x - 2)

⇒ y - 3 = 1/2x - 1

⇒ y = 1/2x - 1 + 3

⇒ y = 1/2x + 2

Therefore, The equation of line passes through the point (2, 3) will be;

⇒ y = 1/2x + 2

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Step-by-step explanation:

In short, they become Martians. Five years later, the war on Earth ends, and a new ship travels through space, its mission being to save the Earthmen stranded on Mars. Much to the surprise of the rescue team, no Earthmen are to be found — only Martians, who have a great affinity for the English language.

hope it help

Answer: To find the total cost of the candy including the sales tax, we first need to calculate the amount of tax by multiplying the cost of the candy by the tax rate.

The cost of the candy is 10.00.

The tax rate is 5%, which can be written as 0.05.

The total cost of the candy would be

10 + (10*0.05) = 10+0.5 = 10.50

So the correct answer is $10.50.

Step-by-step explanation:

Yes, A triangle has sides of lengths 10, 24, and 26 is a right triangle.

A right-angled triangle is a triangle with one of the angles at 90 degrees. A 90-degree angle is called a right angle.

The formula states that in a right triangle:

The square of the hypotenuse is equal to the sum of the square of the base and the square of the altitude.

(Hypotenuse)² = (Base)² + (Altitude)²

c²=a²+b²

The three numbers which satisfy the above formula are the Pythagorean triplets

Properties of right angle:

consider c=26 a=10, b=24 substitute in above formula:

26²=10²+24²

⇒676=100+576

⇒676=676

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Answer:

1/2 of an answer is zero answer.

Step-by-step explanation:

V≈565.49          Step-by-step explanation:

the formula for volume is PI x Raadius squared x Highth

Answer:

Daniel's is correct

Step-by-step explanation:

Daniel split the coin toss into Heads and Tails and has 3 sections for the spinner coming off of each coin toss branch.

In order for an expression, such as x² + 4x + , to become a perfect square trinomial, it must be in the form of a² + 2ab + b².

Perfect squares are whole numbers that are the result of multiplying a given number by itself. For example, 4 is a perfect square because it is the result of multiplying 2 by itself. Similarly, 9 is a perfect square because it is the result of multiplying 3 by itself. Other examples of perfect squares include 16 (4x4), 25 (5x5), 36 (6x6), and so on.

To do this, you must factor the expression. In this case, the expression can be factored into (x + 2)².

Once the expression has been factored into a perfect square trinomial, it can be written as (x + 2)².

This is a perfect square trinomial because it represents the area of a square, as the length of each side is equal to (x + 2).

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Answer:

when x=10 & y=6

10-6=4 so,

x=8

y=4

The probability of the event that the mean amount of water in the 16 bottles is within 5 mL of the population mean is approximately 0.9544, which is closest to 0.95.

The correct answer is: D. P(500 <<510) 0.95.

Here, we have to find the probability that the mean amount of water in the 16 bottles is within 5 mL of the population mean (505 mL), we need to calculate the probability P(500 <x < 510), where x is the sample mean.

Given that the sample size (n) is 16 and the population standard deviation (σ) is 10 mL, we can use the Central Limit Theorem to approximate the sampling distribution of the sample mean.

The Central Limit Theorem states that for a sufficiently large sample size (n ≥ 30), the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.

The mean of the sampling distribution of the sample mean is equal to the population mean (μ) and the standard deviation of the sampling distribution (standard error) is given by σ/√n, where σ is the population standard deviation and n is the sample size.

In this case:

μ = 505 mL (population mean)

σ = 10 mL (population standard deviation)

n = 16 (sample size)

The standard error (SE) of the sample mean is:

SE = σ/√n = 10/√16 = 10/4 = 2.5 mL

Now, we need to find the z-scores for 500 mL and 510 mL:

z₁ = (500 - μ) / SE = (500 - 505) / 2.5 = -2

z₂ = (510 - μ) / SE = (510 - 505) / 2.5 = 2

Using the z-table or a statistical calculator, we can find the probabilities corresponding to these z-scores:

P(z < -2) ≈ 0.0228

P(z < 2) ≈ 0.9772

Now, to find the probability that the sample mean is within 5 mL of the population mean (P(500 <x < 510)), we subtract the probability corresponding to the lower z-score from the probability corresponding to the higher z-score:

P(500 < x < 510) ≈ P(z < 2) - P(z < -2) ≈ 0.9772 - 0.0228 ≈ 0.9544

So, the probability of the event that the mean amount of water in the 16 bottles is within 5 mL of the population mean is approximately 0.9544, which is closest to 0.95.

