1) For number 1, you want to find the area of the square and the circle, then subtract: Area of square - area of circle. That will give you the area of the shaded region.
Area of square: 8² = 64, Area of circle: π4² = 50.27
64 - 50.27 = 13.73 ft²2)
For number 2, subtract the area of the rectangle by the area of the traingle.
Area of rectangle: (10)(6) = 60, Area of triangle:
= 21
60 - 21 = 39 in²3) For number 3, you could either find the entire rectangle and the empty space, and subtract the rectangle by the empty space, or cut the rectangle into sections and find each of the sections, then add them up. I'm going to find the entire rectangle then subtract it by the empty space. I think the problem is set up to be easier that way.
Area of rectangle: (12)(8) = 96, Area of empty space: (4)(4) = 16
96 - 16 = 80 in²
4) Find the area of the rectangle and the area of the semicircle. Subtract the rectangle by the semicircle.
Area of rectangle: (13)(6) = 78, Area of semicircle: π3² / 2 = 14.14
78 - 14.14 = 63.86 yd²
The point (-1, -4) lies in the third quadrant
Answer: 7.5 miles
Step-by-step explanation:
think of it as a triangle; the bold line is the hypotenuse, or x.
8 |\ x
|_\ it's not a good triangle but you get the point
6
and then get out pythagorean theorem: a^2+b^2=c^2
put the numbers in: 8^2 + 6^2 = x^2
do some math:
64+36=x^2
100=x^2 (and then find square root)
10=x
<u>BUT</u>, it said each unit was 3/4 of a mile, so we must multiply 10 by 3/4 to get the actual distance, which is 7.5
Answer:
Here you go!
Step-by-step explanation:
Since we are not yet sure what our number is, we should use a variable to represent that number, and then solve for that variable.
I will use "x" as our variable to represent the number we are trying to find.
Let's take the problem piece by piece.
Six less than four times a number.
If we are using x to represent our number, we know that when we do four times that number we are multiplying x times 4, which is the same as writing "4x."
Next we know that we are taking six less than 4x. Six less than means we will be subtracting 6 from our 4x, which is the same as writing 4x - 6.
Finally, we know that six less than 4x (4x - 6) equals 15. Now we have a full equation:
4x - 6 =15
Now we have to solve for x by getting x by itself:
4x - 6 = 15
add 6 to both sides to move the 6 away from the x
4x = 21
now divide by 4 to get x by itself
x = 21/4, in decimal form this is 5.25
8x - 3 = -19
8x = - 19 + 3
8x = -16
x = -16/8
x = -2
answer: the number is negative 2