What is the solution to this system of equations?
4x-3y=26
3x+2y=11


A:(5,-2)
B:(-2,5)
C:(5,2)
D(8,2)

a) This equation holds true for all x values except x=0, because it would result in division by zero.

b) This equation holds true for all x values except x=0, because it would result in division by zero.

What is inequality?

An inequality is a statement that compares two expressions and is represented by one of the following symbols: < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), ≠ (not equal to).

a) 6x² - x³ = -x² + 2x + 3

b) 6x² - x³ ≤ -x² + 2x + 3

To solve for x in the given inequalities:

a) 6x² - x³ = -x² + 2x + 3

Start by isolating x³ on one side of the equation:

x³ = 6x² + (-x² + 2x + 3)

x³ = 6x² + 2x + 3

Now we can factor out x² from the right side of the equation:

x³ = (x²)(6 + 2/x) + 3

This equation holds true for all x values except x=0, because it would result in division by zero.

b) 6x² - x³ ≤ -x² + 2x + 3

Start by isolating x³ on one side of the inequality:

x³ ≤ 6x² + (-x² + 2x + 3)

x³ ≤ 6x² + 2x + 3

Now we can factor out x² from the right side of the inequality:

x³ ≤ (x²)(6 + 2/x) + 3

This inequality holds true for all x values except x=0, because it would result in division by zero.

Hence,

a) This equation holds true for all x values except x=0, because it would result in division by zero.

b) This equation holds true for all x values except x=0, because it would result in division by zero.

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The slope of this situation is equal to: A. 0.80.

In Geometry, the rate of change of any straight line simply refers to its gradient or slope and it can be calculated by using this mathematical expression;

Rate of change (slope), m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Based on the information provided, we can logically deduce the following slope and data points on the line:

Points on x-axis = 12

Points on y-axis = 9.6.

Substituting the given data points into the slope formula, we have the following;

Rate of change (slope), m = 9.6/12

Rate of change (slope), m = 0.80.

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The probability that an even number is rolled 15 or fewer times when the die is rolled 25 times total can be calculated using the binomial probability formula. In this case, the probability of success is rolling an even number (0.65) and the number of trials is 25.

Using the binomial probability formula, we can calculate the probability of getting 15 or fewer even numbers when the die is rolled 25 times as follows:

P (X <= 15) = P (X = 0) + P (X = 1) + P (X = 2) + ... + P (X = 15)

Where X is the number of even numbers rolled and P(X) is the probability of getting X even numbers.

Using the binomial probability formula:

P(X) = (25 choose X) * (0.65)^X * (0.35)^(25-X)

Plugging in the values, we get:

P(X <= 15) = (25 choose 0) * (0.65)^0 * (0.35)^25 + (25 choose 1) * (0.65)^1 * (0.35)^24 + (25 choose 2) * (0.65)^2 * (0.35)^23 + ... + (25 choose 15) * (0.65)^15 * (0.35)^10

After calculating all the values, we get that the probability of rolling an even number 15 or fewer times when the die is rolled 25 times is about 0.28.

Therefore, the closest answer choice to the probability that an even number is rolled 15 or fewer times when the die is rolled 25 times is 0.25.

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The slope of the line passing through (3, 7) and (-2, -1) is 1.6

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

A linear equation is in the form:

y = mx + b

Where m is the rate of change and b is the initial value

The slope of the line passing through (3, 7) and (-2, -1) is:

Slope = (-1 - 7) / (-2 - 3)

Slope = -8/-5 = 8 / 5

Slope = 1.6

The slope is 1.6

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(15x+7)/(x-1) is the simplified rational expression

What is an expression?

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

Polynomials are algebraic expressions made up of coefficients and variables. Occasionally, variables are referred to as indeterminates. We can execute arithmetic operations on polynomial expressions, such as addition, subtraction, multiplication, and positive integer exponents, but not division by variables.

Factors of 15x²-8x-7 are (15x+7)(x-1)

Factors of  x²–2x+1 are (x-1)²

15x²-8x-7 / x²–2x+1 = (15x+7)(x-1) / (x-1)²  

common factors cancel out

(15x+7)/(x-1) is the simplified rational expression

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The total amount paid with a monthly payment of $100 for a credit of $756.25 at an annual rate of 24.5% is $871.69.

The periodic payment is the amount the car owner pays monthly to offset the balance on the credit card for purchasing new brakes.

