Tutor profile: Pooja S.
Subject: Basic Math
A large soccer field is 115 m long and 85 m wide. What is its area?
To find the area of a rectangle, we multiply the length by the width. For this rectangular field, Area = Length x Width, so Area = (115 m) x (85 m) as given in the problem. This simplifies to Area = 9,775 m^2, and the units become m^2 because we are multiplying the units of m and m together and area is always measured in some units^2.
Pond Water with small organisms inside: (a) identify the piece of matter as a pure substance or a mixture and (b) identify the piece of matter as an element, compound, homogeneous mixture, or heterogeneous mixture.
(a) A pure substance may be made of different elements but has the same composition throughout and every sample would have the exact same properties, such as air, while a mixture is two or more different substances with different properties that can be physically separated. Based on these descriptions, we know pond water with small organisms is a mixture because the water and organisms are physically different and could be separated out with a funnel or other method. (b) An element would be a material made up of only one type of atom, and could be found directly on the periodic table, and a compound is made up of two or more elements chemically bonded together in a fixed ratio. We know that the pond water is neither of these, because the water is not an element (made up of H2O), and the presence of organisms means it is also not just this compound. A homogeneous mixture is the same material and phase of matter (liquid, solid, gas) throughout and a heterogeneous mixture is not uniform and its components can be physically sorted out. The pond water with organisms are two different phases (liquid vs. solid), which means it is a heterogeneous mixture.
If 3x + 8x + 4x = 6x + 63, then what is 5x + 23?
The first step in solving this problem is to temporarily ignore the second question and instead focus on the first equation. In the first equation, 3x + 8x + 4x = 6x + 63, you should first solve for x. To do this, combine the 3x + 8x + 4x on the left side, subtract 6x from both sides to get all the terms with x on the left side, resulting in 3x + 8x + 4x - 6x = 9x. Then we have 9x = 63, so to isolate x divide both sides by 9, which results in x = 7. Now, we can focus back on the second part of the question, what is 5x + 23. Plug in x = 7 to the expression, so 5(7) + 23 = 35 + 23 which simplifies to 58. Therefore, if 3x + 8x + 4x = 6x + 63, then 5x + 23 is 58!
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