The correct answer is: D. P(500 <<510) 0.95

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The scale factor 5/2 takes hexagon J to hexagon K.

From the given two Hexagon's K and L, the Hexagon K is copy to Hexagon K.

The scale factor = the ratio of edges

Scale factor = 20/8 = 30/12 = 5/2

Hence, the scale factor 5/2 takes hexagon J to hexagon K.

Complete question:

Complete question is attached below.

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It is both of the pair of intersecting lines and degenerate hyperbola.

A conic section, conic or quadratic curve is a curve formed by the surface of a cone crossing a plane. The hyperbola, parabola, and ellipse are the three forms of conic sections; the circle is a special case of the ellipse, however it was frequently referred to as a fourth type. Parabolas, ellipses, circles, and hyperbolas are the four main forms of conics. Examine the diagrams below to discover how a conic is defined geometrically. The plane does not travel through the vertex of a non-degenerate conic.

Here,

It consists of a pair of intersecting lines as well as a degenerate hyperbola.

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Answer:

11 feet (Option C)

Step-by-step explanation:

Let the longer side be l and the shorter side be b.

We know that,

→ Perimeter of rectangle = 2 ( longer side + shorter side )

Here,

→ 32 = 2 (l + b)

→ 32 = 2l + 2(5)

→ 32 = 2l + 10

→ 32 - 10 = 2l

→ 22 = 2l

→ [tex] \sf \dfrac{22}{2} [/tex] = l

→ 11 = l

→ 11 feet = longer side

[tex] \therefore [/tex] Length of the longer side is 11 feet.

Answer:

24y + 35

Step-by-step explanation:

Hey there!

8(3y + 5) - 5

= 8(3y) + 8(5) - 5

= 24y + 40 - 5

= 24y + 35

Therefore, the answer is:

Option A. 24y + 35

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Step-by-step explanation:

please refer to the sketch

Answer:

It would take 15 students 6 days to weed the school compound

Step-by-step explanation:

This first step to solving this question is to break down the given rates.

We are told that 10 students take 9 days to weed the school compound. From here we can simplify this by figuring out how long it would take 1 student to weed the compound. Having less people would mean taking a longer time.

1 person is a 1/10 of 10 people. Since we have 10x less people, it should take 10x as long. Therefore it would take 1 person 9x10=90 days to weed a school.

Now the question asks how long it would take 15 people. 15 people is 15x as many as 1 person, so it should take 15x less time to weed the compound. 90/15 = 6

It would take 15 students 6 days to weed the school compound.

Similarly you could have just divided 9 by 1.5 as 15 is 1.5x10, but it is easier to explain the process using the above method.

Hope this helped!

The expression that represents the cost after the discount is

y(c) = (7/50)c

Given is that Charlotte has a loyalty card good for a 14% discount at her local grocery store.

Let the total cost, before tax and discount, of all the items she wants to buy is {c}. Now, let the expression that represents the cost after the discount is given by y(c). We can write -

y(c) = 14% of c

y(c) = (14/100) x c

y(c) = (7/50)c

Therefore, the expression that represents the cost after the discount is

y(c) = (7/50)c.

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Answer:

(-5/2, 1)

Step-by-step explanation:

i hope this helps :)

The number that should be added in the polynomial [tex]x^{3}-6x^{2} +11x+8[/tex]  , so that it is completely divisible by  [tex]x^{2} -3x+2[/tex] is  -14  .

What are Polynomials ?

A polynomial is defined as a type of algebraic expression where the exponents of all the variables is a whole number.

The exponents of the variables in any polynomial is a non-negative integer. A polynomial consists of constants and variables.

the polynomial expression is ⇒ [tex]x^{2} -3x+2[/tex], which can be written in factor form  as  : [tex](x-1)(x-2)[/tex] ,

that means the polynomial is divisible by both x = 1 and x = 2 ;

So , on substituting [tex]x=1[/tex] in the polynomial [tex]x^{3}-6x^{2} +11x+8[/tex] ,

we get , [tex]1^{3}-6\times1^{2} +11\times 1+8[/tex] = 14 ;

on substituting [tex]x=2[/tex] in the polynomial [tex]x^{3}-6x^{2} +11x+8[/tex] ,

we get , [tex]2^{3}-6\times2^{2} +11\times 2+8[/tex] = 14 ;

So , the remainder is 14  .

