State the property that justifies the following statement.
If 12=2 x+8 and 2x+8=3y, then 12=3y.

The conjecture is always true, two right angles are always supplementary.

A pair of angles are supplementary only when the sum of those angles equals to 180°. In such a case each angle is said to be the supplement of another.

In case of parallel lines  and a transversal two co-interior angles are supplementary. The opposite angles of a cyclic quadrilateral are supplementary angles .

For two angles to be supplementary only the sum of the angles matter and they should always be 180°.

The numerical value of right angle is 90° .

Therefore the sum of two right angles will be 90°+ 90° = 180°

So the conjecture which states that two right angles are supplementary will always stand as the sum of two 90°s is always 180°.

Hence the conjecture is true.

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Based on the calculations, the coordinates of the y-intercept are (0, -9).

In Mathematics, the y-intercept of any graph (parabola) occurs at the point where the value of "x" is equal to zero (0). Similarly, the x-intercept refers to the point at which the graph of a function crosses the x-axis and the value of "y" is equal to zero (0).

Mathematically, the slope of any straight line can be calculated by using this formula;

[tex]Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Substituting the given parameters into the formula, we have;

Slope, m = (-4.5 - 3)/(-3 + 8)

Slope, m = -7.5/5

Slope, m = -1.5.

Mathematically, the standard form of the equation of a straight line is given by;

y - y₁ = m(x - x₁)

At point (-8, 3), we have:

y - 3 = -1.5(x + 8)

y - 3 = -1.5x - 12

y = -1.5x - 12 + 3

y = -1.5x - 9

Therefore, the coordinates of the y-intercept are (0, -9).

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The number of teaspoons of strawberry syrup per ounce of milk this recipe use is 0.375 and the number of ounces of milk needed per teaspoon of strawberry syrup is 2.67

The given parameters are

Teaspoons = 3

Ounces of milk = 8

The number of teaspoons of strawberry syrup per ounce of milk this recipe use is calculated as

Rate = Teaspoons/Ounces of milk

So, we have

Rate = 3/8

Evaluate

Rate = 0.375

The number of ounces of milk needed per teaspoon of strawberry syrup is

Rate = Ounces of milk/Teaspoons

So, we have

Rate = 8/3

Evaluate

Rate = 2.67

Hence, the number of teaspoons of strawberry syrup per ounce of milk this recipe use is 0.375 and the number of ounces of milk needed per teaspoon of strawberry syrup is 2.67

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Answer:

m = 8

Step-by-step explanation:

I looked at the line 8 and looked at m and noticed they're literally the same length. so m = 8.

Answer:

1i = 1

4 + i = 4 + 1 = 5

Step-by-step explanation:

hope it's helpful

The graph with two functions with the same end behavior is the bottom one.

The end behavior tell us how the function behaves as x tends to positive and negative infinity.

Now, let's look at the bottom graph on the given image.

You can see that the red graph goes up on the left side, and down on the right side.

And you also can see the same thing for the line, the blue graph,  goes up on the left side, and down on the right side.

So there we can see two graphed equations with the same end behavior, thus, that is the correct option.

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Answer:

B,E,A

Step-by-step explanation:

-3/4

The | \ symbol mean how far it is from 0. - means its negative.

The simplified form of the expression:  9w – 4y – 8w + 1 + y -12 – 2w is -1w – 3y – 11.

Given,

The expression: :  9w – 4y – 8w + 1 + y -12 – 2w

We have to simplify the expression.

A mathematical expression can be simplified by replacing it with an equivalent one that is simpler (often shorter), for example. Algebraic expressions are simplified in computer algebra. Logic optimization involves the simplification of Boolean expressions.

Now simplify:

9w – 4y – 8w + 1 + y – 12 – 2w

= -1w – 4y + 1 + y – 12

= -1w – 3y + 1 – 12

= -1w – 3y – 11

So, the simplified form of the expression:  9w – 4y – 8w + 1 + y -12 – 2w is -1w – 3y – 11.

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The midpoint is at (1 , -7/2 ,1/2)

In the given statement is

To find the midpoint of the line segment joining the pair of points

G(-3,-4,6) and H(5,-3,-5)

Midpoint:

The coordinates of the midpoint of a line segment are the average of the coordinates of the end points.

m = (A +B)/2

If we are given three points and we wish to find the midpoint of those points, we need to use the midpoint formula m =(  [tex]\frac{x_{1}+x_{2} }{2} ,\frac{y_{1}+y_{2} }{2} , \frac{z_{1}+z_{2} }{2}[/tex] )

where:

(x1 , y1 ,z1) are the coordinates of the first point:

(x2 , y2 , z2) are the coordinates of the second point:

Now, We are given the three points G(-3,-4,6) and H(5,-3,-5)

Solving for the midpoint , we have,

m = ([tex]\frac{-3+5}{2},\frac{-4+(-3)}{2} ,\frac{6+(-5)}{2}[/tex])

m = (1 , -7/2 ,1/2)

Therefore, the midpoint is at (1 , -7/2 ,1/2)

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Answer:  shift 2 units right, and 4 units down

==================================================

Explanation:

The x+2 means to shift the point 2 units to the right.

