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Karo-lina-s [1.5K]
3 years ago
12

What is 3/4 of 16/21? worked out please

Mathematics
1 answer:
timofeeve [1]3 years ago
5 0
Of means multiplication

So

\frac{3}{4} \sf{of}  \frac{16}{21}  =  \frac{3}{4} \times  \frac{16}{21}

And then simplify the numerator ad denominator

= \frac{3 \times 16}{4 \times 21} =  \frac{\ 1 \times 16}{4 \times 7}

And simplify the numerator and denominator again

= \frac{\ 1 \times 16}{4 \times 7} = \frac{\ 1 \times 4}{1 \times 7}

And we are finally left with the answer which is \frac{4}{7}
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Dan has five times as many $1 bills as $5 bills. he has a total of 48 bills. how many of each does he have?
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NO LINKS!! Use the method of substitution to solve the system. (If there's no solution, enter no solution). Part 11z​
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Answer:

(x,y)=\left(\; \boxed{-1,-8} \; \right)\quad \textsf{(smaller $x$-value)}

(x,y)=\left(\; \boxed{5,16} \; \right)\quad \textsf{(larger $x$-value)}

Step-by-step explanation:

Given system of equations:

\begin{cases}y=x^2-9\\y=4x-4\end{cases}

To solve by the method of substitution, substitute the first equation into the second equation and rearrange so that the equation equals zero:

\begin{aligned}x^2-9&=4x-4\\x^2-4x-9&=-4\\x^2-4x-5&=0\end{aligned}

Factor the quadratic:

\begin{aligned}x^2-4x-5&=0\\x^2-5x+x-5&=0\\x(x-5)+1(x-5)&=0\\(x+1)(x-5)&=0\end{aligned}

Apply the <u>zero-product property</u> and solve for x:

\implies x+1=0 \implies x=-1

\implies x-5=0 \implies x=5

Substitute the found values of x into the <u>second equation</u> and solve for y:

\begin{aligned}x=-1 \implies y&=4(-1)-4\\y&=-4-4\\y&=-8\end{aligned}

\begin{aligned}x=5 \implies y&=4(5)-4\\y&=20-4\\y&=16\end{aligned}

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1 year ago
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