Given that x and y are integers, explain why the product of x+√y and its conjugate will always be an integer.

Which graph correctly shows the system of equations [tex]\left \{ {{x-2y=4} \atop {y=2x+4}} \right.[/tex] ?

Correct graph for the system of equations is 3rd graph.

We graph the collection of ordered pairs that make up the equation's solution when graphing a system of equations in two variables.

The universal equation for any straight line is y=mx+c. m is the line's slope, and c is the y-intercept.

First, we take the equations as x-2y=4 as equation (1) and y=2x+4 as equation (2).

Now solve the equation (1)

x-2y=4

The equation is not in the form of y=mx+c.

So, we write as y= [tex]\frac{1}{2}[/tex]x-2

Here, slope m=[tex]\frac{1}{2}[/tex] and y-intercept is (0,-2).

If we take x=2 we get y=-1.

y= [tex]\frac{1}{2}[/tex](2)-2

y=1-2

y=-1

Now we have 2 solution for the equation (1) that are (0,-2) and (2,-1).

If we see the third graph in the given options.

There is a blue straight line and that is the line for equation (1) there we can see the points (0,-2) and (2,-1).

Now solve the equation (2)

y=2x+4

The equation is in the form of y=mx+c.

Here, slope m=2 and y-intercept is (0,4).

If we take x=1 we get y=6.

y= 2(1)+4

y=2+4

y=6

Now we have 2 solution for the equation (2) that are (0,4) and (1,6).

If we see the third graph in the given options.

There is a green straight line and that is the line for equation (2) there we can see the points (0,4) and (1,6).

Therefore, the correct graph for the given system of the equation[tex]\left \{ {{x-2y=4} \atop {y=2x+4}} \right.[/tex] is the third graph.

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Answer: Yes √35 +5 is a rational number

Step-by-step explanation:

A rational number is any number that is a fraction, decimal, repeating decimal, or negative decimal.

Answer:

75% filled

Step-by-step explanation:

Each triangle is 50%.

Half of 50% is 25%.

One full triangle, 50%, plus one half triangle, 25%, add up to 75% percent of the two triangles being filled.

The constant of variation is 3.6

The inverse variation property states that , whenever the product of values of two quantities is a constant value then there is opposite variation between these two corresponding values. Or we can also say that if the productive nature of two corresponding values is constant, then one quantity is inversely varies with second quantity. That means, we can say that if one values will increase then other will automatically decrease and vice versa.

Let say if x and y are two values and k is a constant value, then

According to inverse variation

k = xy or y = k/x

In the given question,

Take the order pair (0.9,4)

As it is an inverse variation, we can substitute it

y=k/x  

Now find the constant of variation

4=k/0.9

K=3.6

Therefore, constant of variation is 3.6

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The domain and the range are  −∞ < x < ∞ and −∞ < y < ∞ while the intercept is (2, 0)

The domain of the function is the set of input values of the graph

The range of the function is the set of input values of the graph

The function is given as

g(x) = 3x + 6

The above function is a linear function

This means that the domain and the range of the function are the set of all real values

i.e. −∞ < x < ∞ and −∞ < y < ∞

Calculate x when g(x) = 0 to determine the x-intercept

So, we have

3x + 6 = 0

Divide through by 3

x + 2 = 0

This gives

x = -2

Hence, the domain and the range are  −∞ < x < ∞ and −∞ < y < ∞ while the intercept is (2, 0)

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The solution of the system of equation by elimination method is (-3, 3)

The system of equation can be solved using substitution, elimination and graphical method.

But we are asked to use elimination method.

Therefore,

2x + 6y = 12

2x - 3y=  - 15

Subtract equation(i) from equation(ii)

Therefore,

6y - (-3y) = 12 - (-15)

6y + 3y = 12 + 15

9y = 27

y = 27 / 9

y = 3

Therefore,

2x - 3y =  - 15

2x - 3(3) = - 15

2x - 9 = - 15

2x  = - 15 + 9

2x  = -6

divide both sides by 2

x = - 6 / 2

x = -3

Therefore, the solution of the system of equation by elimination method is (-3, 3)

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The number of adults who have to attend the prom are 53

According to the question we have been given the ratio of number of adults to the number of students attending the prom which is :

                    [tex]\frac{x}{y} = \frac{1}{10}[/tex]          (1)

where, x = number of adults

and y = number of students attending the prom

Now equation (1) can be written as

                  y = 10x    (2)

That is number of students that attend the prom will be 10times the number of adults.

