Sau 18 tháng, số tiền nợ cả gốc lẫn lãi phải trả là $5200. Số tiền gốc là bao nhiêu nếu lãi suất đơn là 8%/năm?

It takes printer A 4 more minutes than printer B to print 40 pages. If working together, the two printers can print 50 pages in

Anastaziya [24]

Answer:

It will take printer A 24 minutes to print 80 pages.

Step-by-step explanation:

It takes printer A 4 more minutes than printer B to print 40 pages.

Let the time it takes printer B be x minutes, since printer A prints at 4 minutes more, it prints at (x + 4) minutes.

Printer A prints at the rate of (40/(x+4)) pages per minute.

Printer B prints at the rate of (40/x) pages per minute.

If working together, the two printers can print 50 pages in 6 minutes

They can print at the rate of 50 pages per 6 minutes, if working together.

Let us add these ratios, the

40/(x + 4) + 40/x = 50/6

Divide by 40

1/(x + 4) + 1/x = 5/24

(x + x + 4)/x(x + 4) = 5/24

2x + 4 = (5/24)(x² + 4x)

48x + 96 = 5x² + 20x

5x² - 28x - 96 = 0

Solving this using the quadratic formula,

x = [-b ± √(b² - 4ac)]/2a

a = 5, b = -28, and c = -96

x = [28 ± √(784 + 1920)]/10

= 28/10 ± √(2704)/10

= 28/10 ± 52/10

x = (28+52)/10 = 80/10 = 8

Or

x = (28 - 52)/10 = -24/10 = -2.4

So, x is either 8 or -2.4

Since we are dealing with time, the realistic value is the positive value, x = 8, then we choose x = 8 minutes.

It takes printer A (x + 4) minutes to print 40 pages.

x + 4 = 12 minutes.

So, it takes it 12 minutes to print 40 pages.

Easily, it will take it twice as much time to print 80 pages.

So, it will take it 24 minutes to print 80 pages.

5 0

3 years ago

A chemist has 200 mL of a 10% sucrose solution. She adds x mL of a 40% sucrose solution. The percent concentration, y, of the fi

user100 [1]

Answer:

The chemist needs to add 400mL of 40% solution.

Step-by-step explanation:

The equation

$y=\frac{0.1(200)+0.4x}{200+x} *100$

gives the percent concentration $y$ of the final mixture, when $x$ mL of the 40% solution are added.

Now we are asked, how many milliliters $x$ of the 40% solution should the chemist add to get final percent concentration $y=30$ ; this is just a matter of solving the equation

$30=\frac{0.1(200)+0.4x}{200+x} *100$

and we solve it the following way:

$30=\frac{0.1(200)+0.4x}{200+x} *100\\\\0.3 =\frac{0.1(200)+0.4x}{200+x}\\\\0.3(200+x)=0.1(200)+0.4x\\\\60+0.3x=20+0.4x\\\\40=0.1x\\\\x=\frac{40}{0.1} \\\\\boxed{x=400\:mL}$

Thus, the chemist needs 400mL of 40% solution to get 30% concentration of the final mixture.

7 0

4 years ago

Ariel swims 2 1/6 miles in every 1/3 hour.Enter the number of miles Ariel swims in 1 hour.

VLD [36.1K]

Answer:

6.5 miles

Step-by-step explanation:

If she travels 2 1/6 in 1/3 hours you would simply multiply by 3 because she would need to travel 2 1/6 miles three times in order for an hour to pass.

7 0

3 years ago

No files please! thanks

BigorU [14]

Answer:

y = $-\frac{1}{3}$

$2\frac{2}{3}=x$

Step-by-step explanation:

To solve a system of equations, solve one or both of the equations for the same variable. Then multiply one of the equations such that the coefficients of one variable are the additive inverse of the variable in the other equation. After doing so, add the two equations, then solve for the other variable using inverse operations. Finally, substitute the value of the other variable into one of the original equations in the system and solve for the unknown variable.

2x + y = 3

y = x - 2

First, manipulate the first equation such that the equation is solved for (y), this can be done using inverse operations,

y = 3 - 2x

y = x - 2

Now multiply the second equation by (2) so that the (x) coefficients are additive inverses of each other,

y = 3 - 2x

2y = 2x - 4

Add the equations,

3y = -1

Inverse operations,

3y = -1

/3 /3

y = $-\frac{1}{3}$

Now back solve, substitute the value of (y) into the equation and solve for (x),

$y=x-3\\$

Substitute,

$(-\frac{1}{3})=x-3$

+3

$2\frac{2}{3}=x$

5 0

3 years ago

Show that (5x-7)2 +140x=(5x+7)2

zhannawk [14.2K]

(5x-7)2 + 140x
= 25x2 - 70x + 14 + 140x
= 25x2 + 70x + 14
= (5x+7)2

8 0

3 years ago