Let's solve the equation:
9x+27 = 9(x+2)+9 ← Distribute 9 to the x and 2
9x+27 = 9x+18+9 ← Combine like terms
9x+27 = 9x + 27 ← Subtract 27 from both sides
9x = 9x
Infinitely many solutions would be correct because no matter what x is, it will always equal each other the both sides of the equation because it is 9 times x on both sides.
Answer:
(82/3, -111/2) or x=82/3, y=-111/2
Step-by-step explanation:
Angle is x. sup - adds up to 180. comp adds up to 90
180-x = 3(90-x)+40
180-x = 270-3x+40
180-x = 310-3x
180+2x = 310
2x = 130
x=65
The coordinate of the point T after the given transformations is; T''(-2, -4)
<h3>How to carry out Translation Transformations?</h3>
We are given the coordinates of the rectangle STUV as;
S(-7, 6)
T(-2, 6)
U(-2, 1)
V(-7, 1)
Now, we are told that all these coordinates are translated using the transformation rule; (x, y) → (x − 2, y − 4)
Thus, the new coordinates using this transformation rule are;
S'(-9, 2)
T'(-4, 2)
U'(-4, -3)
V'(-9, -3)
Now, we are told that these new points are rotated 90° counterclockwise and as such the new coordinates formed will follow the pattern (x, y) → (-y, x).
Thus, our final coordinates are;
S''(-2, -9)
T''(-2, -4)
U''(3, -4)
V''(3, -9)
Thus, the coordinate of the point T after the given transformations is; T''(-2, -4)
Read more about Translation Transformation at; brainly.com/question/4289712
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tl;dr Answer is C
Here we will have to calculate 3 different areas separately.
When calculating the area of the triangle we will use the formula
A = (h*b)/2
A = Area
h = height
b = base
To find the height we do X - Z
23 - 15 = 8 ft
To find the base we do Y - W
19 - 13 = 6 ft
Using the formula above we can now solve for A
A = (8*6)/2
A = (48)/2
A = 24 sq ft
Now we solve the two rectangles using the formula
A = wl
w = width
l = length
We will calculate the area of the left most rectangle first.
We know the length of the rectangle because it's Y - W and we are given the width of the triangle.
w = 15 ft
l = 6 ft
A = 15*6
A = 90 sq ft
Second Rectangle has the width of X and length of W
w = 23 ft
l = 13 ft
A = 23 * 13
A = 299 sq ft
Now we add all the areas to give us the total area of the warehouse.
24 + 90 + 299 = 413 sq ft
Therefore, the answer is C