Now we have been given that there were 477 more students

                  y = x + 477

Now putting the value of y from equation (2) we get

               10x = x+477

                9x = 477

                  x = 53

Thus if the school is expecting the same attendance this year, then total 53 adults have to attend the prom.

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The true statement about the graph of the parabola inequality given as y < x^2 + 2x - 6 is (b) the vertex is located at (-1,-7)

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The parabola inequality is given as

y < x^2 + 2x - 6

Next, we plot the graph of the parabola inequality

To plot this graph, we simply enter the inequality y < x^2 + 2x - 6 in a graphing calculator

From the attached graph, we can see that the vertex of the parabola inequality is at (-1, -7)

Hence, the true statement about the graph of the parabola inequality given as y < x^2 + 2x - 6 is (b) the vertex is located at (-1,-7)

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For the given rational number, y=x-1/x²+4 x+4

Vertical Asymptotes: x= - 2

Horizontal Asymptotes: y = 0

A line that, in analytical geometry, is an asymptote of a curve is one where, when one or both of the x or y coordinates go to infinity, the distance between the curve and the line approaches zero. An asymptote of a curve is a line that is tangent to the curve at a point at infinity in projective geometry and similar settings.

Given,

y=x-1/x²+4 x+4

y = x-1 / (x+2)²

x = -2, x = 0

So the horizontal asymptote will be 0.

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Draw a picture!

You get a right triangle with hypotenuse = 20 ft and horizontal leg = 12 ft

Use the Pythagorean Theorem to find the length of the vertical leg:

vertical leg = √(20²-12²) = √256 = 16 ft

When you are performing multiple transformations it is called a composite transformation.

A number of transformations or sequence of transformations that can be combined into a single transformation is called as composition. The resulting matrix is known as composite matrix. The process of combining is known as concatenation.

A composite transformation (or a composition of transformations) refers to the two or more transformations performed one after the other. For example: a translation followed by a reflection which is again followed by a rotation. Another example can be: a rotation followed by a translation or a rotation followed by a reflection.

Therefore, when you are performing multiple transformations it is called a composite transformation.

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The system of equations has exactly one solution.

Based on the information given, the equation is illustrated as:

2x - 3y = -4

-3x - 3y = 3

Add both equations

5x = -1

Divide

x = -1/5

Since 2x - 3y = -4

2(-1/5) - 3y = 4

-2/5 - 3y = 4

3y = -2/5 - 4

3y = - 4 2/5.

Divide

y = -4 2/5 ÷ 3

y = 1 7/15

Therefore, the system of equations has exactly one solution as the value of x and y are gotten.

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Two parallel lines have equal slope.

Therefore, slope of line y = -2/9x + 6 is equal to the slope of the line joining the points (3,2).

Slope of line is given by :

m= -[(coefficient of x) / (coefficient of y)]

Where m= slope,

Slope of line y = -2/9x + 6

2/9x + y = 6

(m1) slope of equation g = -x/y

                                     = -(2/9)/1

                                     = -2/9

Since equation h is parallel to g

So, m1=m2

That is slope of equation h=slope of equation g

We know,

Equation of the line h having slope=m2= -2/9

passing through the slope of the point (3,2) is,

       y-y1=m(x-x1)

Replace with values x1,y1=(3,2) and m=-2/9

      y-2=(-2/9)(x-3)

We can solve it :      

       9y-18=-2x+6

       2x+9y=6+18

       2x+9y=24

       2x+9y-24=0

Hence,

     2x+9y-24=0 is the equation of h.

Therefore,

Line g has an equation of y = -2/9x + 6. Parallel to line g is line h, which passes through the point (3, 2), then the numbers in the equation of line h is 2x+9y-24=0

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Answer:

Gemma, a scuba diver, begins a dive on the side of a boat 4 feet above sea level. She descends 28 feet.

Step-by-step explanation:

Answer: Papst blue ribbon

Step-by-step explanation:

Ryan lives in a trailer park. He likes to drink papst blue ribbon and not wear satin robes.

The logarithmic expression log₃ 16 changed by the base rule is 2.52.

