Answer:
1. C = 29.52 inches A = 69.63 square inches
2. C = 28.26 inches A = 63.59 square inches
3. Each side of the lawn is 13 yards.
4. 7 is a rational number ([tex]\frac{14}{2}[/tex]), a whole number, and an integer.
5. x = 16
6. h = 12.4
Step-by-step explanation:
1.
π = 3.14
The formula for the circumference of a circle that uses radius is C = 2πr.
C = 2 × 3.14 × 4.7 --- plug in known info
C = 29.516 inches --- solve
C = 29.52 inches
The formula for the area of a circle that uses radius is A = πr².
A = 3.14 × 4.7² --- plug in known info
A = 3.14 × 22.09 --- solve
A = 69.3626 square inches --- solve
A = 69.63 square inches
2.
The formula for the circumference of a circle that uses diameter is C = πd.
C = 3.14 × 9 --- plug in known info
C = 28.26 inches --- solve
To solve for area with the diameter, divide it by 2 and use the radius area formula.
[tex]\frac{9}{2}[/tex]
r = 4.5
A = πr²
A = 3.14 × 4.5² --- plug in known info
A = 3.14 × 20.25 --- solve
A = 63.585 square inches --- solve
A = 63.59 square inches
3.
Because the lawn is square, the length and width of the lawn are equal.
Let x = the length and width.
x × x = 169 --- l × w = area of rectangle
x² = 169 --- x × x is the same as x²
x = 13 --- square root both sides to get rid of square on x
Each side of the lawn is 13 yards.
4.
√49 = 7
Rational number: a number that can be expressed as a simple fraction of 2 integers, 7 = [tex]\frac{14}{2}[/tex]
Irrational number: a number that cannot be expressed as a simple fraction of 2 integers, √2
Whole number: All natural numbers, including 0, up to infinity, 0, 1, 2, 3, 4, 5...
Integer: All whole numbers and their negative counterparts -4, -3, -2, -1, 0, 1, 2, 3, 4…
7 is a rational number ([tex]\frac{14}{2}[/tex]), a whole number, and an integer.
5.
We can solve for x using the Pythagorean theorem: If a triangle is right, a² + b² = c².
12² + x² = 20² --- plug in known info
144 + x² = 400 --- solve
x² = 256 --- subtract 144 from both sides
x = 16 --- square root both sides
6.
Same as problem 5, we will use the Pythagorean theorem to solve.
3² + 12² = h² --- plug in known info
9 + 144 = h² --- solve
153 = h² --- solve
h = 12.36931688 --- square root both sides
h = 12.4 --- round to nearest 10th
