line 1 is y=2x line 2 is y=2x-3 how many solutions are there and whats the coordinates.

AB and CD are not parallel lines.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

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

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

If the slope of AB and CD are equal then the lines are parallel.

A(-3, 5), B(1, 13), C(4, 2), and D(10, 5)

AB=13-5/1+3

=8/4=2

CD=5-2/10-4

=3/6=1/2

As the slope of lines are different, the lines are not parallel.

Hence, AB and CD are not parallel lines.

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If two events are collectively exhaustive, then the probability that both occur at the same time is 1.00 (Option c)

Probability is a quantification of how likely an event is to occur. Typically, probabilities are defined as the chances that a specific outcome will occur out of a given selection of outcomes. A probability is expressed mostly in decimal form, taking values between 0 and 1. Probabilities cannot exceed this particular range of values.

Firstly, To clarify : You are confusing mutually exclusive and jointly collectively exhaustive.

The former describes condition which cannot both (or all) obtain. and so exclude one another.

i.e., "not - (both A and not - A)"

The latter describes conditions, one of which must obtain, and so exhaust the field of possibilities. i.e., "either A or not - A"

I presume you intend to refer to the latter.

Second, to answer your question: If two events - are jointly exhaustive, their probabilities must by definition sum to 1.

It is thus certain, not merely probable, that one or the other will obtain.

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Answer:

If the Esteban's car continues to decrease 20%, by five years the car will be worthless.

20 x 5 is 100. This means that 100%  of the car will have lost its value and will be worthless.

I hope this helps & Good luck <3 !!!

a. The median of Otter 2 's data is greater than the median of Otter 1's data. b. The variability in the data for Otter 1 is greater than the variability in the data for Otter 2.

c. Liz can conclude that Otter 2 generaily eats more food.

In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution.

The median is the value in the middle of a data set, meaning that 50% of data points have a value smaller or equal to the median and 50% of data points have a value higher or equal to the median.

The median for A is 25.5 and 26 for B. This implies that B has higher median than A.

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The graph of equation y = 6 - x - x² is shown in figure.

And, The value of gradient at x = 2 is, - 5.

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

Given that;

The equation is,

⇒ y = 6 - x - x²

Now, The graph of equation y = 6 - x - x² is shown in figure.

Which represent the graph of parabola.

And, The value of gradient at x = 2 is,

⇒ y = 6 - x - x²

⇒ y' (x) = 0 - 1 - 2x

⇒ y' (x) = - 1 - 2x

At x = 2;

⇒ y' (2) = - 1 - 2 × 2

⇒ y ' (2) = - 1 - 4

⇒ y' (2) = - 5

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Answer:An ordered pair contains the coordinates of one point in the coordinate system. A point is named by its ordered pair of the form of (x, y). The first number corresponds to the x-coordinate and the second to the y-coordinate. To graph a point, you draw a dot at the coordinates that corresponds to the ordered pair.

Step-by-step explanation:

Answer:

0.36

Step-by-step explanation:

and I got this answer by using calculator

Answer:

the graph of g(x) will be the same shape as the graph of f(x), but shifted downward by 3 units.

Step-by-step explanation:

The functions g(x) = 4(0.5)^x - 3 and f(x) = 4(0.5)^x are both exponential functions with the same base of 0.5 and the same coefficient of 4.

However, the graph of g(x) will be shifted downward by 3 units compared to the graph of f(x), because of the constant subtraction of 3 at the end of the function. This shift will occur for all values of x, meaning that the distance between the two graphs will remain constant as x changes.

In other words, the graph of g(x) will be the same shape as the graph of f(x), but shifted downward by 3 units.

Answer:

The original price is $ 149.95

Answer:

5 weeks

Step-by-step explanation:

Let factory B produce the same amount of shoes as factory A in w weeks.

then,

70+50w = 120+40w

50w - 40w = 120 - 70

10w = 50

w = 50/10

w = 5

Therefore, in 5 weeks factory B will produce the same amount of shoes as factory A will produce in 5 weeks time.

The ratio of SR and ML and ratio of ST , MN are equal ,so they are similar triangles .

What is triangle ?

