Evaluate \dfrac{3\times a + b}{c} with a=2.3, b=\dfrac25, c=\dfrac45
First, compute the numerator of this fraction. Notice that:
b = \dfrac{2}{5}= 0.4
Therefore :
3 \times a + b = 3 \times 2.3 + 0.4 = 6.9 + 0.4 = 7.3 = \dfrac{73}{10}
We have:
\dfrac{3 \times a + b}{c} = \left(3 \times a + b\right) \times \dfrac{1}{c} =\dfrac{73}{10} \times \dfrac{5}{4}=\dfrac{73}{8}
\dfrac{3\times a + b}{c}=\dfrac{73}{8}
Evaluate \left(\dfrac{3}{5}\right) \times \left(m + \dfrac{n^2}{4}\right) with m = 1.3 and n = 2
We have:
m + \dfrac{n^2}{4} = 1.3 + \dfrac{2^2}{4}= 1.3 + \dfrac{4}{4} = 1.3 + 1 = 2.3
Note that:
2.3 = \dfrac{23}{10}
Therefore:
\dfrac{3}{5} \times 2.3 = \dfrac{3}{5} \times \dfrac{23}{10} = \dfrac{69}{50}
\left(\dfrac{3}{5}\right) \times \left(m + \dfrac{n^2}{4}\right) = \dfrac{69}{50}
Evaluate \dfrac{\left(3 - \left(-4\right)x\right)^2}{y + 15} with x = 2 and y=7
First, compute the numerator:
\left(3 - \left(-4\right)x\right)^2 = \left(3 + 4x\right)^2 = \left(3 + 4 \times 2\right)^2 = \left(3 + 8 \right)^2 = 11^2 = 121
In the denominator:
y+15=7+15=22
Thus:
\dfrac{\left(3 - \left(-4\right)x\right)^2}{y+15} = \dfrac{121}{22}
Simplify:
\dfrac{\left(3 - \left(-4\right)x\right)^2}{y + 15} = \dfrac{11}{2}
Evaluate \dfrac{-4 \times v}{c^2} + 2.6 with v = -2 and c = 4
-4 \times v = -4 \times -2 = 8
c^2 = 4^2 = 16
Thus:
\dfrac{-4 \times v}{c^2} = \dfrac{8}{16}=\dfrac{1}{2} = 0.5
Therefore:
0.5 + 2.6 = 3.1
\dfrac{-4 \times v}{c^2} + 2.6 =3.1
Evaluate \dfrac{6 \times s - t}{t + w} with s = -1, t = 2, and w = .75
First, compute the numerator:
6 \times s - t = 6\times -1 - 2 = -6 - 2 = -8
In the denominator:
t + w = 2 + 0.75 = 2.75
Note that:
2.75 = \dfrac{11}{4}
Therefore:
\dfrac{-8}{11/4} = -8 \times \dfrac{4}{11} = \dfrac{-32}{11}
\dfrac{6 \times s - t}{t + w} = \dfrac{-32}{11}
Evaluate \dfrac{\left(5 - a\right)^2\times 4}{b + \dfrac{2}{3}} with a = 5.5 and b = \dfrac{1}{6}
First, compute the numerator:
\left(5 - a\right)^2 = \left(5 - 5.5\right)^2= \left(-0.5\right)^2 = 0.25
Note that:
0.25 \times 4 = 1
In the denominator:
b + \dfrac{2}{3} = \dfrac{1}{6} + \dfrac{2}{3} = \dfrac{1}{6} + \dfrac{4}{6} = \dfrac{5}{6}
Therefore:
\dfrac{\left(5 - a\right)^2 \times 4}{b + \dfrac{2}{3}} = \dfrac{1}{5/6}= 1 \times \dfrac{6}{5} = \dfrac{6}{5}
\dfrac{\left(5 - a\right)^2\times 4}{b + \dfrac{2}{3}} = \dfrac{6}{5}
Evaluate \dfrac{2 - a \times b}{\left(-3\right)^2 - c + 0.5} with a = -2, b = 0.75, and c = 2.5
First, compute the numerator:
2 - a \times b = 2 - \left(-2\right)\times 0.75 = 2 - \left(-1.5\right) = 3.5
In the denominator:
9 - c + 0.5 = 9 - 2.5 + 0.5 = 6.5 + 0.5 = 7
Therefore:
\dfrac{2 - a \times b}{9 - c + 0.5} = \dfrac{3.5}{7}= \dfrac{1}{2} \text{ or } 0.5
\dfrac{2 - a \times b}{9 - c + 0.5}= 0.5