The periodic payment is determined using an online finance calculator as follows:

N (# of periods) = 1 year

I/Y (Interest per year) = 24.5%

PV (Present Value) = $756.25

PMT (Monthly Payment) = $100

Results:

Sum of all periodic payments = $871.69

Total Interest = $115.44

Thus the total payment made by the car owner is $871.69 with an interest of $115.44.

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Answer:

$830.52

Step-by-step explanation:

I got it right on the test :)

Have great day

Answer:

−16890

Step-by-step explanation:

Simplify the expression.

Answer:

Step-by-step explanation:

Answer:

So the answer is

FMA Assignment 01

1. Jornal

2. Date (Mar) Accounts Title Debit ($) Credit ($)

1 Cash 60,000

Common Stock 60,000

3 Land 23,000

Buildings 9,000

Equipment 6,000

Cash 38,000

5 Advertising Expenses 1,600

Cash 1,600

6 Prepaid Insurance 1,480

Cash 1,480

10 Equipment 26,000

Accounts Payable 26,000

18 Cash 800

Golf Revenue 800

19 Cash (100 x 15) 1,500

Unearned Revenue 1,500

25 Dividends 1,000

Cash 1,000

30 Salaries Expenses 600

Cash 600

30 Accounts Payable 26,000

Cash 26,000

31 Cash 500

Golf Revenue 500

A constant is fixed, which is arbitrary since you don't know what that fixed number is the arbitrary denotes that no particular value has been ascribed.

The order of a differential equation is equal to the number of arbitrary constants in its general solution.

The highest-order derivative that a differential equation has is used to define the equation's order. The highest-order derivative of a differential equation is defined as its degree, which is expressed as a power. The formula:

c1=a1+ib1

and  c2=a2+ib2

the solution will be

y(x)=(a1+ib1+a2+ib2)cos(ax)+i(a1+ib1−a2−ib2)sin(ax)

If and only if

a2=a1

and  b2=−b1

will be the solution real because of complex conjugates using this property.

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Full question

Can arbitrary constants in solutions to 2nd-order linear differential equations be complex?

From the given points, it was found that the slope is m= -3.

You can correlate two data from a function. An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=9x+5. Where:

m= the slope.

b= the constant term that represents the y-intercept.

For the given example: m=9 and b=5.

The question gives some points of the linear function, see below.

x    y

−1  6

0   3

1   0

2  −3

From the given data you can find the slope by solving the system linear equation.

You can write a system linear equation using the points: (-1,6) and (2,-3), for example.

6=m*(-1)+b  (1)

-3=2m+b    (2)

Multiplying equation 2 by -1, you have

6=-m+b  (1)

3= -2m-b    (2)

Summing the previous equation, you have:

9=-3m

m= -9/3

m= -3

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Answer: the answer is A

Step-by-step explanation: I took the text and got it right

To find the value of f(g(-4)), we need to first substitute -4 into the definition of g(x) and then substitute the result into the definition of f(x).

First we substitute -4 into g(x):

g(-4) = 2(-4)^2 + 4(-4) - 8

g(-4) = 2(16) + (-16) - 8

g(-4) = 32 - 16 - 8

g(-4) = 8

Now we substitute 8 into f(x):

f(g(-4)) = f(8) = 2(8) - 4 = 16 - 4 = 12

So the value of f(g(-4)) is 12.

Answer:

28

Step-by-step explanation:

The expression: f(g(-4)) just means calculate the value of g at x = -4 and then calculate what f is equal to at that value g is equal to, so we have to first calculate g(-4) which we can do by substituting in -4 as x.

g(-4) = 2(-4)^2 + 4(-4) - 8

g(-4) = 2(16) - 8 - 8

g(-4) = 32 - 16

g(-4) = 16

Now from here we can substitute 16 as g(-4) in the expression f(g(-4)) which means we want to evaluate g(16) which we can do by substituting in 16 as x.

f(16) = 2(16) - 4

f(16) = 32 - 4

f(16) = 28

So that means f(g(-4)) = 28

The two situations that describe the volume:

A. the amount of shampoo in a bottle.

B. the amount of soap in a bar of soap.

The space occupied by an object in three-dimensional space is called the volume of an object. In simple words, space is taken by an object.

Four phrases are given.

A. the amount of shampoo in a bottle.

This describes the volume.

B. the amount of soap in a bar of soap.

This also describes the volume.

c. the amount of border around a chalkboard.

