a bag contains tiles with the letters a-r-i-t-h-m-e-t-i-c. amelia chooses a tile without looking and doesn't replace it. she cho
2 answers:
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Answer:
x = 4
Step-by-step explanation:
If you do not want to read the explanation go the the next part in bold
Ok so the shorter leg of the triangle is a radius of the circle. ( This is indicated by the point in the middle of the circle.) for the hypotenuse we are given one part of the length (2) The other part also happens to be a radius ( remember that a radius is a line that starts from the center of the triangle to any point of the circumference. ) Also remember that the radius is equal to 3. That being said the hypotenuse = 2+3 which equals 5.
This triangle then happens to be a right triangle. ( A triangle formed by a tangent line and a radius is a right triangle.) This means that we can use the Pythagorean theorem to solve for x.
Below here is where the work is shown
a² + b² = c². where a and b = legs and c = hypotenuse. We are given the hypotenuse (5) and a leg (3) So we plug in what we are given and solve for the missing information. 5² = 3² + b²
5² = 25
3² = 9
we would then have 25 = 9 + b²
Next we subtract 9 from each side
25 - 9 = 16
9 - 9 cancels out
Now we have 16 = b²
finally we want to get rid of the ²
To do so we take the square root of each side
we're left with b = 4 which means that x = 4
Answer:
49.5 square inches
Step-by-step explanation:
We can split the figure into two easier shapes to find the area of; a triangle and a square.
The formula for a triangle is (b*h)1/2. Once we solve we get 24.5 or 24 1/2.
The formula for a square is l*w. Once we solve we get 25.
To find the area of the shaded region, we would add both area and get 49.5 or 49 1/2 square inches.
