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liraira [26]
3 years ago
6

Factor the linear expression. 8x+48x+4 Drag the correct parts of the expression into the boxes.  ( + ) 2x4x8x12x01234

Mathematics
1 answer:
Harlamova29_29 [7]3 years ago
5 0
Yhur answer to this question is       4 • (14x + 1) <span>  hope this helped tho</span>
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Find the locus of a point such that the sum of its distance from the point ( 0 , 2 ) and ( 0 , -2 ) is 6.
jok3333 [9.3K]

Answer:

\displaystyle \frac{x^2}{5}+\frac{y^2}{9}=1

Step-by-step explanation:

We want to find the locus of a point such that the sum of the distance from any point P on the locus to (0, 2) and (0, -2) is 6.

First, we will need the distance formula, given by:

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

Let the point on the locus be P(x, y).

So, the distance from P to (0, 2) will be:

\begin{aligned} d_1&=\sqrt{(x-0)^2+(y-2)^2}\\\\ &=\sqrt{x^2+(y-2)^2}\end{aligned}

And, the distance from P to (0, -2) will be:

\displaystyle \begin{aligned} d_2&=\sqrt{(x-0)^2+(y-(-2))^2}\\\\ &=\sqrt{x^2+(y+2)^2}\end{aligned}

So sum of the two distances must be 6. Therefore:

d_1+d_2=6

Now, by substitution:

(\sqrt{x^2+(y-2)^2})+(\sqrt{x^2+(y+2)^2})=6

Simplify. We can subtract the second term from the left:

\sqrt{x^2+(y-2)^2}=6-\sqrt{x^2+(y+2)^2}

Square both sides:

(x^2+(y-2)^2)=36-12\sqrt{x^2+(y+2)^2}+(x^2+(y+2)^2)

We can cancel the x² terms and continue squaring:

y^2-4y+4=36-12\sqrt{x^2+(y+2)^2}+y^2+4y+4

We can cancel the y² and 4 from both sides. We can also subtract 4y from both sides. This leaves us with:

-8y=36-12\sqrt{x^2+(y+2)^2}

We can divide both sides by -4:

2y=-9+3\sqrt{x^2+(y+2)^2}

Adding 9 to both sides yields:

2y+9=3\sqrt{x^2+(y+2)^2}

And, we will square both sides one final time.

4y^2+36y+81=9(x^2+(y^2+4y+4))

Distribute:

4y^2+36y+81=9x^2+9y^2+36y+36

The 36y will cancel. So:

4y^2+81=9x^2+9y^2+36

Subtracting 4y² and 36 from both sides yields:

9x^2+5y^2=45

And dividing both sides by 45 produces:

\displaystyle \frac{x^2}{5}+\frac{y^2}{9}=1

Therefore, the equation for the locus of a point such that the sum of its distance to (0, 2) and (0, -2) is 6 is given by a vertical ellipse with a major axis length of 3 and a minor axis length of √5, centered on the origin.

5 0
3 years ago
Read 2 more answers
which descriptions from the list below describe the relationship between xyz and uvw check all that apply
Cloud [144]

Answer:

similar and same shape.

Step-by-step explanation:

3 0
2 years ago
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The number of hours, h, that Mr. Hampton works varies directly with the number of tasks, t, he has to perform. If he has 6 tasks
olga2289 [7]

i think its 2.5 because 15/6= 2.5 so 2.5t=h and the equation is kt=h so 2.5 makes the most sense.

I hope this helps

4 0
2 years ago
Mr. Peter's has 80 sheets of colored paper. Seven of his students need the paper for a project. How many sheets does each studen
Julli [10]

Answer:

Each student gets 11 pieces.

Step-by-step explanation:

80 ÷ 7 = 11.42857

80 divided by 7 comes out to a decimal therefore, you will have a remainder. 7 × 11 = 77

The answer would be 11 remainder 3.

8 0
3 years ago
Multiply the polynomials.
slavikrds [6]
<span>(x + 3)(x² – 6x + 5)= x³-6x²+5x+3x²-18x+15 =x³ -3x²-13x+15 Answer B</span>
4 0
2 years ago
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