50 points please show your work and answer all of them

The five rational number between -5/6 and 5/6 are [tex]\frac{-4}{6} ,\ \frac{-3}{6} ,\ \frac{-2}{6} , \ \frac{-1}{6} ,\ \frac{1}{6}[/tex]

We have given two rational numbers [tex]\frac{-5}{6}[/tex] and [tex]\frac{5}{6}[/tex] .

For finding rational number make the denominator of given numbers same.

As the denominator of given numbers is already same so , we don't need to multiply .

Thus , five rational numbers are

 [tex]\frac{-4}{6} ,\ \frac{-3}{6} ,\ \frac{-2}{6} , \ \frac{-1}{6} ,\ \frac{1}{6}[/tex]

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The solution of the inequality is 1<x<2.

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations.

According to the given statement;

2 < 3x - 1 < 5

or, 2 + 1 < 3x - 1 + 1 < 5 + 1

or, 3 < 3x < 6

Divide the whole by 3, we get

or, 3/3 < (3/3)x < 6/3

or, 1 < x < 2

hence, the solution of the inequality is 1<x<2.

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The responses to the questions involving the solution and equations of a straight line are;

6. The slope is -0.5

7. The equation is; y = x + 4

8. y = 7 - 0.25•x

9. The balance after m months is modeled by the equation;

B = 1,800 - 150•m

10. The slope is the monthly payment on the loan

6. The points on the graph in question 6 are; (0, 4), and (4, 2)

The slope is given by the ratio of the rise to the run of the graph as follows;

[tex]Slope = \frac{2 - 4}{0 - 4} = - 0.5[/tex]

7. The equation in slope and intercept form is found as follows;

The given points are;

(-1, 3), and (-3, 1)

The slope and intercept form is presented as follows;

y = m•x + c

The point and slope form is presented as follows;

y - y1 = m•(x - x1)

Where m is the slope of the graph

m = (1 - 3)/(-3 - (-1)) = -2/-2 = 1

Which gives;

y - 3 = 1 × (x - (-1)) = x + 1

y = x + 1 + 3 = x + 4

The equation of the graph in slope and intercept form is; y = x + 4

8. The points are; (-4, 8), (4, 6)

Which gives;

m = (6 - 8)/(4 - (-4)) = -2/8 = -0.25

Therefore;

y - 8 = -0.25•(x - (-4)) = -0.25•x - 1

y = -0.25•x - 1 + 8 = -0.25•x + 7

9. The amount Zachary purchased the computer on loan = $1,800

The balance after 3 months = $1,350

The balance after 5 months = $1,050

Therefore;

The points on the graph of the equation that models the balance are therefore;

(0, 1,800), (3, 1,350), (5, 1,050)

Which gives;

B - 1800 = ((1,350-1,800)/(3-0))•(m - 0)

B - 1800 = -150•m

The equation that models the balance, B, after m months is therefore;

10. The slope, ((1,350-1,800)/(3-0)) = -150, signifies the amount by which the balance reduces each month, which is the same as the amount Zachary pays each month, (the monthly payment).

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Answer:

  5 trumpet players

Step-by-step explanation:

Given there are 10 fewer trumpet players than saxophone players, and the number of saxophone players is 3 times the number of trumpet players, you want to know the number of trumpet players.

Let t represent the number of trumpet players. Then 3t is the number of saxophone players, and the difference in numbers is ...

  3t -t = 10

Collect terms and divide by the coefficient of t:

  2t = 10

  t = 5

There are 5 trumpet players.

__

Additional comment

Check: There are 3 times as many sax players, so 15 of those. That's 10 more than the number of trumpet players.

You could have written the equation as ...

  t +10 = 3t . . . . . . 10 more than the number of trumpets

Sometimes, when ratios are given:

  t : s = 1 : 3

you can think in terms of "ratio units." Here, the difference is 3-1 = 2 ratio units, corresponding to a difference of 10 players. Then the multiplier of the ratio is 10/2 = 5:

  t : s = 1 : 3 = 5 : 15 . . . . . . 5 trumpets and 15 saxophones.

Answer:

2x - 3 = 11

x = -21

Step-by-step explanation:

Answer:

I'm pretty sure it's 5:4 or 5/4. I think this because there are 5 peaches and four oranges.

Answer:

(0,-4)

Step-by-step explanation:

I'm pretty sure it would be (0,-4) though it may be counted wrong. A whole 180° is like if you start from the highest point, you'd be at the lowest point right after the turn. It doesn't really matter the direction with 180° in this case cause it's going to be the same outcome anyways. (Or so I'd think).

Answer:

Step-by-step explanation:

Answer:

first translate triangle FDE down 5 units

second reflect it over the y axis

The image

Step-by-step explanation:

Using proportions, it is found that:

a) You need 15 tablespoons of brown sugar.

b) You need 8 tablespoons of baking soda.

c) You need 10 cups of brown sugar.

d) You need 24 cups of baking soda.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three, that can be either direct(cross multiplication) or inverse(line multiplication), deriving from proportional relationships. One example of application of proportions is for ratio problems.

For this problem, the recipe uses a 2:5 ratio of baking soda to brown sugar, hence:

Hence, for item a, the amount is:

5/2 x 6 = 30/2 = 15.

You need 15 tablespoons of brown sugar.

For item b, the amount is:

2/5 x 20 = 40/5 = 8.

You need 8 tablespoons of baking soda.

For item c, the amount is:

5/2 x 4 = 20/2 = 10.

You need 10 cups of brown sugar.

For item d, the amount is:

2/5 x 60 = 120/5 = 24.

You need 24 cups of baking soda.

