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4 years ago

1. Find the equation of a line that passes through the point (4,1) and is perpendicular to the

Mathematics

1 answer:

slava [35]4 years ago

7 0

Answer:

x - 4y = 0 . . . in standard form

y = (1/4)x . . . in slope-intercept form

Step-by-step explanation:

The slope of the given line is ...

m = (y2 -y1)/(x2 -x1) = (9 -(-7))/(-1 -3) = 16/-4 = -4

The slope of the perpendicular line is the negative reciprocal of this:

desired slope = -1/m = -1/-4 = 1/4

This can be used in the point-slope form of the equation of a line:

y -h = m(x -k) . . . . . line with slope m through point (h, k)

Your perpendicular line has a slope of 1/4 and goes through point (4, 1), so its equation can be written as ...

y -1 = (1/4)(x -4)

y = (1/4)x -1 +1

y = (1/4)x

In standard form, this is ...

4y = x

x -4y = 0

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Last year, an orange tree produced 36 oranges. This year, it produced fewer than 10. What are the possible values for how many f

weeeeeb [17]

Answer:

d : [ 0 , 26 ]

Step-by-step explanation:

Given:-

- The oranges produced last year, x = 36

- The oranges produced this year, y < 10

Find:-

What are the possible values for how many fewer oranges were produced from the tree this year

Solution:-

- The possible values for how many fewer oranges were produced this year relative to last can be determined by solving an inequality that signifies a difference (d) between last year and this year production as follows:

d = x - y

d = 36 - (<10)

- To remove the inequality from Right hand side we we can shift it to left hand side by inverting the inequality sig, since last production is exactly known we have:

d≥36 - 10

d≥ 26

- So the number of oranges produced are at least 26 less than last year and lower bound would be if there is no orange produced this year. Hence, the range is:

d : [ 0 , 26 ]

4 0

3 years ago

Which expression is equivalent to 12(2+3x−6) ?

matrenka [14]

Simplify: 12(2 + 3x - 6)
= (12)(2 + 3x + - 6) = (12)(2) + (12)(3x) + (12)( - 6)
= 24 + 36x - 72
Answer = 36x - 48

2: Factor:

36x - 48
= 12(3x -4)

Answer
= 12(3x -4)

3: <span>12(2+3x−6)

= 12(3x + 2 - 6)

= 12(3x - 4)

Your Answer would be (A).

3x - 4</span>

7 0

3 years ago

Read 2 more answers

What is 82.5 as a fraction in simplest form

tangare [24]

85.5 as a fraction is 85 2/10 which is simplified to 85 1/5

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3 years ago

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Examine the expanded form. y ∙ y ∙ y ∙ y ∙ y ∙ y ∙ y ∙ y ∙ y ∙ y Which represents the expanded form in exponential form? 10y 10y

Drupady [299]

Answer:

$y^{10}$

Step-by-step explanation:

When you do that operation, the <em>y</em>'s become an exponential.

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3 years ago

A system of inequalities is shown.

Doss [256]

The system of inequalities which is represented in the graph shown (see attachment) is:

y ≥ x² -2x -3
y ≤ x +3

<h3>What is an inequality?</h3>

An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following:

Less than (<).

Greater than (>).

Less than or equal to (≤).

Greater than or equal to (≥).

<h3>What is a graph?</h3>

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

By critically observing the graph which models the system of inequalities shown, we can infer and logically deduce the following points:

Both boundary lines on the cartesian coordinate are solid. Thus, the inequalities will both have the "equal to" sign.

The shading occurred above the quadratic boundary line. Thus, the inequalities below the linear boundary line is given by y ≥ x² + and y ≤ x +

In conclusion, we can infer and logically deduce that the system of inequalities which is represented in the graph shown (see attachment) is:

y ≥ x² -2x -3
y ≤ x +3

Read more on graphs here: brainly.com/question/25875680

#SPJ1

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2 years ago