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sertanlavr [38]
1 year ago
14

On a camping trip Trina is going to build a shelter by leading branches up against a rock wall Trina wants her sleeping bag to b

e perpendicular to the wall her saving bag is 6' long and the wall is 8' tall how long will the branches be
Mathematics
1 answer:
tino4ka555 [31]1 year ago
5 0

The Branches should be 10' long.

<h3>What is Pythagoras theorem ?</h3>

Pythagoras theorem states that the sum of the squares of base and perpendicular is equal to the square of hypotenuse.

According to the given question on a camping trip Trina is going to build a shelter by leading branches up against a rock wall Trina wants her saving bag to be perpendicular this means it will form a right angle triangle and we know hypotenuse² = base² + perpendicular².

Here branches is the hypotenuse,wall is perpendicular and saving bag is base.

∴ (Branches)² = (wall)² + (saving bag)²

  (Branches)² = 64 + 36

  (Branches)² = 100

   Branches = 10.

learn more about right angled triangle here :

brainly.com/question/3770177

#SPJ1

You might be interested in
Kyle drew 4 polygons labeled A,B,C, and D. Figure A has twice as many sides as Figure B. Figure B has 3 vertices. Figure C has h
erma4kov [3.2K]

Answer:

Figure A - hexagon

Figure B - triangle

Figure C - rectangle

Figure D - octagon

Step-by-step explanation:

If figure B has 3 vertices (angles), then that means it is a triangle (3 sides)

So that means figure A has 6 sides, (hexagon)

And figure D has 8 vertices, so 8 sides (octagon)

And if C has half as many, that would be 4 (rectangle)

7 0
3 years ago
Find equations of the spheres with center(3, −4, 5) that touch the following planes.a. xy-plane b. yz- plane c. xz-plane
postnew [5]

Answer:

(a) (x - 3)² + (y + 4)² + (z - 5)² = 25

(b) (x - 3)² + (y + 4)² + (z - 5)² = 9

(c) (x - 3)² + (y + 4)² + (z - 5)² = 16

Step-by-step explanation:

The equation of a sphere is given by:

(x - x₀)² + (y - y₀)² + (z - z₀)² = r²            ---------------(i)

Where;

(x₀, y₀, z₀) is the center of the sphere

r is the radius of the sphere

Given:

Sphere centered at (3, -4, 5)

=> (x₀, y₀, z₀) = (3, -4, 5)

(a) To get the equation of the sphere when it touches the xy-plane, we do the following:

i.  Since the sphere touches the xy-plane, it means the z-component of its centre is 0.

Therefore, we have the sphere now centered at (3, -4, 0).

Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (3, -4, 0) as follows;

d = \sqrt{(3-3)^2+ (-4 - (-4))^2 + (0-5)^2}

d = \sqrt{(3-3)^2+ (-4 + 4)^2 + (0-5)^2}

d = \sqrt{(0)^2+ (0)^2 + (-5)^2}

d = \sqrt{(25)}

d = 5

This distance is the radius of the sphere at that point. i.e r = 5

Now substitute this value r = 5 into the general equation of a sphere given in equation (i) above as follows;

(x - 3)² + (y - (-4))² + (z - 5)² = 5²  

(x - 3)² + (y + 4)² + (z - 5)² = 25  

Therefore, the equation of the sphere when it touches the xy plane is:

(x - 3)² + (y + 4)² + (z - 5)² = 25  

(b) To get the equation of the sphere when it touches the yz-plane, we do the following:

i.  Since the sphere touches the yz-plane, it means the x-component of its centre is 0.

Therefore, we have the sphere now centered at (0, -4, 5).

Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (0, -4, 5) as follows;

d = \sqrt{(0-3)^2+ (-4 - (-4))^2 + (5-5)^2}

d = \sqrt{(-3)^2+ (-4 + 4)^2 + (5-5)^2}

d = \sqrt{(-3)^2 + (0)^2+ (0)^2}

d = \sqrt{(9)}

d = 3

This distance is the radius of the sphere at that point. i.e r = 3

Now substitute this value r = 3 into the general equation of a sphere given in equation (i) above as follows;

(x - 3)² + (y - (-4))² + (z - 5)² = 3²  

(x - 3)² + (y + 4)² + (z - 5)² = 9  

Therefore, the equation of the sphere when it touches the yz plane is:

(x - 3)² + (y + 4)² + (z - 5)² = 9  

(b) To get the equation of the sphere when it touches the xz-plane, we do the following:

i.  Since the sphere touches the xz-plane, it means the y-component of its centre is 0.

Therefore, we have the sphere now centered at (3, 0, 5).

Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (3, 0, 5) as follows;

d = \sqrt{(3-3)^2+ (0 - (-4))^2 + (5-5)^2}

d = \sqrt{(3-3)^2+ (0+4)^2 + (5-5)^2}

d = \sqrt{(0)^2 + (4)^2+ (0)^2}

d = \sqrt{(16)}

d = 4

This distance is the radius of the sphere at that point. i.e r = 4

Now substitute this value r = 4 into the general equation of a sphere given in equation (i) above as follows;

(x - 3)² + (y - (-4))² + (z - 5)² = 4²  

(x - 3)² + (y + 4)² + (z - 5)² = 16  

Therefore, the equation of the sphere when it touches the xz plane is:

(x - 3)² + (y + 4)² + (z - 5)² = 16

 

3 0
3 years ago
Consider parallelogram ABCD. Which of the following transformations will change the perimeter of the parallelogram?
jeka57 [31]

In geometry, transformation involves changing the position and/or size of a shape.

<em>The transformation that will change the size of ABCD is dilation.</em>

There are four transformations in geometry:

  • Translation
  • Reflection
  • Rotation
  • Dilation

Of all types of transformation, dilation will change the size of the shape,

The new shape will either be enlarged or reduced

<em>Either ways, the size of the shape will be altered.</em>

<em>When the size is altered, the perimeter will not remain the same.</em>

<em />

Hence. dilation will change the perimeter of ABCD.

Read more about transformations at:

brainly.com/question/11709244

4 0
2 years ago
You sell instruments at a Caribbean music festival. You earn $326 by selling 12 sets of maracas, 6 sets of claves, and xx djembe
ELEN [110]

Answer: An equation we can use to find the number of djembe drums you sold be

12m+6c+dxx=$326

Step-by-step explanation:

Let price of maracas be m

Let the price of claves be c

Let the price of djembe drums be d

Number of maracas = 12 sets

Number of clavas = 6 sets

Number of djembe drums be xx

Total earned amount = $326

According to question,

12m+6c+dxx=$326

Hence, an equation we can use to find the number of djembe drums you sold be

12m+6c+dxx=$326

5 0
3 years ago
Read 2 more answers
Students were asked to explain the first step in solving the equation: 3y + 4 = 16. Susan says multiply by three. Ted says to ad
Juli2301 [7.4K]

Answer:

Nicole is correct

Step-by-step explanation:

They need to get the 3y on one side of the equal sign and the known numbers on the other side. To do this, they must subtract the 4 from both sides.

8 0
2 years ago
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