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Answer: 225 yd³

Step-by-step explanation:

6*4*3=72

3*17*3=153

153+72=225 yd³

Answer:

Step-by-step explanation:

You want the maximum possible number of solutions to the equation

  ||ax -b| +c| = d

The values of 'a' and 'b' represent a vertical scale factor and a horizontal shift, so don't really contribute to the number of possible solutions. That means we can consider only the equation ...

  ||x| +c| = d

Positive c

We know |x| is always positive, and may have the same value for two different values of x. For positive 'c', the outside absolute value function does nothing, so the equation is effectively ...

  |x| = d-c

For d < c, there can be no solutions. For d = c, there will be one solution, and for d > c, there will be two solutions.

Negative c

When 'c' is negative, then sum |x| +c may have either sign. This gives rise to another pair of possible solutions, for a total of four solutions.

The attached graph shows the two cases. The red graph shows the left side expression with c > 0; the purple graph shows the left side expression with c < 0. The orange horizontal line represents a value of 'd'. The number of intersection points with that horizontal line is the number of possible solutions to the given equation.

For c > 0, there are two possible solutions.

For c < 0, there are four possible solutions.

We get that the value of (f + g​)(x​) is 11 x - 1.

Function: a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

We are given the two functions:

f(x) = 4 x + 3

g(x) = 7 x - 4

We need to find:

(f + g​)(x​)

We know that this is equal to

= f(x) +g(x)

Substituting the values, we get that:

= 4 x + 3 + 7x - 4

Combining the like terms, we get that:

= 11 x - 1

Therefore, we get that the value of  (f + g​)(x​) is 11 x - 1.

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Answer:

I don't know I think it's b

Answer:

Not complete, please recheck the question

Answer:

The first one is a function of x. The graph with a straight line up and down (vertical).

Step-by-step explanation:

The number of heavy equipment operators employed is 26 while number of laborers employed is 6

Let x be the number of heavy equipment operators employed

Thus, If thirty-two people were hired, then we can say that;

32 - x represents the number of laborers employed

Thus, the equation to solve for x would be;

136x + 80(32 - x) = 3960

136x + 2560 - 80x = 3960

216x + 2560 = 3960

216x = 3960 - 2560

216x = 1400

x = 1400/216

x ≅ 6

Thus;

32 - x = 32 - 6 = 26

Thus, we conclude that number of heavy equipment operators employed is 26 while number of laborers employed = 6

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The vertex of the function is (1, 0), the maximum is y = 0 and it has no minimum

The function is given as:

y = -2/3|x - 1|

The above function is an absolute value function

An absolute value function is represented as:

y = a|x - h| + k

Where the vertex is

Vertex = (h, k)

By comparing y = a|x - h| + k and y = -2/3|x - 1|, we have

(h, k) = (1, 0) --- vertex

a = -2/3

Because a = -2/3 is negative, then the vertex is a maximum

Hence, the vertex of the function is (1, 0), the maximum is y = 0 and it has no minimum

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Encontrando un factor comun entre los 3 números dados, concluimos que cada pedazo de tronco debe medir 3 metros, y se obtendran 10 pedazos en total.

Sabemos que los troncos miden 15, 9, y 6 metros, si los queremos cortar en pedazos de igual longitud, de tal forma que nada se desperdicie, entonces debemos encontrar un factor comun entre esos 3 numeros.

Los podemos reescribir como:

15 = 3*5

9 = 3*3

6 = 2*3

Entonces el unico factor comun entre las 3 longitudes es 3.

El tronco de 15 metros dará:

15/3 = 5 pedazos de tronco.

El tronco de 9 metros dará:

9/3 = 3 pedazos de tronco.

El tronco de 6 metros dará:

6/3 = 2 pedazos de tronco.

Sumando eso obtenemos 5 + 3 + 2 = 10 pedazos en total.

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Answer:

  x = √65

Step-by-step explanation:

You are given a right triangle with leg lengths 4 and 7, and you are asked for the length of the hypotenuse, x.

The Pythagorean theorem relates the lengths of the sides of a right triangle. It tells you the square of the hypotenuse (x²) is the sum of the squares of the other two sides.

  x² = 4² +7² . . . . . . . . . Pythagorean relation

  x² = 16 +49 = 65 . . . evaluate the expression

  x = √65 . . . . . . . . . . take the square root

The old/Original value of the book before 30% increase in price  is $70

Let us assume the old price of book before30% increase be x

Then the new price of the book after 30% increase would be x+ 30% of x

Which can be simplified as x+ 0.30x

Which further can be simplified 1.30x

As we are provided with the new price of book, we have to equate the above linear equation with the new price of the book

1.30x = $91

To solve the equation we need to move 1.30 from left hand side to right hand side which would change from  to

X= 91/1.30

X=$70

Hence the old value of the book before 30% increase in price   is $70

Correct question is if  30% increase in price of a book and the new price of a book is $91.00. What was the original price of the book?

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Answer: jus subtract untill u find x

Step-by-step explanation:

whether u do to one side do to the other

Answer:the number is 15

if i am correct give me brainliest

Step-by-step explanation:because 5-15=10 the number is 15

Answer:

55%

Step-by-step explanation:

She has ridden 22 out of 40 miles

22/40 is 0.55

0.55 = 55%

She has eight more miles or 45% left to go.

Answer:

100

Step-by-step explanation:

Answer:

34.972 ≈ 35

0.948 ≈ 1

Hope this helps :)

Step-by-step explanation:

To round to the nearest whole number look at the tenths place (the place right after the decimal). If the number is 1,2,3,4 then round down or keep the number the same. If the number is 5,6,7,8,9 then round up.