A new savings account is opened with $400 and gains 3% every year. What is the value of the account at 32 years?

The polynomial p(x) is x³ - 7x - 6 that is (x+1) (x+2)(x - 3)

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

Given that polynomial:

p(x) = x³ - 7x - 6

Known factor: (x+1)

polynomial equation expressed as the sum of linear components.

The degree of polynomial is 3, and when we divide it by a linear equation, the result will be a quadratic.  That quadratic will have 2 solutions.

We can solve the quadratic in two linear factors and as a result we will have the answer.

First of all, we need to divide the polynomial  p(x)with the given factor (x+1) to find the other factors.

x³ - 7x - 6/x+1 = x² - x -6

Solving the quadratic:

x²- x - 6 = x² -3x +2x - 6

x(x-3)+2(x-3)

(x+2)(x-3)

Therefore the polynomial will be p(x) = x³ - 7x - 6 = (x+1) (x+2)(x - 3)

The complete question is : The polynomial p ( x ) = x 3 − 7 x − 6 p(x)=x 3 −7x−6p, left parenthesis, x, right parenthesis, equals, x, cubed, minus, 7, x, minus, 6 has a known factor of ( x + 1 ) (x+1)left parenthesis, x, plus, 1, right parenthesis. Rewrite p ( x ) p(x)p, left parenthesis, x, right parenthesis as a product of linear factors. p ( x ) = p(x)=p, left parenthesis, x, right parenthesis, equals

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Factoring x³ is a relatively straightforward process.

Factory is a quantity or an expression that is multiplied to another quantity or expression to obtain a product. Factor are used in mathematics to solve problems involving multiplication division and equation factor can also be used in financial analysis to calculate interest, payments loan repayments, and another financial transaction factor can also be used to analyze supply and demand market trends and other economic indicators.

The most common way to factor x³ is to use the factorization method. This involves writing x³ as a product of three linear factors, which can be done in the following way:

x³ = x × x × x

Alternatively, you can use the method of grouping to factor x³. This involves writing x³ as a product of two binomials, which can be done in the following way:

x³ = (x × x) × x

You can also use the method of synthetic division to factor x³. This involves dividing the coefficient of x³ by the coefficient of x and then dividing the resulting coefficients by the coefficient of x. This can be done in the following way:

x³ = x² + 0 × x + 0

Once you have factored x³, you can use the factors to solve equations or to find other information related to the equation. In addition, you can use the factored form of x³ to simplify certain expressions.
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Answer:

False

Step-by-step explanation:

[tex]2\sin x \cos x =\sin 2x \implies 4 \sin x \cos x=2\sin 2x \\ \\ \therefore \int 4\sin x \cos x dx=2\int \sin 2x dx \\ \\ 2\int \sin 2x dx=\frac{2}{2}(-\cos 2x)+C=-\cos 2x+C[/tex]

The value of x is 10.

What is expression?

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.

The structure of an expression is:

Expression is (Number/variable, Math Operator, Number/variable)

According to the given question:

EF = 10x+20

FG=36

EG=156

The following expression is true for the given data.

EF+FG = EG

Substitute the given data into the expression

(10x + 20) + (36) = 156

Solve for the unknown value of x

10x + 56 = 156

10x = 100

x = 10

Hence the value of x is 10.

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Triangle ABC is congruent to Triangle CDA using the SSS rule.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

SSS rule states that,

If the three sides of one triangle are equal to the three sides of another triangle, then the triangles are congruent.

To prove:

ΔABC ≅ ΔCDA.

AB = DC ( given)

AD = BC (given)

AC = AC (common to both the triangles)

ΔABC ≅ ΔCDA ( By SSS rule )

Thus,

ΔABC ≅ ΔCDA by SSS rule.

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The point lies in the solution set if x represents the number of children's books and y represents the number of puzzle books Amelie buys (9,5).

To find the point that lies in the solution set, you need to consider the constraints given in the problem. Amelie wants to purchase at least 2 more children's books than puzzle books, which means that the number of children's books should be greater than or equal to the number of puzzle books plus 2. She can afford no more than 15 items total, which means that the total number of children's books and puzzle books should be less than or equal to 15.

Based on these constraints, the point that lies in the solution set is (9,5). This point satisfies both constraints, because the number of children's books (9) is greater than the number of puzzle books (5) plus 2, and the total number of children's books and puzzle books (14) is less than or equal to 15. Therefore, the correct answer is (d) (9,5).

