exercise 1.1.14 in each case either show that the statement is true, or give an example showing it is false. (a) If a linear system has n variables and m equations, then the augmented matrix has n rows. quations • (b) A consistent linear system must have infinitely many solutions. . (c) If a row operation is done to a consistent linear system, the resulting system must be consistent. (d) If a series of row operations on a linear system results in an inconsistent system, the original system is inconsistent.

The point that lies in the solution set of (x - 2)²/25 + (y + 3)²/4 < 1 is B. (3, –2.5)

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

(x - 2)²/25 + (y + 3)²/4 < 1

Also, we have

A. (4, –0.5)

B. (3, –2.5)

C. (–2.5, 4)

D. (–4.5, –3)

Next, we test the options as follows

A. (4, –0.5)

(4 - 2)²/25 + (-0.5 + 3)²/4 < 1

1.7225 < 1  -- false

B. (3, –2.5)

(3 - 2)²/25 + (-2.5 + 3)²/4 < 1

0.1025 < 1   -- true

Hence, the point that lies in the solution set is B. (3, –2.5)

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The given function does not have an end behavior because it is not a polynomial function.

The end behavior of a function refers to how the function behaves or approaches as the input values (x-values) of the function become extremely large (approaching positive infinity) or extremely small (approaching negative infinity).The long term behavior of the function when x moves towards the ends of the coordinate plane can be predicted.

In a polynomial function, the leading coefficient and degree of the function often determine the polynomial function.

The given function is;

f(x) = 2x² - 5 / x² - 1

The end behavior of this function does not exist because this is not a polynomial.

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The function y=x+3 has the greatest y intercept.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The given function is y=x, it has y intercept which is zero

The given function is y=-x, it has y intercept which is zero

Function is y=x+3, it has y intercept which is three

Function is y=2x, it has y intercept which is zero

Hence, the function y=x+3 has the greatest y intercept.

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Answer:

$280

Step-by-step explanation:

7•40=$280

Answer:

y is 0,3

Step-by-step explanation:

To find the x-intercept, substitute in

0

for

y

and solve for

x

. To find the y-intercept, substitute in

0

for

x

Answer:

(0,3)

Step-by-step explanation:

Two methods:

Method 1:  General method for any equation

Method 2: Method specific for parabolas in standard form

Method 1:  General method for any equation

For any two-variable equation to be graphed, the y-intercept is the point where the graph crosses the y-axis.  The y-axis is a vertical line through the origin (0,0).

Any y-intercept is on that line, and to get to that point starting from the origin, one can't travel left or right to get to the y-intercept point (without moving back to the y-axis).  The only movement would be up or down.

Since no left-right movement will happen, the x-coordinate is zero.

For any two-variable equation, the x and y coordinates of any point on the graph are linked by the equation.  If it is known that the x-value is zero, the y-value associated with that x-value is given by substituting zero into the equation everywhere there is an "x", and solving for "y".

[tex]y=-4x^2-x+3[/tex]

[tex]y=-4(0)^2-(0)+3[/tex]

Order of operations requires exponents before multiplication, or addition & subtraction...

[tex]y=-4(0)-(0)+3[/tex]

multiplication...

[tex]y=0-0+3[/tex]

addition & subtraction, from left to right...

[tex]y=3[/tex]

So, when the x-value is zero, the y-value is three.  Therefore, the ordered pair representing that point is (0,3).

Method 2: Method specific for parabolas in standard form

The given equation is the equation for a parabola (as stated in the question), and it is given in "standard form": [tex]y=ax^2+bx+c[/tex], where a, b, and c are real numbers (and a isn't equal to zero, because then the x-squared term would be zero, and the equation would really just be a linear equation).

Note that for our equation, it is in standard form if we rewrite the equation to only use addition, [tex]y=-4x^2+-1x+3[/tex], where [tex]a=-4, ~b=-1 ~ \text{and}~c=3[/tex]

For a parabola in standard form, the y-intercept is always at a height of "c".

So, the y-intercept would be (0,3).

Based on a system of equaitons, the initial opening fee (one-time payment) is $5.00, the monthly maintenance fee is $11.00, while an equation that models Adam's fees over time in months, x is y = 11x + 5.

A system of equations or simultaneous equations are two or more equations solved concurrently or at the same time.

