The matrix associated with the solution to a system of linear equations in x, y, and z is given. Write the solution to the system, if it exists.

Answer:(−1,−4π/3)

Step-by-step explanation:Note that the point is on the circle whose radius is labeled 1, so r=1 or r=−1. Of the choices available, only an angle of −4π3, drawn from the negative x axis plots at the point Q.  So θ=−4π3, and r must be negative, as the angle is measured from the negative x axis. Thus, the polar coordinates are (−1,−4π3).

The rate of change for the cab ride is A = $3 per mile

Given data ,

Change in cost = $55 - $40 = $15

Change in distance = 15 miles - 10 miles = 5 miles

Now, we can divide the change in cost by the change in distance to get the rate of change or cost per mile:

Rate of change or cost per mile = Change in cost / Change in distance

A = $15 / 5 miles

A = $3 per mile

Hence , the rate of change or cost per mile for the cab ride is $3 per mile

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Answer: The relationship between the area of rectangle and area of parallelogram is that they both are equal in area.

Step-by-step explanation:

parallelogram is formed when two parallel lines intersects other two parallel lines and rectangle is a type of parallelogram in which the intersecting lines intersects at right angle.

rectangle and parallelogram shares the same property and If we consider same base and same parallel lines then the area of parallelograms formed is always equal and as I mentioned above rectangle is also a parallelogram.

hence area of rectangle is equal to the area of parallelogram in same base and same parallel lines.

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The media personality's argument is flawed because they are basing their conclusion on a single year's data and ignoring the overall trend of increasing global temperatures. To counter this argument, one can make the following points:

1. While it is true that the annual increase in temperature may be less than the margin of error, the trend of increasing temperatures over several decades cannot be ignored. The margin of error is a statistical concept that takes into account the uncertainty in the measurement, but it does not negate the overall trend.

2. Global temperature records show that the Earth's temperature has been steadily rising over the past century, with the 10 warmest years on record occurring since 2005. This trend cannot be explained by natural variability alone and is consistent with the effects of human-caused climate change.

3. The consequences of rising global temperatures, such as melting glaciers, rising sea levels, and more frequent extreme weather events, are already being felt around the world. Ignoring this trend could have devastating consequences for future generations.

In summary, the media personality's argument is based on a flawed understanding of statistics and ignores the overall trend of increasing global temperatures. The best counterargument is to highlight the overwhelming evidence of climate change and its potential consequences.

The amount more in income tax that Cho pays than Helen each month would be £56.

First, find Helen's yearly salary :

= 1, 720 x  12

= £ 20, 640

Both Cho's and Helen's annual salaries fall within the Basic rate tax bracket.

Cho 's monthly tax would be:

= (( 24, 000 - 12, 570 ) x 20 % ) / 12

= £ 190. 50

Helen's monthly tax :

= (( 20, 640 - 12, 570 ) x 20 % ) / 12

= £ 134.50

The difference is therefore :

= 190. 50 - 134.50

= £56

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Applying the triangle sum theorem, the value of x in the image given is:

x = 33°;   x = 45°

Recall that according to the triangle sum theorem, all three interior angles of a triangle is equal to 180 degrees.

a. x + 21 + (180 - 54) = 180 [triangle sum theorem]

x + 147 = 180

x = 180 - 147

x = 33°

b. (180 - 102) + x + 57 = 180 [triangle sum theorem]

x + 135 = 180

x = 180 - 135

x = 45°

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Answer:

1a+12

Step-by-step explanation:

The percentage of saline solution in brand B is 3%.

Let x be Percentage of saline solution in brand B

We know that the overall volume of saline solution in the combination is 18% of 6 gallons plus x% of (18 - 6) gallons since Danielle blended brands A and B to make a total of 18 gallons of 8% saline solution.

Then the equation is given as,

0.18(6) + 0.01x(18 - 6) = 0.08(18)

Simplifying and solving for x, we get:

1.08 + 0.12x = 1.44

0.12x = 0.36

x = 3

Therefore, the percentage of saline solution in brand B is 3%.

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Step-by-step explanation:

so, the 1 yard is split into 6 equal parts.

each small square has therefore an area of 1/6 × 1/6 yard² = 1/36 yard²

the shaded area is 4×3 = 12 small squares large.

is area is therefore

12 × 1/36 = 1/3 yard²

since 1 yard = 3 ft, 1 × 1 = 1 yard² = 3 × 3 ft² = 9 ft².

and 1/3 yard² = 1/3 × 9 ft² = 3 ft²

so, whatever dimension you need.

the area is

1/3 yard² = 3 ft²

The triangle with the side length of 4.8, 28.6 and 29 is a right triangle.

