Determine if the table shows a proportional relationship. x 42.5 29.2 69.4 y 21.25 14.6 34.7 Yes, it is proportional because the ratios for y over x are all equivalent to one half. Yes, it is proportional because the ratios for y over x are all equivalent to one third. No, it is not proportional because 21.25 over 42.5 is not equal to 29.2 over 14.6. No, it is not proportional because 42.5 over 21.25 is not equal to 34.7 over 69.4.

The values are given as;

1. - 2a - 9 = 6a + 15,  a = -3

2. 14 + 3n = 5n - 6, n = 10

An algebraic expression can simply be described as a mathematical expression that composed of arithmetic operations, such as;

They are also known to be made up of terms, variables, constants, factors and coefficients.

Given the algebraic expression;

- 2a - 9 = 6a + 15

Let's take the following steps;

collect like terms

- 2a - 6a = 15 + 9

add or subtract like terms

-8a = 24

Make 'a' the subject

a = 24/-8

Find the quotient

a = -3

14 + 3n = 5n - 6

collect like terms

3n - 5n = -6 - 14

-2n = -20

Make 'n' the subject of formula

n = 10

Hence, the values are -3 and 10

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Answer :- Constant term

In p(x) = x - 12, 1 is the coefficient of x and -12 is the constant term.

Step-by-step explanation:

Hope this helps..............

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The coordinates for the center of the circle is (-7,-1) and the length of the radius  is 6 units , the correct option is (D)  .

If the equation of the circle is x² + y² + 2fx + 2gy + c = 0

then the center is (-f,-g)

and the radius is √(f²+g²-c)

In the question ,

it is given that the

equation of the circle is x² + y² + 14x + 2y + 14 = 0

So , on comparing it with the general form of equation , we get

2f = 14

f = 7

and 2g = 2

g = 1

hence, the center is (-7,-1) .

the radius is √(7² + 1² - 14)

= √(49 + 1 - 14)

= √(50 - 14)

= √36

= 6

Therefore , The coordinates for the center of the circle is (-7,-1) and the length of the radius  is 6 units .

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Answer:

I think it's (4,5)

Step-by-step explanation:

Since there are 128 fluid ounces in one gallon, we need to divide 14 by 128 to change ounces into gallons.

Since there are 60 minutes per hour, we need to multiply 14 by 60 to change per minute into per hour.

Combining these:  14 fl oz / min x (1 gal / 128 fl oz) x (60 min / hr)  =  6.5625 gal per hour.

Written as a mixed fraction:  6 9/16 gal per hour.

Answer:

Step-by-step explanation:

y=-3x+24

(0,24)

Step-by-step explanation:

79 degrees plus X would make 180 degrees, because these two angles make up a straight angle.

So, 79 + X = 180

    -79          -79

         X=101 degrees.

Y is 79 degrees because it is an alternate interior angle to the other 79 degree angle.

Z is 101 degrees because X and Z are corresponding angles, which means they are equal.

If Z is 101 degrees, Y must be 79 degrees because Y and X make up a straight angle.

Answer:

X is 101 degrees. Y is 79 degrees. Z is 101 degrees.

Hope this helped! :)

For the given parallel lines with transversal ,and the pair of interior angles 72° and (7x +24)°, the value of x = 12°.

As given in the question,

Two parallel lines with transversal are given.

72° and (7x +24)°are pair of interior angles

Simplify the given relation to get the value of x we have,

72° + (7x +24)° =180°

⇒ 7x + (72 +24)° =180°

⇒ 7x + 96° = 180°

⇒ 7x = 180° - 96°

⇒ 7x = 84°

⇒ x = 84° /7

⇒ x = 12°

Therefore, for the given parallel lines with transversal ,and the pair of interior angles 72° and (7x +24)°, the value of x = 12°.

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Answer:

9 inches

Step-by-step explanation:

Set it up like a fraction ratio and solve for x.  as the price (denominator) and amount (numerator) have a set ratio, you can cross-multiply for your answer.

[tex]\frac{13}{52} =\frac{x}{36\\}\\[/tex]

13*36 = 468

468/52 = 9

Another way would be to divide 13 by 52 and multiply by 36, but then you end up with decimals and cross multiplication will be easier in the long run.

