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2 years ago

PLSSSSS SOMEONE ANSWER THIS QUESTION

Mathematics

1 answer:

liq [111]2 years ago

6 0

Answer:

12πx⁴, 15x⁷, 16x⁹

Step-by-step explanation:

Volume of a cylinder: πr²h

Volume of a rectangular prism: whl

Plugging in variables for the volume of a cylinder, we get: 3x²·(2x)²·π

3x²·(2x)² = 3·2·2·x·x·x·x

= 12·x⁴

=12x⁴

Now, we just multiply that by π.

12x⁴·π = 12x⁴π

A monomial is a 1-term polynomial, so 12x⁴π is a monomial.

Plugging in variables for the volume of a rectangular prism, we get: 5x³·3x²·x²

5x³·3x² = 5·3·x·x·x·x·x

= 15·x⁵

= 15x⁵

Now, we just multiply that by x².

15x⁵·x²

= 15·x·x·x·x·x·x·x

= 15·x⁷

=15x⁷

A monomial is a 1-term polynomial, so 15x⁷ is a monomial.

Same steps for the last shape, another rectangular prism:

2x²·2x³·4x⁴

2x²·2x³

= 2·2·x·x·x·x·x

= 4·x⁵

= 4x⁵

Now, we just multiply that by 4x⁴.

4x⁵·4x⁴

= 4·4·x·x·x·x·x·x·x·x·x·

= 16·x⁹

= 16x⁹

A monomial is a 1-term polynomial, so 16x⁹ is a monomial.

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antiseptic1488 [7]

Fraction multiplication involves multiplying the numerators and the denominators to get the numerator and the denominator of the product respectively

Please find the attached diagrams

1. $\dfrac{2}{15}$ , 2. $\dfrac{3}{8}$ , 3. $\dfrac{1}{12}$ , 4. $\dfrac{7}{21}$ , 5. $\dfrac{3}{10}$

6. 51, 7. 1, 8. 22, 9. $\dfrac{36}{55}$ , 10. $5\dfrac{1}{3}$

Reasons:

The process of multiplication of factors using a model includes;

Creating a table that have the number of rows and columns equal to the values in the denominator of the two fractions respectively

Shading the number of columns given by the numerator of the fraction that has a denominator equal to the number of columns in the table

Shading the number of rows given by the numerator of the fraction that has a denominator equal to the number of rows in the table

Ensuring that the common area are shaded to a different color

Simplifying the result

1. $\dfrac{2}{3} \times \dfrac{1}{5} = \dfrac{2}{15}$

2. $\dfrac{1}{2} \times \dfrac{3}{4} = \dfrac{3}{8}$

3. $\dfrac{1}{4} \times \dfrac{2}{6} = \dfrac{2}{24} = \dfrac{1}{12}$

4. $\dfrac{1}{7} \times \dfrac{2}{3} = \dfrac{7}{21}$

5. $\dfrac{4}{8} \times \dfrac{3}{5} = \dfrac{12}{40} = \dfrac{3}{10}$

Second part

6. When calculating fractions, 'of' means to 'multiply by', therefore, we have;

$\dfrac{17}{25} \times 75= \dfrac{17}{25} \times 25 \times 3 = 17 \times 3 = 51$

7. $\dfrac{7}{6} \times \dfrac{24}{28} = \dfrac{7}{6} \times \dfrac{6 \times 4}{7 \times 4} = \dfrac{7}{6} \times \dfrac{6}{7 } = 1$

8. $12 \times 1\dfrac{5}{6} =6 \times 2 \times \dfrac{11}{6} =2 \times {11} = 22$

9. $\dfrac{4}{5} \times \dfrac{9}{11} = \dfrac{4 \times 9}{5 \times 11} = \dfrac{36}{55}$

10. $6\dfrac{2}{3} \times \dfrac{12}{15} =\dfrac{20}{3} \times \dfrac{12}{15} = \dfrac{4 \times 5}{3} \times \dfrac{4 \times 3}{5 \times 3} = \dfrac{4}{3} \times {4} = \dfrac{16}{3} = 5\dfrac{1}{3}$