This describes the perimeter.

D. the amount of wrapping paper covering a gift

This describes the surface area.

Therefore, A and B describe the volume.

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The complete Question:

Choose all the examples that describe volume.

A. the amount of shampoo in a bottle

B. the amount of soap in a bar of soap

c. the amount of border around a chalkboard

D. the amount of wrapping paper covering a gift

The unknown angle in the parallel lines is a follows;

m∠5 = 75 degrees

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, alternate exterior angles, linear angles, vertically opposite angles etc.

Therefore, let's use the angle relationships to find the m∠5 in the parallel lines.

The angle m∠1 and m∠5 are corresponding angles.

Corresponding angles are congruent.

Therefore,

m∠1 = m∠5 = 75 degrees.

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47 square centimeters is equal to 303.225 square inches.

Measure the length and width of an object, such as a rectangle, and multiply the results to get the number in square centimeters. In the event that the length and width are 15 cm and 10 cm, respectively, the formula is 15 cm*10 cm, which equals 150 cm2.

Any number that is multiplied by itself is transformed into a square. A different word for this is a number squared. The symbol for "squared" is 22 since 2 x 2 equals 4.

In mathematics, the squared sign (2), an arithmetic operator, stands in for multiplying an integer by itself. The "square" of an integer is the sum of that number and itself. Therefore, 10,000 square meters are represented by one square centimeter.

1 square inch = 6.4516 square centimeters.

47 in^2 = 47 × 6.4516

= 303.225 sq. cm

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The simplest choice is a linear transformation, for example, the one given by the

matrix [tex]\left[\begin{array}{ccc}-1/2&1&0\\-1/2&0&1\end{array}\right][/tex]

When you represent a three-dimensional object graphically in the plane con paper, the blackboard, or a computer screen), you have to transform spatial coordinates,

[tex]$\mathrm{x} 1$ & \\[/tex]

[tex]$\mathrm{x} 2$[/tex] & into plane coordinates

[tex]$\mathrm{x} 3$[/tex]& [tex]$\mathrm{y} 1$[/tex]& [tex]$\mid$ \\[/tex]

[tex]$\mathrm{x}$[/tex] &[tex]$\mathrm{y} 2$[/tex] &

The simplest choice is a linear transformation, for example, the one given by the

matrix [tex]\left[\begin{array}{ccc}-1/2&1&0\\-1/2&0&1\end{array}\right][/tex]

The complete question is,

When you represent a three-dimensional object graphically in the plane (on paper, the blackboard, or a computer screen), you have to transform spatial coordinates | x 1 | | x 2 | into plane coordinates | y 1 |. | x 3 | | y 2 | The simplest choice is a linear transformation, for example, the one given by the matrix | -1/2 1 0 0 | 1 |.

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No, you are not given enough information to prove that the quadrilateral is a parallelogram.

In order to prove that the quadrilateral is a parallelogram, we must have four points to calculate the lengths of the sides and angles. We need to verify that the opposite sides of the quadrilateral are equal in length and that the opposite angles are equal. We can use the formula for the area of a parallelogram: A = b*h, where b is the length of the base and h is the height of the parallelogram. We can also use the formula for the sum of the angles of a quadrilateral: A1 + A2 + A3 + A4 = 360 degrees. Without having the four points, we cannot calculate the lengths of the sides or angles, so we cannot prove that the quadrilateral is a parallelogram.

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The average of two numbers, A and B, is calculated by adding them together and then dividing by two. In this case, A = 21, B = 20, X = 19, and Y = 20. When we calculate (A + B) / 2, we get 20.00.

1. Add A and B together: 21 + 20 = 41

2. Divide the sum by 2: 41 ÷ 2 = 20.50

3. Round the answer to two decimal places: 20.50 → 20.00

The average of two numbers, A and B, is calculated by adding them together and then dividing by two. This formula is expressed as (A + B) / 2. In this problem, we were given the values A = 21, B = 20, X = 19, and Y = 20. To solve for the average, we first need to add A and B together and get 41. Then we divide this sum by two and get 20.50. To get the final answer, we need to round this value to two decimal places, which results in the answer 20.00. This answer indicates that the average of 21 and 20 is 20.00.

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Without the equation of the graph of the region R, it is not possible to determine the volume of the solid defined by a region R, an isosceles right triangle cross-section, and a line y=k.

The question describes a solid where the base is a region R in the first quadrant, bounded by the graph of y, the x-axis, and the line y = k.