The inverse about an exponential function is a logarithmic or log function. To find an exponent, we could use a log function.

To analyze earthquake magnitudes or compare the magnitudes of 2 distinct earthquakes, we must be able to transform among logarithmic and exponential forms.

Let's use this data to create our log. The logarithmic function is as follows:

Now, for the stated conditions;

= log₃ 16

Using the Base Rule of log functions, the above expression can be written as,

=  ㏒ₓ16/㏒ₓ3

If the base is taken as 10. Then the expression will become.

= ㏒₁₀16 /㏒₁₀3

= 1.204/0.477

= 2.52

Therefore, the value of the given log expression log₃ 16 is obtained as 2.52.

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Answer:

31 units

Step-by-step explanation:

The correct response is [C]: If and only if the angles are nearby, two angles form [a] linear pair.

Think about the response option shown in "Answer choice: [C]":

If and only if the angles are contiguous, two angles constitute a linear pair.

Then, think about the next:

1) "Two additional angles make a linear pair."

Is this a fact? Of course, but not always. (In other words, "sometimes") By definition, a "linear pair" of angles IS supplementary, but not all supplementary pairs of angles are linear pairs. In order for supplementary angles to also be "linear angles," they MUST ALSO BE ADJACENT.

2) "Two vertical angles are next to each other." Is this a fact? It's not true; it never is.

In light of the fact that this biconditional is NOT an acceptable definition, answer choice "C" is the one that is appropriate. This can be determined by looking at all the other options.

Think about the other response options:

The maxim "Two angles are supplementary if and only if the total of their angles measures 180" is the correct response.

is WRONG despite being a nice definition:

1) The total of the measurements of two additional angles is 180 degrees.

2) Two angles are supplementary if the total of their measurements equals 180 degrees.

"Two angles are vertical angles only if they are not close to one other and are produced by two intersecting lines," is the correct response (option B);

is WRONG despite being a nice definition:

1) Nonadjacent angles are those created by two crossing lines when two angles are vertical.

2) Two angles are vertical angles if they are nonadjacent angles created by two intersecting lines.

The sum of two angles equals 90 if and only if both angles are complementary (answer option [D]);

is WRONG despite being a nice definition:

1) The total of two complimentary angles' measurements equals 90 degrees.

2) Two angles are complimentary if the total of their [measured] is 90 degrees.

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Answer:

112

Step-by-step explanation:

Find the lowest common multiple of 14 and 16.

To find the lowest common multiple:

1) Break the numbers down into their prime factors.

14 = [tex]2^{1}[/tex] x [tex]7^{1}[/tex]

16 = 2 x 8 = 2 x 2 x 4 = 2 x 2 x 2 x 2 =  [tex]2^{4}[/tex]

2) Multiply the highest power of each prime number.

We have three numbers, but only two are unique:  [tex]2^{1}[/tex] , [tex]7^{1}[/tex] and  [tex]2^{4}[/tex]

  [tex]2^{4}[/tex] >  [tex]2^{1}[/tex] , so we will use  [tex]2^{4}[/tex]

[tex]7^{1}[/tex] x  [tex]2^{4}[/tex] = 7 x 16 = 112

The product using the distributive property is 12z+8y²-8x+16 in the standard form.

The distributive law, which states that a × (b + c)=(a × b)+(a × c), is generalized by the distributive property of binary operations.

In every scenario, the distributive property can be summed up as follows:

Each summand (or minuend and subtrahend) is multiplied by this factor, and the resulting products are added, to multiply a sum (or difference) by a factor (or subtracted).

This concept states that multiplying the sum of two addends by a number will produce the same outcome as multiplying each addend separately by the number and then adding the results.

Given product: 4×(3z+5+2y²-2x-1)

Using the distributive property we can write it as:

= (4×3z)+(4×5)+(4×2y²)-(4×2x)-(4×1)

= 12z+20+8y²-8x-4

= 12z+8y²-8x+16

So the product using the distributive property is 12z+8y²-8x+16 in the standard form.

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Answer:60 degrees

Step-by-step explanation: hexagon is 360 degrees. has 6 sides. 360 divided by 6= 60 degrees

Answer:

D) 7

Step-by-step explanation:

The answer is D because A, B, and C are not considered numbers that are natural, whole, integers, or fractional. Irrational numbers are numbers that cannot be quantified any other way, do not have repeating decimals, and never end. A good example of this is π or 3.14159265.... you get the picture.

