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Anestetic [448]
3 years ago
12

Leon filled a box with unit cubes. When it was completely filled, the box contained 32 cubes and had no gaps or overlaps. What w

as the volume of the box?
Mathematics
1 answer:
QveST [7]3 years ago
6 0
Leon is filled
Explanation
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Find an equation in point-slope form for the line having the slope m= -5 and containing the point (7,2).
Juli2301 [7.4K]

Answer:

y - 2 = - 5(x - 7)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = - 5 and (a, b) = (7, 2) , thus

y - 2 = - 5(x - 7) ← equation in point- slope form

5 0
3 years ago
Read 2 more answers
The width of a rectangle is 6 kilometers less than twice its length. if its area is 108 square​ kilometers, find the dimensions
Art [367]
Hi there!

Answer:
length = 9 kilometres
Width = 12 kilometres

Let's solve this problem step by step!
To find our answer we need to set up and solve an equation.

Let the length of the rectangle be represented by x.
The width of the rectangle can therefore be expressed by 2x - 6.

The area of a rectangle can be found by using the formula:
A = width × length

Plug in the data from the formula
A = x (2x - 6).

Simplify using rainbow technique.
x(2x - 6) = 2 {x}^{2} - 6x

Now we've found the simplified expression that expresses the area of the rectangle. Therefore, we can now set up and start solve the equation.

2 {x}^{2} - 6x = 108
Subtract 108

2 {x}^{2} - 6x - 108 = 0
Divide by 2.

{x}^{2} - 3x - 54
(x - 9)(x + 6) = 0
Rule AB = 0, gives A is 0 or B is 0.

x - 9 = 0 \\ x = 9 \\ \\ x + 6 = 0 \\ x = - 6

The length of the rectangle, which was represented by x, must be 9 (since it cannot be a negative number).

Length
x = 9
Width
2x - 6 = 2 \times 9- 6 = 18 - 6 = 12

Answer:
length = 9 kilometres
Width = 12 kilometres

~ Hope this helps you!
6 0
3 years ago
A bank is offering you an introductory credit card promotion. Your interest for the first year is 8%. But, at the beginning
Art [367]

Answer:

  • c) $22.50

Explanation:

<u>1. Calculate the monthly interest owed during year 1</u>

<u />

  • <em>Interest for first year: 8%</em>

  • The monthly rate is the yearly rate divided by 12: 8% / 12 = 0.08/12

  • The monthly interest owed is the monthly rate times the balance: (0.08/12)×$1,800 = $12.00

<u>2. Calculate the monthly interest owed during year 2</u>

<u />

  • <em>Interest for second year: 23%</em>

  • The montly rate is the yearly rate divided by 12: 23% / 12 = 0.23/12

  • The monthly interest owed is the monthly rate times the balance: (0.23/12)×$1,800 = $34.50

<u>3. Calculate the difference</u>

  • Difference in the monthly interest owed during year 1 and year 2 = $34.50 - $12.00 = $22.50

Hence, the answer is the option c) $22.50

7 0
3 years ago
Find the inverse of the function y= -3/ x+ 4
Tomtit [17]
Y=4-3/x
y-4=-3/x
(y-4)x=-3
x(y-4)=-3
x=-3/y-4

there's you answer
7 0
3 years ago
Read 2 more answers
Mr. Perry earns 5% commission on each pair of shoes he sells. His commission for the week was $700. What was the total value of
777dan777 [17]
You do $700 x .05 and it equals $35
8 0
3 years ago
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