Answer:
8.35
Step-by-step explanation:
To get absolute value, just make it the opposite
The transformations done are option A. A reflection over the y-axis, then a reflection over the x-axis
Step-by-step explanation:
Step 1:
First, we plot the points of triangle ABC and A''B''C''.
The points of triangle ABC are A (-8, -5), B(-4, -3), and C(-4,-7).
The points of triangle A''B''C'' are A'' (8, 5), B'' (4, 3), and C'' (4,7).
The points of both triangles ABC and A''B''C'' are the same values but different symbols for x and y values.
Step 2:
If a shape is reflected across an axis, the values remain the same but the symbols vary according to the quadrant.
If a shape is translated, all coordinates of all the points vary accordingly.
As triangles ABC and A''B''C'' have exactly the same coordinates it means that two reflections have occurred but no translations have occurred.
So the answer is the option with two reflections. So option A. A reflection over the y-axis, then a reflection over the x-axis is the answer.
Answer:
The correct answer will be option b
Step-by-step explanation:
We know that x = rcos( θ ), and y = rsin( θ ), so let's rewrite this polar equation.
r = 4( x / r ) + 2( y / r ),
r = 4x / r + 2y / r,
r = 4x + 2y / r,
r / 1 = 4x + 2y / r ( Cross - Multiply )
4x + 2y = r²
We also know that r² = x² + y², so let's substitute.
x² + y² = 4x + 2y,
x² - 4x - 2y + y² = 0,
Circle Equation : ( x - 2 )² + ( y - 1 )² = ( √5 )²,
Solution : ( x - 2 )² + ( y - 1 )² = 5
Answer:
c + d = 400
0.2c + 0.5d = 156
Step-by-step explanation:
Let
c = number of liters of 20% acid solution
d = number of liters of 50% acid solution.
c + d = 400 (1)
0.2c + 0.5d = 400(0.39)
0.2c + 0.5d = 156 (2)
From (1)
c = 400 - d
Substitute c = 400 - d into (2)
0.2c + 0.5d = 156 (2)
0.2(400 - d) + 0.5d = 156
80 - 0.2d + 0.5d = 156
- 0.2d + 0.5d = 156 - 80
0.3d = 76
d = 76/0.3
d = 253.33 liters
Substitute d = 253.33 into (1)
c + d = 400
c + 253.33 = 400
c = 400 - 253.33
c = 146.67 liters
Answer:
0.15 / 1.5
Step-by-step explanation:
4 / 3.700 = 1.08
18 / 19 = 0.9
.15 / 1.5 = 0.1
