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Galaxy cluster

for k = 6, the pair of linear equations have infinitely many solutions.

n the above equation a1= k, a2 = 12, b1 = 3, b2 = k, c1 = -(k - 3) and c2 = -k

If a solution has infinitely many solutions, then

⇒ a1 / a2 = b1 / b2 = c1 / c2

For the above pair of equations,

⇒ k / 12 = 3 / k = k - 3 / k

⇒ k/ 12 = 3/ k

⇒ k2 = 36⇒ k = ± 6

Also

⇒ 3/ k = (k - 3)/ k

⇒ 3k = k(k - 3)

⇒ 3k = k2 -3k

Then,

⇒ k2 = 6k

⇒ k = 6

The value of k which satisfies both the equations is 6.

Thus, for k = 6, the pair of linear equations have infinitely many solutions.

The complete question is,

For what values of k will the following pair of linear equations have infinitely many solutions?

kx + 3y - (k – 3) = 0

12x + ky - k = 0

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Answer:

B

Step-by-step explanation:

The identity property of multiplication says that the product of 1 and any number is that number, so it is B , 412x1=412

26 rounded to the nearest 10th is 30. This method is called round-off.

Round-off is the process by which we simplify the number by writing to its nearest number it can be written on the place value of  10th, 100, or 1000, etc.

In round-off, the numbers 0,1,2,3,4 are considered as nearest to the "0" and the numbers 5,6,7,8,9,10 are considered as nearest to the "10" similarly in this question 26 is considered as nearest to the "30".

The number can also be used for numbers as well as decimal numbers so that we can write the decimal number in simplified form. The use of round-off facilitates the number so that we can easily calculate them.

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Answer: To reduce the fraction to lowest terms, we need to divide both the numerator and denominator by their greatest common factor.

In this case, the greatest common factor between the numerator and denominator is x^2y.

So we can divide the numerator and denominator by x^2y to get:

(4x^(4)y^(3))/(-8x^(2)y) = (4x^2y^2)/(-8) = -(1/2) x^2y^2

So the fraction reduced to lowest terms is -(1/2) x^2y^2, which corresponds with option B.

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

Answer:

x = 15 , y = -5

Step-by-step explanation:

refer to attachment for answer

Hope this helps!

-Rishabh

MNP is a triangle, hence. MN and NP's midpoints are Q and R, respectively. MP is measured at 34.

Having three sides, three angles, and three vertices, a triangle is a closed, two-dimensional object. A polygon also includes a triangle. Triangle ΔABC is shown in the image above. Triangle illustrations.

Given:

MNP being a triangle, this. The midpoints of MN and NP are Q and R, respectively.

The lengths of QR and MP are 4x -11 and 9x - 29 respectively.

We must establish the MP's measurement.

x's value is:

The triangle midsegment theorem can be used to find the value of x.

Using the theorem, we've reached;

M P=2(Q R)

Substituting the lengths, we get;

9x - 29 = 2(4x - 11)

9x - 29 = 8x - 22

Subtracting both sides by  8 x, we have;

x - 29 = -22

Adding both sides of the equation by 29 , we get;

x = 7

As a result, x has a value of 7.

Measure of MP: The measure of MP can be obtained by changing x to equal 7 in the MP's length.

We therefore have;

MP = 9(7) - 29

MP = 63 - 29

The measure of MP is 34.

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At age 9, Tammy was taller than Leslie because she was 3.68 inches taller.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

as per the details stated above

that Leslie measured 50 inches at age 9

and Tammy's height may be predicted by the equation

y = 2.2x + 35.5,

where y represents Tammy's height at x years of age,

one must carry out the following computation to establish who was taller at that age:

Tammy = 2.2 x 9 + 35.5

= 18.18 + 35.5

= 53.68.

Tammy was 3.68 inches taller than Leslie at age 9 as a result, Tammy was taller at that age.

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By 3.68 inches, Tammy was taller than Leslie when she was nine years old.

