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monitta
3 years ago
15

Solve the equation without the use of a calculator. please Help!!! Thank you!!! 12x^3-30x=5-2x^2

Mathematics
1 answer:
nata0808 [166]3 years ago
4 0

So, since we have a cubic equation with 4 terms, the first thing we should try is factoring by grouping, so:

12x^3+2x^2-30x+5 =0 \implies \\ 2x^2(6x+1)-5(6x+1)=0 \implies \\ (2x^2-5)(6x+1) = 0

Now that we've factored our equation, we can use ZPP and break it up:

2x^2-5 = 0 \implies \\ 2x^2=5 \implies\\ x^2=\frac{5}{2} \implies\\ x=\pm\frac{\sqrt{5}}{\sqrt{2}}=\pm\frac{\sqrt{10}}{2} \\ \\ 6x+1 =0 \implies \\ 6x=-1 \implies\\ x=\frac{-1}{6}

So, our solutions are:

x\in \{\frac{\sqrt{10}}{2},-\frac{\sqrt{10}}{2},-\frac{1}{6}\}

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An archaeologist at a dig sets up a coordinate system using string. Two similar artifacts are found one at position (1, 4) and t
myrzilka [38]

Given:

Positions of two artifacts are at points (1, 4) and (5, 2).

To find:

The distance between these two artifacts.

Solution:

Distance formula: The distance between two points is

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Using distance formula, the distance between two points (1, 4) and (5, 2) is

d=\sqrt{(5-1)^2+(2-4)^2}

d=\sqrt{(4)^2+(-2)^2}

d=\sqrt{16+4}

d=\sqrt{20}

d=4.4721359

Round to the nearest tenth of a unit.

d\approx 4.5

Therefore, the distance between two artifacts is 4.5 units.

4 0
2 years ago
What is the solution to this equation x-16=-8
arsen [322]
X-16=-8
Add 16 on both sides 
x=-8+16
And solve; your answer will be
x=8
3 0
3 years ago
Solve the equation and explain each step using apropriate Properties<br> -4(3x+6)+6=-30
Lina20 [59]

Answer:

The answer is x=1

Step-by-step explanation:

-4(3x+6)+6=-30

-12x-24+6=-30

-12x-18=-30

-12x-18+18=-30+18

-12x=-12

-12x/-12=-12/-12

x=1

6 0
2 years ago
Find the measure of &lt;BAC​
Orlov [11]

Answer:

56 degrees

Step-by-step explanation:

6 0
2 years ago
A person is standing 200ft from a tower. She can see the top of the tower at a 42 degree angle of elevation. Her eyes are 5ft ab
Oxana [17]

Answer:

C. 185 ft

Step-by-step explanation:

The work is in the attached picture file, if you need it. Basically the question sets up a right triangle, for which the base is 200 and the height is the goal that you are solving for. It is given that the angle between hypotenuse and base is 42 degrees. For this you use tangent to say that

         tan(42) = h / 200

         200 tan (42) = h

         h = 180 feet.

But then you must remember that this triangle starts 5 feet off of the ground. So you add the 5 feet and get 185 feet as the height of the tower.

6 0
2 years ago
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