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3 years ago

Two angles that add up to 90° are called SUPPLEMENTARY angles. TRUE OR FALSE

Mathematics

1 answer:

svet-max [94.6K]3 years ago

3 0

Answer:

This is FALSE. Two supplementary angles add up to 180 degrees.

Step-by-step explanation:

Hope this helped! :-)

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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

What are means of 8/3 = 2/n

Alexus [3.1K]

Answer:

8/3=2/0.75

Step-by-step explanation:

The variable that you are looking for should be the simplified version of the number on the left.

That is where the 2 would come in. Both numbers should be divided by 4 to gat the answer.

8÷4 = 2

3÷4=0.75

5 0

3 years ago

Name two solutions for each inequality.

ahrayia [7]

So,

#1: $n \geq 3 \frac{11}{16} + 4 \frac{1}{2}$

Convert to like improper fractions.
$n \geq \frac{59}{16} + \frac{72}{16}$

Add.
$n \geq \frac{131}{16}\ or\ 8 \frac{3}{16}$

So, one solution could be $8 \frac{3}{16}$ .

Another solution could by 9. There is also 10, 11, 12, etc., and all numbers in between.

#2: $k \ \textless \ 6 \frac{2}{5} * 15$

Convert into improper fraction form.
$k \ \textless \ \frac{32}{5} * 15$

Multiply.
$\frac{(2^5)(3)(5)}{5}$

Cross-cancel, and we have our final result.
$(2^5)(3) = 96$
k < 96

96 is not a solution.

95 is a solution.

So is 94, 93, 92, etc, and all numbers in between.

6 0

3 years ago

2 3/4+1 1/5 i need this for math, im kinda stupid, please dont anwser if you dont know its for a test XD

Oksi-84 [34.3K]

Answer:

3 19/20

Step-by-step explanation:

So...

The first step is to find a common denominator between the 2. The smallest common denominator is 20. So you would do 3/4 times 5/5 which is 15/20. (2 15/20)

1/5 times 4/4 = 4/20(1 4/20)

So the final step is to add them together

2 15/20 + 1 4/20= 3 19/20.

This is the most simplified answer you can get.

5 0

3 years ago

Explain how you could calculate the surface area of a square pyramid.

Damm [24]

Find the area of the base of the pyramid, then find the area of each side then add the areas. hope this help :)

6 0

3 years ago

Read 2 more answers