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4 years ago

5

There are 6 gray keys for every seven blue keys write the possible ratios for gray to black keys

1 answer:

mariarad [96]4 years ago

6 0

6:7 I'm pretty sure. Are there any options?

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A bike was originally $102 and is on sale for 30% off. what is the discounted priice

Anvisha [2.4K]

Answer:

$71.4

Step-by-step explanation:

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3 years ago

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Campbell Middle school has 912 students.How many computers are in this schools computer lab?

Aleksandr [31]

You can't really determine the amount of computers from this question, they're obviously not going to have one computer for everyone so half third, or even a fourth of the school population

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3 years ago

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In the given figure, identify a pair of perpendicular lines.

nexus9112 [7]

Answer:

A

Step-by-step explanation:

The two lines cross the others path to form a right angle.

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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:

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

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3 years ago

0.27 ? 0.3<br><br><<br>><br>=<br>which one is it????

Ira Lisetskai [31]

Answer:

<

Step-by-step explanation:

0.27 is less than 0.3. < is the less than symbol because the "mouth" is pointing towards to the larger number.

6 0

3 years ago

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