As per the data given in the above question are as bellow,

The provided details are,

Given that Tammy's height can be predicted by the equation

y = 2.2x + 35.5,

where y is her height at age x, and Leslie's height at age 9 was 50 inches,

The following computation must be done to establish who was higher at that age:

Leslie is 50.

Tammy = 2.22 x 9.5 + 35.5 = 18.18 + 35.5 = 53.68

Consequently, Tammy was taller at age 9 than Leslie since she was 3.68 inches taller.

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In this study, weight loss would be the dependent variable, as it is being measured or observed as a result of the change in the independent variable, which is the calorie intake (1,300 calories/day).

The independent variable is the factor that is being manipulated or changed in the study, and the dependent variable is the factor that is being measured or observed as a result of that change.

Put simply, an independent variable is just what it sounds like it is. It's a separate factor that can't be affected by the others. One independent variable could be a person's age.

In research, the independent variable might be either (1) quantitative or (2) qualitative. Variables with numeric or scalar ranges are called quantitative. They can be thought of as numerical variables that provide answers to "how many?" or "how often?"

The three primary categories of research variables are the independent variable, the dependent variable, and the controlled variables. Take the case of an automobile driving along a variety of terrains.

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The curve at point P is approximately 0.88.

Slope is a measure of the steepness of a line or a surface and is represented by the letter m. It is calculated by dividing the vertical change in the line or surface by the horizontal change in the line or surface. Slope is used in mathematics, engineering, and other sciences to measure the rate of change between two points.

The slope of the curve at point P can be estimated by evaluating the function at the two points x=1.1 and x=1.3. At x=1.1, the value of y is 2.31 and at x=1.3, the value of y is 3.19. Therefore, the estimated slope of the curve at point P is (3.19-2.31)/(1.3-1.1) = 0.88.

This estimate indicates that the slope of the curve at point P is approximately 0.88.

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Answer: HE WAS PROPOSING A TOAST

1. R

2. N

3. A

4. I

5. H

6. S

7. E

8. G

9. W

10. P

11. O

12. T

Step-by-step explanation:

Answer:

HE WAS PROPOSING A TOAST

Step-by-step explanation:

5. H

7. E

9. W

3. A

6. S

10. P

1. R

11. O

10. P

11. O

6. S

4. I

2. N

8. G

3. A

12. T

11. O

3. A

6. S

12. T

Answer: 3.76

Step-by-step explanation:

6.26 - 2.5 = 3.76

Answer:

3.76

Step-by-step explanation:

Carlos have to travel 105 miles to reach the destination.

The path followed by an object to travel a predetermined distance at a predetermined speed from one place to another is called the distance traveled. As was previously said, the distance formula combines distance, speed, and time.

As per the details share in the above question are as bellow,

The details provided are as follow,

Carlos is traveling by automobile for more than 240 miles.

Carlos has traveled 135 miles so far.

How far must Carlos still travel?

We have to use subtraction method to determine the distance remaining.

Now subtract the total distance by the distance traveled,

Substitute the value in above we get,

=240-135

=105 miles

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The equation of the line in slope intercept form is y=-2/3+7

What is slope intercept form?

You should understand that the slope intercept form of a straight line is one of the most common forms used to represent the equation of a line.

The slope intercept form is used to find the y-intercept and the slope of a straight line

The equation of the line in slope intercept form is written as follows:

y=mx + b

where;

m= slope and

b = y-intercept

Here, m= -2/3 and b = 7

By substitution, the equation is written thus y=-2/3x + 7

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The amount of Dinars Dana would get if she exchanged $63 is 18 Dinars.

The correct answer choice is option D.

