I figured x equals a specific number in every single question involving something like this. X is on all sides, there's no given number.

The solution set for the given inequality (2q/5 + 4 < 2q/-9) is q∈(-∞, - 45/7).

So, 2q/5 + 4 < 2q/ - 9:

Now, solve for the solution set as follows:

Therefore, the solution set for the given inequality is q ∈ ( -∞, - 45/7).

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Answer:

1.25 hours.

68.75 miles from the city

Step-by-step explanation:

Eltan's train (E) is travelling 65mph west.

Dmitri's train (D) is travelling 55mph west.

In terms of vectors, we can write E as 65E and D as 55W

The miles travelled by each is a function of time, T, in hours.

Each train's distance is:

 E:  T*65E

 D:  T*55W

They are 150 miles apart.  They will meet with the combined miles travelled is 150 miles.

 150 miles = T*65E + T*55W

150 miles = T(120 miles/hour)

T = (150 miles/120 miles/hour)

T = 1.25 hours

Make Demitri's train mile 0 and Eitan's train at mile 150 at the start.

They will have travelled the following miles in 1.25 hours:

Demitri:  (1.25hr)(55 m/hr) = 68.75 miles

Eitan:      (1.25hr)(65 m/hr) = 81.25 miles

Total = 150 miles

Dimitri is headed away from the city.  After 1.25 hours, his train will have travelled 68.75 miles when he sees Eitan passing him on the adjacent track (hopefull) headed into the city.  They meet 68.75 miles from the city.

Answer:

question one is B and question 2 is C

Step-by-step explanation:

Answer:

Step-by-step explanation:

triangle area formula: A = 1/2 × b × h

7 +3 = 10 ft

1/2 10 × 4 =

5 × 4 =

20 feet²

1) We need to consider that whenever we have a variable its exponent is raised to the 1st power, even when we don't write it as a superscript.

2) So we can write out the following steps to get that product as x²:

That's why we can write that, applying the property of exponents.

The ascending order of the set of numbers is √3 - 1, 2√10 ÷ 5, √14, 3√2, √19 + 1, 6

Given,

A set of numbers;

3√2, √3 - 1, √19 + 1, 6, 2√10 ÷ 5, √14

We have to arrange this numbers from least to greatest. That is, in ascending order.

Ascending order;

Numbers can be arranged in ascending order, from least value to highest value. The arrangement is left to right. Increasing order is another name for ascending order.

Here,

First we have to find the values of the square roots in the numbers.

3√2 = 4.24

√3 - 1 = 0.73

√19 + 1 = 5.36

6

2√10 ÷ 5 = 1.26

√14 = 3.74

Then,

6 is the greatest number and √3 - 1 is the least number.

That is,

The ascending order of the set of numbers is √3 - 1, 2√10 ÷ 5, √14, 3√2, √19 + 1, 6

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All of the rational numbers that we have in the question that we have here are:

This is the term that is used to refer to the ratio of two numbers that when they are expressed as a ratio of two different numbers, the denominator does not have to be 0.

The rational numbers when they are solved would not give us terminating decimals. That is they would be able to be expressed as fractions.

-√25 = -5

√0.0144 = 0.12

√0.36 = 0.6

√100 = 10

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-√25, √100, √0.36, and √0.0144n are the rational number. Options B, D, E, and F are correct.

As of the given data, numbers are given we have to determine which of the number are rational numbers.

Rational numbers are numbers that can be structured in the form of the fraction of integers. Eg- 5/6, 2/3 etc.

Here,
All the numbers are irrational numbers except -√25, √100, √0.36, and √0.0144 because the number picked out is required rational number.

Thus, -√25, √100, √0.36, and √0.0144n are the rational number. Options B, D, E, and F are correct.

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The equivalent expression of the given expression is [tex]\frac{g^1^5}{8h^6}[/tex].

What is inequality?

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

Consider the given expression, [tex]\frac{(2g^5)^3}{(4h^2)^3}[/tex]

Using the rule, [tex](a^m)^n = a^m^n[/tex]

So, [tex]\frac{(2g^5)^3}{(4h^2)^3} = \frac{8g^1^5}{64h^6}[/tex]

After simplifying  we get,  [tex]\frac{g^1^5}{8h^6}[/tex]

Therefore, the equivalent expression of the given expression is [tex]\frac{g^1^5}{8h^6}[/tex].

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Area of circle A is 113.04 in²

Area of circle B is 200.96  in²

Area of circle C is 452.16  in²

Area of circle B is 254.34  in²

The number of times that the area of Circle D greater than Circle A is 2.25

A circle is a bounded figure which points from its center to its circumference is equidistant.

