All categories

3 years ago

Line segment YV of rectangle YVWX measures 24 units.

Mathematics

2 answers:

oksian1 [2.3K]3 years ago

7 0

Answer: $YX=13.85\ units$

Step-by-step explanation:

<h3> The complete exercise is: "Line segment YV of rectangle YVWX measures 24 units. What is the length of line segment YX?"</h3><h3> The missing figure is attached.</h3>

Since the figure is a rectangle, you know that:

$WV=YX\\\\YV=XW=24$

Notice that the segment YV divides the rectangle into two equal Right triangles.

Knowing the above, you can use the following Trigonometric Identity:

$tan\alpha =\frac{opposite}{adjacent}$

You can identify that:

$\alpha =30\°\\\\opposite=YX\\\\adjacent=YV=24$

Therefore, in order to find the length of the segment YX, you must substitute values into $tan\alpha =\frac{opposite}{adjacent}$ and then you must solve for YX.

You get that this is:

$tan(30\°)=\frac{YX}{24}\\\\(24)(tan(30\°))=YX\\\\YX=13.85$

Nikitich [7]3 years ago

5 0

Answer:

8 StartRoot 3 EndRoot units

You might be interested in

Find the standard form of the equation of the parabola with a focus at (0, 8) and a directrix at y = -8

Gekata [30.6K]

First, let $(x,y)$ be a point in our parabola. Since we know that the focus of our parabola is the point (0,8), we are going to use the distance formula to find the distance between the two points:
$\sqrt{(x-0)^{2}+(y-8)^{2}}$

Next, we are going to find the distance between the directrix and the point in our parabola. Remember that the distance between a point (x,y) of a parabola and its directrix, $y=c$ , is: $|y-c|$ . Since our directrix is y=-8, the distance to our point will be:
$|y-(-8)|$
$|y+8|$

Now, we are going to equate those two distances, and square them to get rid of the square root and the absolute value:
$\sqrt{(x-0)^{2}+(y-8)^{2}}=|y+8|$
$(\sqrt{(x-0)^{2}+(y-8)^{2}})^{2}=|y+8|^{2}$
$(x-0)^{2}+(y-8)^{2}=y+8$

Finally, we can expand and solve for $y$ :
$x^2+y^2-16y+64=y^2+16y+64$
$x^{2}-16y=16y$
$32y=x^{2}$
$y= \frac{1}{32} x^2$

We can conclude that t<span>he standard form of the equation of the parabola with a focus at (0, 8) and a directrix at y = -8 is </span> $y= \frac{1}{32} x^{2}$

3 0

2 years ago

Please show your work

Natasha_Volkova [10]

Answer:

X is equal to 4

5 0

2 years ago

If there are 120 calories in 4 ounces of hot fudge, how many calories are in 8

miss Akunina [59]

Answer:

240 calories

Step-by-step explanation

You're doubling the amount of fudge, so double the amount of calories. You could also think of it as 2 4-oz portions of fudge, then just add the calories (120+120) together.

3 0

3 years ago

The graph of the function f(x) = -(x+3)(x - 1) is shown below. What is true about the domain and range of the function? у The do

Nataly_w [17]

Answer:

The domain will be all real numbers, range will be all real numbers below -3

Step-by-step explanation:

its quadratic so it goes forever left and right. but the vertex has a y value of -3. It is a negative sloped graph, so anything below that is in the range

5 0

3 years ago

How many year apart is 384 BC from 1952 AD

julsineya [31]

BC and BCE are Before Common Era
So what you want to do is add 1952 and 384
1952 + 384 = 2336
So the amount of years between 384 BC and 1952 AD is about 2,336 years
Hope this helps

6 0

3 years ago

Read 2 more answers