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The value of x in the equation 5/3x + 1/3x = 13⅓ + 8/3x is calculated as: x = -20.

To solve an equation is to find the value of the variable by isolating it in such a way that it is moved to one side of the equation.

Given the equation, 5/3x + 1/3x = 13⅓ + 8/3x, to solve this equation, we need to find the value of x by isolating the variable x to one side.

Follow the steps below:

5/3x + 1/3x = 40/3 + 8/3x

2x = 40/3 + 8/3x

Substract both sides by 8/3x:

2x - 8/3x = 40/3 + 8/3x - 8/3x

-2/3x = 40/3

Multiply both sides by -3/2:

-2/3x × -3/2 = 40/3 × -3/2

x = -120/6

x = -20

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So, we ordered 4 size 3 balls for the 7-8 year old team and 11 size 5 balls for the 14 year old team.

To solve this problem, we can set up a system of equations to represent the information given in the problem. Let x be the number of size 3 balls purchased for the 7-8 year old team, and let y be the number of size 5 balls purchased for the 14 year old team.

The first equation will represent the cost of the size 3 balls: 15x = $220.

The second equation will represent the cost of the size 5 balls: 20y = $220.

The third equation will represent the total number of balls purchased: x + y = 12.

Now that we have set up the system of equations, we can solve for x and y using the method of substitution.

First, we can solve the first equation for x: x = $220 / 15 = 12/3 = 4.

Then, we can substitute this value for x in the second equation: 20y = $220 -> y = $220 / 20 = 11.

Finally, we can check our solution by substituting these values for x and y in the third equation: 4 + 11 = 15, which does not equal 12. This means that our solution is incorrect.

To find the correct solution, we can go back and try solving the second equation for y instead: y = $220 / 20 = 11.

Then, we can substitute this value for y in the first equation: 15x = $220 -> x = $220 / 15 = 12/3 = 4.

Finally, we can check our solution by substituting these values for x and y in the third equation: 4 + 11 = 15, which equals 12. This means that our solution is correct: we ordered 4 size 3 balls for the 7-8 year old team and 11 size 5 balls for the 14 year old team.

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The first equation will represent the cost of the size 3 balls: 15x = $220.

The second equation will represent the cost of the size 5 balls: 20y = $220.

The third equation will represent the total number of balls purchased: x + y = 12.

Now that we have set up the system of equations, we can solve for x and y using the method of substitution.

First, we can solve the first equation for x: x = $220 / 15 = 12/3 = 4.

Then, we can substitute this value for x in the second equation: 20y = $220 -> y = $220 / 20 = 11.

Finally, we can check our solution by substituting these values for x and y in the third equation: 4 + 11 = 15, which does not equal 12. This means that our solution is incorrect.

To find the correct solution, we can go back and try solving the second equation for y instead: y = $220 / 20 = 11.

Then, we can substitute this value for y in the first equation: 15x = $220 -> x = $220 / 15 = 12/3 = 4.

Finally, we can check our solution by substituting these values for x and y in the third equation: 4 + 11 = 15, which equals 12. This means that our solution is correct: we ordered 4 size 3 balls for the 7-8 year old team and 11 size 5 balls for the 14 year old team.

No, using divisibility test we find that 3194 is not divisible by 3.

According to the rule of three, if a whole number's digit sum is a multiple of three, the original number is also divisible by three. It is simple to determine if a lower number is divisible by 3 or not using the three-digit multiplication table or skip counting by three (beginning at 0 and adding 3). Without actually dividing larger numbers, we can determine if they are entirely divisible by three or not.

If a whole number's digit sum is a multiple of three or precisely divisible by three, it is said to be divisible by three.

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this question is incomplete, the complete question is

3194 is divisible by 3 yes or no?

An asymptote of a function is a line that the graph of the function gets closer and closer to, but never touches. It is an approaching line that has a fixed slope.

An asymptote of a function is a line that the graph of the function gets closer and closer to, but never touches. It is an approaching line that has a fixed slope. Asymptotes are used to determine the behavior of a function as it approaches infinity or negative infinity. They can be used to help visualize the behavior of the function in the large and small limits. Asymptotes can be either horizontal or vertical. A horizontal asymptote is a line that the graph of the function approaches as it approaches positive or negative infinity, and a vertical asymptote is a line that the graph of the function approaches as it approaches either the positive or negative x-axis. Asymptotes can also be used to describe the behavior of a function near a local minimum or maximum. Asymptotes can be found by looking at the degree and leading coefficient of a polynomial, or by analyzing the behavior of the function at different points.

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The measure of the missing angle in the given isosceles triangle ABC is 70°   .

The Isosceles Triangle is defined as a type of triangle in which the measure of the angle of two sides of the triangle are equal in measure .

In the figure given below , we can see that ,

In triangle ABC , the triangle is an isosceles triangle ,

So , measure of angle B is = x° ;

the measure of angle C is = x° ;

So , By Angle Sum Property Of Triangle ;

∠B + ∠C + ∠A = 180°

x° + x° + 40° = 180° ;

2x + 40 = 180

2x = 180 - 40 ;

2x = 140 ;

x = 140/2 ;

x = 70° .

Therefore , the measure of the missing angle is 70° .

The given question is incomplete , the complete question is

How do you find the measure of the missing angle of the given isosceles triangle ?

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The nature of roots of the given quadratic equation is "real and unequal".

Nature of Roots:

Root type simply means the category to which the root belongs. Roots can be imaginary, real, unequal, or equal. If the discriminant is negative, the root is imaginary.

Depending on the value of the discriminant, we discuss the following cases for the nature of the root:

Case 1: D = 0

If the discriminant is zero (b2 – 4ac = 0), a, b, and c are real, and a≠0, the root of the quadratic equation is ax2 + bx + c = 0 is Real and equal. In this case the root is x = -b/2a. A graph of the equation is tangent to the x-axis at a point.

Case 2: D > 0

If the discriminant is greater than zero (b2 – 4ac > 0), then a, b, and c are real and a≠0, then the root of the quadratic equation ax2 + bx + c = 0 is real and not equal. The equation graph touches the x-axis at two different points.

Case 3: D < 0

If the discriminant is less than zero (b2 – 4ac < 0), a, b, and c are real, and a≠0, then the root of the quadratic equation ax2 + bx + c = 0 is Imaginary and not equal. Roots exist in conjugate pairs. The equation graph does not touch the x-axis.

Case 4: Perfect Square with D > 0

If D > 0 and Perfect Square, the roots of the quadratic equation are real, unequal, and rational.

Case 5: D > 0 and Not Perfect Square

If D > 0 and not perfect square, the roots of the quadratic equation are real, unequal, and irrational.

According to the Question:

The given quadratic equation:

2x²-4x-3 = 0

Here, a = 2, b = - 4 and c = -3

To Find: the nature of roots of the given quadratic equation.

∴ Discriminant, D = b²-4ac

= (-4)² - 4×2×(-3)

= 16 -8(-3)

= 16 + 24

=40

Since,

D = 40 > 0, the roots are real and unequal.

Hence, the nature of roots of the given quadratic equation is "real and unequal".

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To identify whether a mathematical expression represents a "greater than" or "less than" relationship, you can use the following symbols:

Greater than: >

Less than: <

For example, the expression "3 > 2" represents a "greater than" relationship because it means that 3 is greater than 2. Similarly, the expression "5 < 7" represents a "less than" relationship because it means that 5 is less than 7.

You can also use the symbols "greater than or equal to" and "less than or equal to" by using the following symbols:

Greater than or equal to: >=

Less than or equal to: <=

For example, the expression "3 >= 2" represents a "greater than or equal to" relationship because it means that 3 is greater than or equal to 2. Similarly, the expression "5 <= 7" represents a "less than or equal to" relationship because it means that 5 is less than or equal to 7.

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The area of segment enclosed by chord [BC] is 0.94 [tex]cm^{2}[/tex]

Segment and area of a circle segment:

A segment is essentially the area of a circle between the chord and the arc. A circle is a path that a point equidistant from a single point on the plane can follow; this point is known as the circle's center, and the distance between it and that point is known as the circle's radius. A segment is a section of a circle's interior. A sector is the region that a segment encloses and the angle that a segment occupies. By deducting the triangle formed inside the sector from the sector where the segment is located, one can calculate the area of a circular segment.

Given radius and angle subtended by arc on circle is 4 cm and 55° respectively.

So the length of chord [BC] is [tex]\frac{55}{180}[/tex]×π = 3.84 cm.