An equation is a mathematical statement showing the equality or equivalence of two or more algebraic expressions.

While algebraic expressions combine variables with numbers and mathematical operands, equations use the equal symbol (=).

Total Fees after x months

x = # of months    y = total fees ($)

2                                      27

3                                      38 (11 x 3 + 5)

4                                      49 (11 x 4 + 5)

5                                     60

Let w = the monthly maintenance fee

Let z = the one-time opening fee

5w + z = 60 ... Equation 1

2w + z = 27 ... Equation 2

Subtract Equation 2 from Equation 1:

3w = 33

w = 11

b) The monthly maintenance fee is $11.00.

a) The initial (one-time) opening fee is $5.00.

z = 60 - 55

= 5

c) The total fees after x months is y = 11x + 5.

Thus, the one-time opening fee and the monthly maintenance fee can be computed using a system of equations.

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Answer:

A. Using the commutative property

Step-by-step explanation:

Because there is no use of commutative property in the solution process.

Answer:

A) Using Commutative property

Step-by-step explanation:

In step 1, it used distributive property when the number 5 is distributed inside of the equation in the parenthesis.

In Step 4, dividing both sides by 10 to further simplify the equation

In step 2, you combined like terms and it results to the equation in step 3

The coefficient matrix A represents a system of linear equations that has a unique solution.

In a system of linear equations, the unique solution exists when the coefficient matrix has full rank and the determinant of the matrix is non-zero.

The other coefficient matrices listed do not have these properties.

1.  [[6, 0, - 2]

     - 2, 0, 6

        1, - 2, 0]

has a determinant of zero, indicating that the system of equations is dependent and does not have a unique solution.

Similarly, the matrices

[5, 10, 5

 4, 1, 4

- 1, - 2, - 1]

and, [2, 0, - 2

        - 7, 1, 5

          4, - 2, 0]

also do not satisfy the conditions for a unique solution.

Therefore, the coefficient matrix A represents a system of linear equations that has a unique solution.

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Answer:

D

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 3x + 4 ← is in slope- intercept form

with slope m = - 3

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-3}[/tex] = [tex]\frac{1}{3}[/tex] , then

y = [tex]\frac{1}{3}[/tex] x + c ← is the partial equation

to find c substitute (- 1, 5 ) into the partial equation

5 = - [tex]\frac{1}{3}[/tex] + c ( add [tex]\frac{1}{3}[/tex] to both sides )

5 [tex]\frac{1}{3}[/tex] = c ⇒ c = [tex]\frac{16}{3}[/tex]

y = [tex]\frac{1}{3}[/tex] x + [tex]\frac{16}{3}[/tex] ( multiply through by 3 to clear the fractions )

3y = x + 16

The probability that in a sample of 200 Americans, the proportion that uses CNN as their primary news source is at least 0.21 is 49.6%.

The probability is determined using the normal approximation to the binomial distribution.

Given that the sample size is large (n = 200) and the probability of success (p = 0.15) is not too close to 0 or 1, the mean (μ) and standard deviation (σ) of the binomial distribution, will be:

μ = n * p

μ = 200 * 0.15

μ = 30

σ = √(n * p * (1 - p))

σ = √(200 * 0.15 * (1 - 0.15))

σ ≈ 4.29

Then, the z-score corresponding to the proportion of 0.21 is:

z = (x - μ) / σ

z = (0.21 - 0.15) / 4.29

z ≈ 0.014

Using a calculator, the probability of a z-score of 0.014 is approximately 0.504.

Hence, the probability of obtaining a proportion at least 0.21, is:

Probability = 1 - 0.504

Probability ≈ 0.496

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The function that represents the number of comic book as a function of the number of years, t is expressed as y = 30x or f(t) = 30t.

We can use the given data to create a linear equation of the form y = mx + b, where y represents the number of comic books and x represents the number of years.

To find the equation, we can use any two pairs of (x, y) values. Let's use the first and fourth years:

First year: (1, 30)

Fourth year: (4, 120)

The slope, m, of the line can be calculated using the formula:

m = change in y / change in x = (120 - 30) / (4 - 1)

m = 90 / 3

m = 30

The y-intercept, b, can be found by substituting one of the (x, y) values and the slope into the linear equation, y = mx + b:

30 = 30(1) + b

b = 0

Therefore, the equation that represents the number of comic books, y, as a function of the number of years, x, is:

y = 30x

or

f(t) = 30t [where t represents the number of years.]

