Which of the following expressions shows how to rewrite 4 − 5 using the additive inverse and displays the expression correctly on a number line?

Answer:

n = 1

Step-by-step explanation:

[tex]\frac{8}{3}[/tex] = [tex]\frac{19}{6}[/tex] n - [tex]\frac{1}{2}[/tex] n

multiply through by 6 ( the LCM of 3, 6 and 2 ) to clear the fractions

16 = 19n - 3n

16 = 16n ( divide both sides by 16 )

1 = n

Answer:

[tex]0 \leqslant c \leqslant 56[/tex]

Step-by-step explanation:

Since candy costs $7 per pound, and Kayla will buy less than 8 pounds, she will spend no more than $7 × 8, or $56.

18/ 3x+1 is  18x²-2/ 3x²-5x - 2}  in simplest terms.

What are examples of linear equations?

18 x² - 2 / 3x² - 5x - 2

3x² - 5x - 2 = 3x² - ( 6- 1 ) x - 2 = 0

                    ⇒  3x² - 6x + x - 2 = 0

                     ⇒  3x( x - 2 ) + 1 ( x - 2) = 0

                      ⇒ ( 3x + 1 ) ( x - 2 ) = 0

put in equation -

= 18 x² - 2 /  ( 3x + 1 ) ( x - 2 )

= 18/ 3x+1

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Answer:

Step-by-step explanation:

Givens

Flight speed there = 12 feet / second

Flight speed back = 8 feet / second

Total time = 22 minutes

Time at rest = 18 minutes

Time in flight = 22 - 18 = 4 minutes

Equation

Let the time going to the flowerbed = t

12*t + 8*t + 18 = Distance travelled + time at rest.

Answer

12*t + 8*t + 18 = Distance travelled + time at rest

The two numbers which are 5 units away from zero on the number line as required in the task content are; -5 and 5.

It follows from the task content that the numbers which are 5 units away from zero on the number line be identified and plotted.

Hence, given that the numbers in discuss are represented by; x; we have;

| x - 0 | = 5

| x | = 5

Ultimately, x = ±5. where +5 is to the right and -5 is to the left of zero respectively.

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The average interest rate does he pay on the total $32,000 he owes is 9. 5%

From the information given, we have that;

Given the total pay he owes as;

= $22, 000 +$ 10, 000

= $32, 000

The average interest rate is expressed as;

= sum of interest rate for college loan and car/ number of interest rate

Substitute the values

= 8 + 11/ 2

= 19/ 2

Find the quotient

= 9. 5%

Thus, the average interest rate does he pay on the total $32,000 he owes is 9. 5%

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By using collinearity assumptions and addition and subtraction of line segments, the length of the line segment AB is 26 units.

Let A, B, D, F be points lying on the same line such that A(x) ≤ B(x) ≤ D(x) ≤ F(x), where x is the position of each point on a number line. Then, the value of the length of the line segment AB is:

AB = AD + DF - BF

AB = 26 + 8 - 8

AB = 26

Please notice that B(x) = D(x) as AB = AD.

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By elimination, the solution of the system of equations, 6x - 3y = 3 and 5x - 5y = 10, is (-1 , -3).

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

First, simplify both equations by dividing the first equation by 3 and the second equation by 5.

6x - 3y = 3 ⇒ 2x - y = 1     (equation 1)

5x - 5y = 10 ⇒ x - y = 2     (equation 2)

Use the elimination method since subtracting the two equations will eliminate the variable y.

2x - y = 1     (equation 1)

 x - y = 2     (equation 2)

x        = -1

x = -1

Substitute the value of x to any of the two equation and solve for y.

6x - 3y = 3     (equation 1)

6(-1) - 3y = 3

-3y = 3 + 6

-3y = 9

y = -3

Hence, the solution of the system of equations is (-1 , -3).

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Answer:

where is the equal to sign????

an=a1+d(n−1)  is the explicit and a recursive formula for each sequence .

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.

Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.

An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.

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The length of seesaw will be equal to 11 feet.

It is given that midpoint of the seesaw is 13.5 feet from the swing set and swing set is 8 feet from the edge of the seesaw.

We have to find out the length of seesaw.

What do you mean by midpoint of a line segment ?

The midpoint is halfway between the two end points , whose x value is halfway between the two x values and y value is halfway between the two y values.

As per the question ;

The midpoint of the seesaw is 13.5 feet from the swing set.

and

The swing set is 8 feet from the edge of the seesaw.

So ;

The distance from the midpoint to the edge will be ;

13.5 – 8 = 5.5.

And

The length of the seesaw will be ;

= 2× (5.5)

= 11 feet

Thus , the length of seesaw will be equal to 11 feet.

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Answer:

6n2-15=150-15

6n2-15=135

6n2=150

divied both side by 6

n2=25

sqrt both side

n=-5 or 5 bc sqrt so 2 answer

Step-by-step explanation:

Answer:

f (x^2-4)  =  2x^2 - 5

Step-by-step explanation:

Yes , Triangles are all tessellated. The triangle's three corners (A, B, and C) meet together to form a 180° angle, or a straight line, which is why the image is successful.

Is a triangle capable of tessellation?

To create a regular tessellation, it is necessary that the tiles may fill 360 degrees around a point (all the tiles regular polygons with same number of sides) Only 60 degree angle triangles, 90 degree squares, and 120 degree hexagons will work.

Every vertex, edge, and tile in a regular tesselation are identical.

However, there are semiregular tesselations that use more than one regular polygon, but since they must be able to fill 360 degrees around a point, it turns out that only the octagon (8 sides, 135 degrees) and dodecagon can be used as additional polygons (12sides, 150 deg).

Note that just these 5 tesselations can be utilized to fill the plane entirely with regular polygons.

Each vertex in the semiregular tessellations is the same.

Eight of them are (3,3,3,3,6), (3,3,3,4,4), (3,4,6,4), (3,6,3,6), (3,12,12), and (4,6,12). (4,8,8)

The Octagon & square tiling (4,8,8) is a very common floor tiling.

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Answer:

X=2

Step-by-step explanation:

Add four to both sides

2x-4=0

2x-4+4=0+4

Add the numbers 2x = 4

2x =4

2x/2 = 4/2

cancel the terms

divide the numbers

= x=2

The 9th term of the geometric sequence can be determined by using the nth term of geometric sequence formula: an=arn-1

Geometric sequence is the series of number in which each term is determined by multiplying the common ratio with the preceding term.

In the formula, an=arn-1, a is the first term, n is the number of terms, and r is the common ratio.

The geometric sequence from the part b is 2,4,8,…

The first term a = 2

The common ratio r = 2

The number of term n = 9

Hence, to find the 9th term,

a9=2(2)9-1

a9=2(2)8

a9=512

The 9th term of the geometric sequence 2,4,8,… is 512

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Using translation concepts, the function g is given as follows:

g(x) = -|x - 4| + 1

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

In this problem, we have that function g(x) is the function f(x) vertically compressed by a factor of 2, hence:

g(x) = 0.5f(x)

g(x) = 0.5(-2|x - 4| + 2)

g(x) = -|x - 4| + 1

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Answer:

D. 52 45

Step-by-step explanation:

Answer:

no solution

Step-by-step explanation:

5n + 1 = 5n - 1 ( subtract 1 from both sides )

5n = 5n - 2 ( subtract 5n from both sides )

0 = - 2 ← not possible

this indicates that the equation has no solution

The slope of the line that contains the  points G(-4,3), H(-4,7) is not defined.

Slope of a line containing two points (a,b) and (c,d) is denoted  by

[tex]slope=\frac{d-b}{c-a}[/tex]

In the given question

The points given are G(-4,3), H(-4,7)

a=-4, b= 3  and c= -4 and d=7

Substituting the values in formula of slope we get

[tex]slope=\frac{d-b}{c-a}[/tex]

[tex]slope=\frac{7-3}{-4-(-4)}\\ \\ =\frac{4}{-4+4} \\ \\ =\frac{4}{0}[/tex]

Since the division of any number by zero is not defined .

Therefore , the slope of the line that contains the  points G(-4,3), H(-4,7) is not defined.

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The mean height of the given sample of values is approximately 65.20.

