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3 years ago

Please solve each quotient

Mathematics

1 answer:

kakasveta [241]3 years ago

8 0

Answer:

Step-by-step explanation:

13. 1.75 14. 2.5 15, 40.5

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6: REDUCE to simplest term. 4/1 + 15/2

vovangra [49]

Answer:

$\frac{4}{15}+\:\frac{1}{2}$ in the simplest term is:

$\frac{4}{15}+\frac{1}{2}=\frac{23}{30}$

Step-by-step explanation:

Given the expression

$\frac{4}{15}+\:\frac{1}{2}$

Thus, solving to reduce to the simplest term

$\frac{4}{15}+\frac{1}{2}$

LCM of 15, 2: 30

Adjusting fraction based on the LCM

so the expression becomes

$\frac{4}{15}+\:\frac{1}{2}=\frac{8}{30}+\frac{15}{30}$

Apply the fraction rule: $\frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}$

$=\frac{8+15}{30}$

Add the numbers: 8+15 = 23

$=\frac{23}{30}$

Therefore, $\frac{4}{15}+\:\frac{1}{2}$ in the simplest term is:

$\frac{4}{15}+\frac{1}{2}=\frac{23}{30}$

4 0

3 years ago

A machine in a chocolate factory is set to squirt out a predetermined amount of molten chocolate. When the machine is set to x,

frez [133]

Answer:

Sorry I need Points but I also need help

Step-by-step explanation:

3 0

3 years ago

3^x= 3*2^x solve this equation

kompoz [17]

In the equation

$3^x = 3\cdot 2^x$

divide both sides by $2^x$ to get

$\dfrac{3^x}{2^x} = 3 \cdot \dfrac{2^x}{2^x} \\\\ \implies \left(\dfrac32\right)^x = 3$

Take the base-3/2 logarithm of both sides:

$\log_{3/2}\left(\dfrac32\right)^x = \log_{3/2}(3) \\\\ \implies x \log_{3/2}\left(\dfrac 32\right) = \log_{3/2}(3) \\\\ \implies \boxed{x = \log_{3/2}(3)}$

Alternatively, you can divide both sides by $3^x$ :

$\dfrac{3^x}{3^x} = \dfrac{3\cdot 2^x}{3^x} \\\\ \implies 1 = 3 \cdot\left(\dfrac23\right)^x \\\\ \implies \left(\dfrac23\right)^x = \dfrac13$

Then take the base-2/3 logarith of both sides to get

$\log_{2/3}\left(2/3\right)^x = \log_{2/3}\left(\dfrac13\right) \\\\ \implies x \log_{2/3}\left(\dfrac23\right) = \log_{2/3}\left(\dfrac13\right) \\\\ \implies x = \log_{2/3}\left(\dfrac13\right) \\\\ \implies x = \log_{2/3}\left(3^{-1}\right) \\\\ \implies \boxed{x = -\log_{2/3}(3)}$