For instance, the point (5,13) moves to (7,13) after adding 2 to the x coordinate.

The y-4 means to shift the point 4 units down. Example: (10,8) moves to (10,4) after subtracting 4 from the y coordinate.

Overall, (x,y)→(x+2,y-4) means "shift 2 units right, and 4 units down"

------------

Example:

Let's apply the rule to the point (1, 7)

(x,y)→(x+2,y-4)

(1,7)→(1+2,7-4)

(1,7)→(3,3)

The equation of the line in slope-intercept form is y + 2 = (5 / 3) · (x + 5).

Linear equations are first order polynomials whose slope-intercept form is introduced below:

y - y₁ = m · (x - x₁)       (1)

Where:

And the slope of the line is determined by the secant line formula:

m = Δy / Δx                (2)

Now we proceed to determine the equation of the line in slope-intercept form:

m = [5 - (-5)] / [4 - (- 2)]

m = 10 / 6

m = 5 / 3

y + 2 = (5 / 3) · (x + 5)

The equation of the line in slope-intercept form is y + 2 = (5 / 3) · (x + 5).

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80.94cm² is the area of the parallelogram.

The formula of the area of a parallelogram: bh (base × height)

Now, substitute the values in the formula as follows:

Therefore, the area of a parallelogram is 80.94cm².

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The domain of the function will be - 2 ≤ x < 0. And the range of the function will be 0 ≤ y < 1. Then the relationship between x and y will be y = √(2² - x²).

The domain means all the possible values of x and the range means all the possible values of y.

A relation is shown in each graph. Every ordered pair in the relationship has a first and second number that are both real numbers.

From the figure, the domain of the function will be - 2 ≤ x < 0. And the range of the function will be 0 ≤ y < 1.

The function is a part of the circle, then the relationship between x and y will be as,

y = √(2² - x²)

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Answer:

Step-by-step explanation:

Answer:

y = -2x + 9

Step-by-step explanation:

1) Use the equation y = mx + c (m being gradient and c being y-intercept)

2) Substitute all the values to get 7 = -2(1) + c

3) Solve to get c:

4) Final answer: y = -2x + 9

The sum of the first ten terms of any Fibonacci-like sequence is 88.

The Fibonacci numbers, sometimes known as Fn in mathematics, are a series. Each number in the Fibonacci sequence is composed of the sum of the two numbers before it. Typically, the sequence begins with 0 and 1.

means

0+1 = 1

1+1 = 2

1+2 = 3

2+3 = 5,like this.

The Fibonacci sequence includes the numbers 0, 1, 1, 2, 3, 5, 8, 13, 21 and so on.

Sum = 0 + 1 + 1 + 2 + 3 + 5 + 8 + 13 + 21 + 34 = 88 is what we get when we add up the numbers in the series.

The first ten Fibonacci numbers sum is 88.

Hence, The sum of the first ten terms of any Fibonacci-like sequence is 88.

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Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100.

The number 1/3 as a percentage is 33.33 %.

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The percent sign, %, is frequently used to indicate it. There is no unit of measurement for a percentage. It is a dimensionless number (pure number).

Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.

Let the number be 1/3 then

1/3 = 0.3333

To find percentage multiply it by 100, we get

So, 0.3333 × 100 = 33.33 %

Therefore, the number 1/3 as a percentage is 33.33 %.

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The sequence  1,4,9,16, . . . is neither an arithmetic nor a geometric sequence. In fact, it is a quadratic sequence. The next two terms are: 25 and 36

Given a sequence:

  1,4,9,16, . . . .

To determine whether the sequence is an arithmetic, geometric, or neither, we need to check the relation between two consecutive terms.

Arithmetic sequence:

   a(n) = a(n-1) + d

or a(n) - a(n-1) = d  for all n

where d is a constant and is usually called common difference.

Geometric sequence:

   a(n) = a(n -1) . r

or a(n)/a(n-1) = r, for all n

In the given sequence:

a(1) = 1

a(2) = 4

a(3) = 9

a(4) = 16

Check the difference:

a(2) - a(1) = 4 - 1 = 3

a(3) - a(2) = 9 - 4 = 5

Since the difference between 2 consecutive sequence is not a constant, then the sequence is not an arithmetic one.

Check the ratio:

a(2)/a(1) = 4

a(3)/a(2) = 9/4

Since the ratio of 2 consecutive sequence is not a constant, then the sequence is not a geometric one.

Thus the given sequence is neither an arithmetic, nor a geometric sequence. In fact, it is a quadratic sequence. Notice that:

a(n) = n²

Hence, the next two terms are: 25 and 36

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Answer:

Step-by-step explanation:

  The photo and poster of known dimensions are similar figures at a ratio of 4.