It is also mentioned that each cross section perpendicular to the y-axis is an isosceles right triangle with the right angle on the x-axis and one leg in the XY-plane.

However, the equation of the graph of the region R is not given, which makes it impossible to determine the range of y over which the solid is defined and therefore, calculate the volume of the solid. It's very important to have the equation of the graph of the region R to find the volume of the solid.

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The question is -

Let R be the region In the first quadrant bounded by the "graph of y the !-axis, and the line y The region R Is the base of a solid For the solid, each cross section perpendicular [tex]t_0[/tex] to the y-axis Is an isosceles right triangle with the right angle on the !-axis and one leg in the 1y-plane What is Ithe volume of the solid?

Answer:

Expression: 5y+3x+9

Coefficients: (of y) 5, (of x) 3

Constant: 9

Hope this helps :)

Step-by-step explanation:

The coefficient(s) of an equation will always be the number that sits next to/attached to a variable. The constant of an equation will always be the number(s) that stands alone.

All terms should be shifted to the left and set to zero. After that, make each factor equal to zero. [tex]C=\frac{P}{1+M}$$[/tex]

P=C+M C

As C + M C = P, rewrite the equation.

C+M C=P

Add C to the equation on both sides. .MC=P−C

Simplify M C = P C by dividing each term by C.

Divide each phrase into [tex]$M C|=| \boldsymbol{P}-\boldsymbol{C}$[/tex] by C

[tex]\frac{M C}{C C} \equiv \frac{P}{C}+\frac{-C}{C}$$[/tex]

C's common factor should be cancelled.

[tex]$M=\frac{P}{C}+\frac{-C}{C}$[/tex]

M=PC−1

An equation that is mostly made up of letters is said to be literal. Literal equations include those found in formulas. Each variable acts as a "literal" representation of an essential element of the overall relationship that the equation expresses. For instance, P = 2L + 2W is a formula for expressing a rectangle's perimeter.

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An Interval is all the numbers between two given numbers. 95% confidence level would result in a wider confidence interval.

What is interval in math?

Given data :

confidence interval = ( -11.98, -4.52)

-11.98≤x≤-4.52, [-11.98,-4.52], and {x∈ℝ|-11.98≤x≤-4.52} all mean that x is between -11.98 and -4.52 and could be either endpoint.

95% confidence level would result in a wider confidence interval. Increasing the confidence level increases the length of the confidence interval.

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Ridge regression is a type of linear regression used to reduce the effects of multi-collinearity. It is used with 1000 labeled examples to minimize the sum of the squared errors of the model.

Ridge regression is a type of linear regression used to reduce the effects of multi-collinearity. It adds a penalty term to the cost function that penalizes large coefficients, thus reducing their magnitude. The penalty term is a regularization term that is added to the cost function to minimize overfitting. To use ridge regression, one must select a value for the regularization parameter. This parameter determines how much the model weights the penalty term, and is usually determined through cross-validation. With 1000 labeled examples, ridge regression can be used to minimize the sum of the squared errors of the model. The model is then trained on the data, and predictions can be made. Ridge regression is a powerful tool for reducing the effects of multi-collinearity, and can be used to accurately model relationships between variables.

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The height of the tree is 8 feet.

Triangles which has the same shape but are different in size are said to be similar triangles for example all equilateral triangles are similar triangle.  

It is also defined as if the corresponding sides of two triangles are in proportion then the two triangles are said to be a similar triangles. The symbol ‘~’ is used to denote the similarity between two triangles.

If two triangles ΔABC and ΔXYZ are two similar triangles then the condition between corresponding sides is given by

Here we have

John's height is 6 feet

He standing 4 feet from a tree

Johns's shadow is 12 feet long  

We can represent the whole scenario as two similar triangles

[ Picture is given below ]

As we know in Similar triangles the ratio of corresponding sides is equal

Let 'x' be the height of the tree

From given figure  

=> AC: DE = BC: EB  

=> x : 6 = 16 : 12

=> x/6 = 16/12

=> 12x = 16 × 6  

Divided by 6

=> 2x = 16

Divided by 2

=> x = 8

Therefore,

The height of the tree is 8 feet.

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The vertex for the graph is at (2, 0).

A parabola is formed by cutting a right circular cone in half along a plane perpendicular to the cone's generator. It is a locus of a moving point whose separation from the focus is equal to its separation from a stationary line (directrix)

Focus is a fixed point.

