Given that a solution containing 12% alcohol is to be mixed with a solution containing 4% alcohol to make 20 gallons of solution containing 9% alcohol.

Let x gallons of 12% alcohol be mixed with y gallons of 4% alcohol.

Total gallons $= x+y = 20$

Alcohol content in the total mixture $= 0.12x+0.04y =9% of x+y$

$0.12x+0.4y=0.09(20)\\12x+4y = 180$

b) Two equations are

$x+y = 20\\12x+4y = 180$

c) This is of the form Ax = B

where A = $\left[\begin{array}{ccc}1&1\\12&4\end{array}\right]$

Inverse is $\frac{1}{4-12} \left[\begin{array}{ccc}4&-1\\-12&12\end{array}\right]\\=\frac{-1}{8} \left[\begin{array}{ccc}4&-1\\-12&12\end{array}\right]\\$

Solution set is A inverse *B

= $x \ 12.5\\y \ 7.5$

7 0

3 years ago

Can someone pls answer 150 divided by 30

Svetlanka [38]

Answer:

Step-by-step explanation:

150/30 = 15/3 = 5

Good luck!

4 0

3 years ago

Read 2 more answers

Any volunteer please help

den301095 [7]

Answer:

Part A)

The equation in the point-slope form is:

$y-11=\frac{4}{3}\left(x-\left(-2\right)\right)$

Part B)

The graph of the equation is attached below.

Step-by-step explanation:

Part A)

Given

The point = (-2, 11)

m = 4/3

The point-slope form of the line equation is

$y-y_1=m\left(x-x_1\right)$

Here, m is the slope and (x₁, y₁) is the point

substituting the values m = 4/3 and the point (-2, 11) in the point-slope form of the line equation

$y-y_1=m\left(x-x_1\right)$

$y-11=\frac{4}{3}\left(x-\left(-2\right)\right)$

Thus, the equation in the point-slope form is:

$y-11=\frac{4}{3}\left(x-\left(-2\right)\right)$

Part B)

As we have determined the point-slope form which passes through the point (-2, 11) and has a slope m = 4/3

The graph of the equation is attached below.

5 0

3 years ago

Elizabeth lives in San Francisco and works in Mountain View. In the morning, she has 3 transportation options (take a bus, a cab

Lesechka [4]

Answer:

4/9

Step-by-step explanation:

The possibilities of transportation: (The first will be for morning, second will be for afternoon)

B, B

B, C

B, T

C, B

C, C

C, T

T, B

T, C

T, T

It is clearly seen that there are 9 transportation options.

(Using cab 1 time we have BC, CB, CT, TC. So four of the transportation methods use cab one time.)

Therefore, the probability that she will use a cab only once is 4/9.

6 0

3 years ago

One number is 4 times another number and their product is 64. How would that be written in equation form?​

One number is 4 times another number and their product is 64. How would that be written in equation form?