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3 years ago

Expand and simplify: 3x(2x-3)^2 - (x+4)

Mathematics

1 answer:

Crazy boy [7]3 years ago

7 0

$3x(2x-3)^2 - (x+4)=\\
3x(4x^2-12x+9)-x-4=\\
12x^3-36x^2+27x-x-4=\\
12x^3-36x^2+26x-4$

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Which is the most reasonable estimate for the depth of a lake: 6 millimeters,6 centimeters, or 6 meters? explain?

aniked [119]

6 meters, both mm and cm are too small to be reasonable, as lakes are deep enough to have boats on and to swim in.

7 0

3 years ago

Triangle ABC is formed by two parallel lines and two other intersecting lines. Find the measure of each angle A, B, and of the t

Mamont248 [21]

Answer:

A = 61°

B = 72°

C = 47°

Step-by-step explanation:

Well, first of all, we can see that:

$61^{\circ}+47^{\circ}+B^{\circ}=180^{\circ}$

So, we can find angle B.

$B=180^{\circ}-47^{\circ}-61^{\circ}$

$B=72^{\circ}$

Now, we can see to that angle C is just 47°

Finally, we know that the sum of all angles in a triangle is 180°, so we have:

$B+A+C=180^{\circ}$

$A=180^{\circ}-47^{\circ}-72^{\circ}$

$A=61^{\circ}$

I hope it helps you!

6 0

3 years ago

The function d(t)=300,000t represents the distance (in kilometers) that light travels in t seconds.

Korolek [52]

Answer:

a. The light travels 4,500,000 kilometers in 15 seconds

b. It takes the light 40 seconds to travel 12 million kilometers

Step-by-step explanation:

- The function d(t) = 300,000 t represents the distance in kilometers

that light travel in t seconds

- We need to find how far the light travels in 15 seconds

∵ d(t) = 300,000 t

∵ t = 15 seconds

- Substitute the value of t in the function above

∴ d(t) = 300,000 (15)

∴ d(t) = 4,500,000 kilometers

The light travels 4,500,000 kilometers in 15 seconds

- We need to find how long does it takes the light to travel 12 million

kilometers

∵ d(t) = 12 million kilometers = 12,000,000 km

∵ d(t) = 300,000 t

- Substitute the value of d(t) in the function

∴ 12,000,000 = 300,000 t

- Divide both sides by 300,000

∴ t = 40 seconds

It takes the light 40 seconds to travel 12 million kilometers

3 0

3 years ago

5x-2y=12 6x+2y=32 find the solution

diamong [38]

Answer:

(4,4)

Step-by-step explanation:

There are two ways that you can solve this. You can solve it with the help of technology or you can solve it traditionally. I will show how to do it in both ways so you can pick which way you want to solve it.

Traditional Method:

5x - 2y = 12

6x + 2y = 32

Look at the variables and numbers in both equations. One of them has to be the same value but have to have opposite signs. The 2y in both equations are the same value but have different signs. That's what we want. We can add everything in the equation now. (5x + 6x), (-2y + 2y), and (12 + 32).

11x = 44

To get x alone, Divide each side by 11. Then we will get the value of x.

11/11x = 44/11

x = 4

Horray! We got x, but what about y? Pick one of the equations. I will go with 5x - 2y = 12. Substitute the x value inside the equation.

5(4) - 2y = 12

20 - 2y = 12

-2y = -8

y = 4

Good! We figured out y. Now we know the solution! The solution is (4,4).

Technology Method:

Grab a graphing calculator. Enter the equations. You will see two lines. Look at where they intersect. The point where they intersect is the solution. That line is (4,4). You could also do this on a piece of paper by graphing the equations.

I hope this helps! Let me know if you need any more help or if I got anything wrong.

3 0

3 years ago

Y varies directly with square root of(x+5) .. . y=4 when x = -1 find y when x=11

velikii [3]

Answer:

y varies as √(x+5)

Step-by-step explanation:

y varies as √(x+5)

y= k√(x+5)

k is a constant connecting the two sides.

therefore

k=y/√(x+5)

k=4/√(-1+5)

k= 4/√4

k=4/2

k=2

Y when x=11

y=k√(x+5)

y=2√(11+5)

y=2√16

y=2*4

y=8

3 0

3 years ago