Rodney is given two linear equations: x – y = 11 and 2x + y = 19. What is the value of x in the solution to the system of equations?
3/4
9
10
41/3

O a² + 10² 5² =25 + 100 =2a ,2a=125 , a=\sqrt{125} , a=11.18 m

Therefore, the missing side (a) is 11.18 m.

We are trying to find the missing side (a) of the triangle shown in the diagram.

To do this, we will use the Pythagorean Theorem, which states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the longest side.

The two shorter sides of the triangle are 5 m and 10 m.

We will use the Pythagorean Theorem to calculate the missing side (a).

First, we need to square the lengths of the two shorter sides:

5² = 25

10² = 100

Next, we add the squares of the two shorter sides together:

25 + 100 = 125

Finally, we take the square root of the sum to find the length of the missing side:

√125 = 11.18 m

Therefore, the missing side (a) is 11.18 m.

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Answer:

5509 yes votes

Step-by-step explanation:

We will start by adding together our ratio, so we know how many voters there were in a total ratio, so we can divide our total number of people by it, and then multiply it by the number of people who said yes (7 people).

Our ratio was 7:4, so adding those two numbers together gives us 11. Then, dividing 8657 by 11 gives us:

8657 / 11 = 787

Now, we will multiply 787 by 7, since that was the number of people who said yes:

787 * 7 = 5509

So, there were 5509 yes votes.

Hope this helped!

Answer: 187.567 < 187.68

Step-by-step explanation:

0.6 is larger than 0.5 so 187.68 is bigger than 187.567

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The equation of the line passing through the points (0, 3) and (-5, 0) is y = -3/5 x + 3

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

Here,

To find the equation of the line passing through the points (0, 3) and (-5, 0), we can use the slope-intercept form and the slope formula:

m = (y2 - y1) / (x2 - x1) = (0 - 3) / (-5 - 0) = -3/5

where (x1, y1) = (0, 3) and (x2, y2) = (-5, 0) are the coordinates of the given points.

Now we can substitute the value of m and the coordinates of one of the points into the equation of the line to find the value of b:

y = mx + b

3 = (-3/5)*0 + b

b = 3

So the equation of the line passing through the points (0, 3) and (-5, 0) is:

y = -3/5 x + 3

We can also convert the equation to point-slope form as :

y - y1 = m(x - x1)

y - 3 = (-3/5)(x - 0)

y - 3 = -3/5 x

y = -3/5 x + 3

Hence, the equation of the line passing through the points (0, 3) and (-5, 0) is y = -3/5 x + 3

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Answer:

3

Step-by-step explanation:

3 can divide both 153 and 48

Answer: If Pedro starts reading at page 20 and reads at an average rate of 25 pages per hour, and Bella starts reading at the same time but starts at page 60 and reads at an average rate of 18 pages per hour,

We can use the formula: distance = rate x time

To find out when they will meet we need to find out when they are on the same page.

let's say t be the time in hours, Pedro will be reading t25 pages, and Bella will be reading t18 pages.

So we can write the equation: 20+t25 = 60+t18

Solving this equation we get t = 2

So, they will meet after 2 hours.

Pedro will be on page 20+225 = 70, and Bella will be on page 60+218 = 96

So they will meet at page 70 when Pedro reaches that page after 2 hours of reading, which means Bella will have read 26 pages more than Pedro on that point.

Step-by-step explanation:

Answer: it will be improper

Step-by-step explanation:11/4

Answer:11/4

Step-by-step explanation:it is improper.

As rain drop and sink through the rock, it often solvates some of the iron. It conveys that iron along with it as it continues to seep through the rock and soil.

When the rainwater becomes groundwater or dart into freshwater sources like lakes and rivers, it may become the part of the local water supply.

Municipal water systems that get their water from these sources can end up with high levels of iron in their water, and the riddle they have set up to remove bacteria and other harmful contaminants may not always riddle it out.