1 Dinar = $3.50.

x Dinar = $63

Equate the ratio

1 : 3.50 = x : 63

1/3.50 = x / 63

cross product

1 × 63 = 3.50 × x

63 = 3.50x

divide both sides by 3.50

x = 63/3.50

x = 18 Dinar

Therefore, Dana will exchange 18 Dinars for $63

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The measure of the angle ∠XYZ in the right-angle triangle will be 66.42 degrees.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

In the right-angle triangle, the measure of the angle ∠XYZ will be given as,

cos ∠XYZ = 6 / 15

cos ∠XYZ = 0.40

∠XYZ = cos⁻¹ (0.40)

∠XYZ = 66.42°

The measure of the angle ∠XYZ in the right-angle triangle will be 66.42 degrees.

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Simple geometric forms are used to create composite figures. Divide a composite figure or any irregularly shaped figure into straightforward, non-overlapping figures to get its area. To determine the overall area of the composite figure, first calculate the areas of each simpler figure separately.

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Step-by-step explanation:

I don't see any defined inequality here in the text.

but I can tell you what's in the picture. and how the correct inequality would look like.

the function, for which we need to define the range (all valid y-values) is moving between y = 2 and y = -2, including these 2 values.

the inequality shown is

-9 < y < -4

the values -4 and -9 are not included (indicated by the dotted lines).

so, we need to change that to

-2 <= y <= 2

please consider the "<=" signs, as both values have to be included, because the function is clearly also producing -2 and +2 values.

FYI

it would also be correct to write

2 >= y >= -2

Part 1:

MyFone Cellular company: C = 30 + 0.05m

Cellphones R Us company: C = 35 + 0.03m

What does a math equation mean?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Part 2:

If your monthly budget is $50 for cell phone service, we can find the number of text messages that can be sent with each company by using the equation for each company's monthly bill and setting it equal to $50.

MyFone Cellular company: 50 = 30 + 0.05m, so m = 600

Cellphones R Us company: 50 = 35 + 0.03m, so m = 1250

In this scenario, Cellphones R Us company would give you the most text messages.

Part 3:

To find the number of text messages at which the monthly bill is the same for each company, we can set the two equations equal to each other and solve for m.

30 + 0.05m = 35 + 0.03m

0.02m = 5

m = 250

At 250 text messages, the monthly bill for both companies would be the same.

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The simplified equation for -5x - 4y = 3, would be y = 1.25 x - 0. 75

The equation of 5x - 4y = 3 is a more complicated version of a linear equation which is meant to be in the slope - intercept form.

The slope - intercept form is:
y = mx + b

Where :

m = slope

b = y - intercept

The equation, 5x - 4y = 3, in that form is :
5x - 4y = 3

5x - 3 = 4 y

( 5x - 3 ) / 4 = 4 y / 4

5/ 4 x - 3 / 4 = y

1. 25x - 0.75 = y

y = 1.25 x - 0. 75

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The first part of the question is:
Simplify 5x - 4y = 3

The solution of the system of equations y = x² + 6x + 9 and y = -x + 3 is (-6, 9) and (-1, 4)        

An equation shows the relationship between numbers and variables in an expression.

From the system of equation:

y = x² + 6x + 9   (1)

And:

y = -x + 3      (2)

Using substitution method, substitute y = -x + 3 into equation 1:

-x + 3 = x² + 6x + 9  

x² + 6x + x + 9 - 3 = 0

x² + 7x + 6 = 0

x² + x + 6x + 6 = 0

x(x + 1) + 6(x + 1) = 0

(x + 6)(x + 1) = 0

x = -6 or x = -1

substitute value of x to get y:

when x = -6; y = -(-6) + 3 = 9        

when x = -1; y = -(-1) + 3 = 4

The solution is (-6, 9) and (-1, 4)        

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The number conjecture that proves the given assertion is;

D) Let (2a + 1) be one odd number, and let (2b + 1) be the other odd number. (2a + 1) + (2b + 1) = 2a + 2b + 2 = 2(a + b + 1). Because 2(a + b + 1) is a multiple of 2, it is an even number.

Number Conjecture is also called Goldbach conjecture which is defined as a number theory that states that every even counting number greater than 2 is equal to the sum of two prime numbers.