Required area of segment enclosed = Area of segment subtended by arc [BC] - area of ΔABC

>semi-perimeter of ΔABC is [tex]\frac{(4+4+3.84)}{2} = 5.92[/tex]

>Area of ΔABC is [tex]\sqrt{5.92*(5.92-4)*(5.92-4)*(5.92-3.84)} = 6.74 cm^{2}[/tex]

>Area of segment subtended by arc {BC} = θ/360° × π[tex]r^{2}[/tex]

                                                                     =[tex]\frac{55}{180}[/tex]×16π

                                                                     = 7.68[tex]cm^{2}[/tex]

∴The area of segment enclosed by chord [BC] is [tex]7.68-6.74 = 0.94 cm^{2}[/tex]

The area of segment enclosed by chord [BC] is 0.94 [tex]cm^{2}[/tex]

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The value of other Zeroes are -1/2,2

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable)

Algebraic expressions known as polynomials can have exponents that are multiplied, divided, or added. Polynomials come in various varieties. Monomial, binomial, and trinomial, respectively. A monomial is a polynomial with only one term. A polynomial having two dissimilar terms is called a binomial.

Given ,

p(x)=2x ³ +3x² −11x−6

Since x=−3 is a zero of p(x)

So, by factor theorem x+3 is a factor of p(x)

Now, if we divide 2x³+3x²−11x−6 by x+3, quotient is 2x² −3x−2 and remainder is 0.

Therefore,

2x³+3x² −11x=(x+3)(2x² −3x−2)

=(x+3)(2x+1)(x−2)

for other zeroes of p(x)

2x+1=0,x−2=0

Hence the other zeroes are − 1/2,2

The complete question is : Find all the other zeros of the polynomial p(x)=2x³ +3x ² −11x−6 if one of its zero is −3.

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the residual plot below suggests that this violation is Heteroscedasticity

The residual is the discrepancy between the actual value and the model's estimated value. The fundamental premise of regression or time series analysis is that the residual variance or quantity should be constant. As a result, there shouldn't be any patterns visible in the residual scatter plot.

The residuals scatter plot reveals a pattern. The dispersion of residuals is growing at higher values of Docs. As a result, residual variance is not constant.

Heteroscedasticity is present when the residual variance is non-constant. Regression makes the supposition that the residual variance should be constant (Homosceasticity). Consequently, the scatter plot of residuals violates the heteroscedasticity condition.

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Answer:

B

Step-by-step explanation:

Answer: B, √60 .

Step-by-step explanation: Irrational numbers are numbers that can not be written in the form of a/b. To further explain, this includes any decimals that go on forever and are non-repeating, such as pi 3.14159... Numbers that have repeating numbers like 5.5555555 are rational, so don't get confused between the two! The square root of 60 is 7.74596669 making it the only irrational number here.

The slope of the given function 4x + 2y = -10 is equal to -2.

As given in the question,

Given function is equal to 4x + 2y = -10

Standard form  of the equation in slope intercept form is given by :

y = mx  + c

'm' is the slope of the function

'c' is the value of y-intercept.

Now simplify the given function in standard form we have,

4x + 2y = -10

⇒2y = -4x -10

⇒ y = (-4x -10 ) / 2

⇒ y = -2x - 5

Compare with the standard form we get,

Slope of the function m = -2.

Therefore, the slope of the given function 4x + 2y = -10 is given by m = -2.

The given question is incomplete , the complete question is:

What is the slope of the function 4x + 2y =- 10?

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The standard form of linear equation in two variables is Ax + By = C.

The standard form of linear equation in two variables is Ax + By = C, where A, B and C are constants and A and B are not both zero. This equation can be used to represent a line on a graph, which can be found by plotting any two points that satisfy the equation.

To calculate the equation of a line in standard form, first identify two points on the line. For example, point (x1, y1) and point (x2, y2). Then, calculate the slope of the line using the formula m = (y2 - y1) / (x2 - x1). The slope determines the constants A and B for the equation. A = m and B = -1. Finally, calculate the constant C by substituting one of the two points into the equation. C = Ax1 + By1.

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a. The probability that a randomly selected home run was hit to right field is 0.286.

b. The probability that a randomly selected home run was hit to left field is 0.031.

c. Yes it was unusual for this player to hit a home run to left field.

From the information, the baseball player hit 63 home runs in a season. Of the 63 home runs, 18 went to right field, 25 went to right center field, 9 went to center field, 9 went to left center field, and 2 went to left field.

The probability that a randomly selected home run was hit to right field is:

= 18 / 63

= 0.286.

The probability that a randomly selected home run was hit to left field is:

= 2 / 63

= 0.031.

It was unusual for this player to hit a home run to left field as the chance is 3%.

