A line goes through the points (-4,6) and (-2,3). A line perpendicular to
that line is:

Answers

Answer 1

Answer:

The equation of the line perpendicular to the given line that passes through the point (-4, 6) is y = (2/3)x + 26/3.

Here, we have to find a line that is perpendicular to the given line, we need to determine the slope of the given line and then find the negative reciprocal of that slope.

Perpendicular lines have slopes that are negative reciprocals of each other.

Given points: (-4, 6) and (-2, 3)

The slope of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:

$m = (y_2 - y_1) / (x_2 - x_1)$

Let's plug in the values:

$m_1 = (3 - 6) / (-2 - (-4))\nm_1 = (-3) / (2)\nm_1 = -3/2$

The negative reciprocal of a number is the negative value of its reciprocal.

The reciprocal of a number a is 1/a.

So, the negative reciprocal of $m_1$ is:

$m_2 = -1 / m_1\nm_2 = -1 / (-3/2)\nm_2 = -1 * (-2/3)\nm_2 = 2/3$

The perpendicular line has a slope of 2/3.

Now, we have the slope of the line perpendicular to the given line.

To find the equation of this perpendicular line, we also need a point on the line.

We can use one of the given points from the original line.

Let's use the point (-4, 6):

Use the point-slope form of a line to write the equation of the perpendicular line:

$y - y_1 = m_2(x - x_1)$

Substitute the values:

y - 6 = (2/3)(x - (-4))

y - 6 = (2/3)(x + 4)

Now, if we want to put the equation in slope-intercept form (y = mx + b), we can simplify further:

y - 6 = (2/3)x + 8/3

Add 6 to both sides:

y = (2/3)x + 8/3 + 6

y = (2/3)x + 8/3 + 18/3

y = (2/3)x + 26/3

So, the equation of the line perpendicular to the given line that passes through the point (-4, 6) is y = (2/3)x + 26/3.

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Answer 2

Answer:

Answer: A line with a slope of 2

Step-by-step explanation: the slope of the line is -1/2 so the negative reciprcal of the slope is 2 (It would be perpendicular to it)

i used m=y2-y2/x2-x1 to figure ou the slope and -(x/y) as the negative reciprcal for the perpendicular line.

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7. The $5 gift cards are given away first. Inhow many ways can these cards be given to 3
of the 9 volunteers? Is this a combination or a
permutation? Explain.
Answer choices:
a. 84; combination because the order does
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b. 504; combination because the order
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C. 84; permutation because the winners
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d. 504; permutation because the winners
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Answers

Answer:

Step-by-step explanation:

Final answer:

The $5 gift cards can be given to 3 of the 9 volunteers in 84 different ways.

Explanation:

This is a combination problem because the order in which the gift cards are given does not matter.

To find the number of ways the gift cards can be given to 3 of the 9 volunteers, we can use the combination formula:

C(n,r) = n! / (r!(n-r)!)

In this case, n = 9 (the number of volunteers) and r = 3 (the number of gift cards to be given).

Plugging in the values, we get:

C(9,3) = 9! / (3!(9-3)!) = 84

Therefore, there are 84 ways to give the $5 gift cards to 3 of the 9 volunteers.

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Please 20 points I need it fast

Answers

Answer: irrational numbers

Step-by-step explanation:

because i had the same test

Solve the equation x+10=30

Answers

get x alone on one side and solve

x = 30 - 10
x = 20

X+10=30
Subtract 10 from both sides
X+10=30
-10 -10
X=20
Answer:
X=20

Please help me with this

Answers

Seems like I've done a few of these already today.

a[1] = 4, d=6

Formula: a[n] = 4 + 6(n-1)

a[40]=4 + 6(39) = 238

Table: 4 10 16 22 28 34 ... a[40]=238

--------

a[23]=25, d=3

a[n] = a[1] + d(n-1)

25=a[23]=a[1] + 3(22)

a[1] = 25 - 66 = -41

Table: -41 -38 -35 -32 -29 -26

Let's check a[23]= -41 + 3(22)= 25, good

Formula: a[n] = -41 + 3(n-1)

What is the area of this figure.

Answers

Answer: 95cm^2

Step-by-step explanation:

Make smaller shapes then add all the areas up together at the end.

6*4 = 24cm^2

3*2 = 6cm^2

For the base of the triangle:

10+3 = 13cm^2

Area of a triangle = (b*h)/2

(13*10)/2 = 65cm^2

65cm^2 + 13cm^2 + 24cm^2 = 95cm^2

The ratio of girls to boys in one of Mr. Pryslak's grade 9 Mathematics dasses is 4:3. If there are 9boys in the class, how many girls are there?
Help me