The heights of the 15 students are as follows:

{59, 61, 62, 63, 63, 64, 65, 65, 66, 67, 67, 67, 67, 69, 73}

To find the mean (average) height of the given values, we need to add up all the heights and then divide the sum by the total number of heights:

59 + 61 + 62 + 63 + 63 + 64 + 65 + 65 + 66 + 67 + 67 + 67 + 67 + 69 + 73

= 978

So, the mean height can be calculated as:

Mean height = Total height / Number of heights = 923 / 15 = 65.2

Therefore, the mean height is approximately 65.20.

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The naive forecast for day 6 is 94.

The naive forecast for the nth period is calculated as follows.

Forecast period Yn=Yn−1​

Period Sales Naive Forecasts

1         90                   -

2         97                  90

3         92                  97

4         90                  92

5         94                  90

6                            94

Hence, the naive forecast for day 6 is 94.

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The Slope-intercept form of the given equation is y = -3x + 18 .

An equation in Slope-intercept form is of the form

[tex]y = mx + b[/tex]

where m is the slope and b is the y intercept.

Now, the given equation is (y/9) + (x/3) = 2

Taking LCM on the left hand side of the equation, we get

⇒ [tex](3y+9x)/(2y) = 2[/tex]

⇒ 3y + 9x = 54

⇒ 3y = 54 - 9x

Dividing both side of the equation by 3, we get

⇒ y = [tex](54 - 9x)/3[/tex]

⇒ y = 18 - 3x

⇒ y = -3x + 18

∴ The equation y = -3x + 18 is in Slope-intercept form.

In the equation the slope is -3 and the y-intercept is 18.

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Answer:

  g(f(x)) = 6x -9

Step-by-step explanation:

Given f(x) = 3x –5 and g(x) = 2x +1, you want to find g(f(x)).

A function is evaluated by simplifying the result of substituting the argument for the function's variable.

  g(f(x)) = 2·f(x) +1 = 2(3x -5) +1 = 6x -10 +1

  g(f(x)) = 6x -9

Answer:

22 :)

Step-by-step explanation:

I've attached an image to help break down the answer. (credit to cymath.com)

Hope this helps!

Using the given information, the equation of the circle with center located at point (2 , 1) and passes through the point (6 , 4) is (x - 2)^2 + (y - 1)^2 = 25

Using the distance formula, get the radius of the circle by solving for the distance between the center (2 , 1) and the point (6 , 4).

radius = distance = √(x2 - x1)^2 + (y2 - y1)^2

radius = √(6 - 2)^2 + (4 - 1)^2

radius= √16 + 9

radius = √25

radius = 5

The standard form of the equation of the circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.

(x - h)^2 + (y - k)^2 = r^2

where (h , k) = (2 , 1)

r = 5

(x - 2)^2 + (y - 1)^2 = 5^2

(x - 2)^2 + (y - 1)^2 = 25

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The Gary's score after getting stuck in the dust storm will be -35 points.

It is given in the problem that,

The points gained by Gary by jumping over a crater = 20 points

And then,

The points lost by Gary for getting stuck in a dust storm = 45 points

We need to find,

The Gary's score after getting stuck in the dust storm

As in the beginning of the game, Gary's account had 20 points but as he then stuck in the dust storm he lost 45 points, which means he has lost points more than he had. So, now Gary would have negative points left in his account in the game

= 10 - 45

= - 35

Hence, the Gary's score after getting stuck in the dust storm will be -35 points.

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The equation and the solution are 2 = -8 * -x and x = 1/4, respectively

On the model, we have the following representations

[1][1]          [-1][-1][-1][-1][-1][-1][-1][-1][-x]

When represented as an equation, we have the following equation

So, we have

2 = -8 * -x

Evaluate the product in the above equation

So, we have

2 = 8x

Divide both sides of the above equation by 8

So, we have

1/4 = x

Rewrite the above expression as

x = 1/4

Hence, the equation and the solution are 2 = -8 * -x and x = 1/4, respectively

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The arithmetic mean of two terms in an arithmetic sequence is 42 .

One term is 30 then other term is

42 = (x+30)/2

x=54

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.

Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.

An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.

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