The median value is the 11th score which is 84%.Changing 49% to 69% will increase the mean but the median will not change.

The three measures of central tendency used in statistics are mean, median, and mode. While describing a set of data, we always specify the focal point of any data set. The measure of central tendency is this. Every day, data are presented to us. We discover them in books, articles, bank statements, phone and utility bills, as well as in newspapers. There are so many; they are all around us. The challenge now is if we can identify some key characteristics of the data by focusing on only a few data points. The means, medians, and modes—measures of central tendency or averages—can be used to do this. When describing a set of data, a measure of central tendency locates the set's center.

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Answer:

IT WAS NOT D!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Step-by-step explanation:

Answer:

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

Find the midpoint of the segment and its slope to determine the perpendicular line passing through the midpoint.

The midpoint has coordinates:

The slope:

We know perpendicular lines have opposite/reciprocal slopes.

So the slope of the perpendicular bisector is:

Use the coordinates of the midpoint and point-slope equation to determine the line:

Answer:

[tex]y=-\dfrac{5}{2}x+9[/tex]

Step-by-step explanation:

A perpendicular bisector is a line that intersects another line segment perpendicularly and divides it into two equal parts.

Given endpoints of the line segment:

Substitute the given endpoints into the slope formula to find the slope of the line segment:

[tex]\implies \textsf{Slope $m$}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{6-2}{7-(-3)}=\dfrac{4}{10}=\dfrac{2}{5}[/tex]

If two lines are perpendicular to each other, their slopes are negative reciprocals.  

Therefore, the slope of the perpendicular line is -⁵/₂.

Find the midpoint of the given line segment by substituting the given endpoints into the midpoint formula:

[tex]\implies \textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)[/tex]

[tex]\implies \textsf{Midpoint}=\left(\dfrac{7-3}{2},\dfrac{6+2}{2}\right)[/tex]

[tex]\implies \textsf{Midpoint}=\left(\dfrac{4}{2},\dfrac{8}{2}\right)[/tex]

[tex]\implies \textsf{Midpoint}=\left(2,4\right)[/tex]

To find the equation of the perpendicular bisector, substitute the found slope and midpoint into the point-slope form of a linear equation:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-4=-\dfrac{5}{2}(x-2)[/tex]

[tex]\implies y-4=-\dfrac{5}{2}x+5[/tex]

[tex]\implies y=-\dfrac{5}{2}x+9[/tex]

Therefore, the equation for the perpendicular bisector of the line segment whose endpoints are (-3, 2) and (7, 6) is:

[tex]\boxed{y=-\dfrac{5}{2}x+9}[/tex]

Answer:

Q4) 20

Q5) 48%

hope this helps

Answer:

slope = -1/9

Step-by-step explanation:

Hope this helps!!!

Scientific notation the

Answer:

B

Step-by-step explanation:

[tex]f(x) = 7( { \frac{1}{2} })^{3x} \\ f(x) = 7 ({ \frac{1 \times 1 \times 1}{2 \times 2 \times 2} })^{x} \\ f(x) = 7 ({ \frac{1}{8} })^{x} [/tex]

To make a poster you have to keep the ratio between lenght and height (otherwise it will look weird)

This is:

Answer: 7.3924E14

Step-by-step explanation:

Answer: (52,72) (52 adults and 72 children)

Step-by-step explanation:

1) Create 2 formulas that show the information show above, 2.5x+2y=274 showing how the x is how many adults paid for a ticket and y is how many children paid for a ticket. The second formula being x+y=124 meaning the combination of children and adults equal 124 people.

2) Take those formulas and input them into a graph as shown in the picture (Graph 1)

3) Find the common point shown on the graph (should be the middle grey dot if on Desmos as shown (Graph 2)

4) The common point is (52, 72)

And if you plug these numbers in by replacing the x's and y's i shown in step 1 they bring an output of 274 and 124

Hope this helps :)

Answer:

G

Step-by-step explanation:

the domain is the interval or set of all valid x values.

we see x starts at -3 and goes up to +1.

but x = 1 has the be excluded (the hollow point tells us that, a filled point says "include").

therefore, the -3 <= x < 1 answer is correct

The number of followers Rita has is 13086.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The number of followers Rida has = 6,218

92 people stop following Rida's blog.

