The triangles are similar by SAS principle.
<h3>How to know similar triangles?</h3>
Similar triangles have the same shape but may have different sizes.
In similar triangles, corresponding sides are always in the same ratio.
The corresponding angles are congruent.
Therefore, using SAS ratio,
6 / 8 = 8 × 3 / 32
6 / 8 = 24 / 32 = 3 / 4
Therefore, the corresponding sides are a ratio of each other.
Therefore, the triangles are similar by SAS principles because the two triangles have two pairs of sides in the same ratio and the included angles are also equal
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Answer:
Clockwise rotation 90 ° about origin
R_{90, clockwise, origin}(x,y) -> (y,-x)
J(-4,1) therefore
R_{90, clockwise, origin}J(-4,1) -> J'(1,+4) this answer was form other person credits to him/her
Step-by-step explanation:
Given:
Let x be the whole amount inherited.
1/2 * x - invested with Bernie Madoff
1/3 * x - lost due to identity theft
1/8 * x - lost in casino
40,000 - remainder
x - x/2 - x/3 - x/8 = 40,000
LCM:
2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24
3: 3, 6, 9, 12, 15, 18, 21, 24
8: 8, 16, 24,
x * 24/24 = 24x / 24
x/2 * 12/12 = 12x / 24
x/3 * 8/8 = 8x / 24
x/8 * 3/3 = 3x / 24
40,000 * 24/24 = 960,000 / 24
24x/24 - 12x/24 - 8x/24 - 3x/24 = 960,000/24
(24x - 12x - 8x - 3x)/24 = 960,000/24
x/24 = 960,000/24
24 * x/24 = 24 * 960,000/24
x = 960,000
x = 960,000 initial inheritance
x/2 = 960,000/2 = 480,000 invested with Bernie Madoff
x/3 = 960,000/3 = 320,000 lost due to identity theft
x/8 = 960,000/8 = 120,000 lost in the casino
40,000 - remaining amount.
960k - 480k - 320k - 120k = 40k
40k = 40k
Factor out the -3
(-3)(x^2-2x+3)
In order to graph the equation, you need some coordinates,
So, put x = 0,
2y = 6. y = 3. Coordinate = (0, 3)
Now, put y = 0,
-x = 6
x = -6 Coordinate (-6, 0)
In short, Just mark that two points and draw a line, graph is done
Hope this helps!
