This is why brainly is lame

If four desk lamps cost $120 what is the average cost per lamp?

Nookie1986 [14]

$30 each. Unless that's not the answer you are looking for.

8 0

2 years ago

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Simplify this expression (a^8a^6)^1/7/a^2

ArbitrLikvidat [17]

Answer: 1

Step-by-step explanation: Whenever you take the power of a power, the find the answer you can multiply the two exponents, for example:

(x^3)^4 = x^12

We will use that here.

a^8a^6 = a^14

((a^14)^1/7) = (a^2)/a^2

Our answer is 1

7 0

3 years ago

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

2 years ago

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Select the reason why these triangles are

Elden [556K]

Answer:

B. SAS

Step-by-step explanation:

In the given diagram, it would be observed that each side of the bigger triangle are multiplied by a factor of $\frac{1}{3}$ to give the values of each corresponding sides of the smaller triangle. But the included angle of the two triangles are the same.

Therefore, the reason why the triangles are similar is because of side-angle-side (SAS) relations. The correct option is B.

4 0

3 years ago

In 2003 the population of Africa was about 7.7 million people which is 2million more than 3 times the population in 1950

shtirl [24]

The answer to the question is 1.9 million in 1950.

5 0

2 years ago