A right angle triangle is a triangle that has one of its angles as 90 degrees.

The sum of angles in a triangle is 180 degrees.

The sides of a right angle triangle can be found using Pythagoras's theorem as follows:

c² = a² + b²

where

Therefore, lets check if the triangle is a right triangle using Pythagoras's theorem as follows:

4.8² + 28.6² = 29²

23.04 + 817.96 = 841

841 = 841

Therefore, the triangle is a right triangle.

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Only [tex]0.03125 ml[/tex] of the technetium-99m will be left after 24 hours.

After 6 hours, half of the original amount will decay.

After another, leaves 1/4 of the original amount.

After another, leaves 1/8 of the original amount.

After another, leaves 1/16 of the original amount.

We will below formula calculate the amount of technetium-99m left after 24 hours: N = N0 * (1/2)^(t/T)

N = 0.5 * (1/2)^(24/6)

N = 0.5 * (1/2)^4

N = 0.5 * 1/16

N = 0.03125 ml

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The rules for the two graphs above are: A. first graph: y = 3 + x; second graph : y = 6 + x.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of graph 1;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (4 - 3)/(1 - 0)

Slope (m) = 1/1

Slope (m) = 1

At data point (0, 3) and a slope of 1, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 3 = 1(x - 0)  

y = x + 3

Next, we would determine the slope of graph 2;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (7 - 6)/(1 - 0)

Slope (m) = 1/1

Slope (m) = 1

At data point (0, 6) and a slope of 1, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 6 = 1(x - 0)  

y = x + 6

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The equivalent expression to the given expression [tex]2^{3x}[/tex] - 4  is equal to 8ˣ - 4.

The expression is equal to,

[tex]2^{3x}[/tex] - 4

Simplify the expression using the law of exponent we get,

yᵃᵇ = (yᵃ)ᵇ

Here  in the expression the value of y = 2,

Value of a = 3

and the value of b = x

Substitute the value in the formula we get,

= ( 2³ )ˣ - 4

value of the exponent 2³ = 2 × 2 × 2

                                          = 8

This implies the equivalent expression is,

= 8ˣ - 4

Therefore, the value of the given expression is equivalent to 8ˣ - 4.

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The quantity of candy that Eric ate would be = 14/15

The quantity of Candy Kim had = 2⅓ pounds.

The quantity of Kims candy that Eric ate = 2/5

That is 2/5 of 2⅓.

The actual quantity of candy that Eric ate = 2/5× 7/3 = 14/15

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The total cost of repainting the 4 walls and floor of the pool would be $2800

Given that;

A swimming pool is in the shape of a right rectangular prism. the pool is 40 feet long,20 feet wide and 4 feet deep the cost of repainting the pool is $2.50 per square foot.

Here, The first step is to calculate the total surface area of the pool, which includes the four walls and the floor.

The area of the floor is simply the length times the width:

Area of floor = 40 ft x 20 ft = 800 square feet

The area of each of the four walls is the height times the width:

Area of each wall = 4 ft x 20 ft = 80 square feet

Since there are four walls, the total area of the walls is:

Total area of walls = 4 x 80 sq ft = 320 square feet

To find the total surface area of the pool, we add the area of the floor to the area of the walls:

Total surface area = Area of floor + Total area of walls

Total surface area = 800 sq ft + 320 sq ft = 1120 square feet

Finally, we can calculate the total cost of repainting the pool by multiplying the total surface area by the cost per square foot:

Total cost = Total surface area x Cost per square foot

Total cost = 1120 sq ft x $2.50/sq ft

Total cost = $2800

Therefore, the total cost of repainting the 4 walls and floor of the pool would be $2800

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The solutions to the quadratic equation 3y(-2y+x)-5y(-7x+y) are y = -16x + 32x√2 and y = -16x - 32x√2

To solve the quadratic equation 3y(-2y+x)-5y(-7x+y), we first need to simplify it by distributing the terms inside the parentheses:

3y(-2y+x) = -6y² + 3xy

-5y(-7x+y) = 35xy - 5y²

Next, we can substitute these expressions back into the original equation and simplify it further:

3y(-2y+x)-5y(-7x+y) = (-6y² + 3xy) - (35xy - 5y²) = -6y² + 3xy - 35xy + 5y² = -y² - 32xy

Now, we have simplified the quadratic equation to the standard form of ax² + bx + c = 0, where a = -1, b = -32x, and c = 0. To solve for y, we can use the quadratic formula:

y = (-b ± √(b² - 4ac)) / 2a

Plugging in the values for a, b, and c, we get:

y = (-(-32x) ± √((-32x)² - 4(-1)(0))) / 2(-1) = (32x ± √(1024x²)) / (-2)

Simplifying further, we get:

y = -16x ± 32x√2

In conclusion, we can simplify the given quadratic equation by distributing the terms inside the parentheses, and then rearrange it to the standard form ax² + bx + c = 0. We can then use the quadratic formula to solve for y, and simplify the solutions.

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Answer:

Part A:

1. Computation of Basic EPS

Basic EPS = (Net Income - Preferred Dividends) / Weighted Average Shares Outstanding²

Net Income = $120,000

Preferred Dividends = 4% x $50,000 = $2,000

Weighted Average Shares Outstanding = 100,000 (assuming no change in common stock during the year)

Basic EPS = ($120,000 - $2,000) / 100,000

Basic EPS = $1.18

2. Individual dilution/anti-dilution with decision making

We need to check if any of the convertible securities or stock options are dilutive or anti-dilutive by comparing their impact on EPS with the basic EPS.

Convertible Preferred: Each preferred share can be converted into 1.9 common shares (1,900 / 1,000). The conversion would increase the common shares outstanding by 1,900 and decrease the preferred dividends by $2,000.

EPS after conversion = ($120,000 - $0) / (100,000 + 1,900)

EPS after conversion = $1.16

Since this is lower than the basic EPS of $1.18, the convertible preferred is dilutive and should be included in the diluted EPS calculation.

Stock Options - A: Each option can be exercised at $12 to buy one common share when the average market price is $11. This means that the options are out of the money and would not be exercised by the holders. Therefore, they have no impact on EPS and are anti-dilutive.

Stock Options - B: Each option can be exercised at $7 to buy one common share when the average market price is $8. This means that the options are in the money and would be exercised by the holders. The exercise would increase the common shares outstanding by 4,000 and generate cash proceeds of $28,000 ($7 x 4,000). The cash proceeds can be used to buy back some common shares at the market price of $8. The number of shares bought back is 3,500 ($28,000 / $8). The net increase in common shares outstanding is 500 (4,000 - 3,500).

EPS after exercise = ($120,000 - $2,000) / (100,000 + 500)

EPS after exercise = $1.17

Since this is lower than the basic EPS of $1.18, the stock options - B are dilutive and should be included in the diluted EPS calculation.

Convertible Bonds: Each bond can be converted into 40 common shares (40,000 / 1,000). The conversion would increase the common shares outstanding by 40,000 and decrease the interest expense by $50,000 ($1,000,000 x 5%). The interest expense is net of tax, so we need to multiply it by (1 - tax rate) to get the after-tax amount. The tax rate is 30%.

EPS after conversion = ($120,000 - $2,000 + $50,000 x (1 - 0.3)) / (100,000 + 40,000)

EPS after conversion = $1.19

Since this is higher than the basic EPS of $1.18, the convertible bonds are anti-dilutive and should be excluded from the diluted EPS calculation.

3. Ranking of potential dilutors

We need to rank the potential dilutors from the most dilutive to the least dilutive based on their impact on EPS.

The most dilutive security is the convertible preferred with an EPS of $1.16.

The second most dilutive security is the stock options - B with an EPS of $1.17.

The least dilutive security is the convertible bonds with an EPS of $1.19.

4. Step-by-step inclusion of individual dilutors to arrive at reportable EPS with decision making.

We need to include the potential dilutors in order of their dilution until we reach a point where the next security would be anti-dilutive.

The first security to include is the convertible preferred.

EPS with convertible preferred = ($120,000 - $0) / (100,000 + 1,900)

EPS with convertible preferred = $1.16

The next security to include is the stock options - B.

EPS with stock options - B = ($120,000 - $0) / (100,000 + 1,900 + 500)

EPS with stock options

The expression is simplified to √5

From the information given, we have that;

logₐ x = 3

logₐ y = 4

logₐ z = 5

Given that the expression is;

logₐ [tex]\sqrt[4]{\frac{y^3z^6}{x^4z^-^2} }[/tex]

Now, we have to substitute the value of the logarithm into the expression.

We have;

[tex]\sqrt[4]{\frac{4^35^6}{3^45^-^2} }[/tex]

Find the value of the index forms and substitute;

[tex]\sqrt[4]{\frac{64(625)}{81(1/25)} }[/tex]

Multiply the values and expand the bracket

3(5)/3(5^⁻²/4)

multiply the values

15/3(5^-1/2)

Find the square root of the denominator, we have

15/3(√5)⁻¹

5/√5

Rationalize the surd form, we get;

5√5/5

Then, we have;√5

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Step-by-step explanation:

a) 11*5=55

15*5=75

8*5+5=45

b) No, because (55+75+45=175°) and the perimeter of a triangle is 180°

The correct statements from the box plot are given as follows:

A box and whisker plots shows these five features from a data-set, listed as follows:

Hence the correct statements are given as follows:

The false statements are given as follows:

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The value of segment x is determined as 13.6 units.

option B

The value of length x is calculated as follows;

x² = 8 x ( 8 + 15)

From the diagram given, the length of the sides are as follows;

8, 15 and segment x

The value of segment x is calculated as follows;

x² = 8 x 23

x² = 184

x = √ ( 184 )

x = 13.6 units

Thus, the value of x is determined by applying the principle of tangent theorem.

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The order of steps of constructing an inscribed circle of a triangle:

Commence the process by sketching a line that cuts one angle of the triangle in two and intersects the opposing side at some point. Through this action, a pair of miniature triangles with congruent figures materialize.

Subsequently, draft an additional bisector for another angle of the triangle. The second dividing line needs to meet the side opposite to the situated angle at a specific location.

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Answer:

c and d

Step-by-step explanation:

it is a 2d object

so it can only be measured in 2 directions (up and side) it has no depth as it is 2 dimensional. and it is round and cannot have a point.

Answer:

D. It is a two-dimensional object.

The statement D is true about the figure above. The figure is a circle, which is a two-dimensional object.

Statement A is not true. A point is a location in space, but a circle is a shape that takes up space and has a defined area.

Statement B is not true either. A circle has only one measurement, which is its radius or diameter. The radius is the distance from the center of the circle to any point on its circumference, while the diameter is the distance across the circle through its center.

Statement C is also not true. A circle cannot "grow" into a three-dimensional object because it is a two-dimensional object that exists in a flat plane. However, multiple circles can be stacked on top of each other to form a cylinder, which is a three-dimensional object.

75% of students of a class answered Question No. 1 correct and 55% answered Question No. 1 correct and 20% answered neither question correctly . 50 is the percentage of students who only answered one question

A percentage is a quantity or ratio that is expressed as a fraction of 100. It is symbolised by the '%' percentage sign. 'pct' or 'pc' are the acronyms used to indicate the percentage. In sense, the percentage is measured in terms of 100 and is defined as the amount of one quantity that is made up of another.

Students answer Q.1 or Q.2 or both correctly = ( 100 - 20) = 80%

x% students answered both correctly

( 75 - x) + ( 55 - x) + x = 80

130 - x = 80

x = 50

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Your question is incomplete but most probably your full question was,

75% of students of a class answered Question No. 1 correct and 55% answered Question No. 1 correct and 20% answered neither question correctly . What percent of students answered both question correctly ?

The tangent at any point of a circle is perpendicular to the radius through the point of contact by showing that line PQ coincides with the radius OP.

Let us assume that we have a circle with center O and radius r.

Let P be any point on the circle .

And let Q be the point of intersection of the tangent to the circle at P and the radius OP,

To prove that PQ is perpendicular to OP.

First, we observe that OP is a radius of the circle and therefore its length is r.

Since PQ is tangent to the circle at point P,

It is perpendicular to the radius drawn from the center of the circle to point P.

As the tangent to a circle is perpendicular to the radius drawn to the point of contact.

This implies, angle QOP is a right angle.

Next, triangle OPQ is a right triangle with right angle at Q.

By the Pythagorean Theorem, we have,

OP²= OQ² + PQ²

Substituting r for OP and noting that OQ = r since Q is on the radius. we have,

⇒ r² = r²+ PQ²

Subtracting r² from both sides, we get,

⇒ PQ² = 0

This implies that PQ = 0,

In other words, that point Q coincides with point P.

PQ is a line that coincides with the radius OP.

And since angle QOP is a right angle, we can conclude that PQ is perpendicular to OP.

Therefore, it is proved that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

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The above question is incomplete, the complete question is:

Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

Step-by-step explanation:

Arithmetic sequence with  d = 2    a1 = -6

a20 = -6 + 2(20-1) = 32

Answer: The spinner is probably because 5 was spun approximately 200 times

Step-by-step explanation:

3. The factored polynomial is p(x) = (x - 1)(x - 5)

4. The factored polynomial is p(x) = (x + 3)²

A polynomial is a mathematical expression in which the power of the unknown is greater than or equal to 2.

3. To factorize the polynomial using the graph, we see that the polynomial cuts the x - axis at x = 1 and x = 5.

This implies that its factors are (x - 1) and (x - 5)

So, the factored polynomial is p(x) = (x - 1)(x - 5)

4. To factorize the polynomial using the graph, we see that the polynomial touches the x - axis at only one point x = -3. So,it has repeated roots

This implies that its factors are (x - (-3)) = (x + 3) twice

So, the factored polynomial is p(x) = (x + 3)²

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