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astra-53 [7]
3 years ago
5

Given triangle ABC with coordinates A(−2, 7), B(−2, 4), and C(−4, 3), and its image A′B′C′ with A′(2, 3), B′(−1, 3), and C′(−2,

1), find the line of reflection.
The line of reflection is at y =
Mathematics
1 answer:
Setler [38]3 years ago
6 0

Answer:

y = x + 5

Step-by-step explanation:

given an obtuse scalene triangle (∆ABC) with vertices A(-2,7), B(-2,4), and C(-4,3) (representing the preimage of the reflection). And congruent triangle (∆A'B'C') with vertices A'(2,3), B'(-1,3), and C'(-2,1) (representing the image of the reflection / triangle after the reflection).

The easiest way to look at this is by taking the inverse of each point on the preimage (swapping y and x coordinates) and the adding 5 to the y and subtracting 5 from the x to get the image.

You can test this, and you will see that this will match with vertices of the image.

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An equation is shown below.
spayn [35]

Answer:

Step-by-step explanation:

6 0
3 years ago
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The perimeter of a rectangle is 24 inches. Find the dimension If the length of the rectangle is 3 inches more than it’s width.
GuDViN [60]

Answer:

length is 7.5 and width is 4.5

Step-by-step explanation:

Its given that perimeter of the triangle is 24 units.

The condition is that length is 3 units more than the width.

l=w+3;

Formula for perimeter is 2(l+w).

so ,

2(w+w+3)=24,

2w+3=12,

w=4.5,

l=w+3=7.5

Hence for the given conditions length is 7.5 and width is 4.5.

8 0
3 years ago
Steve invests in a circus production. The cost includes an overhead of $84,000, plus production costs of $2000 per performance.
Dima020 [189]

Answer:

14

Step-by-step explanation:

Given that Steve  invests in a circus production. The cost includes an overhead of $84,000, plus production costs of $2000 per performance. A sold-out performance brings in $8000.

Sales per performance =8000

Production cost per performance =2000

Contribution per performance = 8000-2000=6000

Overhead costs = 84000

Break even units = overhead cost/contribution per performance

= \frac{84000}{6000} \\=14

14 performances should be done to break even

3 0
3 years ago
What is the slope of the line? 2 x − 5 y = 9
Alex777 [14]

Answer:

The slope of this line is -2

Step-by-step explanation:

2x - 5y  =9

-5y = -2x + 9 (Subtract 2x from each side)

y= -2x + 14 (add 5 to each side)

-2 is the slope

4 0
3 years ago
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What is the f of x over the g of x when f(x) = 6x3 − 19x2 + 16x − 4 and g(x) = x − 2? (2 points)
VikaD [51]
You're being asked to divide 6x^3 - 19x^2 + 16x - 4 by x - 2.

Try using synthetic division, if you know it:

     _______________
2  /   6    -19    16    -4
              12     -14    4
    --------------------------
        6     -7       2     0

6, -7 and 2 are the coefficients of the quotient.  The quotient (answer to this question) is

6x^2 - 7x + 2
4 0
3 years ago
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