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3 years ago

Solve ? -4-4(-x-1)=-4(6+2x)

Mathematics

1 answer:

soldier1979 [14.2K]3 years ago

7 0

$-4-4(-x-1)=-4(6+2x)\\\\-4+4x+4=-24-8x\\\\4x=-24-8x \ \ /+8x\\\\12x=-24 \ \ /:12\\\\\huge\boxed{x=-2}$

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A loan company charges $30 interest for a one month loan of $500. Find the annual interest they are charging

xz_007 [3.2K]

Answer:

$360

Step-by-step explanation:

If the company charges $30 for $500 in one month.

The interest they will be changing for a year = 30*12 = $360 interest.

It's just simple, multipling the the interest value by 12 to get it's annual interest value.

4 0

4 years ago

A tank is filled at a constant rate. 10 minutes after filling is started, the tank contains 4.8L of water. After 35 minutes the

Mashcka [7]

Answer:

Part A)

0.1 liters per minute.

Part B)

There was initially 3.8 liters of water.

$\displaystyle V(t) = 0.1(t - 10) + 4.8$

Part C)

562 minutes.

Step-by-step explanation:

A tank is filled at a constant rate. After 10 minutes, the tank contains 4.8 L of water and after 35 minutes, the tank contains 7.3 L of water.

Part A)

We can represent the current data with two points: (10, 4.8) and (35, 7.3). The x-coordinate is measured in minutes since the tank began to be filled and the y-coordinate is measured in how full the tank is in liters.

To find the rate at which the tank is being filled, find the slope between the two points:

$\displaystyle m = \frac{\Delta y}{\Delta x} = \frac{(7.3)-(4.8)}{(35)-(10)} = \frac{2.5}{25} = 0.1$

In other words, the rate at which the tank is being filled is 0.1 liters per minute.

Part B)

To find the function of the volume of the tank, we can use the point-slope form to first find its equation:

$\displaystyle y - y_1 = m( x - x_1)$

Where m is the slope/rate of change and (x₁, y₁) is a point.

We will substitute 0.1 for m and let (10, 4.8) be the point. Hence:

$\displaystyle y - (4.8) = 0.1(x - 10)$

Simplify:

$\displaystyle y = 0.1(x-10) + 4.8$

Since y represent how full the tank is and x represent the time in minutes since the tank began to be filled, we can substitute y for V(t) and x for t. Thus, our function is:

$\displaystyle V(t) = 0.1(t - 10) + 4.8$

The initial volume is when t = 0. Evaluate:

$\displaystyle V(0) = 0.1 ((0) - 10) + 4.8 = 3.8$

There was initially 3.8 liters of water.

Part C)

To find how long it will take for the tank to be completely filled given its maximum capacity of 60 liters, we can let V(t) = 60 and solve for t. Hence:

$60 = 0.1(t - 10) + 4.8$

Subtract:

$55.2 = 0.1(t - 10)$

Divide:

$552 = t - 10$

Add. Therefore:

$t = 562\text{ minutes}$

It will take 562 minutes for the tank to be completely filled.

8 0

3 years ago

Slope of (-20,9) (14,9)

skelet666 [1.2K]

Y2-y1/x2-x1 is slope so

9-9/14-(-20) so you get 0/34 which means there is no slope since they have the same y (the equation would be y=0x+9 therefore y=9)
Which makes sense since the equation is a straight line

3 0

3 years ago

Determine the length of GH. Round to the nearest tenth. 3.9 cm G 52 642 H

sesenic [268]

Answer:

|GH| = 5,7 cm

Step-by-step explanation:

To know |GH|, you first need to find the length of |GD|.

We can calculate |GD| by;

cosG = |GC| / |GD|

<=> |GD| = |GC| / cosG

=> |GD| = 3,9 cm/ 0,62 = 6,33 cm

We now can easily calculate |GH| with the sinus of angle D;

sinD = |GH| / |GD|

<=> |GH| = sinD.|GD|

=> |GH| = 0,899.6,33 cm = 5,694 cm => 5,7 cm

I hope i did not make a mistake ...

5 0

3 years ago

For the following right triangle, find the side length x.

never [62]

Answer:

x = 10

Explanation:

Using Pythagoras Theorem:

a² + b² = c²

Solve:

8² + 6² = x²

x² = 64 + 36

x² = 100

x = √100

x = 10

8 0

2 years ago

Read 2 more answers

Solve ? -4-4(-x-1)=-4(6+2x)​

Solve ? -4-4(-x-1)=-4(6+2x)