Triangle can be defined in which it consists of three sides , three angles and sum of three angles is always 180 degrees.

In given two triangles,

RST and NLM

In the triangle RST ,

The sum of angles is 180

so,

44  + 15 + S = 180

S =   180 - 59

S = 121

And similarly in the triangle NLM,

N + 121 + 44 = 180

N = 180 - 165

N = 15

Therefore, The values of given angles S and N are 121 , 15 respectively

SR / ML  = 3.61 / 5.415 = 0.667
ST / MN = 9.71 / 14.565 = 0.667

Hence, The ratio of SR and ML and ratio of ST , MN are equal ,so they are similar triangles .

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Answer:

225

Step-by-step explanation:

(x+y)^2, if x=6 and y=9

Put 6 in place of x and 9 in place of y.

(6+9)^2 According to order of operations, add the 6+9 first.

(6+9)^2

= 15^2

= 225

The approximate area of the remaining cardboard would be = 246 cm². That is option B.

To calculate the area of the remaining cardboard = (area of rectangle) - 2(area of circle)

The formula that is used to calculate the area of rectangle = length×width

where length = 14 cm

width = 18cm

area = 14×18 = 252 cm²

The area of the 2 circle formula;

= 2(πr²)

where π = 3.14

r = 2/2 = 1

area = 2(3.14) = 6.28

Area of the remaining cardboard

= 252 cm²- 6.28

= 245.72

= 246 cm²

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Answer:

Step-by-step explanation:

1. The Louisiana Purchase

2. The War of 1812

3. The Missouri Compromise

4. Trail of Tears

Hope this helped!

The box plot that represents the data-set is given as follows:

Option B.

From left to right, the five features of the box and whisker plot are listed as follows

The data-set in this problem has 11 elements, hence:

The quartiles are the mean of each half, hence:

Meaning that the second plot is correct.

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(a) The angle measurement of first unknown angle is c = 80 degrees

(b) The angle measurement of second unknown angle is y = 110 degrees

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

(a) You can pick pair of starting angles a = 30 degrees and b = 70 degrees

The angle measurement of first unknown angle will be:

a + b + c = 180  (sum of angles in a triangle is 180 degrees)

c = 180 - a - b

c = 180 - 30 - 70

c = 80 degrees

(b) The angle measurement of second unknown angle will be:

y = 180 - b  (sum of angles on a straight line is 180 degrees)

y = 180 - 70

y = 110 degrees

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Answer:

x=-2

Step-by-step explanation:

if we find sum of same variables ,

3x-2x+y-y=-8+6

x=-2

Answer:

  (c)  A line graph, because it would show the association or relationship between two variables

Step-by-step explanation:

You want to know if scatter plot or a line graph more appropriate to construct for seeing the relationship between a manatee's weight and height.

The variables involved are "weight" and "height". Notice that "time" is not involved. (This eliminates choices B and D.)

A line graph is useful for showing how one variable relates to another as the value of one variable changes. It would be useful for plotting the weight and height of one animal as it changes during the animal's lifetime.

When multiple animals are involved, a scatter plot might be more helpful for showing the relationship.

The context is given as "a manatee's weight and height", not "manatees' weight and height." Hence it seems we can assume that we're looking at data for only one animal.

The appropriate graph would be ...

  A line graph, because it would show the association or relationship between two variables — choice C.

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The algorithms are a problem solving tool in Python because it  provides a wide range of built-in algorithms that can be used to solve many common problems.

The Algorithms are a fundamental problem solving tool in Python . An algorithm is a set of instructions that are executed in a specific order to solve a particular problem. In Python, algorithms can be implemented in the form of functions or methods.

So , In addition to the built in algorithms, Python also provides a rich collection of third party libraries that contain various algorithms that can be used to solve complex problems.

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The given question is incomplete , the complete question is

How are algorithms a problem solving tool in Python ?

The value of complex number |2 - 3i| will be, 3.605

A complex number is one that has the formula a + bi, where I is the imaginary unit and a and b are real numbers. A and b are the real and imaginary halves of a complex number, respectively.

In order to expand the real number system to include answers to polynomial equations that couldn't be solved with just real numbers, complex numbers were first introduced. Many branches of mathematics and science, such as computer science, physics, and engineering, are based on the idea of a complex number.