Area of a circle = πr²

Where :

Area of circle A = 3.14 x 6² = 113.04 in²

Area of circle B = 3.14 x (6 + 2)² = 200.96  in²

Area of circle C = 3.14 x (8 + 4)² = 452.16  in²

Area of circle B = 3.14 x (12 - 3)² = 254.34  in²

Number of time that is the area of Circle D greater than Circle A = 254.34  in² / 113.04 in² = 2.25

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two lines are perpendicular when their slope is inverted and have the opposite sign

the general form of the equation line is-3,1

where m is the slope

rewrite

so, the slope 3/8

the slope of the other line is

to write the new equation of the line we use the slope and replace the point (-3,1)

now, replace b and the slope to create the line

Answer:

[tex]\dfrac{x-7}{9}[/tex]

which corresponds to choice
C :   [tex]f^{\small -1}(x)\ =\ \frac{1}{9}x\ -\ \frac{7}{9}[/tex]

Step-by-step explanation:

The inverse of a function y = f(x) can be found by interchanging x and y and solving for y

Let y = f(x)

y = 9x + 7

Interchange x and y:

x = 9y + 7

9y + 7 = x  (switch sides)

subtract 7 both sides
→  9y + 7 - 7 = x - 9

→ 9y = x - 9

Divide both sides by 9

→ [tex]y = \dfrac{x - 7}{9} = \dfrac{x}{9} - \dfrac{7}{9}[/tex]

which corresponds to choice C

Answer:

g = 5

Step-by-step explanation:

8g - 7 = 18 + 3g

add 7 to both sides:

8g - 7 + 7 = 18 + 3g + 7

8g = 25 + 3g

subtract 3g from both sides:

8g - 3g = 25 + 3g - 3g

5g = 25

divide both sides by 5:

5g/5 = 25/5

g = 5

Answer:

4.10 + 2.50x = 36.60

x = 13 miles

Step-by-step explanation:

I hope this helped

have a good day ^^

A set of data is given. It is required to find the first, second, and third quartile.

The given data is:

Recall that the lower quartile Q₁, or the first quartile, is the median of the lower half of the data in a set.

The lower half is:

Find the median of the lower half to get the first quartile, Q₁:

Hence, Q₁=9.

Recall that the second quartile Q₂ is the same as the median of the data.

The median is the middle element or the mean of two middle elements in a numerical data set with the elements ordered by their value.

Notice that the middle number is 15.

Hence, second quartile Q₂=15.

The upper quartile Q₃, or the third quartile, is the median of the upper half of the data in a set.

The upper half of the data is:

Calculate the median to find the third quartile, Q₃:

It follows that Q₃=17

The complete table is shown below:

The question asks us to solve the following system of equations by elimination:

Solution

Answer

The solution to the system of equation is:

x = -8

y = 9

Answer:

Step-by-step explanation:

From the ellipse equation

the length of the major axis is equal to 2a. By comparing this equation with the given one, we can note that

Then, the length of the major axis is 2x7 = 14

Answer: 1

Step-by-step explanation:

[tex]\lim_{x \to -6} f(x) \neq -1[/tex] because the left and right hand limits are not the same.

[tex]\lim_{x \to -1} f(x) \neq -1[/tex] because the left and right hand limits are not the same.

However, somewhere between 1 and 2, the limit does equal -1 because the left and right hand limits are the same.

Answer:

1) y = 3x + 5

2) y = -12x + 2

3) y = 5/4 - 5

4) y = -6x + 3

Step-by-step explanation:

ANSWER:

STEP-BY-STEP EXPLANATION:

We have the following function:

We calculate the inverse function as follows:

Answer:

Step-by-step explanation:

0 mixed berry smoothies and 70 milkshakes

Answer:

Step-by-step explanation:

x y

2 12

6 8

10 4

14 0

18 -4

The slope is the Rise/Run, or change in y over the change in x.  Pick any two points.  I'll choose (2,12) and (18,-4),

Rise = (-4 - 12) = -16

Run = (18 - 2) = 16

Slope = Rise/Run = -16/15, or -1

The equation becomes y = -1x + b

To find b, use any of the points in the equation and solve for b.  I'll use (14,0):

y = -1x + b

0 = -1(14) + b

b = 14

The equation is y = -x + 14

See the attached graph.

The perimeter of the rectangle is 6.89

Perimeter of the rectangle:

The perimeter (P) of a rectangle is the total length of all the sides of the rectangle.

