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professor190 [17]
3 years ago
11

A rectangular prism has a volume of 36 cubic units. Which set of dimensions could make this prism?

Mathematics
2 answers:
xenn [34]3 years ago
6 0
9 units, 2 units, 2 units
Kaylis [27]3 years ago
3 0
2 units, 3 units, 6 units

36 units, 1 unit, 1 unit

9 units, 2 units, 2 units

12 units, 3 units, 1 unit

All options stated above would result in a volume of 36 cubic units.
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What is the missing constant term in the perfect square that starts with x2+18xx^2+18xx2+18xx, squared, plus, 18, x ?
katrin2010 [14]

Answer:

81

Step-by-step explanation:

Given the expression: x^2+18x

To make it a perfect square, we follow the following steps.

Divide the coefficient of x by 2

  • Coefficient of x=18, 18/2=9

Square It

  • 9 X 9=81

Add it to the expression

  • x^2+18x+81

This is written as a perfect square as: (x+9)^2

The constant term required therefore is 81.

4 0
3 years ago
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Given the following three points, find by the hand the quadratic function they represent (0,6, (2,16, (3,33)
Lisa [10]

Answer:

f(x) = 4x^2 - 3x + 6

Step-by-step explanation:

Quadratic function is given as f(x) = ax^2 + bx + c

Let's find a, b and c:

Substituting (0, 6):

6 = a(0)^2 + b(0) + c

6 = 0 + 0 + c

c = 6

Now that we know the value of c, let's derive 2 system of equations we would use to solve for a and b simultaneously as follows.

Substituting (2, 16), and c = 6

f(x) = ax^2 + bx + c

16 = a(2)^2 + b(2) + 6

16 = 4a + 2b + 6

16 - 6 = 4a + 2b + 6 - 6

10 = 4a + 2b

10 = 2(2a + b)

\frac{10}{2} = \frac{2(2a + b)}{2}

5 = 2a + b

2a + b = 5 => (Equation 1)

Substituting (3, 33), and c = 6

f(x) = ax^2 + bx + x

33 = a(3)^2 + b(3) + 6

33 = 9a + 3b + 6

33 - 6 = 9a + 3b + 6 - 6

27 = 9a + 3b

27 = 3(3a + b)

\frac{27}{3} = \frac{3(3a + b)}{3}

9 = 3a + b

3a + b = 9 => (Equation 2)

Subtract equation 1 from equation 2 to solve simultaneously for a and b.

3a + b = 9

2a + b = 5

a = 4

Replace a with 4 in equation 2.

2a + b = 5

2(4) + b = 5

8 + b = 5

8 + b - 8 = 5 - 8

b = -3

The quadratic function that represents the given 3 points would be as follows:

f(x) = ax^2 + bx + c

f(x) = (4)x^2 + (-3)x + 6

f(x) = 4x^2 - 3x + 6

6 0
3 years ago
How will the solution of the system y > 2x + Two-thirds and y < 2x + One-third change if the inequality sign on both inequ
blagie [28]

Answer:

Step-by-step explanation:344x-5-p-0-9-but=pmc+m2 something like that

8 0
2 years ago
A large appliance such as a water heater is only running when it has clicked on and is actually heating water. The time your wat
mafiozo [28]

a) Total cost (per day) ≈ $1.40

​b) Total cost (per year) ≈ $510

c) New annual cost = $327

d) The number of years that the water heater pays for itself is; approximately 4 years

<h3>How to calculate Energy Bill?</h3>

Wattage per hour = 4200 Watts per hour

Number of hours per day = 3 hours

Cost per unit = $0.11 per kilowatt-hour

Savings rate = 36%

Cost water heater = $1,100

a) The total wattage is the product of the wattage per hour and the number of hours;

Total wattage (per day) = Wattage per hour × Number of hours

= 4,200 watts per hour × 3 hours

= 12,600 watt-hours

= 12.6 kilowatt-hours

​

The total cost is then the product of the total wattage and the cost per unit:

Total cost (per day) = Total wattage × Cost per unit

Total cost (per day) = 12.6 kilowatt-hours × $0.11 per kilowatt-hour

Total cost (per day) = $1.386

Total cost (per day) ≈ $1.40

​

b) The total cost in a year is the product of the total cost in a day and the number of days in a year. There are 365 days in a year (assuming no leap year).

Total cost (per year) = Total cost (per day) × Number of days in a year

Total cost (per year) = $1.40 × 365

Total cost (per year) = $511

Total cost (per year) ≈ $510

​

c) We are told that this new water heater saves 36% of annual cost. Thus;

Amount saved = 36% * 510 = $183.6

Thus;

New annual cost = $510 - $183 = $327

d) The number of years that the water heater pays for itself is;

1100/327 = 3.36 or approximately 4 years

Read more about Energy Costs at; brainly.com/question/14277272

#SPJ1

6 0
1 year ago
There are 14 red, 10 yellow, 5 green, and 3 purple candies in a bag. What is the probability that a candy chosen at random is no
ch4aika [34]

Answer: 9/16

Work Shown:

14 red + 10 yellow + 5 green + 3 purple = 32 total

(32 total) - (14 red) = 18 that aren't red

18/32 = 9/16 is the probability of picking something that isn't red.

8 0
3 years ago
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