This means,

6218 - 92 = 6126

417 people start following Rida's blog.

This means,

6126 + 417 = 6543

The number of followers doubles.

This means,

6543 x 2 = 13086

Thus,

The number of followers Rita has is 13086.

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Answer:

63.7 inches to nearest tenth.

Step-by-step explanation:

The legs of the right triangles formed are 21 inches and 1/2*18 = 9 inches.

So, the hypotenuse (which is one of the congruent sides of the isosceles triangle)

= √(21^2 + 9^2

= √522 inches

Therefore, the triangles perimeter

= 2 * √522 + 18

= 63.695 inches.

Option C and Option D are the appropriate measurements of center and spread for the dataset.

The mean, median, and mode are three examples of center-of-data measurements.

Included in the spread measurements are range, mean deviation, variance, and standard deviation.

The given data is displayed as a box plot with the minimum, maximum, median, Q1 and Q3 values.

The median is the most accurate measurement of the middle of the data.

The interquartile range is the appropriate way to measure spread.

In conclusion, the median and interquartile range, respectively, are the most suitable measures of the data set's center and dispersion.

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Applying the distributive property and precedence of operations, the results to each side of the expression is of 2/5, hence they property holds.

The left-hand side of the expression is defined as follows:

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

Applying the distributive property, 2/5 multiplies each term as follows:

2/5(4/3-1/3) = 8/15 - 2/15

(multiplication of fractions -> multiply numerators and denominators with themselves).

They have common denominator, then the subtraction of the fractions is calculated as follows:

2/5(4/3-1/3) = 8/15 - 2/15 = 6/15

6 and 15 are divisible by 3, hence the fraction is simplified as follows:

6/15 = 2/5.

The right-hand side of the expression is given as follows:

2/5 x 4/3 - 2/5 x 1/3

We have two operations, subtraction and multiplication. The multiplication has higher precedence, hence:

2/5 x 4/3 - 2/5 x 1/3 = 8/15 - 2/15

Then the procedure is the same as the left-hand side, obtaining an equal result, and so the distributive property holds.

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

We need to solve:

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Thus, the final answer is 34.9.

2.

Answer:120 dollars

Step-by-step explanation:

Explanation

To answer the question, we have to understand the different parts of an algebraic expression

An expression containing variables, numbers, and operation symbols is called an algebraic expression. is an example of an algebraic expression. Each expression is made up of terms. A term can be a signed number, a variable, or a constant multiplied by a variable or variables.

We are given the algebraic expression:

For the given question

The difference means the result of subtracting one number from another or How much one number differs from another, so we have

Then

The coefficient is is a number or any symbol representing a constant value that is multiplied by the variable of a single term or the terms of a polynomial, so we have

Also

A quotient is a number resulting from the division of one number by another, so we have

Finally,

A product is the result of multiplication or an expression that identifies factors to be multiplied.

Thus, we have

Answer:

X=ℝ, Y=ℝ

Step-by-step explanation:

Parallel means they have the same slope so it can be anything on the x-axis, perpendicular meaning opposite slope which is y=.

Answer:

[tex]6x - \frac{3}{X^2} + 2[/tex]

Step-by-step explanation:

Hope this is correct and helps you! :))

It is true to state that segments 6 5 8 could form a triangle. Where AC = 6, CB =5 and BA = 8. See the explanation for the same below.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. Triangle ABC denotes a triangle with vertices A, B, and C.

The total lengths of any two sides must always be larger than the length of the third side in order to make a triangle.

This is shown as follows:

6 + 5 = 11 > 8

5 + 8 = 13 > 6

8 + 6 = 14 > 5

Given that the side lengths meet the preceding criterion, a result, the supplied segments may be used to build a triangle.

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True, the segments 6, 5, and 8 form a triangle.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Let ABC is a triangle

AB=6

BC=5

CA=8

To form a triangle the sum of any two sides must be greater than the third side.

AB+BC>CA

6+5>8

11>8

BC+CA>AB

5+8>6

13>6

CA+AB>BC

8+6>5

14>5

It satisfies the condition for forming a triangle.

Hence the segments form a triangle.

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