Therefore , -14 should be added in the given polynomial .

The given question is incomplete , the complete question is

What should be added in the polynomial x³ -6x² +11x +8 so that it is completely divisible by x² -3x +2 ?

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Function: This means that 2.7 x 10^3 is about 201.593 times smaller than 5.481 x 10^5. This can also be expressed as 0.049 or 4.9%.

A function is a mathematical relation between two sets of values, usually between an input and an output. It can be thought of as a machine that takes a certain input and produces a certain output.

2.7 x 10^3 is about 0.049 times smaller than 5.481 x 10^5.
To determine this, we can divide the two numbers. 5.481 x 10^5 divided by 2.7 x 10^3 equals about 201.593.
This means that 2.7 x 10^3 is about 201.593 times smaller than 5.481 x 10^5. This can also be expressed as 0.049 or 4.9%.

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Answer:

1 solution

Step-by-step explanation:

y=16, r=-21/2

This system of equations have no solution, the correct option is A.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree. A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

We are given that;

y = 12 + 1 + 3

y = -2r – 5

Now,

We can simplify the first equation by adding 12 + 1 + 3 to get y = 16. Then we can compare the coefficients of r and y in both equations.

We can see that the coefficients of r are different (-2 and 0), but the coefficients of y are the same (1 and 1).

This means that the graphs of the equations are parallel lines with different y-intercepts (16 and -5).

Therefore, the answer will be the system of equations has no solution.

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The vertex of the equation is (0, -1), the line of symmetry is x = 0 and the y-intercept is (0,-1).

For the equation f(x) = [tex]-3x^7[/tex] + 2x - 1, the vertex is the highest or lowest point on the parabola and it can be found by completing the square method.

To find the line of symmetry, we can set the function equal to zero and solve for x. The x-coordinate of the vertex is the same as the line of symmetry.

The y-intercept is the point at which the parabola crosses the y-axis, and it can be found by setting x equal to zero and solving for y.

The vertex of the parabola:

The line of symmetry:

The y-intercept:

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So the number of parcels that Helen delivered on Monday ​is 120 parcels.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

An equality of two ratios is a percentage. We use proportions to construct comparable ratios and find solutions to problems involving unknown numbers.

If on Wednesday Helen delivered 50% fewer parcels than on Tuesday, then on Tuesday Helen delivered 72 / (1 - 0.5) = 72 * 2 = 144 parcels.

On Tuesday Helen delivered 20% more parcels than on Monday, so the number of parcels Helen delivered on Monday is (144 / 1.2) = 120

So Helen delivered 120 parcels on Monday.

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Answer:

35

Step-by-step explanation:

x + 55 = 90

x = 90 - 55

x = 35

When we subtract 3xy from 5 we will get 3xy - 5.Both are different 3xy is a polynomial in xy and 5 is a constant we can not simplify further.

First, let's try to learn subtraction in the case of polynomials.

3xy is a polynomial.

5 is a constant.

Polynomials can be subtracted using a method that involves changing the signs to the opposite sign. The process resembles adding polynomials. Depending on the specific equation, we transform the sign while subtracting polynomials to either positive or negative. Learn more about subtracting polynomials, their techniques, procedures, and examples by reading on.

For instance, subtract 5x + 8y - 20z from 4x - 10y + 15z.

The polynomials should first be arranged in standard form. In this illustration, it has already been set up.

Place them horizontally in step two.

(4x - 10y + 15z) - (5x + 8y - 20z)

Step 3: By using parenthesis, modify the second polynomial's sign.

4x-10y-15z, and 5x+8y 20z

Step 4: Group terms that are similar together.

4x - 5x - 10y - 8y + 15z + 20z

Step 5: Resolve the problem

-x - 18y + 35z

As a result, we get -x - 18y + 35z when we subtract 4x - 10y + 15z from 5x + 8y - 20z.

In the same way, if we subtract 3xy from 5 we will get 3xy - 5.

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Answer:

13x-39=39

13x=78

 the answer is x=6