1/√2
Step-by-step explanation:
Imagine a right-angled triangle, for e.g. Triangle ABC,
Where
B = 90°
Remember your Toa Cah Soh.
sin 45° = opposite / hypotenuse
If theta = 45°
Angles A and C = 45° (Sum of angles in a triangle equal = 180°)
Since theta are the same, we can also deduce that the length AB and BC are the same.
Take for example AB = BC = 1 = opposite
By the Pythagorean theorem,
AB² + BC² = AC²
1² + 1² = AC²
2 = AC²
AC = √2 = hypotenuse
Therefore:
sin 45° = opposite / hypotenuse
sin 45° = 1/√2
Answer:
75%
Step-by-step explanation:
Think of it this way. 3 quarters is 75 cents. It's the same as 3/4, since 4 quarters makes $1.00.
Find the LCD and then combine
Answer: 41/5 or 8.2 in decimal form
Answer:
As many as 7 apples or as few as 4 apples could be green.
Step-by-step explanation:
Laura picks 7 apples.Some apples are red and some are green. Fewer than 4 of the apples are red. How many of laura's apples could be green?
x = total number of red apples
y = total number of green apples
Fewer than 4 of the apples are red.
x<4
That means that 3 or less of the apples are red
So, 7 - 3 = 4
That means that 4 or more apples are green.
7≥y≥4
That means that as many as 7 apples or as few as 4 apples could be green.
Answer:
C (x, y) -> (x + 7, y + 8); scale factor = 3
Step-by-step explanation:
The translation can be found by subtracting the coordinates of the original center from those of the center of the image. The scale factor will be the ratio of the radii.
__
<h3>translation</h3>
We note the center coordinates are I(-3, -6) and I'(4, 2). Then the translation is ...
I' -I = (4, 2) -(-3, -6) = (4 +3, 2 +6) = (7, 8)
(x, y) ⇒ (x +7, y +8)
<h3>scale factor</h3>
The radius of each circle can be found by counting the grid squares from the center to the circle. It works best to do this along a horizontal or vertical line.
The radius of circle I is 2; the radius of circle I' is 6. The scale factor is ...
scale factor = 6/2 = 3
