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sweet [91]
3 years ago
6

2 - 2n = 3n + 17 solve n

Mathematics
1 answer:
Masja [62]3 years ago
4 0

Answer:

n = -3

Step-by-step explanation:

2 - 2n = 3n + 17

-2                -2

-2n = 3n + 15

-3n    -3n

<u>-5n = 15</u>

-5       -5

n = -3


Hope this helps you!!! :)

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0.884 in standard form
Arada [10]

Answer:

8.84×10⁻

Step-by-step explanation:

To write a number in standard form we need to write down a number between 1 and 10, then × 10(to the power of a number). Therefore, the standard form of 0.884 is ¹.8.84×10⁻.

Have a great day

7 0
3 years ago
Let $A = (4,-1)$, $B = (6,2)$, and $C = (-1,2)$. There exists a point $X$ and a constant $k$ such that for any point $P$,
goldfiish [28.3K]

Answer:

k=32

Step-by-step explanation:

Given the points:

A = (4,-1)$, $B = (6,2)$, and $C = (-1,2)$.

The first step is to find the <u>Centroid</u> of the triangle.

Centroid, X

=\left(\dfrac{x_1+x_2+x_3}{3} ,\dfrac{y_1+y_2+y_3}{3} \right)\\=\left(\dfrac{4+6+(-1)}{3} ,\dfrac{-1+2+2}{3} \right)\\=\left(\dfrac{9}{3} ,\dfrac{3}{3} \right)=(3,1)

Next, let P be a point (x,y)

Using the <u>distance formula, </u>\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}<u />

<u />PA^2=(x-4)^2+(y-(-1))^2\\PB^2=(x-6)^2+(y-2)^2\\PC^2=(x-(-1))^2+(y-2)^2\\PX^2=(x-3)^2+(y-1)^2\\<u />

On Substitution into: PA^2 + PB^2 + PC^2 = 3PX^2 + k

(x-4)^2+(y-(-1))^2+(x-6)^2+(y-2)^2+(x-(-1))^2+(y-2)^2=3[(x-3)^2+(y-1)^2]+k

Let us simplify the LHS first

\\LHS: x^2-8x+16+y^2+2y+1+x^2-12x+36+y^2\\-4y+4+x^2+2x+1+y^2-4y+4\\=3x^2-18x+3y^2-6y+62

Also, the Right Hand Side

RHS:3[(x-3)^2+(y-1)^2]+k\\=3[x^2-6x+9+y^2-2y+1]+k\\=3x^2-18x+27+3y^2-6y+3+k\\=3x^2+3y^2-18x-6y+30+k

Therefore:

3x^2-18x+3y^2-6y+62=3x^2+3y^2-18x-6y+30+k\\k=3x^2-18x+3y^2-6y+62-3x^2-3y^2+18x+6y-30\\k=3x^2-3x^2+3y^2-3y^2-18x+18x+62-30\\k=32

7 0
3 years ago
Question 2 (1 point)<br> What is the value of x if AABC is equilateral?
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Answer:

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Step-by-step explanation:

Given that,

AB = 7.5x

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ΔABC is an equilateral triangle.For an equilateral triangle, all sides are equal. ATQ,

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Taking like terms together

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Hence, the value of x is equal to 2.

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What is the measurement of the angle x ?
kogti [31]

Answer:

62 degrees

Step-by-step explanation:

180 = x + 118

180 - 118 = x

62 = x

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4 years ago
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