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Hatshy [7]
3 years ago
14

What is the product of 9 and -7?

Mathematics
1 answer:
kolezko [41]3 years ago
3 0

Answer:

The product of 9 and -7 is -63

Step-by-step explanation:

Hope This Helped!

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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
3# Find the missing variable (s). Round to the nearest tenth.
rewona [7]

Answer:


Step-by-step explanation:


This triangle is already positioned to match trig functions (also known as circular functions).


Point A is origin, side AC (length x) is on X axis,

side CB (length y) is parallel to Y axis.


***** You just remember *****


cos is horizontal, on X axis,

sin is vertical, on Y axis.

To get from unit triangle with hypotenuse 1,

horizontal side cos(θ), vertical side sin(θ), you multiply all sides by same number, namely, the specified length of the hypotenuse.


***** that's all you need to know *****


Draw a unit circle centered at A, mark point Y at intersection of circle and AB, and drop a vertical line from Y crossing X axis at X.


Then radial segment AY is 1, AB is 10

horizontal segment AX is cos(32°), AC is 10AX

vertical segment XY is sin(32°), CB is 10XY.


So x = 10 cos(32°), y= 10 sin(32°).




7 0
3 years ago
18. Solve the inequality. Show your work.<br> –6b &gt; 42 or 4b &gt; –4
grigory [225]
-6b > 42 = b<-7
or
4b > -4 = b>-1
Hope this helps.
6 0
3 years ago
Read 2 more answers
SOMEBODY HELPPPPPPPPPP BE FAST
Paul [167]

The answer 30, 40, 50

Forms a right triangle

Hope this helps!

5 0
2 years ago
Chris paid $36 for 3 tanktops and 2 shirts. a shirt cost 3 times as much as a tank top. how much did chris pay for the 2 shirts?
devlian [24]

Answer:

$72

Step-by-step explanation:

36/3=12

1 tanktop=$12

12*3=36

1 shirt equals=$36

36*2=72

2 shirts=$72

4 0
3 years ago
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