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3 years ago

A line segment's measurement(s) include which of the following?

Mathematics

1 answer:

Effectus [21]3 years ago

7 0

Answer:

D. Length

Step-by-step explanation:

We measure the length of a line segment, and thus, the correct answer is given by option D.

The length of a line segment is the distance between it's endpoints, using the formula for the distance between two points given below.

Distance between two points:

Suppose that we have two points, $(x_1,y_1)$ and $(x_2,y_2)$ . The distance between them is given by:

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

You might be interested in

Which of the following is a solution to the equation x - 5/7 = -3/7

podryga [215]

Solve the equation:

      5       3
x – —— = – ——
      7       7

   5
Add —— to both sides, so you get x isolated at the left-hand side:
   7

      5       5       3 5
x – —— + —— = – —— + ——
      7        7           7       7

          3 5
x = – —— + ——
      7    7

Now, add those fractions at the right-hand side of the equation:

          – 3 + 5
x = —————
         7

        2
x = ——    <——— this is the answer (first option: 2/7).
        7

I hope this helps. =)

8 0

3 years ago

Use the coordinate plane to help you identify the length of each leg then use the Pythagorean Theorem to find the length of CD

Nitella [24]

Answer:

CE= 9cm, DE= 5cm, CD= 10.2956cm

Step-by-step explanation:

Let E be the point of the other triangle.

Using Pythagoras' Theorem,

CD= square root symbol (CE^2 + DE^2)

= square root symbol (9^2+5^2)

= 10.2956cm (6 sf)

7 0

2 years ago

EXAMPLE 5 Find the maximum value of the function f(x, y, z) = x + 2y + 9z on the curve of intersection of the plane x − y + z =

geniusboy [140]

The Lagrangian,

$L(x,y,z,\lambda,\mu)=x+2y+9z-\lambda(x-y+z-1)-\mu(x^2+y^2-1)$

has critical points where its partial derivatives vanish:

$L_x=1-\lambda-2\mu x=0$

$L_y=2+\lambda-2\mu y=0$

$L_z=9-\lambda=0$

$L_\lambda=x-y+z-1=0$

$L_\mu=x^2+y^2-1=0$

$L_z=0$ tells us $\lambda=9$ , so that

$L_x=0\implies-8-2\mu x=0\implies x=-\dfrac4\mu$

$L_y=0\implies11-2\mu y=0\implies y=\dfrac{11}{2\mu}$

Then with $L_\mu=0$ , we get

$x^2+y^2=\dfrac{16}{\mu^2}+\dfrac{121}{4\mu^2}=1\implies\mu=\pm\dfrac{\sqrt{185}}2$

and $L_\lambda=0$ tells us

$x-y+z=-\dfrac4\mu-\dfrac{11}{2\mu}+z=1\implies z=1+\dfrac{19}{2\mu}$

Then there are two critical points, $\left(\pm\frac8{\sqrt{185}},\mp\frac{11}{\sqrt{185}},1\pm\frac{19}{\sqrt{185}}\right)$ . The critical point with the negative $x$ -coordinates gives the maximum value, $9+\sqrt{185}$ .