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The volume of the triangular prism is V = 18ft³

The volume of the prism is equal to the area of the triangular face, times the length of the prism, which is 9ft.

Remember that the area of a triangle of base B and height H is:

A = B*H/2

Here we can see that the base is 2ft and the height is 2ft, then the area of the triangular face is:

A = 2ft*2ft/2 = 2ft²

And thus, the volume of the prism is:

V = 2ft²*9ft

V = 18ft³

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The probability that exactly 1 buyer would prefer green P ( A ) = 0.1854

Given data ,

A researcher wishes to conduct a study of the color preferences of new car buyers

And , 30 % of this population prefers the color green

where 20 buyers are randomly selected

Now , binomial distribution problem with n = 20, p = 0.30 and we want to find the probability of exactly 1 buyer preferring green.

The formula for the probability mass function of a binomial distribution is:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where (n choose k) = n! / (k! * (n-k)!)

Plugging in the values, we get:

P(X = 1) = (20 choose 1) * 0.30¹ * 0.70¹⁹

= 20 * 0.30 * 0.70¹⁹

= 0.1854 (rounded to four decimal places)

Hence , the probability that exactly 1 buyer would prefer green is 0.1854

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The ball has traveled approximately 25.24 feet Horizontally.The correct answer is D. 25.2 ft.

The horizontal distance traveled by the soccer ball after 0.9 seconds, we can use the equation:

horizontal distance = initial velocity * time * cos(angle)

Substituting the given values:

initial velocity = 39 ft/s

time = 0.9 s

angle = 44°

horizontal distance = 39 ft/s * 0.9 s * cos(44°)

Calculating:

horizontal distance ≈ 39 ft/s * 0.9 s * 0.71934 ≈ 25.24 ft

Therefore, after 0.9 seconds, the ball has traveled approximately 25.24 feet horizontally.

The correct answer is D. 25.2 ft.

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The required reference angle of 13π/8 is 3π/8.

The reference angle of an angle in standard position is the positive acute angle formed between the terminal side of the angle and the x-axis.

Given an angle of 13π/8, we can determine its reference angle as follows:

Angle: 13π/8

Since the angle is in the fourth quadrant, we subtract it from 2π (one full revolution) to find the reference angle:

Reference angle: 2π - 13π/8 = 3π/8

Therefore, the reference angle of 13π/8 is 3π/8.

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Answer: b: 58-22=36

A=37 68-22-9

d=99 37+62

c=29 34-9

Step-by-step explanation:

The type of model that best fits the situation of a $500 raise in salary each year is a linear model.

In a linear model, the dependent variable changes a constant amount for constant increments of the independent variable.

In the given case, the dependent variable is the salary and the independent variable is the year.

You may build a table to show that for increments of 1 year the increments of the salary is $500:

Year         Salary        Change in year         Change in salary

2010           A                           -                                       -

2011           A + 500     2011 - 2010 = 1          A + 500 - 500 = 500

2012          A + 1,000   2012 - 2011 = 1          A + 1,000 - (A + 500) = 500

So, you can see that every year the salary increases the same amount ($500).

In general, a linear model is represented by the general equation y = mx + b, where x is the change of y per unit change of x, and b is the initial value (y-intercept).              

In this case, m = $500 and b is the starting salary: y = 500x + b.

Answer: 216

Step-by-step explanation:

592-376

592-300= 292

292-70= 222

222-6= 216

Answer:18

Step-by-step explanation:

The equation for each circle is given as follows:

36) (x - 2)² + (y - 15)² = 4.

37) (x + 8)² + (y + 18)² = 25.

38) (x - 11)² + (y + 9)² = 49.

39) (x - 13)² + (y + 8)² = 36.

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

For item 36, the center is given as follows:

(-3, 11)

After the translation, the center will be given as follows:

(2, 15)

Hence the equation is given as follows:

(x - 2)² + (y - 15)² = 4.

For item 37, the center is given as follows:

(-3, -14)

After the translation, the center will be given as follows:

(-8, -18)

Hence the equation is given as follows:

(x + 8)² + (y + 18)² = 25.

For item 38, the center is given as follows:

(11, -9).

Hence:

(x - 11)² + (y + 9)² = r².