Hope this helps!

Answer: 12346

Step-by-step explanation:

Firstly, to round the decimal number 12345.6789 to its nearest whole number we will look at the tenth place. the digit to the immediate right of the decimal point.

Here in the given example 12345.6789, the tenth digit is 6.

If the tenth place digit is equal to or more than 5 we will round up and if it is less than 5 we will round down.

If the hundredth digit of the decimal number is equal to or more than 5, then round up.

Since the tenth digit 6 is >= 5 we will round up i.e. ( ones place digit + 1 ) and the remaining all digits next to the decimal point are removed.

Therefore, the number 12345.6789 rounded to the nearest whole number is 12346. if this is wrong im sorry but i think this is how i even double checked.

log₄x²y³ = log x² + log y² is solution of this logarithmic function.

What is an example of a logarithmic function?

What distinguishes exponential from logarithmic growth?

we use property [ log ( mn) = log +  log n ] in equation -

log₄x²y³ = log x² + log y²

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Given that,

Mass of earth = 5.9 × 10²⁴ kg

Mass of   = 4.9 ×  10²⁴ kg

a) Combined mass of earth and

5.9 × 10²⁴ +  4.9 ×  10²⁴ = 10.8 × 10²⁴

b) If the mass of the sun =  1.9 × 10³⁰

Let's say the total gain of earth and  combined x

so it will equal the mass.

Then,

10.8 × 10²⁴ + x = 1.9 × 10³⁰

x = 18989.2 kg

Hence "Combined mass of earth and venues is 10.8 × 10²⁴ and there are a total of 18989.2 kg taking earth and venue to equal to the sun.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

For example = 2 + 8 + 9

Subtraction = Minus of any two or more numbers with each other called subtraction.

For example = 4 - 8

Division = divide any two numbers or variable called division.

For example 4/8

Multiplication = to multiply any two or more numbers or variables called multiplication.

For example 5 × 7.

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Since the difference between consecutive terms is the same, the sequence is an arithmetic sequence, hence Mai is correct.

The sequence is missing, and has these following information:

We also have that:

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

[tex]a_n = a_1 + (n - 1)d[/tex]

From the values os the function, we have that:

The rate of change is the same, hence sequence is an arithmetic sequence, and Mai is correct.

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Answer:

the answer is false

Step-by-step explanation:

this is an example: 22+1=23  23 is not an even number

Answer:

B. False

Step-by-step explanation:

Let the even number be x_e and odd be x_o

[tex]{ \tt{ = x _{e} + 1}}[/tex]

Assume the range is 2 ≤ x ≤ 4

[tex]{ \tt{x _{2} = 2 + 1}} \\ { \tt{x_{2} = 3 \: (odd)}}[/tex]

[tex]{ \tt{ x_{4} = 4 + 1}} \\{ \tt{x _{4} = 5 \: (odd)}}[/tex]

Therefore:

[tex]{ \tt{x _{n + 1} = x _{e} + n \: \: gives \: odd}}[/tex]

Hence;

[tex]{ \tt{ x_{e} + 1 = x _{o} }}[/tex]

Answer:

2. 7x^2 + 4x + 2x

4. -x - 6

6. 4x^2

8. 7x - 2

10. 10x^2 + 5

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Answer:

The larger figures are 3 times the size of the smaller figures.

Scale factor = 3?

Step-by-step explanation:

Answer:

The scale factor is 3 :)

Step-by-step explanation:

The smaller figure multiplied by 3 is the larger figure.

Answer:

x=5

Step-by-step explanation:

STEP

1

:

STEP

2

:

Pulling out like terms

2.1     Pull out like factors :

  4x - 8  =   4 • (x - 2)

Equation at the end of step

2

:

 (0 -  12 • (x - 2)) -  -36  = 0

STEP

3

:

STEP

4

:

Pulling out like terms

4.1     Pull out like factors :

  60 - 12x  =   -12 • (x - 5)

Equation at the end of step

4

:

 -12 • (x - 5)  = 0

STEP

5

:

Equations which are never true:

5.1      Solve :    -12   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

5.2      Solve  :    x-5 = 0

Add  5  to both sides of the equation :

                     x = 5