Directrix is the name for fixed lines.

Given the graph is a parabola,

A parabola's vertex is the location where its symmetry line and parabola intersect. The vertices of a parabola whose equation is provided in standard form will be the lowest (lowest point) and highest (highest point) points on the graph, respectively.

The minimum point in graph is (2, 0)

Hence vertex is (2, 0).

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The complete question is in image,

Answer:

Step-by-step explanation:bmmmv m

Answer:

h = 6 m

Step-by-step explanation:

the area (A) of a trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂)

where h is the perpendicular height between the bases b₁ and b₂

given A = 51 , b₁ = 10 and b₂ = 7 , then

[tex]\frac{1}{2}[/tex] h (10 + 7) = 51 ( multiply both sides by 2 to clear the fraction )

17h = 102 ( divide both sides by 17 )

h = 6 m

Find the height of the trapezoid.

if the area of the trapezoid is [tex]51m^{2}[/tex] and parallel sides are [tex]7m[/tex] and [tex]10m[/tex].

To find the height of the trapezoid, substitute the area and parallel sides into the formula for the area of the trapezoid.

Trapezoid area formula is

[tex]L=\frac{1}{2}(number of parallel sides)(height)\\ L=\frac{1}{2} (a+b)(t)[/tex]

The next step is substitute the area and parallel sides into the formula for the area of the trapezoid.

[tex]51=\frac{1}{2}(7+10)(t)[/tex]

Complete the arithmetic operation

[tex]51=\frac{1}{2}(17)(t)\\ 51=\frac{17}{2}(t)[/tex]

Multiply each side by [tex]\frac{2}{17}[/tex]

[tex]51(\frac{2}{17}) =\frac{17}{2}(\frac{2}{17})(t)\\ 6=t[/tex]

So the height of the trapezoid is [tex]6m[/tex]

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It is false that x is a function of y

The given equation to be used to determine the truth and falsity of the statement is given as:

The given parameters are function of x

x = y²

determine whether the relation represents y as a function of x

x^2 + y^2 =25

x = y²

Set y = 2

x = (2)²

Taking the square root of the value

x = 4

Set y = -2

x = (-2)²

x = 4

From the experiment, the different values of y give the same x value.

therefore, this means that x is not a function of y

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Answer:

22.386

Step-by-step explanation:

The volume of the container is (x+6)(x-2)(x-1) cubic feet and it can be express as the form of polynomial.

Six faces make up the three-dimensional shape of a rectangular prism. The prism's faces are all rectangles. The shape of a rectangular prism is cuboidal.

There are two sets of parallel and congruent bases in this polyhedron. It has eight vertices, 12 sides, and six faces. Rectangular prisms are also known as a right rectangular prism, rectangular parallelepiped, and rectangular hexahedron.

Right rectangular prisms and oblique prisms are the two primary varieties of rectangular prisms. The bases of a right rectangular prism are parallel to the other faces.

The volume of a rectangular prism is simply the product of its three dimensions: in your case, the volume of the prism is, given x

[tex](x+6)(x-2)(x-1)[/tex]

A polynomial is a sum (with some coefficients) of powers of x, so, if we expand the product just written, we have.

[tex]=(x+6)(x-2)(x-1)\\\\=(x^2-2x+6x-12)(x-1)\\\\=(x^3+4x^2-12x-x^2-4x+12)\\\\=(x^3+3x^2-16x+12)[/tex]

Which is a polynomial and expresses the volume of the prism.

the complete question is,

How do you write a polynomial that represents the volume of a box that is a rectangular prism has the dimensions length x+6, width x-2, and height x-1?

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The class interval [15-19] has the greatest frequency, and the class interval [10-14] has the least frequency

From the question, we have the following parameters that can be used in our computation:

10. 9. 5. 19. 17

13. 2. 0. 4. 10

1. 16. 9. 7. 3

15. 17. 18. 16. 6

Using a class of 5, we have the following class intervals

0 - 4, 5 - 9, 10 - 14 and 15 - 19

When the frequencies of each class are counted, we have the following table

Interval Midpoint Frequency R/F        C/F

0 - 4 2           5                 5/20 5

5 - 9 7           5                 5/20 10

10 - 14 12           3                 3/20 13

15 - 19 17            7                 7/20 20

using the above as a guide, we have the following:

The class interval [15-19] has the greatest frequency 7

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