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Inga [223]
3 years ago
11

From examples 9 and​ 10, what is the connection between function notation to evaluate a function at certain values and ordered p

air solutions of the​ function?
Mathematics
1 answer:
Reika [66]3 years ago
7 0
What are examples 9 and 10?
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The length of a rectangle is 5 ft less than three times the width, and the area of the rectangle is 50 ft². Find the dimensions
Mariulka [41]

Answer

Length = 10 ft

Width = 5 ft

Explanation

Area of the rectangle given = 50 ft²

Let the width of the rectangle be x

So this means the length of the rectangle will be 3x - 5

What to find:

The dimensions of the rectangle.

Step-by-step solution:

Area of a rectangle = length x width

i.e A = L x W

Put A = 50, L = 3x - 5, W = x into the formula.

\begin{gathered} 50=(3x-5)x \\ 50=3x^2-5x \\ 3x^2-5x-50=0 \end{gathered}

The quadratic equation can now be solve using factorization method:

\begin{gathered} 3x^2-5x-50=0 \\ 3x^2-15x+10x-50=0 \\ 3x(x-5)+10(x-5)=0 \\ (3x+10)(x-5)=0 \\ 3x+10=0\text{ }or\text{ }x-5=0 \\ 3x=-10\text{ }or\text{ }x=5 \\ x=-\frac{10}{3}\text{ }or\text{ }x=5 \end{gathered}

Since the dimension can not be negative, hence the value of x will be = 5.

Therefore, the dimensions of the rectangle will be:

\begin{gathered} Length=3x-5=3(5)-5=15-5=10\text{ }ft \\  \\ Width=x=5\text{ }ft \end{gathered}

7 0
1 year ago
A particular sawdust pile has a base diameter of 25 feet when the height is 20 feet. Find the volume of this sawdust pile when i
Artist 52 [7]

The volume of the sawdust pile is 11,039.06 ft³.

<h3>What is the volume of the pile?
</h3>

The shape of the sawdust pile would be a cone. The diameter is always proportional to its height.

Diameter = k x height

where k is equivalent to the rate of increase of the diameter with respect to the increase in height.

25= k20

k = 25 / 20

k = 1.25

Diameter when height is 30 ft = 1.25x 30 = 35.50 feet

Volume of the sawdust = \frac{1}{3}πr²h

Where:

  • π = 3.14
  • r = radius = diameter / 2 = 35.50 / 2 = 18.75
  • h = 30

\frac{1}{3} x 3.14 x 18.75² x 30 = 11,039.06 ft³

To learn more about the volume of a cone, please check: brainly.com/question/13705125

#SPJ1

4 0
1 year ago
The measurement of a rectangular room on a scale drawing are 8cm x 6cm. If the scale use is 1 : 400, calculate the actual area o
rosijanka [135]

Answer:

768 m²

Step-by-step explanation:

8 x 400 = 3200 cm = 32 m

6 x 400 = 2400 cm = 24m

32 x 24 = 768 m²

8 0
3 years ago
I asked my dad how to solve this question and he part helped me and I was like ohhhhhhhhhhh so now I want you to solve it. I'll
matrenka [14]

Answer:

Whats the question? I can surely answer it.

3 0
3 years ago
I had a dream of a beautiful cupcake tree, growing 4 loveee cupcakes every 12 hours for 36 hours. Please make my dream come true
weqwewe [10]

Answer: sounds sweet:)

Step-by-step explanation:

7 0
3 years ago
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