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lys-0071 [83]
3 years ago
14

Triangle ABC has vertices A(-2, 3), B(0, 3), and C(-1,-1). Find the coordinates of the image after a reflection over the

Mathematics
1 answer:
motikmotik3 years ago
8 0

<u>Given</u>:

Given that the triangle ABC has vertices A(-2,3), B(0,3) and C(-1,-1).

We need to determine the coordinates of the image after a reflection over the x - axis.

Let A'B'C' denote the coordinates of the triangle after a reflection over the x - axis.

<u>Coordinates of the point A':</u>

The general rule to reflect the coordinate across the x - axis is given by

(x,y)\rightarrow (x,-y)

Substituting the point A(-2,3), we get;

(-2,3)\rightarrow (-2,-3)

Thus, the coordinates of the point A' is (-2,-3)

<u>Coordinates of the point B':</u>

The general rule to reflect the coordinate across the x - axis is given by

(x,y)\rightarrow (x,-y)

Substituting the point B(0,3), we get;

(0,3)\rightarrow (0,-3)

Thus, the coordinates of the point B' is (0,-3)

<u>Coordinates of the point C':</u>

The general rule to reflect the coordinate across the x - axis is given by

(x,y)\rightarrow (x,-y)

Substituting the point C(-1,-1), we get;

(-1,-1)\rightarrow (-1,1)

Thus, the coordinates of the point C' is (-1,1)

Hence, the coordinates of the image after a reflection over the x - axis is A'(-2,-3), B(0,-3) and C(-1,1)

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Y-1/4x=-1 <br> y-2=4x <br> one solution, no solution or infinite solution?
alexandr1967 [171]

Answer:

One solution

Step-by-step explanation:

To start, let's simplify the equations to slope-intercept form

y - 1/4x = =1

  +1/4x     +1/4x

y           = 1/4x - 1

y - 2 = 4x

  +2          +2

y       = 4x + 2

As you can see, the equations do not have anything in common worth mentioning. The slopes are different and the y-intercepts are different, so there must be only one solution.

Feel free to ask me any questions in the comments! :D

7 0
2 years ago
To speed the process of surveying, surveyors use brass metal plates to record important information. The benchmarks, as they are
Agata [3.3K]

Answer:

Feet Above Sea Level

Step-by-step explanation:

A benchmark is a term in Surveying and Geo informatics, that describes a point of reference established at a known elevation which serves as basis in which other elevation or topographical point can be measured.

Therefore, when determining the benchmark, it's height is calculated relative to the vertical datum of the area, typically mean sea level, which is then recorded in FEET ABOVE SEA LEVEL.

Hence, Benchmarks measurements refer to FEET ABOVE SEA LEVEL.

5 0
3 years ago
Thanh purchased crawfish and shrimp at a local seafood market to use at her restaurant. At the market, crawfish cost $3 per poun
irina1246 [14]

Answer:

22 pounds

Step-by-step explanation:

c+s=52, c = 52-s

3c+5s=200

3(52-s) +5s = 200

156 - 3s +5s = 200

5s-3s = 200-156

2s = 44

Shrimp = 44/2 = 22 pounds

3 0
2 years ago
Try it solve the equation<br> -3x - 6 = 6
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2 years ago
Read 2 more answers
Factor f(x) = 15x^3 - 15x^2 - 90x completely and determine the exact value(s) of the zero(s) and enter them as a comma separated
Illusion [34]

Answer:

x=-2,0,3

Step-by-step explanation:

We have been given a function f(x)=15x^3-15x^2-90x. We are asked to find the zeros of our given function.

To find the zeros of our given function, we will equate our given function by 0 as shown below:

15x^3-15x^2-90x=0

Now, we will factor our equation. We can see that all terms of our equation a common factor that is 15x.

Upon factoring out 15x, we will get:

15x(x^2-x-6)=0

Now, we will split the middle term of our equation into parts, whose sum is -1 and whose product is -6. We know such two numbers are -3\text{ and }2.

15x(x^2-3x+2x-6)=0

15x((x^2-3x)+(2x-6))=0

15x(x(x-3)+2(x-3))=0

15x(x-3)(x+2)=0

Now, we will use zero product property to find the zeros of our given function.

15x=0\text{ (or) }(x-3)=0\text{ (or) }(x+2)=0

15x=0\text{ (or) }x-3=0\text{ (or) }x+2=0

\frac{15x}{15}=\frac{0}{15}\text{ (or) }x-3=0\text{ (or) }x+2=0

x=0\text{ (or) }x=3\text{ (or) }x=-2

Therefore, the zeros of our given function are x=-2,0,3.

7 0
3 years ago
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