Point (18, -9) is on the circle, hence the radius squared is obtained as follows:

r² = (18 - 11)² + (-9 + 9)²

r² = 49.

Hence the equation is:

(x - 11)² + (y + 9)² = 49.

For item 39, the center is given as follows:

(13, -8).

Hence the equation is:

(x - 13)² + (y + 8)² = r².

Point (7, -8) is on the circumference of the circle, hence the radius squared is obtained as follows:

r² = (7 - 13)² + (-8 + 8)²

r² = 36.

Hence the equation is given as follows:

(x - 13)² + (y + 8)² = 36.

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The output of the program for the variable z is -22 or it returns an error if z = x - 25y

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

x = 1

x = 3

z = x - 25y

print(z)

The value of the variable y is not given

So, the program would return an error

However, if the complete program is as follows (removing the variable y)

x = 1

x = 3

z = x - 25

print(z)

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

The final value of x is 3

So, we have

z = 3 - 25

Evaluate

z = -22

This means that the output of the program for z is -22

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The vertical distance between the two points given are (2, 11/3) and (2, -4/3) is 5 units.

The two points given are (2, 11/3) and (2, -4/3). These points have the same x-coordinate of 2, which means they lie on a vertical line. The vertical distance between the two points is simply the difference between their y-coordinates.

So, the vertical distance between the two points is:

11/3 - (-4/3) = 15/3 = 5

This means that if we were to draw a line segment connecting the two points, the length of the segment would be 5 units, and the segment would be parallel to the y-axis.

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Answer: A) [tex]f(x)=\frac{6x^2-x+4}{2x^2-1}[/tex]

Step-by-step explanation:

Line [tex]y=L[/tex] is a horizontal asymptote of the function [tex]y=f(x)[/tex], if either [tex]\lim_{x \to \infty} f(x)=L[/tex] or [tex]\lim_{x \to \infty} f(x)=L[/tex], and [tex]L[/tex] is finite.

calculate the limits:

[tex]\lim_{x \to \infty} (\frac{6x^2-x+4}{2x^2-1})=3[/tex]

[tex]\lim_{x \to -\infty} (\frac{6x^2-x+4}{2x^2-1})=3[/tex]

Thus, the horizontal asymptote is [tex]y=3[/tex]

Answer:

The answer is 8

Step-by-step explanation:

/x/ // /8/

x=8

The length of the side of the square in simplest form is 2sqrt(14).

The area of a square is given by the formula [tex]A = s^2[/tex], where A is the area and s is the length of a side.

We are given that the area of the square is 56 units, so we can set up the equation:

[tex]56 = s^2[/tex]

To solve for s, we can take the square root of both sides of the equation:

sqrt(56) = [tex]sqrt(s^2)[/tex]

We can simplify the square root of 56 by factoring it:

sqrt(56) = sqrt(222*7) = 2sqrt(14)

So, we have:

2sqrt(14) = s

This is an improper fraction because the numerator is larger than the denominator. Therefore, the length of the side of the square in simplest form is 2sqrt(14).

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The expected value of the given variable with the probability distribution is 7

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

The probability distribution on the table of values

The expected value of the variable is calculated as

Expected value = ∑x * P(x)

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

Expected value = 2 * 1/36 + 3 * 1/18 + 4 * 1/12 + 5 * 1/9 + 6 * 5/36 + 7 * 1/6 + 8 * 5/36 + 9 * 1/9 + 10 * 1/12 + 11 * 1/18 + 12 * 1/36

Evaluate

Expected value = 7

Hence, the expected value of the variable is 7

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Answer:

10

Step-by-step explanation:

300 plus 200 is 500

80 minus 30 is 50

500 divided by 50 is 10

The length of side CB to one decimal place is 89.3.

To find the length of side CB in the given triangle, we can use the sine rule. The sine rule states that in a triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

In this case, we have the angle C as 53° and the side opposite to it, side CB, as the unknown. Let's denote the length of side CB as x.

According to the sine rule:

sin(C) / x = sin(A) / AB

We know that angle A is 37° and AB is 120 units. Plugging in the values:

sin(53°) / x = sin(37°) / 120

To find x, we can rearrange the equation:

x = (120 * sin(53°)) / sin(37°)

Calculating this expression gives us:

x ≈ 89.32

Rounding this value to one decimal place, the length of side CB is approximately 89.3.

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