Answer:
Yes triangle ABC and DEF are similar.
Step-by-step explanation:
One rule of triangles is that all the angles in a triangle will add up to 180 degrees.
Now, first, you will figure out the remaining angle in triangle ABC.
- Add up 35 and 20. (35 + 20 =55)
- Subtract 55 from 180 (180-55= 125)
- When you add 125, 35, and 20, you get 180, which should happen due to the rule of all angles in a triangle add up to 180.
Now, in triangle DEF, one angle is 125 and the other is 35. To find the other angle add 125 and 35 and subtract the sum of those two numbers from 180.
- 125 + 35 = 160
- 180-160= 20
The remaining angle is 20 degrees
As you can see, triangle ABC shares the same angles as triangle DEF.
This tells you that triangle ABC and triangle DEF are both similar due to the fact that they have the same measurements of triangles.
You can also tell they are similar because two angles in triangle ABC equal two angles in triangle DEF because of the Angle-Angle (AA) Similarity
I hope this explanation helped and have a good day!
Answer:
The equation of the circle is
(x + 2)² + (y + 2)² = 9
Centered at (-2, -2), with radius of 3 units.
Step-by-step explanation:
The general equation of a circle is given as
(x - h)² + (y - k)² = r²
Where (h, k) is the center of the circle, and r is the radius.
Looking at the graph, the center is the red dot. It corresponds to -2 on the y-axis, and -2 on the x-axis. So, the center (h, k) is (-2, -2).
The radius is the distance from the center of the circle to the edge of the circle. The red dot is the edge of the circle, there are 3 lines that represent 3 units, so we have a radius of 3 units.
Using these in the general equation, we have
[x - (-2)]² + [y - (-2)]² = 3²
(x + 2)² + (y + 2)² = 9
And this is the equation.
Answer:
-3
Step-by-step explanation:
5*3=15
15-18= -3
For the first one, subtracting the membership fee, we have 9 dollars to buy as many 1.50 dollar videos as possible. 9/1.50 works well as 6, so he can buy 6.
Subtract 160 from 480 to get 320, and divide that by 80 to get 4 days
We can do some guess and check here. If he buys 2 t shirts, that's 12*2=24 and 41-24=17. 17 is not a factor of 5, so that doesn't work. If he buys 3, that's 12*3=36 and 41-36=5. 5 is a factor of 5, so that works!
