Answer:
- B. $5 for each vinyl, $4 for each CD, and $1 for each electronic download
Step-by-step explanation:
Let the prices be
- Vinyl - x
- CD - y
- Electronic download - z
<u>Set the following equations based on the number of purchased items</u>
Sarah
Jamie
Frank
- 6x + 6z = 36 (<em>note: it can't be 30, corrected in the process of solution</em>)
Solve by substitution, simplify the third equation first
Substitute the value of x into the first two equations
3(6 - z) + 4y + z = 32
⇒ 18 - 3z + 4y + z = 32
⇒ 4y - 2z = 14
⇒ 2y - z = 7
⇒ z = 2y - 7
2(6 - z) + 5y + 7z = 37
⇒ 12 - 2z + 5y + 7z = 37
⇒ 5y + 5z = 25
⇒ y + z = 5
Solve by substitution again to get
- y + 2y - 7 = 5
- 3y = 12
- y = 4
Find z
Find x
The solution is
Correct choice is B
Answer:
Part A) The volume of the entire cone is 
Part B) see the explanation
Step-by-step explanation:
Part A) we know that
The volume of a cone is equal to

where
r is the radius of the base of the cone
h is the height of the cone
In this problem triangle ABD is similar to triangle ACE
Remember that If two figures are similar, then the ratio of its corresponding sides is proportional
so

substitute the given values

solve for x

To find out the volume of the entire cone we have


substitute in the formula


Part B) How did you determine the value for x in triangle ACE
In this problem triangle ABD is similar to triangle ACE
If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
so

substitute the given values and solve for x
By definition, the area is given by:

Where,
w: width
l: length
We have two expressions for the length:
Since the length is the same, we equate both expressions:

From here, we clear the value of c:


Then, we have that the width is given by:

Substituting the value of c we have:

Finally, the area is given by:

Answer:
he should order 140 square feet
7 because I just know like how kould you not know that