A proportion is a value that allows us to know variable values of a set of elements that are related by means of a constant.

  If we want to know if these two figures are similar or proportional, they must be at a ratio, (both dimensions), for this we formulate the following:

 This will generate an equation:

2x = 8

3x = 8

  When solving for both values of "x" it must be exactly the same:

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Step-by-step explanation:

Value from:

1 shilling coins

=

1

(

21

−

3

x

)

=

21

−

3

x

5 shilling coins

=

5

(

2

x

)

=

10

x

10 shilling coins

=

10

(

x

)

=

10

x

Total value

=

72

shillings

i.e.

21

−

3

x

+

10

x

+

10

x

=

72

shillings

−

3

x

+

10

x

+

10

x

=

72

−

21

17

x

=

51

x

=

51

17

x

=

3

∴

Mary has

3 10

shilling coins.

Square root is a factor that, when multiplied by itself, equals the original value.

The values of -√38 = -6.16 then -√38  <  6.

In mathematics, a square root is a factor that, when multiplied by itself, equals the original value. Any time the idea of an object's square is mentioned, square roots can be considered more widely. These include square matrices and function spaces, among other mathematical structures.

Even though it is only one of the two square roots of a positive number, the term "square root" is occasionally used to describe the major square root of a positive number.

Let the values of -√38 = -6.16 then -√38  <  6

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The line of best fit for pork production in China in x years after 2000 is given by:

y = 2053.17x + 39758.67.

The values of the table are missing, and are given as follows:

To find the equation, we need to insert the points (x,y) in the calculator.

For this problem, we insert the points (Year - 2000, Production) given in the table, and the line of best fit, using a calculator, is given by:

y = 2053.17x + 39758.67.

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Equations x - 5 = -2, -3/5 + x = 12/5, -14x = -42, x/4 = 6/8 will be placed in the x =3 column and equations x/3 = 9, -6 + x = -9 will be placed in the x 73 column.

Here, we are given 6 equations, let us solve each one-

1. x/3 = 9

x= 9 3

x= 27

=x3

2.-6 + x = -9

x= -9 + 6

x

x= -3

X+ 3

3.

3. x - 5 = -2 x= -2 + 5

x=3 4.-3/5 + x = 12/5

x= 12/5 + 3/5

x= 15/5

= x= 3

5. -14x = -42

x= -42/-14

x = 42/14

= x= 3

6. x/4 = 6/8

X/4 = 3/4

x = 12/4

x= 3

Thus, equations x - 5 = -2, -3/5 + x = 12/5, -14x = -42, x/4 = 6/8 will be placed in the x =3 column and equations x/3 = 9, -6 + x = -9 will be placed in the x 73 column.

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The slope of the line containing (4,2) and (4,-3) is 1.

The slope of a straight line can be written as follows,

m = ( [tex]y_{2} - y_{1}[/tex])/([tex]x_{2} - x_{1}[/tex])                 equation1

The line is containing the points (5,-1) and (2,-4). So, we can write

[tex]y_{2}[/tex] = -4 , [tex]y_{1}[/tex] = -1 , [tex]x_{1}[/tex] = 5 , and [tex]x_{2}[/tex] = 2 .

On substituting the values of variables in equation1, we will get

m = (-4-(-1))/(2-5) = (-3/-3) = 1.

As the slope of a line is 1 , so we can conclude that the given line is a straight line.

Here,

m = the slope of the line

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex]  ) are the first coordinates.

( [tex]x_{2}[/tex] , [tex]y_{2}[/tex]  )are the second coordinates.

The slope of the line containing (5 , -1) and ( 2 , -4 ) is 1.

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The equation of line which contains points (2,4) and (0,-2) will be y = 3x - 2.

It is given that a line contains points (2,4) and (0,-2).

We have to find out the equation of the line.

What is the equation of line in slope intercept form ?

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

As per the question ;

Line contains points (2,4) and (0,-2)

We know that slope intercept form of line is ;

y = mx + c

∴  (2,4) and (0,-2) must satisfy the equation because the line contains them.

So ,

For x = 2 and y = 4 ;

the equation y = mx + c becomes ;

4 = 2m + c ------ ------ ------ ---- (1)

Also ;

For x = 0 and y = -2 ;

the equation y = mx + c becomes ;

-2 = 0 + c

or

c = -2

Put the value of c in equation 1 ;

i.e.,

4 = 2m - 2

2m = 6

or

m = 3

So ,

the equation of line which contains points (2,4) and (0,-2) will be ;

y = (3 × x) - 2

y = 3x -2

Thus , the equation of line which contains points (2,4) and (0,-2) will be y = 3x - 2.

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Answer:

It would be at the coordinates 4,5

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

Area of rectangle - area of semicircle =

 25 x17 - 1/2 pi (3.5)^2 = 405.8 mm^2 to the nearest tenth ...

Answer:

Yes, Triangle A

Step-by-step explanation: