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Sedaia [141]
2 years ago
13

If the slope of a line is -1 and two points on the line are (-9, 3) and (-10, r), what is the value of r?

Mathematics
1 answer:
ANEK [815]2 years ago
6 0

Answer:

r=4

Step-by-step explanation:

We know that the slope of the line is -1.

We also know that the line passes through (-9, 3) and (-10, r).

We want to find the value of r.

First, let's figure out the equation of our line. We can use the point-slope form:

y-y_1=m(x-x_1)

Where m is the slope and (x₁, y₁) is a point.

So, let's substitute -1 for m. Since we know the point (-9, 3), let's use this for (x₁, y₁).

Substitute:

y-(3)=-1(x-(-9))

Simplify:

y-3=-(x+9)

Distribute:

y-3=-x-9

Add 3 to both sides. So, our equation is:

y=-x-6

It passes through (-10, r) and we want to find the value of r. So, let's substitute -10 for x and r for y, since -10 is our x and r is our y. So:

r=-(-10)-6

Evaluate for r. Distribute:

r=10-6

Subtract:

r=4

So, the value of r is 4.

And we're done!

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Point D(-3.5) is a vertex of triangle DEF.After a rotation of the triangle about the origin, D' is located at (3,-5).Which of th
Nimfa-mama [501]
<h3>Answer: 180 degrees</h3>

note: it doesn't matter if its clockwise or counterclockwise when it comes to 180 degree rotations.

========================================

Explanation:

The rule for 180 degree rotations is

(x,y) ---> (-x, -y)

So the x and y coordinates flip in sign from positive to negative, or vice versa.

Point D ' (-3, 5) rotates to D ' (3, -5) following this rule

-----------------

A further detailed break down might look like this

x = -3 becomes -x = -(-3) = 3

y = 5 becomes -y = -5

(-3, 5) ----> (3, -5)

6 0
3 years ago
The length of a rectangle is 6 yards longer than its width. If the perimeter of the rectangle is 32 yd, find its area in square
ddd [48]
Let, width = x
Length = x + 6

Now, perimeter, 2(l+b) = 2(x+6+x)
2(2x+6) = 32
4x + 12 = 32
4x = 20
x = 5 &
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As rectangle's dimensions are 11*5, it's area would be: 11 * 5 = 55 yards²

So, your final answer is 55 Yd²

Hope this helps!
8 0
3 years ago
Find the center and radius of the circle represented by the equation below.
valina [46]

Answer:

radius 4

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Step-by-step explanation:

(x - h)^2 + (y - k)^2 = r^2

coordinates of the center (h, k) and the radius is (r)

x² + y²- 6x - 12y +29=0

x² - 6x + y²- 12y +29=0

(x² - 6x) + (y²- 12y) +29=0

complete the square

(x² - 6x) + 9 + (y²- 12y) +36 +29=  + 9  +36

(x² - 6x + 9) + (y²- 12y + 36) = + 9  +36 -29

(x-3)^2 + (y-6)^2 = 16

(x - h)^2 + (y - k)^2 = r^2

coordinates of the center (h, k) and the radius is (r)

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varsitytutors

3 0
1 year ago
Read 2 more answers
Nathan is 3 years older than Olivia. Determine the equation if n represents the age of Nathan and o represents the age of Olivia
Arte-miy333 [17]

Answer: A, n=o+3

Step-by-step explanation:

Nathan (n) is 3 years older than Olivia (o) so Nathan's age would equal Olivia's age plus 3 years.

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6 0
2 years ago
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Solve the following system: <br> 3x + 2y = 7 <br> -4.5x - 3y = -10.5
valentina_108 [34]

Answer:

<u>infinitely many solutions</u>

Step-by-step explanation:

The system of equations :

  1. 3x + 2y = 7
  2. -4.5x - 3y = -10.5

Multiplying Equation 1 times 3 and Equation 2 times 2 :

  • 9x + 6y = 21
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Putting the equations in standard form after simplifying :

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  2. -6y = 9x - 21 ⇒ <u>y = -1.5x + 3.5</u>

<u />

As both equations are the same, the system will have <u>infinitely many solutions</u>.

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