Now, when we multiply any number by two, it will become even. We can also see that, if we divide any number by two without a remainder, it will be even. In this question, we can say that;

Let (2a + 1) be one odd number.

Let (2b + 1) be the other odd number. Thus;

(2a + 1) + (2b + 1) =

2a + 2b + 2 =

2(a + b + 1).

This is due to the fact that 2(a + b + 1) is a multiple of 2, it is an even number.

Substituting any odd number in a and b gives you an even number

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The missing options are;

A) Every time you add two odd numbers, the sum is an even number.

B) Look at these different examples: 5 + 3 = 8, 15 + 7 = 22, 21 + 13 = 34. So the sum of two odd numbers must be even.

C) Let a and b both represent odd numbers, and let a + b be an even number. Therefore, a + b = b + a, which shows that the sum of two odd numbers is even.

D) Let (2a + 1) be one odd number, and let (2b + 1) be the other odd number. (2a + 1) + (2b + 1) = 2a + 2b + 2 = 2(a + b + 1). Because 2(a + b + 1) is a multiple of 2, it is an even number.

The required value of z in the given system of equations is 4. Option D is correct.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
3x + 5y - z = 15 - - - - (1)

x + 2y = 8 - - - - -(2)

x - 3y + 2z = - 9 - - - - (3)

multiply equation 1 by 2 and add with equation 3,
6x + x + 10y -3y -2z + 2z = 30 - 9
7x + 7y = 21
x + y = 3 - - - -(4)

Subtract equation 4 from 2
y = 5
Now, from equation 4
x + 5 = 3
x = -2

From equation 1
3(-2) + 5(5) - z = 15
-6 + 25 - z = 15
z = 10 - 6
z = 4

Thus, The required value of z in the given system of equations is 4. Option D is correct.

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The number of cords in 1 m³ are 0.3 based on their dimensions 8 ft, 4 ft and 4 ft.

Number of cords will be calculated by the formula -

Number of cords = total volume ÷ volume of one cord

Total volume is 1 m³

Volume of one cord is further given by the formula -

Volume of one cord = length × breadth × height

Keep the values in formula -

Volume of one cord = 8 × 4 × 4

Performing multiplication on Right Hand Side of the equation

Volume of one cord = 128 ft³

As per the known information, 1 feet is 0.305 meter

So, 1 ft³ = 0.028 m³

Volume of one cord = 128 × 0.028

Performing multiplication

Volume of one cord = 3.63 m³

Now calculating the number of cords

Number of cords = 1/3.63

Performing division

Number of cords = 0.3

Thus, there are 0.3 cord.

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The graph for [tex]y=5\sqrt{x}-2x[/tex] has been attached below. The solution has been obtained using graphing the function.

What is graphing of a function?

Drawing the graph of an applicable function is the process of graphing a function. While graphing simple functions like direct, quadratic,etc. is fairly easy, complex functions like rational, logarithmic,etc. bear some complexity and an understanding of certain fine ideas. Every point on the curve will satisfy the function equation if the curve represents the function.

We are given [tex]y=5\sqrt{x}-2x[/tex]

The range is given as [0,12]

The graph obtained has been attached below.

It is observed that graph of the function is increasing gradually and then decreasing.

Hence, the graph of the function is increasing gradually and then decreasing.

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Solving systems of equations by elimination involves manipulating equations so that the variables may be canceled out, resulting in a simpler equation that can be solved. This method is used to solve systems of equations with two or more variables.

Solving systems of equations by elimination is a method of finding the solutions to systems of equations with two or more variables. To do this, the equations are manipulated so that the two variables can be canceled out, resulting in a simpler equation. This simpler equation can then be solved using basic arithmetic. Depending on the equations, different methods may be used to manipulate them, such as adding them together or subtracting one from the other. Once the variables have been canceled out, the resulting equation can be solved to find the solution. This method of solving systems of equations can be used for linear equations, quadratic equations, and even more complex systems of equations.

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