Determine whether the ordered pair (1,4)is a solution of the linear inequality y-4x<0.

Answer:

y=3

Step-by-step explanation:

The required line will be y = 3 which is passing through points (6,3) and (-4,3)

The slope of the line is defined as the gradient of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

Assume two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)

To determine the line of passing through points (6,3) and (-4,3)

We have been given two points :(6,3) and (-4,3)

Let the required line will be:

(y - y₁) =  [(y₂ - y₁)/(x₂ -x₁ )](x -x₁  )

Here

x₁ = 6, y₁ = 3

x₂ = -4, y₂ = 3

(y - y₁) =  [(y₂ - y₁)/(x₂ -x₁ )](x -x₁  )

Substitute values in the above formula

(y - 3) =  [(3 - 3)/(-4 -6 )](x -6 )

(y - 3) =  [(0)/(-10 )](x -6 )

(y - 3) = 0

y = 3

Therefore, the required line will be y = 3

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Answer: The answer is biased :)

Final answer:

To write a rational number as a repeating decimal, perform long division. -7/9 as a repeating decimal is -0.7777..., 11/15 is 0.7333..., and 8/3 is 2.6666...

Explanation:

To write a rational number as a repeating decimal, you need to perform a long division. Let's go through each of the given rational numbers:

1. -7/9

When you divide -7 by 9, you get -0.7777… with the 7s repeating. So, -7/9 as a repeating decimal is -0.7777…

2. 11/15

When you divide 11 by 15, you get 0.7333… with the 3s repeating. So, 11/15 as a repeating decimal is 0.7333…

3. 8/3

When you divide 8 by 3, you get 2.6666… with the 6s repeating. So, 8/3 as a repeating decimal is 2.6666…

Final answer:

To find the product of three consecutive nonzero integers, multiply the first number by the next two numbers in the sequence.

Explanation:

If the first integer is n, the next will be n+1 and the next to it will be n+2

The product of three consecutive nonzero integers can be calculated using the formula:

n * (n+1) * (n+2)= n(n^2 + 3n+ 2)=n^3 +3n^2 + 2n

where 'n' represents the first integer. For example, if we take 'n' as 2, the three consecutive nonzero integers would be 2, 3, and 4. So, the product would be 2 * 3 * 4 = 24= (2)^3+  3*(2)^2+ 2*2

The value of x is 15.

For given question,

Two of the angles in a parallelogram measure 5x° and 7x°

The measure of an angle opposite to 5x° is also 5x°

Similarly the measure of an angle opposite to 7x° is also 7x°

So, we have the four angles of parallelogram as 5x°, 7x°, 5x°, 7x°

We know, the sum of all angles of quadrilateral is 360°

⇒ 5x° + 7x° + 5x° + 7x° = 360°

⇒ (5 + 7 + 5 + 7) x = 360

⇒ 24x = 360

⇒ x = 15

Therefore, the value of x is 15.

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Answer:

Atleast 53

Step-by-step explanation:

We are given that your basketball team has a goal  to collect atleast 160 blanket for a shelter.

Team member bought blankets on Monday =42

Team member bought blankets on Wednesday=65

We have to write an inequality and find the number of blankets  has to collect on Friday.

Let x be the number of blankets  bought by team members on Friday

According to question

[tex]42+65+x \geq 160[/tex]

[tex]107+x \geq 160[/tex]

Subtract 107 on both sides

[tex]107-107+x\geq 160-107[/tex]

[tex]x\geq 53[/tex]

Hence, team members bought atleast 53 blankets on Friday .

The number of hours will they be 280 miles apart will be 2 hours.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

Two vehicles leave new york simultaneously going in inverse headings. one goes at a typical speed of 77 mph and the other at 63 mph.

The relative speed is given as,

S = 77 + 63

S = 140 miles per hour

The number of hours will they be 280 miles apart will be calculated as,

Time = 280 / 140

Time = 2 hours

The number of hours will they be 280 miles apart will be 2 hours.

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The solution for given equation 17=-13-8x is x = -15/4.

In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .

The given equation is,

17 = -13 - 8x

Now to solve the equation following steps are followed :

adding 13 both the sides of the equation,

17 + 13 = -13 - 8x + 13

or, 17 + 13 = -13  + 13 - 8x

Solving them we get,

30 = - 8x

or, - 8x = 30

multiplying -1 both side

- 8x*(-1) = 30*(-1)

Solving them we get,

8x = -30

dividing both side by 2

8x/2 = -30/2

Solving them we get,

4x = -15

dividing both side by 4

4x/4 = -15/4

Solving them we get

x = -15/4

Hence,the solution for given equation 17=-13-8x is x = -15/4.

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Answer: supplementary, complementary, neither.

Step-by-step explanation:

Answer:

Given inequality,

[tex]x+y<1[/tex]

For graphing the inequality :

The related equation of the given inequality,

x + y = 1

Having the x-intercept = (1,0),

y-intercept = (0,1),

Also, at (0,0),

0 + 0 < 1 ( True )

⇒ The area of the given inequality x + y < 1 must contain the origin.

Now, '<' show the dotted line.

Thus, by the above explanation we can plot the graph of the given inequality.