What is the bare minimum needed to write the equation of a line?

The solution to the compound inequality is x > -3. The correct option is the third option x > -3

From the question, we are to solve the given compound inequality

2x - 2 > -8 or -4x ≤ -36

Solving the first inequality

2x - 2 > -8

Add 2 to both sides of the inequality

2x -2 + 2 > -8 + 2

2x > -6

Divide both sides by 2

2x/2 > -6/2

x > -3

Solving the second inequality

-4x ≤ -36

Divide both sides of the inequality

-4x/-4 ≤ -36/-4

x ≥ 9

From the two solutions, we can conclude that x > -3

Hence, the solution is x > -3

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The property used in expression 3 x 5 = 5 x 3 will be ''Commutative property''.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 3 x 5 = 5 x 3

Now,

We know that;

The commutative property is defined as;

⇒ a x b = b x a

Hence, In the expression,

⇒ 3 x 5 = 5 x 3

The commutative property is used.

Thus, The property used in expression 3 x 5 = 5 x 3 will be ''Commutative property''.

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The crew will take 6 hours to mulch 12 flower gardens.

Given, that

A landscaping crew can mulch 3 flower gardens in 1(1/2) hours i.e. 3/2 hours.

so, 3 flower gardens mulch = 3/2 hours

Now, we are asked that how long will it take the crew to mulch 12 flower gardens.

As, 3 flower gardens mulch = 3/2 hours

1 flower garden mulch = (3/2)×(1/3) hours

1 flower garden mulch = 1/2 hour

12 flower gardens mulch = (1/2)×12 hours

12 flower gardens mulch = 6 hours

So, it will take 6 hours by the crew to mulch 12 flower gardens.

Hence, the crew will take 6 hours to mulch 12 flower gardens.

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If the mill starts out with 490 tons of grain , then the amount of grain that remains to be sold after milling is 450.8 ton.

In the question ,

it is given that ,

the percent of grain that is lost due to spillage = 3%

the percent of grain that is lost due to mildew = 5%

the total percent of grain lost = grain lost due to spillage + grain lost due to mildew

= 3% + 5%

= 8% of total grain  

given that amount of grain =  490 tons .

amount of grain lost = 8% of 490

= 0.08 * 490

= 39.2 ton ,

So , 39.2 ton of grains is lost .

the amount of grain remain to be sold = 490 - 39.2 = 450.8 ton

Therefore , If the mill starts out with 490 tons of grain , then the amount of grain that remains to be sold after milling is 450.8 ton   .

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The slopes of both lines that passes through the given points are different, therefore: d. No, they are not perpendicular because their slopes are not reciprocals.

For any two lines that passes through two set of points to be perpendicular to each other, their slopes must have a product that is equal to -1, or be negative reciprocals.

Find the slope of the line that passes through P(0, –9) and Q(2, –8):

Slope of PQ (m) = (-8 -(-9)) / (2 - 0)

m = 1/2

Find the slope of the line that passes through R(1, 4) and S(3, 3):

Slope of RS (m) = (3 - 4) / (3 - 1)

m = -1/2

The slope of both lines are not equal neither are they negative reciprocals of each other. Therefore: d. No, their slopes are not reciprocals.

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The measure of angle B is 40 degrees.

In this question, we have been given angle A and angle B are supplementary angles.

m∠A=(4x−16)°

and m∠B=(x+1)°

since angle A and angle B are supplementary angles,

angle A + angle B = 180°

So we get an equation,

(4x − 16)° + (x + 1)° = 180°

5x - 16 + 1 = 180

5x = 180 + 15

5x = 195

x = 39

So, x + 1 = 39 + 1

              = 40°

Therefore, the measure of angle B is 40 degrees.

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Answer: 8%

Step-by-step explanation: Rate = Interest 484 ÷ Principle (550) x Time (11), with this formula the answer is 8%.

Answer:

  450

Step-by-step explanation:

You want the value of (5 × 10⁰) × (9 × 10¹).

  (5 × 10⁰) × (9 × 10¹) = (5) × (9×10) = 450

__

Additional comment

Any number to the 0 power is 1. Any number to the power of 1 is that number.

Your calculator can help you evaluate numerical expressions.

According to question, project managers can assess the outcomes to identify any hazards the project might encounter after it is completely executed.

These risks are frequently examined by project managers and stakeholders to decide whether they are controllable and whether it is worthwhile to move on with the entire project. An organization can control the risk of a novel concept and spot any flaws through a pilot project before significant resources are spent.

On the other hand, a trial is a limited implementation before you launch the pilot project broadly. All the advantages of a pilot project are present, but they are more thorough, and the team is frequently able to test out more features and observe the results on a wider scale.

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Answer:

The answer is the screenshot shown.

Step-by-step explanation:

How to graph it in that is to check the given first.

y= -5x

x = 0

y = -5

-

So you will have to plot the line at 0 for x and for y, you should put it at -5

James has $37.67 now after all his expenses

James had $x, his brother had $y, and his sister had $z when the morning began.

By using algebra,

James's sibling had twice as much money as James.

Now, x =y/2..... (i)

James had $27 fewer dollars than his sister did.

So, x = z - 27 ........ (ii)

⇒  {From equation (1)}

⇒ y/2 = z -27

⇒ y = 2z - 54

⇒ 2z - y =54 ..........(3)

Now, James and his sister each received $12 from his brother.

James now has $(x + 12), his brother now has $(y -24), and his sister now has $(z + 12).

Given that James' sister has twice as much money as James' brother after payoff,

So, z+12/2 = y-24

⇒ z + 12 = 2y - 48

⇒ 2y - z = 50 ......... (4)

The result of resolving equations (3) and (4) is

3y = 54 + 100 = 154

⇒ y =  51.33.

The result of equation (3) is now z = 52.67.

And from equation (1), x = 51.3/2= 25.67

So, now, James has (25.67 + 12) = $37.67

Hence, James has $37.67 now after all his expenses

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The equation to represent the area of the desk is A=3.5 x 12.  The length of the large office desk is 12.

The area a rectangle occupies on a two-dimensional plane is known as the area of the rectangle. A quadrilateral, a type of two-dimensional shape with four sides and four vertices, is what a rectangle is.

A large office desk is given, with area 42 ft^2. The shape of the desk is rectangle. The area of the rectangle is given by A=l*w.

Given, the area is 42 ft^2.

w=3.5 feet.

A= 42

42=3.5*l

l=42/3.5

l=12 feet.

The length of the rectangular desk is 12 feet. The equation to represent the area of the large office desk is A=12*3.5.

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The exact value of the trigonometric equation cos 0.5θ is equal to 2 / 3.

In this problem we have the exact value of a trigonometric function, from which we must determine the exact value of the half angle by means of the following equation:

cos 0.5θ = √[(1 - cos θ) / 2]

If we know that cos θ = 0.8 and cos 0.5θ > 0, then the exact value of the cosine of the half angle is:

cos 0.5θ = √[[1 - (1 / 9)] / 2]

cos 0.5θ = √[(8 / 9) / 2]

cos 0.5θ = √(8 / 18)

cos 0.5θ = √(4 / 9)

cos 0.5θ = 2 / 3

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If y is exactly proportional to x, then the value of y at x=16 is 40 if y=5 when x=2.

[tex]&y \propto x \\[/tex]

[tex]&y=k x[/tex]

When x = 2, y = 5

[tex]&5=k(2) \\[/tex]

therefore

[tex]k=\frac{5}{2}[/tex]

When x = 16,

[tex]&y=\left(\frac{5}{2}\right) \\[/tex]

y = 40

Hence, If y is exactly proportional to x, then the value of y at x=16 is 40 if y=5 when x=2.

The complete question is:

If y is directly proportional to x and y=5 when x=2, what is the value of y when x=16?

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Answer:

-1

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

1 foot = 12 inches

Jana can jump 36 inches!

Divide this by 12 to get the feet:

36 / 12 = 3

Check: 12 + 12 = 24 + 12 = 36

so, Jana can jump 3 feet above the ground

Multiplying vector v we get 2.5v =  (-10, 10).

What is the vector?

A vector is a quantity or phenomenon with two distinct properties: magnitude and direction. The term can also refer to a quantity's mathematical or geometrical representation. In nature, vectors include velocity, momentum, force, electromagnetic fields, and weight.

The magnitude of a vector indicates the vector's length. It is typically represented by an arrow pointing in the vector's direction. A vector a is defined as a1 ^ii^ + b1 ^jj^ + c1 ^kk^, where a1, b1, and c1 are its constituents.

We have,

v = (-4,4)

2.5v = ?

Multiplying vector v by 2.5 we get,

2.5v =  (-10, 10)

Hence, by Multiplying vector v we get 2.5v =  (-10, 10).

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Using the standard form of the equation of line, the slope of the line represented by the equation 3x-4y=7 is 3/4.

In the given question,

We have to find the slope of the line represented by the equation 3x-4y=7.

The given equation is 3x-4y=7.

To find the slope we first express the given equation in the form of standard equation of line.

The standard form of equation is y=mx+c where m is slope of the equation.

Now expressing the equation in standard form.

3x-4y=7

Subtract 3x on both side

3x-4y-3x=7-3x

-4y=7-3x

Divide by -4 on both side

-4/-4 y=7/-4 - (-3)/(-4) x

Simplifying

y=3/4x-7/4

Now comparing from the standard equation to find the slope(m).

m = 3/4

Hence, the slope of the line represented by the equation 3x-4y=7 is 3/4.

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8,16,24

Given:

the relation between number of sandwiches and time is :

y = 8x

where, y is number of sandwiches

x is time

For 1 hour,

y = 8*1

y = 8.

For 2 hour,

y = 8*2

y = 16.

For 3 hour,

y = 8*3

y = 24.

#123

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sandwiches eaten by Jimmy in consecutive hours are 8, 16, and 24.

Given info;

Jimmy consistently consumes sandwiches. The linear equation y = 8x represents the number of sandwiches(y) that he can consume in an hour(x).

To know how many sandwiches he ate in consecutive hours;

Case(1):

y = 8x

x = 1 hour

y = 8*1

  = 8

Case(2):

y = 8x

x = 2 hours

y = 8*2

  = 16

Case(3):

y = 8x

x = 3 hours

y = 8*3

  = 24

Therefore, sandwiches eaten by Jimmy in consecutive hours are 8, 16, and 24.

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By using the formula for area of triangle using coordinates, the following results are obtained

13) Area of triangle = [tex]\frac{15}{2} \ sq. units[/tex]

14) Area of triangle = [tex]\frac{49}{2} \ sq. units[/tex]

What is area of triangle?

Area of a triangle is the total space taken by the triangle. If the coordinates of triangle are [tex](x_1, y_1), (x_2, _2) \ and \ (x_3, y_3)[/tex], then area of triangle is calculated by the formula

Area of triangle = [tex]\frac{1}{2}|x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|[/tex]

13) The given coordinates are E (3, 1), F(3, -2) and G(-2, 2)

Area of triangle =

[tex]\frac{1}{2}|3(-2-2) + 3(2-1) + (-2)(1 -(-2))|\\\\\frac{1}{2}|3(-4) + 3(1) -2(3)|\\\\\frac{1}{2}|-12 + 3 - 6|\\\\\frac{1}{2}|-15|\\\\\frac{15}{2} \ sq. units[/tex]

14) The given coordinates are E (-3, 4), F(4, 4) and G(3, -3)

Area of triangle =

[tex]\frac{1}{2}|(-3)(4-(-3)) + 4(-3-4) + 3(4-4)|\\\\\frac{1}{2}|(-3)(7)+4(-7)+3(0)]\\\\\frac{1}{2}|-21-28+0|\\\\\frac{1}{2}|-49|\\\\\frac{49}{2} \ sq. units[/tex]

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The domain of the function in the graph is {yl1≤y≤9}.  Option b is the correct answer.

Graph:

The domain of a function is the collection of all conceivable values that can be used as inputs, or alternatively, it is the full range of potential values for independent variables.

A graph is an organized visual representation of any data in mathematics. The relationship between the variable quantities is depicted on the graph. In a graph theory, the set of items that are somehow connected to one another is represented by a graph. The vertices or nodes of the objects are essentially mathematical notions, and the edges between the nodes represent the relationships between the nodes. In mathematics and statistics, there are various types of graphs that are used to visually display data. The study of points and lines is known as graph theory. It is a branch of mathematics that focuses on the investigation of graphs. The mathematical truth is shown visually in this picture. Relationships are studied using graph theory.

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Thus, Bao age is 27.

acc to our question-

hence,Thus, Bao age is 27.

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Hence the complete table is ,

=>  laps        Miles

       3             3.75

       7              8.75

       8              10

      13              16.25

What is miles ?

   A mile is a unit of length that is exactly equal to 5280 feet, or 1760 yards, and was standardised as exactly 1609.344 metres by an International agreement in 1959. It is the largest unit commonly used to measure the distance between distant locations.

Here the distance 2 laps = 2.5 miles. Then ,

=> 1 laps = 2.5/2 = 1.25 miles.

Now 3 laps = 3*1.25 = 3.75 miles

Here n laps = 8.75 miles .

=> n* 1.25 = 8.75

=> n = 7 laps .

Now 8 laps = 8*1.25 = 10 miles.

And n laps = 16.25

=> n = 16.25/1.25 = 13 laps. miles

Hence the complete table is ,

=>   laps        Miles

       3             3.75

       7              8.75

       8              10

      13              16.25

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Answer: Mean :286.6 Median:294 Mode:169, 294, 188, 295, 487

Answer: 1.467

Step-by-step explanation: All you had to do was divide 22 by 15.

Answer:

-7x>=22-1

-7x>=21

x>=21/-7

x>=-3

The GCF of the questions are as follows:

1. 2

2. 12

3. 2

4. 3y

5. 4

6. 2x

7. 1

8. 4ab

9. 7c

10. 1

11. (x+9)(x-9)

12. (x+2)(x-2)

13. (x+12)(x-12)

14. (1+7x)(1-7x)

15. (4x+5)(4x-5)

16. (3x+10)(3x-10)

17. (6x+7)(6x-7)

18. 2(x+5)(x-5)

19. (2x+10)(2x-10)

20. (4x+10)(4x-10)

Define GCF.

The term "greatest common factor" is abbreviated as "GCF." As the greatest number that is a factor of two or more other numbers, the GCF is thus named. The greatest factor that 24 and 36 share, for instance, is 12, hence the GCF of 24 and 36 is 12. 12 is the highest common factor between 24 and 36, while there are others. Since we frequently utilize fractions in our daily lives and hence frequently employ the greatest common factors (GCF), this makes GCF incredibly handy.

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Charlie needs to sell 1000 packages per month in order to pay himself a monthly salary of $5000. By using the Equation concept we solved this problem.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

Let the number of packages that Charlie needs to sell is ‘x’

So, According to the question , the below equation has been formed,

10x – (1500 + 3.50x) = 5000

10x – 1500 – 3.50x = 5000

6.50x = 5000+1500

6.50x = 6500

x = 6500/6.50

x = 1000 packages.

So that is how we calculated the number of packages that Charlie needs to sell per month.

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Answer:75 ft

Step-by-step explanation:sea level is represented as 0. going from 0 to -75 is 75 ft