Answer:Dilation involves changing the size of a shape.
The true statement is that the locations of E' and F' are E' (−12, 0) and F' (0, 6), and lines g and g' are parallel.
The given parameters are:
--- the scale factor
Multiply the coordinates of point E and F by the scale factor (k), to determine the new coordinates of E and F.
Given that line g is represented by points E and F; line g' would be represented by points E' and F'
So, both lines would be parallel.
Hence, the true option is (d)
Step-by-step explanation:
9514 1404 393
Answer:
x = 10
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relation ...
Sin = Opposite/Hypotenuse
sin(30°) = 5/x
Solving for x, we get ...
x = 5/sin(30) = 5/0.5
x = 10
_____
It can be helpful to remember that the side ratios in a 30°-60°-90° triangle are ...
1 : √3 : 2
That is, the hypotenuse is 2 times the length of the side opposite the 30° angle. Here, that means x = 2×5 = 10, as we found above.
Answer: 3060 ft^2
Step-by-step explanation:
We will calculate the surface area of the rectangular prism and the triangular prism separately and then subtract off the face that isn't on the surface.
For the rectangular prism:
SA= Ph + 2B
P = 36+36+10+10
P = 92
B = 36*10 = 360
SA = 92*20+2*360
SA = 1840+720
SA = 2560
We subtract off the face on the right of the rectangular prism because it isn't on the surface so we get 2560-200 = 2360
Now for the triangular prism:
SA= Ph + 2B
P = 15+20+25
P = 60
B = 15*20/2
B = 150
SA = 60*10+2*150
SA = 600+300
SA = 900
Again we subtract off the face on the left bescause it's not on the surface so we get 900-200 = 700
Therefore, the total surface area = 2360+700 = 3060 ft^2
Answer:
Because the triangle is isosceles, the base angles are congruent. Since the sum of angles in a triangle is 180° we can write:
24 + x + x = 180
24 + 2x = 180
2x = 156
x = 78°