The formula for the perimeter of the rectangle is

P = 2(l + w)

The letter ‘P’ denotes the perimeter of a rectangle. Let l denote the length and w denote the width of the rectangle.

Given,

Here we have the graph with the following points:

(-3/2, -1 7/9), (7/2, -1 7/9), (7/2, 3 2/9), and (-3/2 3 2/9)

Now we need to find the perimeter of the rectangle.

To calculate the perimeter, first we have to find the length and width of the rectangle.

To calculate the length, we have to use the values of x axis,

That is,

=> -3/2 + 7/2

=> (-3+7)/2

=> 4/2

=> 2

Therefore, the length of the rectangle is 2.

Now, we have to find the width of the rectangle using the y axis coordinates,

=> -1 7/9 + 3 2/9

Convert the mixed fraction into normal form, then we get,

=> -16/9 + 29/9

=> (-16 + 29)/9

=> 13/9

Therefore, the width of the rectangle is 13/9

Now, we have to use this to calculate the perimeter of the triangle,

P = 2 (2 + 13/9)

P = 2 ((18+13)/9)

P = 2 (31/9)

P = 62/9

P = 6.89

Therefore, the perimeter of the rectangle is 6.89.

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PLUG IN THE VALUES OF THE VARIABLES IN THE RIGHT POSITIONS AND SIMPLIFY.

[tex] \frac{1}{2} (12 - 4) \times \frac{1}{4} \\ = \frac{1}{2} (8) \times \frac{1}{4} \\ = \frac{8}{2} \times \frac{1}{4} \\ = \frac{8}{8} \\ = 1[/tex]

THE ANSWER IS OPTION B.

The linear equation that passes through the points (14, 15) and (20, 24) crosses the y-axis at y = -6.

A general linear equation can be written as:

y = m*x + b

Where m is the slope and b is the y-intercept.

If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope can be written as:

m = (y₂ - y₁)/(x₂ - x₁).

In this case the line passes through (14, 15) and (20, 24) so the slope is:

m = (24 - 15)/(20 - 14) = 9/6 = 3/2

y = (3/2)*x + b

To find the y-intercept we can replace the values of one of the points, like (14, 15)

15 = (3/2)*14 + b

15 = 3*7 + b

15 = 21 + b

15 - 21 = b

-6 = b

The y-intercept is -6.

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Answer:

4th option

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - [tex]\frac{2}{3}[/tex] x + 8 ← is in slope- intercept form

with slope m = - [tex]\frac{2}{3}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{2}{3} }[/tex] = [tex]\frac{3}{2}[/tex] , then

y = [tex]\frac{3}{2}[/tex] x + c ← is the partial equation

to find c substitute (- 6, 2 ) into the partial equation

2 = - 9 + c ⇒ c = 2 + 9 = 11

y = [tex]\frac{3}{2}[/tex] x + 11 ← equation of perpendicular line

Answer:

I miss you

Step-by-step explanation:

The solution of the inequality is b ≥ -17.

Given inequality:-

b + 5 ≥ -12

We have to find the solution of the inequality.

Subtracting 5 from the given inequality, we get

b + 5 - 5 ≥ -12 - 5

b + (5 - 5) ≥ -17

b + 0 ≥ -17

b ≥ -17

Hence, b can be equal to or greater than -17.

Inequality

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.

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The equation of the line in slope-intercept form would be; y = -12x + 18

If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as:

y = MX +c

To find the slope of a line, we the rate at which the value of 'y' is increasing as we increase the value of 'x' by one unit.

We have been given the point (1,6) and (2,-6)

y-y₁ = m(x-x₁)

m = (-6-6)/(2 -1)

m = -12/1

Now substitute;

y-y₁ = m(x-x₁)

y- 6 = -12(x- 1)

y- 6 = -12x + 12

y = -12x + 18

Hence, the equation of the line in slope-intercept form would be; y = -12x + 18

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Jane decides to randomly interview 10 freshmen from each of the dorms, these people are her Sample.

What is Sample?

Sampling is the process of choosing a portion of a statistical population to estimate attributes of the entire population in statistics, quality control, and survey methods. Statisticians try to get samples that are typical of the population under consideration.

A little sample or amount of someone or something that is inspected, analyzed, or otherwise investigated to learn more about the rest.

Given: Jane wants to know what percentage of freshmen at her college purchase clothing with college logos. She decides to randomly interview 10 freshmen from each of the dorms.

Therefore, by the above information, these people are her Sample.

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Surface area of a rectangular prism formula

where w is width, l is length, and h is height.

Substituting with w = 4 ft, l = 6 ft, and h = 10 ft, we get: