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Tema [17]
1 year ago
13

HELP PLEASE ASAP!!! James has 822 feet of rope. There are 19 teams of hikers. If James gives an equal amount of rope to each tea

m, how much rope will each team receive?
Mathematics
1 answer:
padilas [110]1 year ago
6 0
<h2>Hello, there today we will be solving your problem</h2>

_____________________

\huge\blue{\mid{\fbox{\tt{Answer}}\mid}}

  • 43 \frac{5}{19}

\huge\blue{\mid{\fbox{\tt{Explanation}}\mid}}

<em>         Since James has 822 feet of rope all we have to do is divide that among 19 different teams. </em>

<h3>Definitions</h3>

Division<em> - Division, otherwise known as the inverse of multiplication separates a certain number into what it has been divided by.</em>

Fraction -<em> A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, or three-quarters.</em>

Improper Fraction - <em>An improper fraction has a numerator greater than the denominator. For example, </em>\frac{3}{2}<em> is an improper fraction, but 2/3 is a proper fraction, whose denominator is greater than the numerator.</em>

Mixed Number - <em>A mixed number is a whole number, and a proper fraction represented together. It generally represents a number between any two whole numbers. Look at the given image, it represents a fraction that is greater than 1 but less than 2.</em>

_____________________

<h3><em>Now we can solve this equation</em></h3>
  1. Step one - Division   822\div19=\frac{822}{19}
  2. Step two - Turn the improper fraction into a mixed number 822\div19=43 R5
  3. Step three - Turn the remainder back into a fraction 43 \frac{5}{19}
<h3><em>Your answer is  </em>43\frac{5}{19}</h3>
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A rectangle has perimeter 28cm. Its area is 42sq.cm. Determine the dimensions of the rectangle. Include a diagram in your soluti
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The dimensions of the rectangle are: b=9.65 cm and h=4.35 cm or b=4.35 cm and h= 9.65 cm.

<h3>Quadrilaterals</h3>

There are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example, in a rectangle,  the opposite sides are equal and parallel and their interior angles are equal to 90°.

The area of a rectangle is equal to base x height (A=bh). The perimeter of a geometric figure is the sum of its sides. Thus, for a rectangle, the perimeter is 2b+2h.

<h3>System of Linear Equations</h3>

System of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.

The question gives:

Perimeter=28cm

Area= 42 cm²

If the perimeter is the sum of all sides of the rectangle, you have:

Perimeter= 2b+2h=28

If the area of the rectangle is 42cm², you have:

Area=bh=42 cm²

You can write a system of linear equations.

2b+2h=28 (1)

bh=42 (2)

From equation 2, you have  b=\frac{42}{h}. Then, you can replace it in equation 1.

2*\frac{42}{h}+2h=28 \\ \\ 84+2h^2=28h\\ \\ 2h^2-28h+84=0 \; dividing\; by\; 2\\ \\ h^2-14h+42=0

Now, you should solve the quadratic equation.

h_{1,\:2}=\frac{-\left(-14\right)\pm \sqrt{\left(-14\right)^2-4\cdot \:1\cdot \:42}}{2\cdot \:1}

h_{1,\:2}=\frac{-\left(-14\right)\pm \:2\sqrt{7}}{2\cdot \:1}

h_1=\frac{-\left(-14\right)+2\sqrt{7}}{2\cdot \:1}=7+\sqrt{7}=9.65 cm

h_2=\frac{-\left(-14\right)-2\sqrt{7}}{2\cdot \:1}=7-\sqrt{7}=4.35cm

If h1=9.65 cm, then b_1=\frac{42}{9.65} =4.35 cm, and if  h2=4.35 cm, then b_1=\frac{42}{4.35} =9.65 cm.

Read more about the quadratic function here:

brainly.com/question/1497716

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