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4 years ago

Do the ratios 8/50 and 4/10 form a proportion

1 answer:

7 0

Cross multiply:
8 * 10 = 50 * 4

Simplifying
8 * 10 = 50 * 4

Multiply 8 * 10
80 = 50 * 4

Multiply 50 * 4
80 = 200

Solving
80 = 200

Couldn't find a variable to solve for.

This equation is invalid, the left and right sides are not equal, therefore there is no solution

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A chemist wants to make 100 liters of a 44% acid solution. She has solutions that are 20% acid and 60% acid.

alexgriva [62]

the first solution is 20% acid, and say we'll be using "x" liters, so how many liters of just acid are in it? well 20% of "x" or namely 0.2x. Likewise for the 60% acid solution, if we had "y" liters of it, the amount of only acid in it is 0.6y.

$\begin{array}{lcccl} &\stackrel{solution}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{liters of }}{amount}\\ \cline{2-4}&\\ \textit{1st solution}&x&0.20&0.2x\\ \textit{2nd solution}&y&0.60&0.6y\\ \cline{2-4}&\\ mixture&100&0.44&44 \end{array}~\hfill \begin{cases} x+y=100\\\\ 0.2x+0.6y=44 \end{cases}$

$x+y=100\implies y=100-x~\hfill \stackrel{\textit{substituting on the 2nd equation}}{0.2x+0.6(100-x)=44} \\\\\\ 0.2x+60-0.6x=44\implies -0.4x+60=44\implies -0.4x=-16 \\\\\\ x=\cfrac{-16}{-0.4}\implies \boxed{x=40}~\hfill \boxed{\stackrel{100-40}{y=60}}$

7 0

2 years ago

Tell whether the ratios form a proportion.

qaws [65]

5:16 is no
24:15 is no
3:12 is yes

3 0

3 years ago

What is the linear function equation represented by the graph?

igor_vitrenko [27]

Look at the picture.

The point-slope form of a line:

$y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (0, 1) and (2, 0). Substitute:

$m=\dfrac{0-1}{2-0}=\dfrac{-1}{2}=-\dfrac{1}{2}\\\\y-1=-\dfrac{1}{2}(x-0)\\\\y-1=-\dfrac{1}{2}x\qquad|+1\\\\y=-\dfrac{1}{2}x+1$

Answer: $f(x)=-\dfrac{1}{2}x+1$

5 0

3 years ago

Mary is 5 years older than bob. If the sum of their ages is 39 write and solve an equation to find ages. Please help me with a c

nikdorinn [45]

5x=39 x stands for the age of bob so 39/5 =7.8 which is rounded up to 8 and if you multiply 8 by 5 you get 40 but if you multiply 7.8 by 5 you get 39 so his age would be 7.8 years old.

4 0

3 years ago

Read 2 more answers

What does n = in 10=6+n/2

Pani-rosa [81]

Answer:

n = 8

Step-by-step explanation:

10=6+n/2

Switch sides

6 + n/2 = 10

Subtract 6 from both sides

6 + n/2 -6 = 10-6

Simplify

n/2 = 4

Multiply both sides by 2

2n/2 = 4 times 2

n = 8

Hope this helps!

8 0

3 years ago