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4 years ago

Find the slope between the two points. (3,7) and (-4,2)?

Mathematics

1 answer:

muminat4 years ago

5 0

Answer:

rise: 9 run: -1 so 9/-1 is your slope

Step-by-step explanation:

do you need the equation or just the rise/run?

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What is the measurement of the longest line segment in a right rectangular prism that is 26 inches long, 2 inches wide, and 2 in

EastWind [94]

Answer:

$6\sqrt{19} \approx 26.153$ inches.

Step-by-step explanation:

The longest line segment in a right rectangular prism is the diagonal that connects two opposite vertices. On the first diagram attached, the green line segment connecting A and G is one such diagonals. The goal is to find the length of segment $\mathsf{AG}$ .

In this diagram (not to scale,) $\mathsf{AB} = 26$ (length of prism,) $\mathsf{AC} = 2$ (width of prism,) $\mathsf{AE} = 2$ (height of prism.)

Pythagorean Theorem can help find the length of $\mathsf{AG}$ , one of the longest line segments in this prism. However, note that this theorem is intended for right triangles in 2D, not the diagonal in a 3D prism. The workaround is to simply apply this theorem on two different right triangles.

Start by finding the length of line segment $\mathsf{AD}$ . That's the black dotted line in the diagram. In right triangle $\triangle\mathsf{ABD}$ (second diagram,)

Segment $\mathsf{AD}$ is the hypotenuse.
One of the legs of $\triangle\mathsf{ABD}$ is $\mathsf{AB}$ . The length of $\mathsf{AB}$ is $26$ , same as the length of this prism.
Segment $\mathsf{BD}$ is the other leg of this triangle. The length of $\mathsf{BD}$ is $2$ , same as the width of this prism.

Apply the Pythagorean Theorem to right triangle $\triangle\mathsf{ABD}$ to find the length of $\mathsf{AB}$ , the hypotenuse of this triangle:

$\mathsf{AD} = \sqrt{\mathsf{AB}^2 + \mathsf{BD}^2} = \sqrt{26^2 + 2^2}$ .

Consider right triangle $\triangle \mathsf{ADG}$ (third diagram.) In this triangle,

Segment $\mathsf{AG}$ is the hypotenuse, while
$\mathsf{AD}$ and $\mathsf{DG}$ are the two legs.

$\mathsf{AD} = \sqrt{26^2 + 2^2}$ . The length of segment $\mathsf{DG}$ is the same as the height of the rectangular prism, $2$ (inches.) Apply the Pythagorean Theorem to right triangle $\triangle \mathsf{ADG}$ to find the length of the hypotenuse $\mathsf{AG}$ :

$\begin{aligned}\mathsf{AG} &= \sqrt{\mathsf{AD}^2 + \mathsf{GD}^2} \\ &= \sqrt{\left(\sqrt{26^2 + 2^2}\right)^2 + 2^2}\\ &= \sqrt{\left(26^2 + 2^2\right) + 2^2} \\&= 6\sqrt{19} \\&\approx 26.153\end{aligned}$ .

Hence, the length of the longest line segment in this prism is $6\sqrt{19} \approx 26.153$ inches.

5 0

3 years ago

The segments shown below could form a triangle.

Setler79 [48]

Answer:

a is the answer, also it's true.

3 0

3 years ago

Find an irrational number between -10 and -10.1.

Pavlova-9 [17]

Between two rational numbers there are an infinite number of irrational numbers.

Example:

$- 5 \sqrt{3} -\sqrt{2}= 5 \times 1.7320508 - 1.41421356 \approx -10.0744676\\\\
-10.1 \ \textless \ -10,0744676 \ \textless \ -10$

6 0

3 years ago

654x67<br> Quien me ayuda please

Likurg_2 [28]

The answer is 43,818

3 0

4 years ago

Read 2 more answers

Solve the inequality, <br> x + 6.56 > 25.2

pogonyaev

Answer: x>18.64

Step-by-step explanation:

x+6.56-6.56>25.2-6.56

x>18.64

7 0

3 years ago

Find the slope between the two points. (3,7) and (-4,2)?​

Find the slope between the two points. (3,7) and (-4,2)?