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3 years ago

What is the range of the function? Graph in link.

Mathematics

1 answer:

murzikaleks [220]3 years ago

4 0

Answer: Option D: R = {3, 9, 12}

Step-by-step explanation:

The range of a function is the set of the possible outputs of a function:

if we have the function f(x) = y, the values of x are the domain, and the values of y are the range.

In the image, the set at the right is the output, so the set in the right is the range.

such that we have the pairs (-2,3) (2, 3) (3, 9) (4, 12)

So the range will be R = {3, 9, 12}

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does anyone know how to do this. im dumb and need help please i will put 30points if someone actually helps

Oksana_A [137]

Answer:

1 =98

2 = 49

3 = 63

Step-by-step explanation:

Assuming 1 is at the center since it has the dot

<1 = arc 98

<1 = 98

We can find angle 2

<2 = 1/2 the intercepted arc

<2 = 1/2 (98)

<2 = 49

We can find angle 3

Angle formed by 2 chords

<3 = 1/2(arc 70 + arc56)

<3 = 1/2(70+56)

<3 =1/2 (126)

<3 = 63

3 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

3 years ago

Read 2 more answers

LAN mailed a package that weighed 5.63 pounds . what is the first step in rounding this number to the nearest tenth? what is the

ankoles [38]

For this case we must follow the following rules of rounding

1) If the previous number is greater than or equal to five, then the next number increases by one unit

2) If the previous number is less than five, then the next number stays the same

Therefore, the steps for rounding to the nearest tenth is:

1) We observe that 3 is less than 5.

2) Therefore, the next number stays the same

Rounding to the nearest tenth is:

5.6

Answer:

1) We observe that 3 is less than 5.

2) Therefore, the next number stays the same

5.6

7 0

3 years ago

Ratio equivalents to 1:2

nata0808 [166]

2:4 3:6 4:8

Any ratio equals 1:2 as long as you can divide the first number by itself to get 1 and the second number with the 1st number.
Example
2:4
Divide the first number by 2 and you get 1
Divide the second number by 2 and you get 2
So the ratio equals 1:2

Please make me brainliest

3 0

2 years ago

Read 2 more answers

2/5 times 2/3 = what

Luda [366]

Answer:

16/15

Step-by-step explanation:

5 0

3 years ago