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The end behavior of the graph would be that it would approach negative infinity as x approaches positive infinity, and negative infinity as x approaches negative infinity.

When the degree of a polynomial is even and the leading coefficient is negative, the end behavior of the graph is that it will approach negative infinity as x increases or decreases without bound in either direction. This is because the degree of the polynomial is even and the coefficient is negative, meaning that the leading term will always be negative. Since the leading term is always negative, the graph will approach negative infinity as x increases or decreases without bound in either direction. This is the general behavior of a polynomial with even degree and a negative leading coefficient.

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Answer:

The answer is A but I must put very much more characters in order to fulfill the character limit

The number that is 10 more than 40 is 50, using addition.

Addition (usually signified by the plus symbol +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division.The addition of two whole numbers results in the total amount or sum of those values combined. The example in the adjacent image shows a combination of three apples and two apples, making a total of five apples. This observation is equivalent to the mathematical expression "3 + 2 = 5" (that is, "3 plus 2 is equal to 5").

Besides counting items, addition can also be defined and executed without referring to concrete objects, using abstractions called numbers instead, such as integers, real numbers and complex numbers. Addition belongs to arithmetic, a branch of mathematics. In algebra, another area of mathematics, addition can also be performed on abstract objects such as vectors, matrices, subspaces and subgroups.

Here, what we can do is use addition to find the number that is 10 more than 40.  

We can do 10 + 40 = 50.

Hence, the number that is 10 more than 40 = 50.

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Besides counting items, addition can also be defined and executed without referring to concrete objects, using abstractions called numbers instead, such as integers, real numbers and complex numbers. Addition belongs to arithmetic, a branch of mathematics. In algebra, another area of mathematics, addition can also be performed on abstract objects such as vectors, matrices, subspaces and subgroups.

Here, what we can do is use addition to find the number that is 10 more than 40.  

We can do 10 + 40 = 50.

Hence, the number that is 10 more than 40 = 50.

We constantly gauge a prism's height perpendicular to the plane of its base. That holds true even when a prism is tilted or turned on its side.

Volume of a prism is equal to base area into height.

A prism's total surface area is equal to the sum of its two bases' surfaces and lateral surface area.

Without bases, the prism's faces are parallelograms or rectangles. And any n-sided polygon, whether a triangle, square, rectangle, or other, might serve as the prism's basis.

Dimensions of a prism. the separation between a prism's two bases. The technically smallest line segment between the bases . The term "altitude" also relates to how long this part is.

Any prism's volume is equal to V = BH, where B is its base's area and H is its height.

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Answer:

1

Step-by-step explanation:

The square root of 1 is called 1.

In mathematics, the square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 4 is 2, because 2 x 2 = 4. The square root of 9 is 3, because 3 x 3 = 9.

The square root of 1 is 1, because 1 x 1 = 1. Therefore, the square root of 1 is simply called 1.

In slope intercept form, Equation 14x-20y=-13 can be written as 13 + 4y/20 = y.

The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation. The slope, m, is a measure of how steep a line is. The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables.

Given,

Equation

14x-20y=-13

In slope intercept form

13 + 4x = 20y

13 + 4y/20 = y

In slope intercept form, Equation 14x-20y=-13 can be written as 13 + 4y/20 = y.

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First make the graph of the functions, then  if the two graphs are symmetric with respect to the line y = x (mirror images over y = x ), then they are inverse functions.

Symmetric

A figure or shape that can be divided into two equal parts by a line is called symmetric figures.

Inverse Functions

The inverse function of a function f  is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by F^-1.

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The surface area of the net of the triangular prism in the space provided,

2400cm².

Prism is a polyhedron with two identical ends in three dimensions.

Surface area = (Perimeter of the base × Length of the prism) + (2 × Base                Area)

                     = (S₁ + S₂+ S₃)l + bh

where, b is the bottom edge of the base triangle, h is the height of the base triangle, l is the length of the prism and S₁, S₂, and S₃ are the three edges (sides) of the base triangle (bh) is the combined area of the two triangular faces [2 × (1/2 × bh)] = bh.

The side of the triangle is S₁ = 8, S₂= 15, and S₃= 17.

The rectangular's base = 20 and height = 8

Substituting all the values in the formula:

Surface area

= (Perimeter of the base × Length of the prism) + (2 × Base Area)

= [ ( 15 +17+8) x 20] + (20 x 80)

= 800 + 1600

= 2400 cm²

Therefore, the surface area of the prism is 2400 cm².

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