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Non-vertical parallel lines have equal slopes, while slopes of non-vertical, non-horizontal perpendicular lines are negative reciprocals of each other. Vertical lines are defined as having an infinite slope, thus they must be non-vertical to consider their slopes.

When considering the slopes of lines on a graph with perpendicular axes, like the x-axis and the y-axis, we can draw several conclusions about parallel and perpendicular lines. If two non-vertical lines are parallel, their slopes are equal, because the tilt of the lines with respect to the horizontal axis is the same. For example, if we have two equations of lines in the form y = mx + b, where m represents the slope and b represents the y-intercept, parallel lines would have the same value of m.

If two lines are perpendicular and neither line is parallel to an axis, then their slopes are negative reciprocals of one another. This holds true because the product of the slopes of two perpendicular lines is -1. For example, if the slope of one line is a, the slope of the line perpendicular to it will be -1/a.

It is necessary for the lines to be non-vertical because a vertical line does not have a well-defined slope; its slope is considered infinite. Therefore, the definition of perpendicular lines in terms of slope only applies to non-vertical lines.

Answer:

22 + 5 ÷ 9 = 3

Proof:

27/9

= 3

the number is 22

Answer:

y = -(1/2)x + 2

Step-by-step explanation:

2y = -x + 4

y = (-x + 4)/2

y = -(1/2)x + 2

Answer:

314 mile²

Step-by-step explanation:

area = πr² = 3.14 x 10² = 314 mile²

Answer:

320

Step-by-step explanation:

j u s t a g u e s s b u t i t h i n k i t s r i g h t

To find the area percentage increase when the area of a parallelogram increased from 40 to 128 square centimeters, calculate the percentage change as 220%.

The area percentage increase can be calculated as follows:

A function from x to y represents a situation where each x value is linked to a unique y value. This can be represented in a mapping diagram, such as with the points (1,5), (2,10), (3,7), and (4,14). Such a diagram showcases the fact that different x values trigger different y values, demonstrating the dependence of y on x.

A function from x to y implies that when the value of x changes, it directly influences the value of y. One way to represent this is through a mapping diagram.

A mapping diagram that represents a function can be visualised as each value of x corresponding to a unique value of y. For example, refer to the following points: (1,5), (2,10), (3,7), and (4,14). Here, every x value is paired with a unique y value. When these points are plotted, there's no x value that corresponds to more than one y value, demonstrating the dependence of y on x.

Therefore, a function from x to y is represented by a mapping diagram where different x values are linked to unique y values, showing the dependency of y values on the x values.

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Answer:

x = -2

Step-by-step explanation:

Answer:

33/4

Step-by-step explanation:

8x4 +1 = 33

Answer:

33/4

Step-by-step explanation:

Answer:

Step-by-step explanation:

7/12 is greater than 1/3 because it has a greater numerator and denominator it is less than 2/3 because the numerator is smaller

Multiply the weight by the amount they took out:

4 2/5 x 5/8

Rewrite as 22/5 x 5/8

(22 x 5) / (5 x 8)

Simplify:

110/40

Rewrite as a proper fraction:

2 3/4 ounces.

Answer:

42

Step-by-step explanation:

120*35=4200

4200/100=42

9y - 4 - 11y + 7

Terms: 9y, -4, -11y, 7

Like terms: 9y and -11y

Coefficient : 9, -11

Constants: 7, -4

Solution:

Given expression is:

9y - 4 - 11y + 7

We have to find the terms, like terms, coefficient and constants

Each term in the expression is called terms

It includes, numbers, variables also

Terms : 9y and -4 and -11y and 7

A coefficient is a number used to multiply a variable

Here the terms with variables are 9y and -11y

Coefficient : 9, -11

"Like terms" are terms whose variables are the same and thier powers is also same

Like terms : 9y and -11y

The constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number

Constants: 7 and -4

Answer:

vertex (-3 , 7)

Step-by-step explanation:

vertex (h, k)     f(x) = a | x - h | + k

f(x) = |x + 3|+ 7 ,    h = - 3 and k = 7

vertex (-3 , 7)

The value of vertex of the graph would be,

⇒ (-3 , 7)

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

We know that;

Standard form of equation is,

⇒  f(x) = a | x - h | + k

Where, vertex = (h, k)  

Here, The equation of graph is,

f(x) = |x + 3|+ 7 ,    

And, h = - 3 and k = 7

Thus, The value of vertex of the graph would be,

⇒ (-3 , 7)

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Answer:

Step-by-step explanation:

When learning about commutative and associative properties, we learn that ...

  a + b = b + a . . . . . addition is commutative

  ab = ba . . . . . . . . . multiplication is commutative

But we also know that ...

  a - b ≠ b - a . . . . . . subtraction is not commutative

  a/b  ≠ b/a . . . . . . . . division is not commutative

__

We also learn that ...

  a + (b+c) = (a+b) +c . . . . addition is associative

  a(bc) = (ab)c . . . . . multiplication is associative

And of course, ...

  a - (b -c) ≠ (a -b) -c . . . . subtraction is not associative

  a/(b/c) ≠ (a/b)/c . . . . . . . division is not associative

_____

However, you can use associative and commutative properties in problems involving subtraction and division if you write the expression properly:

  a - (b - c) = a +(-(b -c)) = a +((-b) +c) = (a +(-b)) +c . . . . keeping the sign with the value makes it an addition problem, so the associative property can apply

  (a/b)/c = (a(1/b))(1/c) = a(1/b·1/c) = writing the division as multiplication by a reciprocal makes it so the associative property can apply

Answer:

addition

multiplication

Answer:

200- software (x)          225- video game (y)    = 425 items

Step-by-step explanation:

software- 200 = $10,000      video-225 = $7,875

                              total= $17,875

200x + 225y = $17,875

Answer: She earns 482.50

Step-by-step explanation:

Answer:

the answer to the inequality is x>-6

Step-by-step explanation:

x+8>2

x>2-8

x>-6

Answer:1

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

360 is a full turn so, 360 divided by 60 is 6

Answer:

x = 7.002 or 7

Step-by-step explanation:

5x/3 + 1/3 = 12

        - 1/3  - 1/3

5x/3 = 11 2/3

3(5x/3) = 3(11 2/3)

5x = 35.01

x = 7.002 or 7

The tip i will leave is of 6 dollars.

Percentage is the value per hundredth. Suppose we have 500 dollars and we need find 50% of it.We know 50% of 500 dollars is half of it which is 250 dollars.

To find 50% of 500 dollars we put the the given percentage on numerator and divide by hundred and multiply it by the given amount.

∴ (50/100)×500

= 250 dollars.

According to the given question

You go out to dinner and the bill is $40 and you want to leave the server a 15% tip.

We have to find what is 15% of 40 dollars which is

= (15/100)×40 dollars.

= 6 dollars.

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Answer:

when you have two fractions that equal each other you want to solve by using cross multiply

What cross multiply is, is when you multiply diagonally so:

8/x=14/7

you would take 14*x and 8*7

14x=56 (you would then divide each side by 14)

x=4 (14/14=1, 56/14=4)

8/4=14/7

To check your work you could simplify

8/4=2

14/7=2

2=2, which is true

x=4

Hope this helps ;)

Answer:

6

Step-by-step explanation:

The function that represents the interest on this loan after years is Interest = Principal × Rate × Time.

The function that represents the interest on this loan after years can be calculated using the formula for simple interest:

Interest = Principal × Rate × Time

In this case, the principal is $8,000, the rate is unknown, and the time is 2 years. The interest paid back is $8,160, so we can rewrite the formula as:

$8,160 = $8,000 × Rate × 2

Dividing both sides of the equation by $8,000 × 2 gives:

Rate = $8,160 / ($8,000 × 2)

Solving this equation gives a rate of 0.51, or 51%.

Answer:

B, hope this helps you!

The general strategy for solving an equation of the form x/a = b is to multiply both sides by a.

A mathematical statement that two expressions are equal: it is either an identity in which the variables can assume any value, or a conditional equation in which the variables have only certain values (roots) the act of regarding as equal .

Solving equations is computing the value of the unknown variable still balancing the equation on both sides.

The general strategy for solving an equation of the form x/a = b

To solve this equation we will multiply both sides by a

On multiplying

x = ab

Therefore Option B. multiply both sides by a is the correct answer.

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Answer:

Plumber A has greater initial fee

Step-by-step explanation:

Plumber B:

Hourly charge = 160 - 105 = $55

Initial charge = 105 - 55 = $50

Equation: y = 50 + 55x

Answer:

C

Step-by-step explanation:

For plumber A : y = 100 + 30x

For plumber B :

Let the total charge be y

Initial charge be x

Hourly rate be za

For total price = 105 in 1hr

105 = x + a ........(1)

For 160 total charge in 2hrs

160 = x + 2a .........(2)

Substracting (1) from (2)

160 - 105 = 2a - a

55 = a

Substituting a = 55 in (1)

105 = x + a

105 = x + 55

x = 105 - 55

x = 50

:- equation for total charge is

y = 50 + 55a

Answer:

1370.75

Step-by-step explanation:

Final answer:

The expression (889 x 27) + 50 is greater than 889 x 27, because adding 50 to any product will always result in a larger number.

Explanation:

The student's question is asking to compare the result of the expression (889 x 27) + 50 with 889 x 27, without actually calculating the precise values.

First, let's evaluate the structure of the expressions. When we have an expression of the form (a x b) + c, adding any number c to the original product of a and b will always result in a value greater than the original product. This is a basic property of arithmetic progression.

Based on this property, we know that (889 x 27) + 50 is definitely greater than 889 x 27 because we are adding a positive number (50) to the original product, hence the sum must be larger.

Answer:

y = x - 4

Step-by-step explanation:

equation of a line can be expressed as

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

(x - 5)/(10 - 5) = (y - 2)/(-3 - 2)

cross multiplying,

-5(x - 5) = 5(y - 2)

clearing the parentheses

-5x + 10 = 5y - 10

hence,

5y = 5x - 20

y = x - 4

Answer:

81

Step-by-step explanation:

To find the 21 st term substitute n = 21 into the formula

[tex]x_{21}[/tex] = 4(21) - 3 = 84 - 3 = 81