Simple the expression ( 3k + 4 1/5) + 8 3/5

Mathematics

1 answer:

lesantik [10]2 years ago

7 0

Answer:

$3k+12\frac{4}{5}$

Step-by-step explanation:

$(3k+12\frac{4}{5})$

Convert mixed numbers to improper fractions:

$a\frac{b}{c}=\frac{a*c+b}{c}$

$4\frac{1}{5}=\frac{4*5+1}{5}$

$=\frac{21}{5}$

$=(3k+\frac{21}{5} )+\frac{43}{5}$

Add the fractions

$\frac{21}{5}+\frac{43}{5}$

$\frac{21}{5} \frac{43}{5} =\frac{64}{5}$

$=3k+\frac{64}{5}$

Divide 64 by 5

$\frac{64}{5}$ $12.8 or 12\frac{4}{5}$

$=3k+12\frac{4}{5}$

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VARVARA [1.3K]

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3 years ago

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What is the volume of the composite figure? Explain your work. A complete answer should include how you broke up the figure, whi

Sphinxa [80]

Answer:

$15,000\:\mathrm{mm^3}$

Step-by-step explanation:

The composite figure consists of a square prism and a trapezoidal prism. By adding the volume of each, we obtain the volume of the composite figure.

The volume of the square prism is given by $V=s^2\cdot h$ , where $s$ is the base length and $h$ is the height. Substituting given values, we have: $V=14^2\cdot 30=196\cdot 30=5,880\:\mathrm{mm^3}$

The volume of a trapezoidal prism is given by $V=\frac{b_1+b_2}{2}\cdot l\cdot h$ , where $b_1$ and $b_2$ are bases of the trapezoid, $l$ is the length of the height of the trapezoid and $h$ is the height. This may look very confusing, but to break it down, we're finding the area of the trapezoid (base) and multiplying it by the height. The area of a trapezoid is given by the average of the bases ( $\frac{b_1+b_2}{2}$ ) multiplied by the trapezoid's height ( $l$ ).