Wells that portray water from aquifers with high iron content may contain high iron concentrations as well.

Iron in water generally takes two types of ferrous iron, which is soluble in water, and next one is ferric iron, which is insoluble.

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A graph of each function is shown in the image attached below.

The number of commercials (x) is equal to 7 commercials while the number of movies (y) is equal to 2 movies.

In order to graphically solve the system of equations, we would write two (2) equations that models the situation by assigning variables to the number of commercials and number of movies respectively, and then translate the word problem into algebraic equation as follows:

Since Victoria would earn $40 every time one of her songs is played in a commercial and $140 every time one of her songs is played in a movie, an equation which models it is;

40x + 140y = 560

Additionally, Victoria earned a total of $560 in royalties on 9 commercials and movies;

x + y = 9

Next, we would use an online graphing calculator to plot the above system of equations with a point of intersection at (7, 2) as shown in the image attached below.

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A man crosses a distance of 48 meters while going round a quadrilateral field twice. For 24 m cost of fencing the field is  $42.

Perimeter of the field is the total lengths of its boundary = 48/2 m = 24 m

For 1 m, cost of fencing the field = $1.75

Therefore, for 24 m cost of fencing the field = $(1.75 × 24) = $42

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Answer:

x ≥ -3 3/4

Step-by-step explanation:

-1/3x + 1/2 ≥ -3/4

1/3x ≥ -5/4

x ≥ -3 3/4

Researchers frequently select a level of significance of 0.05. The reason for this is that if we chose a lower threshold of significance, we will have less room to reject the null hypothesis and so a higher likelihood of making a type 2 error.

On the other hand, if the degree of significance is higher, more type 1 errors are made, leading us to reject the hypothesis even though it is correct. Therefore, 0.05 is a balanced level that is neither significantly greater nor significantly smaller. The health care and nutrition-related industries are mostly included in some of the studies where we require a lower level of importance. This type of industry has a higher error rate, which causes more fatalities and negative side effects.

We can use a higher level of relevance in a variety of circumstances, such as the entertainment and marketing-related industries. The reason for this is that even if there are more potential for error, it won't harm the person; instead, it just affects the information, which we can assess using common sense.

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The area for the trapezoid is 35 square inches. Last option

The formula for the decomposition method of finding trapezoid is given as: ( x + y ) / h

The variables are given as

x = 3

y = 4

h = 5

we would have to fix the values into the formula in order to get the area of the trapezoid

Hence we would have

( 3 + 4) * 5

7 * 5

= 35 square units

Hence the area of the trapezoid by decomposition is given as 35 square units.

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As long as they are not all on the same line, three points can define a plane in a three-dimensional space.

Intersecting Space with Planes A plane just divides space into two distinct regions. Space is divided into a maximum of four sections by two planes. Space can only be divided into eight sections by three planes.

One line has the ability to split a plane into two regions; two non-parallel lines have the ability to divide a plane into four regions; three non-parallel lines have the ability to divide a plane into seven regions; and so on.

Four unique, nonintersecting zones can be created by selecting three separate points on a circle and connecting each pair of them with a chord.

Three points can define a plane in a three-dimensional space as long as they are not all on the same line.

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One line can divide a plane into two regions, two non-parallel lines can divide a plane into 4 regions and three non-parallel lines can divide into 7 regions.

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A graph which could represent a cubic function include the following: C. Graph C.

In Mathematics, a function is a mathematical expression which can be used for defining and showing the relationship that exist between two or more variables in a data set.

In Mathematics, a cubic function is sometimes referred to as a cubic polynomial and it can be defined as a type of polynomial in which the degree of the highest term (coefficient or exponent) is equal to three (3).

In this context, we can reasonably infer and logically deduce that a graph that represents a cubic function is graph C because it models this polynomial y = x³.

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The height define how long the attribute is and the width specify about the breadth of the attributes.

Given:

Arty's height is 63 inches.

