Question

1. duane kicked a 45-yard field goal. how many feet is 45 yards?

• 4. explain why is a square a regular quadrilateral?
• 5. a regular hexagon has a perimeter of 36 inches. how long is each side?

1. $\frac{1}{4} = \frac{?}{100}$
2. $\frac{8 \times 8}{8 + 8}$

• 8. $5\frac{2}{3} + 3\frac{3}{4}$
• 9. $\frac{1}{2} + \frac{2}{3} + \frac{1}{4}$

1. $\frac{9}{10} - \frac{1}{2}$

• 11. $6\frac{1}{2} - 2\frac{7}{8}$

1. compare: $2 \times 0.4 \bigcirc 2 + 0.4$
2. $4.8 \times 0.35$
3. $1 \div 0.4$
4. how many $0.12 pencils can mr. velazquez buy for $4.80?
5. estimate round the product of 0.33 and 0.38 to the nearest hundredth.
6. multiply the length by the width to find the area of this rectangle.

• 18. conclude is every rectangle a parallelogram?

1. analyze what is the twelfth prime number?
2. the area of a square is 9 cm²

Explanation:

Step1: Convert yards to feet

1 yard = 3 feet, so $45 \times 3$

Step2: Calculate the product

$45 \times 3 = 135$
---

Step1: Define regular quadrilateral

A regular quadrilateral has 4 equal sides and 4 equal angles.

Step2: Match square properties

A square has 4 congruent sides and 4 right (equal) angles.
---

Step1: Divide perimeter by 6

A regular hexagon has 6 equal sides, so $\frac{36}{6}$

Step2: Compute the quotient

$\frac{36}{6} = 6$
---

Step1: Find equivalent fraction

$\frac{1}{4} = \frac{1 \times 25}{4 \times 25}$

Step2: Calculate numerator

$\frac{25}{100}$, so? = 25
---

Step1: Simplify numerator and denominator

$8 \times 8 = 64$, $8 + 8 = 16$, so $\frac{64}{16}$

Step2: Divide to get result

$\frac{64}{16} = 4$
---

Step1: Convert to improper fractions

$5\frac{2}{3} = \frac{17}{3}$, $3\frac{3}{4} = \frac{15}{4}$

Step2: Find common denominator

LCD of 3 and 4 is 12: $\frac{17 \times 4}{12} + \frac{15 \times 3}{12} = \frac{68}{12} + \frac{45}{12}$

Step3: Add fractions

$\frac{68 + 45}{12} = \frac{113}{12} = 9\frac{5}{12}$
---

Step1: Find common denominator

LCD of 2, 3, 4 is 12: $\frac{6}{12} + \frac{8}{12} + \frac{3}{12}$

Step2: Add numerators

$\frac{6 + 8 + 3}{12} = \frac{17}{12} = 1\frac{5}{12}$
---

Step1: Find common denominator

LCD of 10 and 2 is 10: $\frac{9}{10} - \frac{5}{10}$

Step2: Subtract fractions

$\frac{9 - 5}{10} = \frac{4}{10} = \frac{2}{5}$
---

Step1: Convert to improper fractions

$6\frac{1}{2} = \frac{13}{2}$, $2\frac{7}{8} = \frac{23}{8}$

Step2: Find common denominator

LCD of 2 and 8 is 8: $\frac{52}{8} - \frac{23}{8}$

Step3: Subtract fractions

$\frac{52 - 23}{8} = \frac{29}{8} = 3\frac{5}{8}$
---

Step1: Calculate both expressions

$2 \times 0.4 = 0.8$, $2 + 0.4 = 2.4$

Step2: Compare values

$0.8 < 2.4$, so use $<$
---

Step1: Multiply decimals directly

$4.8 \times 0.35 = 1.68$
---

Step1: Divide 1 by 0.4

$1 \div 0.4 = \frac{10}{4} = 2.5$
---

Step1: Divide total cost by unit cost

$\frac{4.80}{0.12}$

Step2: Compute the quotient

$\frac{4.80}{0.12} = 40$
---

Step1: Calculate the product

$0.33 \times 0.38 = 0.1254$

Step2: Round to nearest hundredth

$0.1254 \approx 0.13$
---

Step1: Multiply length and width

$\frac{3}{4} \times \frac{1}{2}$

Step2: Compute the product

$\frac{3 \times 1}{4 \times 2} = \frac{3}{8}$
---

Step1: Define parallelogram

A parallelogram has 2 pairs of parallel sides.

Step2: Match rectangle properties

A rectangle has 2 pairs of parallel sides.
---

Step1: List primes in order

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37

Step2: Count to 12th prime

The 12th prime is 37
---

Step1: Find side length of square

Area $A = s^2$, so $s = \sqrt{9} = 3$ cm

Step2: (If finding perimeter, optional)

Perimeter $= 4 \times 3 = 12$ cm

Answer:

1. 135 feet
2. A square has 4 equal sides and 4 equal right angles, meeting the definition of a regular quadrilateral.
3. 6 inches
4. 25
5. 4
6. $9\frac{5}{12}$
7. $1\frac{5}{12}$
8. $\frac{2}{5}$
9. $3\frac{5}{8}$
10. $2 \times 0.4 < 2 + 0.4$
11. 1.68
12. 2.5
13. 40 pencils
14. 0.13
15. $\frac{3}{8}$ square inches
16. Yes, every rectangle is a parallelogram because it has two pairs of parallel sides.
17. 37
18. (If finding side length: 3 cm; if finding perimeter: 12 cm)