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3 years ago

Instructions: Find the missing length indicated.

Mathematics

1 answer:

nata0808 [166]3 years ago

8 0

Answer:

x = 12

Step-by-step explanation:

By applying geometric root theorem in the given triangle,

$\frac{BD}{DC}= \frac{AD}{BD}$

$BD^2=AD\times DC$

$x^{2} =16\times 9$

$x=\sqrt{144}$

$x=12$

Therefore, x = 12 will be the answer.

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Find the value of x.<br> 28°

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3 years ago

Three cars are driving on a racetrack. The mean speed of the three cars is 100 miles per hour. Car X drives 101 miles per hour a

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Answer:

Less than 100. Z=83

Step-by-step explanation:

The mean is the average found by adding the sum of the data points and dividing by the number of them. Here there are 3 cars whose speeds are 101, 116, and Z or unknown. The mean of them is 100. Solve for Z.

100 =(101+116+Z)/3

300=217+Z

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3 years ago

Emma is 14 years younger than twice fred age. Emma is 34. How old is fred

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Answer:

24 years old

Step-by-step explanation:

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3 years ago

Read 2 more answers

Eliza bought 2 2/4 yards of fabric. She cut off 3/4 yards to make an art project. What fraction offabric is left?

mina [271]

Answer:

7/4 or 1 3/4

Step-by-step explanation:

Think of 2 2/4 to be 10/4 because you need to multiply the 2 to the 4 which makes 8 and then add 2 to get 10/4.

When you get 10/4 subtract it with 3/4 to get 7/4.

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3 years ago

Find the area of the triangle with the given vertices. Use the fact that the area of the triangle having u and v as adjacent sid

Gnom [1K]

Answer:

The area of the triangle is $A=\sqrt{\frac{4027}{2}}$

Step-by-step explanation:

Using the fact that the area of the triangle having u and v as adjacent sides is given by

$A=\frac{1}{2}||{\bf u} \times {\bf v} ||$

We know that we want to take a cross product to compute the area of the triangle, but we need to be careful because it doesn't make sense if we take the cross product of points.

The first step is to build some vectors that describe this triangle.

According with the graph we can build the vectors:

${\bf AB}$ and ${\bf AC}$

The vector ${\bf AB}$ is the difference of point B minus point A

${\bf AB}=(5-3,5-5,0-9)=(2,0,-9)$

and the vector ${\bf AC}$ is the difference of point C minus point A

${\bf AC}=(-4-3,0-5,2-9)=(-7,-5,-7)$

Next we need to find the cross product of this vectors.

${\bf AB} \times {\bf AC}=\begin{pmatrix}2&0&-9\end{pmatrix}\times \begin{pmatrix}-7&-5&-7\end{pmatrix}$

This is the definition of cross product of two vectors in space:

Let ${\bf u} = u_1{\bf i}+u_2{\bf j}+u_3{\bf k}$ and ${\bf v} = v_1{\bf i}+v_2{\bf j}+v_3{\bf k}$ be vectors in space. The cross product of ${\bf u}$ and ${\bf v}$ is the vector

${\bf u} \times {\bf v}=(u_2v_3-u_3v_2){\bf i}-(u_1v_3-u_3v_1){\bf j}+(u_1v_2-u_2v_1){\bf k}$

Applying this definition we get

${\bf AB} \times {\bf AC}=\begin{pmatrix}2&0&-9\end{pmatrix}\times \begin{pmatrix}-7&-5&-7\end{pmatrix}$

$\begin{pmatrix}0\cdot \left(-7\right)-\left(-9\left(-5\right)\right)&-9\left(-7\right)-2\left(-7\right)&2\left(-5\right)-0\cdot \left(-7\right)\end{pmatrix}\\\\\begin{pmatrix}-45&77&-10\end{pmatrix}$

$||{\bf AB} \times {\bf AC}||=\sqrt{(-45)^2+(77)^2+(-10)^2} \\\\||{\bf AB} \times {\bf AC}||=\sqrt{2025+5929+100}\\\\||{\bf AB} \times {\bf AC}||=\sqrt{8054}$

The area of the triangle is

$A=\frac{1}{2}||{\bf AB} \times {\bf AC} ||=\frac{1}{2}\sqrt{8054}=\sqrt{\frac{4027}{2}}$

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4 years ago