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2 years ago

Line r passes through points (8,10) and (2,3). Line s is perpendicular to r. What is the slope of line S?

Mathematics

1 answer:

Zepler [3.9K]2 years ago

5 0

Answer:

$-\dfrac67$

Step-by-step explanation:

slope of r:

$a_r=\dfrac{10-3}{8-2}=\dfrac76$

s is perpendicular to r:

$s\perp r\ \ \implies\ \ a_s\cdot a_r=-1\\\\a_s\cdot\dfrac76=-1\\\\a_s=-\dfrac67$

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Which of the expressions below can be factored using the difference of squares method?

Dmitry [639]

Answer: A. $9x^2 - 16y^2$ .

Step-by-step explanation:

A difference of squares problem is factored as : $a^2 - b^2 = (a + b)(a - b)$
For this both terms in the form of squares and a minus sign between them.

From all the options only option A has both terms square and they minus sign between them.

Also, $9x^2 - 16y^2= (3x)^2-(4y)^2=(3x+4y)(3x-4y)$

Here a= 3x and b= 4

Hence, the correct answer is A. $9x^2 - 16y^2$ .

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3 years ago

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Bess [88]

4+4+1 is the answer

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2 years ago

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A cable car begins its trip by moving up a hill. As it moves up, it gains elevation at a constant rate of 50 feet/minute until i

asambeis [7]

Answer:

he cable car's elevation will be 750 feet after 15 minutes

Step-by-step explanation:

Given:

elevation, e =2,000 feet

rate, I = 50 feet/minute

The equation that models the car's elevation, e, after t minutes is e = |t

The cable car's elevation will be 750 feet after how many minutes?

since, e = It

for 2,000 feet = 50 feet/minute * t

t = 2000/50 =40minutes

using the same constant rate, I for 750ft, T =

since, e = It

for 750 feet = 50 feet/minute * t

t = 750/50 =15minutes

3 0

3 years ago

Find the line y=a+bx which best approximates the data points

Vika [28.1K]

Answer:

y = 11.84x - 32.71

Step-by-step explanation:

Here, the given data points,

(−3,−70),(−1,−42),(1,−21),(2,−9),(4,14),

Let x represents the input value and y represents the output value,

So, the table that represents the given situation is,

x -3 -1 1 2 4

y -70 -42 -21 -9 14

By the above table,

$\sum x=3$

$\sum y=-128$

$\sum xy = 269$

$\sum x^2=31$

$\sum y^2 = 7382$

Let the equation of the line is,

y = bx + a

Where,

$a=\frac{\sum y \sum x^2 - \sum x\sum xy}{n(\sum x^2)-(sum x)^2}$

$b=\frac{n\sum xy - \sum x \sumy}{n(\sum x^2)-(\sum x)^2}$

n = number of data points = 5,

By substituting the values we get,

a = - 32.70547945 ≈ - 32.71,

b = 11.84246575 ≈ 11.84,

Hence, the equation of line would be,

y = 11.84x - 32.71

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2 years ago

Consider the function represented by the equation y-6x-9=0. Which answer shows the equation written in function notation with x

Marta_Voda [28]

Answer:

A. f(x) = 6x + 9

Step-by-step explanation:

The given equation is:

y - 6x - 9 = 0

We have to write this equation in function notation with x as the independent variable. This means that y will be replaced by f(x) and all other terms will be carried to the other side of the equation to get the desired function notation.

y - 6x - 9 = 0

y = 6x + 9

f(x) = 6x + 9

Therefore, option A gives the correct answer.

5 0

3 years ago

Read 2 more answers