Solve the problem.
How much money needs to be invested now to get $2000 after 4 years at 8%
compounded quarterly? Express your answer to the nearest dollar.
A) $584
B) $1457
C) $1848
D) $2746

The equation is therefore in Standard Form: 2  Degree :Quadratic  number of terms :Binomial

There are numerous ways to define an equation in mathematics .In algebra, a statement that mathematically establishes the equality of two mathematical expressions is known as an equation. Take into consideration the equation 3x + 5 = 14, in which 3x + 5 and 14 are two variables that are separated by the word "equal." Even the most elementary and simple algebraic equations use mathematical variables.

To construct a polynomial in standard form in this instance, you begin writing with the term having the highest degree, or exponent (in this example, the

2[tex]x^{2}[/tex] +x

word), and after that, in descending order. due to the two

[tex]x^{2}[/tex] is used to the greatest degree:

You look at the highest exponent, or degree, to categorize a polynomial. Considering that 2 is the highest exponent,

That is a quadratic equation. First few are as follows:

1- linear

2- quadratic

3- cubic

4- quartic

5- quintic

Count the terms in the polynomial to categorize it according to its term count: There are two terms in this polynomial,

2[tex]x^{2}[/tex]and x

. This is therefore a binomial.

Monomial is one term.

binary two terms

trinomial, 3 terms

4-plus terms; polynomial

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You can compute amplitude as well, but this is quicker. There will be a reflection in the x axis, as shown by the negative sign before the number 2.

The maximum displacement or distance made by a point on a vibrating body or wave relative to its equilibrium location is known as the amplitude in physics. It is equivalent to one-half of the vibration path's length.

Amplitude:

[tex]Found right in the equation the first number:\\ y=-2-cos2(x+4)-1[/tex]

You can compute it as well, but this is quicker. There will be a reflection in the x axis, as shown by the negative sign before the number 2.

Period:

[tex]First find k in equation:\\ y=−2cos2−(x+4)−1[/tex]

Then use this equation:

[tex]period=2\pi /k\\period=2\pi /2\\period=\pi[/tex]

Phase Shift:

[tex]y=-2cos2(x+4)-1[/tex]

The graph will move 4 units to the left, according to this section of the equation.

Vertical Translation:

[tex]y=-2cos2(x+4)-1[/tex]

The -1 tells you that the graph will shift 1 unit down.

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The coordinates after the reflection of the points will be(7, -3).

The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse.

Given that, (-7,3) is reflected across the x-axis, and then the y-axis.

When reflected across x-axis, it will be (-7, -3)

And again when reflected across y-axis it will be (7, -3)

Hence, The coordinates after the reflection of the points will be(7, -3)

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Answer:

The second option/ B

Step-by-step explanation:

6 coins plus 4 coins is 10 coins, and you can’t forget the x amount of pennies.

Answer:

slope is undefined

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (16, - 9 ) and (x₂, y₂ ) = (16, 13 )

m = [tex]\frac{13-(-9)}{16-16}[/tex] = [tex]\frac{13+9}{0}[/tex] = [tex]\frac{22}{0}[/tex]

since division by zero is undefined then slope of line is undefined.

Answer:

[tex]\boxed{0}[/tex]

_________________________________________________________

For degrees, coterminal angle formula is: θ ± 360 * n For radians, coterminal angle formula is: θ ± 2π * n In the above formulas, n refers to a multiple of full rotations, which equals to 360 degrees or 2π.

⇒ θ ± 360

⇒  θ ± 2π

⇒ 0 360 degrees or 2π.

Therefore, your answer is 0

_____________________

Hope this helps!

Please mark me brainless!

The simplest definition of point-slope form is a line equation expressed using a single line point and the line's slope.

When the line to be examined's slope is known, and the provided point also serves as the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). B stands in for the y value of the y-intercept point in the formula.

An equation for a line stated using a single point on the line and the line's slope is a straightforward definition of point-slope form.

The slope is defined as the rise over run, or the proportion of the change in the y values over the change in the x values, and the point form is denoted by the letters (x,y).

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Answer:

x=−10,y=−5

Step-by-step explanation:

The required age of Liza's sister is given as 6 years.

Given that,
Liza is one year older than her sister. In four years she will be 3 times as old as she is now. How old is her sister now is to be determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
Let the age of Liza be x and of her sister be y,
According to the question,
x = y + 1
After 4 years,
4 + (y + 1) = 3(y + 1)
5 + y = 3y + 1
y = 2
The age of her sister now,
y = 2 + 4 = 6 years.

Thus, the required age of her sister is given as 6 years.

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josh is 3 years older than 4 times kim's age. the sum of their ages is less than 43. inequality for the situation, then the oldest age kim could be.

4k + 3 < 43

k < 10

We are given that Josh is 3 years older than 4 times Kim's age. We can express this as 4k + 3, where k represents Kim's age. We are told that the sum of their ages is less than 43, so we can write this as an inequality: 4k + 3 < 43. To find the oldest age Kim could be, we can solve this inequality for k. To do this, we subtract 3 from both sides, giving us 4k < 40. Finally, we divide both sides by 4, giving us k < 10. Therefore, the oldest age Kim could be is 10.

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The expression that represents her overall change in depth is given as follows:

-10 + 10.

The changes in depth are represented using integer numbers, as follows:

Liz dives 10 feet below the surface of the water, hence the integer number is of:

-10.

Then she returns to the surface, that is, moving 10 feet in the direction of the surface, hence the integer number is given as follows:

10.

Then the addition operation that represents her overall change in depth

-10 + 10.

Which has a result of zero, as she finished at the same place that she started.

The problem is given by the image shown at the end of the answer.

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Answer: -6

Step-by-step explanation:

(0,y)

at y intercept, x is 0. therefore sub x with 0 and solve

y= 3(0)-12/0+2

= -12/2

=-6

If you graph a linear characteristic you may get a immediately line. There also are nonlinear functions. If you graph the coordinates of a nonlinear characteristic you may now no longer get a immediately line.

One of the very best ways (however now no longer the handiest way) to differentiate among a linear and a nonlinear characteristic is to have a take a observe the graph of the characteristic.

A linear equation is an equation with  variables whose graph is a line. The graph of the linear equation is a hard and fast of factors withinside the coordinate aircraft that every one are answers to the equation. If all variables constitute actual numbers you can graph the equation via way of means of plotting sufficient factors to understand a sample after which join the factors to encompass all factors.

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all because all of the equianlangular triangles are equal

R is equivalence relation and cl (-7) = cl(5)

cl (-6) = cl (0)

cl (-2) = cl(1) = cl(4) = cl( 7)

A reflexive, symmetric, transitive binary connection is an equivalence relation. One such illustration of an equivalence relation is the relation of equipollence between line segments in geometry.

demonstrate the equivalence of R. We must demonstrate

1). reflexive

x +2x = 3x and 3/ 3x  = 3/x +2x

(x,x) ∈ R

R is reflexive

2). symmetric

let (x,y )  ∈ R

x + 2y = 3a for some a ∈ R

consider y +2x = y + 2(3a - 2y)

6a - 3y = 3(2a - y) = 3k

3/y +2x

so (y,x)  ∈ R

R is symmetric

3). transitive

(x,y) and (y,x) ∈ R

3/x+2y and 3/y+2x

x+2y =3a and y +2x = 2b for some a,b

consider x+2z = 3a - 2y + 2 (3b-y/2)

3a +3b -3y

3(a+b-y)

3/x+2z

(x,z) ∈ R

R is tansitive

so R is equivalence relation

b).S = (-7, -6, -2,0,1,4,5,7)

cl (x) = { y∈ z , x∈ y }

cl (x) = {y∈ z , x +2y = 3a}

cl (x) =  {y∈ z , y = 3a - x /2}

cl (-7) = {y∈ z , y = 3a +7  /2}

cl (-7) = cl(5)

cl (-6) = cl (0)

cl (-2) = cl(1) = cl(4) = cl( 7)

R is equivalence relation

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The value of the central angle of the given arc of the circle is ; θ = 162°

The central angle  of an arc of a circle is defined as an angle between two radii with the vertex at the center. The central angle of an arc is  also called the central angle subtended by the arc.

We are given the circumference of the circle as 10 and the length of the arc as 9.

Now, the formula for circumference of a circle is;

C = 2πr

where r is radius

The formula for length of the arc is;

L = θ/360 * 2πr

Plugging in the relevant values, we have;

9/2 = (θ/360) * 10

θ = (360 * 9)/(10 * 2)

θ = 162°

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(a) The total score of Jesse's card is 1

(b) The value of each of the two cards can either be 0 or cards with different signs

In the question,

(a) Jesse's card are 3 , -5 , 9 and -6

We have to find the total

You should know that,

Adding a positive integer is like addition but adding a negative integer is like subtraction

So, Total score = 3 + (-5) + 9 + (-6)

=> 3 - 5 + 9 - 6

=> 1

Jesse's total score is 1

(b) Jesse has picked two cards which are not affecting her total score

So, either he got two zeroes or two cards with opposite signs with same magnitudes

Like 1 and -1 etc.

The two doesn't affect his score because their effect got cancelled out

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A) Acceleration Direction

The net force is acting down the surface, as seen in the figure. As a result, the acceleration vector should likewise be directed down the surface.

Labeling the vector of acceleration

The acceleration vector is depicted below:

B)  Determine the velocity vector

According to the free-body diagram, an item should be on an inclined surface with a tension force pulling it down. When a kinetic frictional force is directed up to the surface, the item is said to be sliding down the slope. As a result, the velocity vector should be oriented upside down.

Determine the direction of the velocity vector

The velocity vector is indicated in the picture below:

C) Describe a real-world thing

The diagram shows an item on an inclined surface, with the kinetic force directed up to the surface. As a result, the item may be thought of as a box being pulled down by a rope down an inclined slope.

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Full Question

Problems 35 through 40 show a free-body diagram. For each:

a. Redraw the diagram

b Identify the direction of the acceleration vector  and show it as a vector next to your diagram. Or, if appropriate, write

c. If possible, identify the direction of the velocity vector and show it as a labeled vector.

d Write a short description of a real object for which this is the correct free-body diagram. Use Examples 5.4, 5.5, and 5.6 as models of what a description should be like.

If the sample size increases while the variability remains the same, then the standard error decreases.

Standard error is defined as the measures of the preciseness of an estimate of a population mean. It can be calculated by dividing the sample standard deviation by the square root of the sample size.

SE = SD / √n

where SE = standard error

SD = sample standard deviation

n = sample size

Variability refers to the statistical dispersion of data which is expressed through the range, variance, or standard deviation.

Increasing the sample size, n, while having the same variability, will result to a lower value for the standard error.

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Equation s/12 = 6 represents the equation on how many stones were used for the order. On solving we get 72 stones.

How to form an equation for a word problem?

Follow these steps:

Understand the problem. Understand all the words used in stating the problem. Understand what you are asked to find.

Translate the problem to an equation. Assign a variable (or variables) to represent the unknown.

Carry out the plan and solve the problem.

According to the given question:

Leslie's most recent order included a total of 6 bracelets.

It takes 12 stone to make one bracelet.

Let the total number of stones be s.

If one bracelet requires 12 stones then 6 bracelets requires 12 x 6 stones

Therefore, s = 12 x 6 or s/12 = 6

On solving to get value of s we get 12 x 6 = 72 stones.

Hence s/12 = 6 represents the equation on how many stones were used for the order. On solving we get 72 stones.

Complete question:

Leslie creates designer bracelets with gemstones. Her most recent order included a total of 6 bracelets. It takes 12 stone to make one bracelet.

Write and solve an equation that represents how many stones were used for the order.

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The two solutions of the equation:

(6x - 12)/3 + 4 = 18/x

Are x = 3 and x = -3

Here we have the following equation:

(6x - 12)/3 + 4 = 18/x

Notice that in the right side we have x on a denominator, then x can not be zero, so x ≠ 0.

Now, let's start by simplifying the left side:

(6x - 12)/3+  4 = 18/x

2x - 4 + 4 = 18/x

2x = 18/x

Now we can multiply both sides by x so we get:

2x^2 = 18

Now divide both sides by 2:

x^2 = 18/2

x^2 = 9

Finally, apply the square root in both sides:

√x^2 = ±√9

x = ±3

The two solutions are x = 3 and x = -3

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Step-by-step explanation:

since triangles are congurent

4z- 32 = 36

z = 68/4

z= 17

6x - 29 = 115

6x = 144

x = 24

and u can find y by triangle property...... similarly.....I'm too lazy to do that

Answer:

See below

Step-by-step explanation:

You start at the origin which is the very middle of where the x and y axis cross.  The first number tells you to go right 3 spaces and the second number tells you to go 2 spaces.

The remainder when f(x) is divided by x + 5 is 3.

What is an Equations?

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

we discovered that the polynomial equation is the equation that results from equating a polynomial function to zero. A linear equation results from equating a function to zero if it is a linear polynomial. We get a quadratic equation if the function is a quadratic polynomial.

f(x) = ax^3 + bx^2 + cx + d

In the polynomial above, a, b, c, and d are constants and f(-5)=3.

- 5 is the root of the given polynomial when remainder is 3 so we get the one factor of the given polynomial and that is,

x-(-5)=(x+5)

That is if f(-5)=3 it means that the remainder when f(x) is

divided by (x-(-5))=x+5 is 3

Hence, The remainder when f(x) is divided by x + 5 is 3

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Probability can be used to make predictions or decisions in a variety of situations, such as in gambling, finance, and science. In these situations, probabilities can be calculated based on statistical data or by using mathematical models.

