Where is the circumcenter of this acute triangle located?

8) A school community had planned to reduce the number of grade 9 students per class room by constructing additional class rooms

Allisa [31]

Step-by-step explanation:

Let "c" be the original number of classrooms.

The 1200/c was the original number of students per classroom.

----

Equation:

1200/(c-4) = (1200/c)+10

Multiply thru by c(c-4)

---

1200c = 1200(c-4)+10c(c-4)

---

1200c = 1200c-4800 + 10c^2-40c

----

10c^2-40c-4800 = 0

c^2-4c-480 = 0

Factor:

(c-24)(c+20) = 0

---

Positive solution:

c = 24 (# of classrooms originaly planned)

7 0

2 years ago

2. Standard 6.NS.B

weqwewe [10]

Answer:

4 packages of hot dogs and 5 packages of hot dog buns.

Step-by-step explanation:

Find the least common multiple of 10 and 8, which is 40.

5 0

3 years ago

A container manufacturer plans to make rectangular boxes whose bottom and top measure x by 4x. The container must contain 12ft^3

zheka24 [161]

The height of the container should be equal to 2.57 cm, so as to minimize cost.

<h3>How to calculate the height?</h3>

First of all, we would determine the volume of the rectangular container by using this formula:

Volume = l × w × h

Where:

l represents the length.

w represents the width.

h represents the height.

Substituting the given parameters into the formula, we have;

Volume = x × 4x × h

Volume = 4x²h

At a volume of 12 ft³, we have:

12 = 4x²h

h = 12/4x²

h = 3/x²

For the total area of top and bottom, we have:

Area = (x × 4x) + (x × 4x)

Area = 4x² + 4x²

Area = 8x² sq. units.

Thus, the cost of top and bottom is given by:

Cost = 8x² × 1.50

Cost = $12x²

For the total area of all four sides, we have:

Area = (x × h) + (x × h) + (4x × h) + (4x × h)

Area = xh + xh + 4xh + 4xh

Area = 10xh sq. units.

Thus, the cost of all four sides is given by:

Cost = 10xh × 4.50

Cost = $45xh.

Also, the cost function would be given by:

C(x) = 12x² + 10xh

C(x) = 12x² + 10x(3/x²)

C(x) = 12x² + 30/x

Taking the first derivative, we have:

dC/dx = 24x - 30/x²

24x = 30/x²

24x³ = 30

x³ = 30/24

x = 1.08

Therefore, the height will be:

h = 3/x²

h = 3/1.08²

h = 3/1.1664

Height, h = 2.57 cm.

Read more on minimum height here: brainly.com/question/27308167

#SPJ1

5 0

1 year ago

The vertices of square RSTV have coordinates R(-1,5), S(-3,1), T(-7,3), and V(-5,7). What is the perimeter of RSTV?

kompoz [17]

The perimeter of square RSTV is: 17.88 units

Further explanation:

As the given figure is a square, all of its sides will be equal. So we have to find one side to find the perimeter.

Given

R(-1,5), S(-3,1), T(-7,3), and V(-5,7)

The distance formula will be used to find the side

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^@}$

Let x be one side of square

$RS=x=\sqrt{(-3-(-1))^2+(1-5)^2}\\=\sqrt{-3+1)^2+(-4)^2}\\=\sqrt(-2)^2+(-4)^2}\\=\sqrt{4+16}\\=\sqrt{20}\\=4.47$

Let P be the perimeter of square

P= 4x

P=4*4.47

=17.88 units

The perimeter of square RSTV is: 17.88 units

Keywords: Perimeter, Distance Formula

Learn more about perimeter at:

#LearnwithBrainly

6 0

3 years ago

How long in days is a mega second? Hi, I'm helping my little brother with a maths assignment at the moment and I couldn't quite

Marat540 [252]

I've heard of milliseconds, microseconds and nanoseconds, but never a megasecond. By the way:
<span>1 second = 1000 milliseconds </span>
<span>1 second = 1,000,000 microseconds </span>
<span>1 second = 1e+009 nanoseconds
</span>

8 0

3 years ago