State whether each sentence is true or false. If false, replace the underlined term to make a true sentence.
A right solid has an axis that is also an altitude.

the horizontally shrunk function by a scale factor K = 3 is modeled by:

g(x) =  |3*x| + 5

For any function f(x), we define a horizontal shrink or compression by a scale factor K as:

g(x) = f(K*x)

In this case the function is:

f(x) = |x| + 5

And the scale factor is K = 3.

Then we can write the compression as:

g(x) = f(3*x)

Replacing the actual function we will get:

g(x) = f(3*x) = |3*x| + 5

Then the horizontally shrunk function by a scale factor K = 3 is modeled by:

g(x) =  |3*x| + 5

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Answer:

B,E,A

Step-by-step explanation:

The formula for the temperature in ºC is:

[tex]C = \frac{5}{9}(F - 32)[/tex]

As shown in the problem, the rule is as follows:

F(C) = 9C/5 + 32.

We want to find the temperature in Celsius given the Fahrenheit temperature, hence we have to solve for C the above formula, hence:

9C/5 = F - 32

9C = 5(F - 32)

C = 5/9(F - 32).

For better notation I will use Latex, as follows:

[tex]C = \frac{5}{9}(F - 32)[/tex]

The above formula is the formula for the temperature in ºC.

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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 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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The first five terms of a geometric sequence with first term 2 and common ratio (-2) are 2, -4, 8, -16, 32

The given parameters:

a₁ = 2, r = -2

r is the common ratio, hence, the given sequence is a geometric sequence.

In a geometric sequence, the formula for the nth term is given by:

       a(n) = a(1) . rⁿ⁻¹

We can also find the terms using recursive formula. The nth term of a geometric sequence is equal to the (n-1)th term times the common ratio, r. Mathematically,

       a(n) = a(n -1) . r

Let us start from n = 1

a(1) = 2  (given)

a(2) = a(1) . r = 2 . (-2) = -4

a(3) = a(2) . r = -4 . (-2) = 8

a(4) = a(3) . r = 8 . (-2) = -16

a(5) = a(4) . r = -16 . (-2) = 32

Thus, the first five terms are 2, -4, 8, -16, 32

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The algebraic expression (z+0)+y+0 is equivalent to (z+y) by the identity property of addition.

An algebraic expression is a simple and random combination of  constants and variables .

An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number).

The identity property of addition states that when a constant number is added to zero the value of the expression remains the same.

Since the absolute value of 0 is nothing so adding or subtracting zero from a constant does not change the value of the constant.

I.e, g+0=0 here the value of g does not change.

Given (z+0)+y+0

We know from the identity property of addition:

z+0=z and y+0=y

Therefore the value of the expression is (z+y) .

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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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Answer:

It would be at the coordinates 4,5

Step-by-step explanation:

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 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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Answer:

53degree

82+45=127

We know

There is 180 degree in the angle

For the missing value

180-127= 53

Answer:

Answer is in the attached screenshot! :)

Step-by-step explanation:

Please let me know if you have any questions! :)

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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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:

Answer:

Yes, Triangle A

Step-by-step explanation:

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 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)

-3/4

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

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

Answer:

1i = 1

4 + i = 4 + 1 = 5

Step-by-step explanation:

hope it's helpful

The probability that the point of the spinner land on blue is 8.34%.

A pie chart is a type of chart that shows data in a circular graph.

We recognise that the pie's total value is always 100%. It is additionally recognized that a circle has a circumference of 360°. As a result, the sum of all the data equals 360°. Depending on these, there seem to be two main pie chart formulas:

On complete rotation of circle forms 360 degrees at the centre.

The total percentage of the all the colours is 100%.

Divide the value of blue by 3.6 because 360 degrees /100 percent = 3.6.

The total percentage of blue shown by the pointer of spinner is 30%.

Probability P (pointer landing on blue) = 30/3.6

Probability P (pointer landing on blue) = 8.333... = 8.4 (approx.)

Therefore, the probability that the pointer lands on the blue is 8.4.

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Answer:

The answer is 4x+(any number other than 4)

Step-by-step explanation:

If there are no solutions, then the equation will be equal to 4x + (any number other than 4).

Examples: 4x + 1, 4x + 2, 4x + 3

Based on the percent gratuity to the florist and the cost being rounded to the nearest ten, the amount of the tip is $9

When the cost for the florist is rounded to the nearest 10, it goes from $94 to $90.

When the percentage gratuity is rounded to the nearest ten, it goes from 12% to 10%.

The approximate tip is:

= 10% x 90

= $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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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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Answer:

subtract 4from each side

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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