Suppose Julian's height is x inches.

As Arty's height is 3 inches less than 1.5 times Julian's height.

⇒ 1.5x - 3 = 63

1.5x = 63 + 3

1.5x = 66

x = 44

Hence, the Julian's height is 44 inches.

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6  is the length of segment AC in right-angled triangle .

What is a right-angle triangle, exactly?

A right-angled triangle is a particular kind of triangle in which one of the angles is 90 degrees. The combined angles of the other two are 90 degrees.

               Perpendicular and the triangle's base make up the sides that the right angle is formed from. The hypotenuse, or third side, is the longest of the three. It is also known as the hypotenuse.

  let length of AC is x

   BC + CD = AC + DE

  4 + 8 = X + 6

     12 = X + 6

       X = 6

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Two equivalent fractions to 2/25 are given as follows:

4/50 and 8/100.

A fraction is a numerical representation of the division of the two terms x and y, as follows:

Fraction = x/y.

The terms are classified as follows:

Two fractions are called equivalent when the ratio between their numerators and denominators is the same.

The fraction in this problem is defined as follows:

2/25.

To obtain an equivalent fraction, we multiply both the numerator and denominator by the same constant, hence:

The problem asks for two equivalent fractions to 2/25.

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Answer:

Equilateral Triangle

Step-by-step explanation:

Answer:

Equilateral

Step-by-step explanation:

The Answer to this given question is a Equilateral

Reason : The sides of an equilateral triangle are congruent, which means that all sides are of equal length.

The order for the process of Statistcal Method will be Identify the research objective, Collect the data needed to Answer the Research question, Describe the data, and Perform Inference.

For any statistics method, we first must have an objective as to why are we conducting that research. Hence the first process has to be Identifying the research objective.

For any statistical method, samples need to be drawn to conduct statistic tests. This essentially requires data to work with. Hence, Collecting the data needed to Answer the Research question must be the next step.

After data is collected, numerous tests are possible to be performed on any set of data but to select the most appropriate statistic, we need to first understand the nature, range, and limitations of the data. Hence, the net step should be to describe the data.

The last step out of the available step would be to perform the inference since this is the only other step possible from the ones mentioned.

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Answer: i) dy/dx of x = 1

ii) dy/dx of xy = y

iii) dy/dx of y = 2y

iv) dy/dx of xy = 2xy

Step-by-step explanation:

Since the points on this graph represent a relationship between x- and y-values, a statement about the relationship which is true include the following: A, it cannot be proportional because the straight line through the points does not go through the origin.

In Mathematics, the graph of any proportional relationship between two (2) variables is always characterized by a straight line with the data points starting from the origin (0, 0) and passes through other unique data points on the cartesian coordinate.

By critically observing the graph which shows a relationship between the x-values and y-values, we can logically deduce that it does not start from the origin (0, 0) and as such, it does not represent a proportional relationship.

In this context, we can reasonably infer and logically conclude that cost is not proportional to area in the situation represented by this graph.

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1100 Absolute is a 30.55% increment relative percent

To find an Increment percentage in population we need the Number of increases in population.

4700- 3600 = 1100

That is absolutely increased number.

For relative increment, we need to find the Percentage -

so the population in 2007 was 3600

so  percentage = 1100/3600*100

=> 30.55%

SO Relative increase =  30.55%

Here we can see that percent is the way to analyze the change, Increment/decrease in terms of 100 as it multiple the fractional changes in quantity by 100 to make it out of 100. So percentage simply means out of 100.

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The length of the midsegment of 28. is 17 units and 29. is 27 units.

A line drawn by joining the midpoints of any two of the triangle's sides is known as the midsegment. All three sides of a triangle can be divided in half, with the midpoint being the point that is equally spaced from either vertex, regardless of whether the triangle is a right triangle, isosceles triangle, or sometimes an equilateral triangle.

If the slope and sides are same then we can cut the midsegment ad paste it such that it becomes an rectangle.

28. Now the length of the rectangle = n + 12 + n + 12 = 4n + 6 + 2n - 2

⇒ 2n + 24 = 6n +4

⇒ 20 = 4n

⇒ n = 20/4

⇒ n = 5

Length of midsegment = 5 + 12

                                       =  17 units

29. Now the length of the rectangle = 2n+ 11 + 2n+ 11 = 5n - 2 + n + 8

⇒ 4n + 22 = 6n + 6

⇒ 16  = 2n

⇒ n = 16/2

⇒ n = 8

Length of midsegment = 2(8) + 11

                                       =  27 units

Thus, he length of the midsegment of 28. is 17 units and 29. is 27 units.

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Answer:

1.23 calculator on cellphone do have that apps

Answer: 1.23

Step-by-step explanation: To find this answer, we need to move the decimal place. So, the 7 will move 1 place to the right of the 7, and then the decimal place will move to the right of the 8. So, now it should look like this:

[tex]\frac{08.61}{7}[/tex]

Then, divide using long division. You should get 1.23. To check, you can multiply 1.23 by 7, to get the dividend, 0.861. I hope this helped!

The eigenvalues of the matrix are -1,1,3 and the corresponding eigenvectors are [-1,2,2], [1,-1,-1], [1,1,1] respectively.

The matrix is given as

2 1 -1

3 2 -3

3 1 -2

To find the eigenvalues and eigenvectors of a matrix A, we need to solve the following equation:

Av = λv

where v is the eigenvector and λ is the eigenvalue.

So, we have

(2 1 -1) (x) = λ (x)

(3 2 -3) (y) (y)

(3 1 -2) (z) (z)

We can find the eigenvalues by solving the characteristic equation which is det(A-λI) = 0.

The characteristic equation for the above matrix is

(2-λ)((-λ-2)(-λ+1) - 2) - 3(1)(-λ+1) + 3(1)(-λ-2) = 0

Solving the above equation we get λ = -1,1,3

Now we can find the eigenvectors for each eigenvalue.

For λ = -1

(2 1 -1) (x) = -1 (x)

(3 2 -3) (y) (y)

(3 1 -2) (z) (z)

Solving the above equation we get x = -1, y = 2 and z = 2. So the eigenvector is [-1,2,2].

For λ = 1

(2 1 -1) (x) = 1 (x)

(3 2 -3) (y) (y)

(3 1 -2) (z) (z)

Solving the above equation we get x = 1, y = -1 and z = -1. So the eigenvector is [1,-1,-1].

For λ = 3

(2 1 -1) (x) = 3 (x)

(3 2 -3) (y) (y)

(3 1 -2) (z) (z)

Solving the above equation we get x = 1, y = 1 and z = 1. So the eigenvector is [1,1,1].

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Answer:

Step-by-step explanation

since they are complementary their angles should add up to 90.

18+(8x-28)=90

you solve from there

add common values

8x-10+90

add 10 to both sides

8x=100

divide by 8

x=12.5

The answer is:

Work/explanation:

Since we're given both angles, we can set up an equation and find x.

The sum of two complementary angles is 90°.

Now, set up the equation:

[tex]\sf{8x-28+18=90}[/tex]

[tex]\sf{8x-10=90}[/tex]

Add 10 on each side

[tex]\sf{8x=100}[/tex]

Divide each side by 8

[tex]\sf{x=12.5}[/tex]

The required missing number is 51.02

Any progression in which the ratio of adjacent terms is fixed is a Geometric Progression. The general form of representation of a geometric sequence is a, ar, ar2, ar3, ar4, ar5, .....

Given here the numbers 140,100,71.4, ,36.44

clearly 140/100=100/71.4=1.4

Thus the given set of numbers form a geometric progression with common ratio 1.4

Therefore the complete set of numbers are 140,100,71.4,51.02,36.44

Hence, the required numbers is 51.02

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a)The probability Space, S = {(1,1) (1,2) (1,3) (1,4) (1,5) (1,6), (2, 1) (2, 2) (2,3) (2,5) (2,4),(2,6), (3,1) (3,2) ,(3,3), (3,4) (3,5)(3,6), (4,1) (4,2) (4,3) (4,4) (4,5) (4,6), (5,1) (5,2) (5,3) (5,4) (5,5) (5,6),(6,1) (6,2) (6,3) (6,4) (6,5) (6,4), (6,5),(6,6)}

b) i) Probability that the sum of the rolls is even, P(A) = 0.5

ii)Probability that first roll is equal to the second, P(B) 0.166

iii) Probability that the first roll is larger than the second, P(C) = 0.4166.

We have a pair of dice are rolled, then the Sample space is same as probability space.

a) The probability space , S is a non-empty set contains all possible outcomes. The probability space is written as

S = {(1,1) (1,2) (1,3) (1,4) (1,5) (1,6), (2, 1) (2, 2) (2,3) (2,5) (2,4),(2,6), (3,1) (3,2) ,(3,3), (3,4) (3,5)(3,6), (4,1) (4,2) (4,3) (4,4) (4,5) (4,6), (5,1) (5,2) (5,3) (5,4) (5,5) (5,6),(6,1) (6,2) (6,3) (6,4) (6,5) (6,4), (6,5),(6,6)}

b) Total possible outcomes from rolling = 36

Let us consider the events,

A : sum of the rolls is even

B : first roll is equal to the second

C : first roll is larger than the second.

Now, favourable outcomes for event A = 18

i) Probability (Sum is even), P( A) = 18/36

= 0.5

Favourable outcomes for event B = 6 = { (1,1),(2,2),(3,3),(4,4), (4,1) (4,2) (4,3), (5,5),(6,6)}

ii) So, Probability that first roll is equal to the second, P(B) = 6/36 = 0.166

Favourable outcomes for event C = 15 = { (2,1),(3,2),(3,1),(4,1),(5,1) (5,2) (5,3) (5,4),(6,1) (6,2) (6,3) (6,4) (6,5) (6,4), (6,5)}

iii) So, probability that the first roll is larger than the second, P(C) = 15/36

= 0.4166.

Hence, we get all required probabilities.

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The probability of P(Sum is even)=0.5, P(the first roll is equal to the second)=[tex]\frac{1}{6}[/tex], P(the first roll is larger than the second)=0.4167.

A pair of dice are rolled

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur.

a) Sample space,

[tex]$$\begin{aligned}S= & \left\{\begin{array}{l}(1,1)(1,2)(1,3)(1,4)(1,5)(1,6) \\(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)\end{array}\right. \\& (3,1)(3,2)(3,3)(3,4)(3,5)(3,6) \\& (4,1)(4,2)(4,3)(4,4)(4,5)(4,6) \\& (5,1)(5,2)(5,3)(5,4)(5,5)(5,6) \\& (6,1)(6,2)(6,3)(6,4)(6,5)(6,2)\}\end{aligned}$$[/tex]

(b).

(i).The probability of each of the following events

Probability of event to happen

⇒P(Sum is even)=[tex]\frac{18}{36} =\frac{1}{2}[/tex]=0.5

⇒P(Sum is even)=0.5

(ii). P(the first roll is equal to the second)=[tex]\frac{6}{36} =\frac{1}{6}[/tex]

⇒P(the first roll is equal to the second)=[tex]\frac{1}{6}[/tex]

(iii). P(the first roll is larger than the second)=[tex]\frac{15}{36}=0.4167[/tex]

⇒P(the first roll is larger than the second)=0.4167

Therefore, the P(Sum is even)=0.5, P(the first roll is equal to the second)=[tex]\frac{1}{6}[/tex], P(the first roll is larger than the second)=0.4167.

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