The absolute value of a complex number "a + bi" can be calculated as the square root of the sum of the squares of its real and imaginary parts:

|a + bi| = √(a² + b²)

In this case, a = 2 and b = -3, so:

|2 - 3i| = √(2 + (-3)²)

          = √(4 + 9)

          = √(13)

          = approximately 3.6055

So, the value of |2 - 3i| is approximately 3.6055.

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Answer:

2√21

Step-by-step explanation:

let the sides of bigger triangle be a, b and d.

then,

a²= b² + d² [ by Pythagoras theorem]

13² = 9² + d²

d² = 13² - 9²

d²= 169 - 81

d² = 88

d = √88

Now, the sides of smaller triangle are c, x, and d

by Pythagoras theorem,

d² = c²+x²

(√88)² = 2² + x²

88 - 4 = x²

x² = 84

x = √84

x= 2x2x3x7

x = 2√21

Therefore, the value of x is 2√21

Hope it's helpful..

Answer: $546.60 (*this was the actual number but I rounded it $546.644444444)

Step-by-step explanation:

Divide: $245.99/0.45 = 546.644444444

You can double check your answer by multiplying 546.644444444 by 0.45 and you will get $245.99

If you multiply by $546.60 you will get $245.97 since you rounded

Find the difference between the starting and ending values:

    72 - 60 = 12

Divide that difference by the starting value:

    12 ÷ 60 = 0.2

Convert that to a percent:

   0.2 = 20%

The number of teachers increased by 20%.

The key is to divide the difference by the original number, not the ending number.

The solution of AB = BC  for A, assuming that A,B and C are square matrices and B is invertible is [tex]A = BCB^{-1}[/tex]

We have to solve the equation

AB = BC , given that these all are square matrices and B is invertible.

Write the required Equation:

 AB = BC

Multiply both sides by inverse of B

The multiplicative inverse of a matrix is the matrix that gives you the identity matrix when multiplied by the original matrix.

Matrix multiplied by an identity matrix, the result is always the same original non-identity (non-unit) matrix, and thus, as explained before, the identity matrix gets the nickname of "unit matrix"

[tex]ABB^{-1} = BCB^{-1}\\AI = BCB^{-1}\\A = BCB^{-1}[/tex]

so the solution of AB = BC is [tex]A = BCB^{-1}[/tex]

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Answer:

B. 1/12

Step-by-step explanation:

1/8 × 5/6 = 5/48 × 4/5 = 1/12

To validate a min-heap, you can follow these steps: Start at the root, Check each subtree, Repeat the process recursively, If any node violates the min-heap property, then the heap is not valid.

Start at the root: Verify that the value at the root node is the minimum value in the heap. This is the defining property of a min-heap. Check each subtree: For each subtree, check that the value at the root of the subtree is less than or equal to the values of its child nodes. If this property holds true for all subtrees, the heap is a valid min-heap. Repeat the process recursively: Continue the above steps for each subtree until all nodes have been checked. If any node violates the min-heap property, then the heap is not valid. In that case, you can either rebuild the heap or identify the specific node or subtree that violates the property and fix it. In summary, to validate a min-heap, you need to check that the root node contains the minimum value, and each subtree obeys the min-heap property. You can check the property recursively until all nodes have been verified, and identify any nodes that violate the property for correction.

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Answer: 124950

Step-by-step explanation:

So, let’s look at this logically. For first place, you can any one of the 51 runners finish there. For 2nd place, you can have any one of the remaining 50 runners finish there. For 3rd place, you can have any one of the 49 runners who haven’t finished finish there. runners who haven’t finished finish doesn’t matter .So, you take all of the possibilities, and times them together, 51*50*40 different possibilities.Now, if you want a generic equation, you can run it through this equation, x being the number of possibilities, and n being the number of ones your choosing:

(51!)/(51-3)!

Answer:

y=12-5x

Step-by-step explanation:

We know that 12 is our original number so we put that first. X represents the number of hours. And 5 is how much its dropping per hour. Y would be our final answer. If you sub in for x the amount of hours outside and multiply it by 5, that's how many degrees it dropped.