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9966 [12]
3 years ago
5

Sasha's grandmother loves to travel. She sends Sasha postcards from all around the world. Sasha keeps the postcards in a special

box. The box has a square base and a square pyramid for a lid.What is the combined volume inside the box and lid?

Mathematics
1 answer:
Alinara [238K]3 years ago
6 0
To find the total volume of the box, you will find the volumes of each separate piece.

Use the formulas for finding the volumes of each:

V = 1/3 Bh (pyramid);  B stands for the area of the base shape
      1/3 x 8 x 8 x 3
V = 64 cubic inches

V = Bh (prism)
      8 x 8 x 4
V = 256 cubic inches

256 + 64 = 320 cubic inches

The total volume of the box is 320 cubic inches.
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Can you please help me with this problem?
Hoochie [10]
Here you have to find which each variable is, for this you start of picking one equation,

x + 2y + 6z = 4
-3x + 2y - 2 = -4
4x + 2z = 16

depending the equation you pick you multiply that by a certain number that will give you the opposite of one of the other equations,
-1(x + 2y + 6z = 4)
= -x -2y - 6z = -4

With this you add or subtract it with the equation that has the same number or variable, or both,
In this case it will be the equation,
-3x + 2y + 6z = 4
You can use this one or the third equation since both have a positive 2y which will cancel with -2y from the new equation,
-x - 2y - 6z = -4
-3x + 2y -z = -4

= -4x -7z = -8
Now you since you just eliminated the variable (y) you now have 2 variables, and the last equation has only 2 variables, meaning now you find the answer to those to equations,

-4x -7z = -8
4x + 2z = 16

= -5z = 8
Now leave the variable by itself,
z = 8/5
Now you found the variable (z), with this just substitute on one of the equations we used to find (z) so you can find (x), after that substitute those answered to on of the original equations so you can find (y)




6 0
3 years ago
A triangle is to be dilated with the origin as the center of dilation and with a scale factor of 2. Which answer choice correctl
saveliy_v [14]

Answer:

All the coordinates are changed to

(x, y) ⇒ (2x, 2y)

Step-by-step explanation:

Given - A triangle is to be dilated with the origin as the center of dilation and with a scale factor of 2.

To find -  Which answer choice correctly maps this dilation algebraically?​

Proof -

Let ABC is a triangle where A, B, C are the vertices of the triangle respectively.

Now,

Let the coordinates be (x, y)

If a triangle is to be dilated with the origin as the center of dilation and with a scale factor of a , then the coordinated be changes as

(x, y) ⇒ (ax, ay)

Here given , a = 2

So, all the coordinates are changed to

(x, y) ⇒ (2x, 2y)

3 0
3 years ago
Raul crosses Main Street when he walks home from school. The graph of the function d(t)=4|t-0.75) shows Raul's distance, in mile
lina2011 [118]

Answer: does someone have it cause I’m stuck to

Step-by-step explanation:

7 0
3 years ago
A boat is heading towards a lighthouse,
larisa86 [58]

Answer: 920.3 ft

Step-by-step explanation:

\tan 7^{\circ}=\frac{113}{x} \\ \\ x(\tan 7^{\circ})=113 \\ \\ x=\frac{113}{\tan 7^{\circ}} \approx \boxed{920.3 \text{ ft}}

4 0
1 year ago
The sum of the first n terms of an arithmetic sequence is n/2(4n + 20).
lesantik [10]

Answer:

(a).

S_{n} =  \frac{n}{2} (4n + 20) \\  \\S _{n - 1} =  \frac{(n - 1)}{2} (4n - 4 + 20) \\  \\ S _{n - 1} =  \frac{(n - 1)}{2} (4n + 16) \\  \\S _{n - 1} = \frac{(n - 1)(4n + 16)}{2}  \\   \\  { \boxed{S _{n - 1} =  {2 {n}^{2} + 6n - 8}}} \\

(b).

from general equation:

S _{n - 1} =  \frac{(n - 1)}{2} (4n + 16)

first term is 4n

common difference:

16 =  \{(n - 1) - 1 \}d \\ 16 = (n - 2)d \\ d =  \frac{16}{n - 2}

8 0
3 years ago
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