To determine the probability of each of the five smallest y values, we can use the probability of each possible outcome and the number of ways that outcome can occur.

P(y = 1) = probability that the first component is defect-free = 0.8

P(y = 2) = probability that the first component is defective and the second component is defect-free = (1 - 0.8) * 0.8 = 0.16

P(y = 3) = probability that the first two components are defective and the third component is defect-free = (1 - 0.8) * (1 - 0.8) * 0.8 = 0.032

P(y = 4) = probability that the first three components are defective and the fourth component is defect-free = (1 - 0.8) * (1 - 0.8) * (1 - 0.8) * 0.8 = 0.0064

P(y = 5) = probability that the first four components are defective and the fifth component is defect-free = (1 - 0.8) * (1 - 0.8) * (1 - 0.8) * (1 - 0.8) * 0.8 = 0.00128

We can see that the probability of each y value is simply the probability of the previous y value multiplied by (1 - 0.8) = 0.2. This means that the probability distribution of y is given by the formula P(y) = 0.2^(y - 1) * 0.8.

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A is a 7x7 matrix with three eigen values. One eigenspace is two-dimensional and one of the other eigenspaces is three dimensional, then it is possible that A is not diagonalizable. The given statement is true.

There are three eigen-spaces, since A has three eigen values, the dimension of each of the eigen value is atleast one as there is atleast one non-zero eigen vector in them.

It is given that one of the eigen space has dimension 2 and other one has dimension 3.

A 7 x 7 matrix is diagonalizable if and only if the sum of the eigenspaces' dimension is 7. The given matrix is diagonalizable if and only if the third eigen space has dimension 2.

In A, if the sum of dimensions of eigenspace is not equal to the number of columns, then A is not diagonalizable.

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Answer:

$3.78

Step-by-step explanation:

To find the new price of the speaker after the sale, you can use the following formula:

New price = (1 + discount percentage) * (original price - discount amount)

In this case, the discount percentage is 40%, or 0.4, and the discount amount is 40% of the original price, or 0.4 * $4.50 = $1.80. Plugging these values into the formula, we get:

New price = (1 + 0.4) * ($4.50 - $1.80)

= 1.4 * $2.70

= $3.78

So the new price of the speaker after the sale and the subsequent price increase is $3.78.

The required value of 'a' in the equation of proportionality is 32.

What is direct proportion?

Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value.

It is symbolised by the proportional sign ∝.

For instance, if x and y are two quantities or variables that are intimately linked to one another, we can say x & y. The ratio of x and y becomes equal to a constant when the proportionality sign is removed, for example, x/y = C, where C is a constant.

Given, a = 8b

When b = 4 then

So, a = 8*4 = 32

Hence, the required value of 'a' in the equation of proportionality is 32.

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The formula for the volume of a circular cone:

If the height(h) of the circular cone is given then,

V = 1/3 * π * r² * h

If the slant height(l) of the circular cone is given then,

V = 1/3 * π * r² * √(l² - r²)

the volume of a cone if the height is 10 cm and the diameter is 6 cm is 94.25 cubic centimeters

We know that a right circular cone has a circular base with the apex above the center of the base.

For a right circular cone, with radius r and height h

The formula for the volume of a right circular cone is,

V = 1/3 * π * r² * h

We need to find the the volume of a right circular cone with a circumference.

We know that circumference C = 2πr

From circumference we find the radius of circular base.

Then using the formula for the volume of a right circular cone, we find the volume.

The volume of a circular cone:

If the height(h) of the circular cone is given then,

V = 1/3 * π * r² * h

If the slant height(l) of the circular cone is given then,

V = 1/3 * π * r² * √(l² - r²)

Now we need to find the the volume of a cone if the height is 10 cm and the diameter is 6 cm

From diameter, the radius of the circular base of the cone would be,

r = 6/2

r = 3 cm

also, h = 10 cm

So, V = 1/3 * π * 3² * 10

V = 94.25 cu.cm.

Therefore, the volume of a cone if the height is 10 cm and the diameter is 6 cm is 94.25 cubic centimeters

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None of the solutions are appropriate since the result of the equation z + (z+6) will be equal to 2z + 6.

A mathematical expression is the result of combining a number of mathematical symbols with an arithmetic operator, a variable, and a constraint.

In a different sense, expression is highly helpful in identifying the root or end value of a constraint.

for instance, 3x + 5y

The expression restriction is denoted by the symbols = or, >.

Given the phrase,

z + (z+6)

opening the bracket

z + z + 6

⇒ 2z + 6

Hence

"2z + 6 will be the value of the equation z + (z+6)."

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