Area of a square = length²
A = x²
16 = x²; x = 4
dA/dx = 2x cm²/s
dx/dt = 6 cm/s
Using chain rule:
dA/dt = dA/dx * dx/dt
dA/dt = 2x * 6
dA/dt = 12x
At x = 4,
dA/dt = 12(4) = 48 cm²/s
Check the picture below.
since in a rhombus the diagonals bisect each other, thus EC = EA.
now, the rhombus is simply 4 congruent triangles, we know the base and height of one of them, thus
![\bf \textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh~~ \begin{cases} b=8\\ h=15 \end{cases}\implies A=\cfrac{1}{2}(8)(15)\implies A=60 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of all 4 triangles}}{4(60)\implies 240}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Barea%20of%20a%20triangle%7D%5C%5C%5C%5C%20A%3D%5Ccfrac%7B1%7D%7B2%7Dbh~~%20%5Cbegin%7Bcases%7D%20b%3D8%5C%5C%20h%3D15%20%5Cend%7Bcases%7D%5Cimplies%20A%3D%5Ccfrac%7B1%7D%7B2%7D%288%29%2815%29%5Cimplies%20A%3D60%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Barea%20of%20all%204%20triangles%7D%7D%7B4%2860%29%5Cimplies%20240%7D)
These are just a few of the things you will learn in 6th grade. You will learn how to write a two- variable equation, how to identify the graph of an equation, graphing two-variable equations. how to interpret a graph and a word problem, and how to write an equation from a graph using a table, two-dimensional figures,Identify and classify polygons, Measure and classify angles,Estimate angle measurements, Classify triangles, Identify trapezoids, Classify quadrilaterals, Graph triangles and quadrilaterals, Find missing angles in triangles, and a lot more subjects. <span><span><span>Find missing angles in quadrilaterals
</span><span>Sums of angles in polygons
</span><span>Lines, line segments, and rays
</span><span>Name angles
</span><span>Complementary and supplementary angles
</span><span>Transversal of parallel lines
</span><span>Find lengths and measures of bisected line segments and angles
</span><span>Parts of a circle
</span><span>Central angles of circles</span></span>Symmetry and transformations
<span><span>Symmetry
</span><span>Reflection, rotation, and translation
</span><span>Translations: graph the image
</span><span>Reflections: graph the image
</span><span>Rotations: graph the image
</span><span>Similar and congruent figures
</span><span>Find side lengths of similar figures</span></span>Three-dimensional figures
<span><span>Identify polyhedra
</span><span>Which figure is being described
</span><span>Nets of three-dimensional figures
</span><span>Front, side, and top view</span></span>Geometric measurement
<span><span>Perimeter
</span><span>Area of rectangles and squares
</span><span>Area of triangles
</span><span>Area of parallelograms and trapezoids
</span><span>Area of quadrilaterals
</span><span>Area of compound figures
</span><span>Area between two rectangles
</span><span>Area between two triangles
</span><span>Rectangles: relationship between perimeter and area
</span><span>compare area and perimeter of two figures
</span><span>Circles: calculate area, circumference, radius, and diameter
</span><span>Circles: word problems
</span><span>Area between two circles
</span><span>Volume of cubes and rectangular prisms
</span><span>Surface area of cubes and rectangular prisms
</span><span>Volume and surface area of triangular prisms
</span><span>Volume and surface area of cylinders
</span><span>Relate volume and surface area
</span><span>Semicircles: calculate area, perimeter, radius, and diameter
</span><span>Quarter circles: calculate area, perimeter, and radius
</span><span>Area of compound figures with triangles, semicircles, and quarter circles</span></span>Data and graphs
<span><span>Interpret pictographs
</span><span>Create pictographs
</span><span>Interpret line plots
</span><span>Create line plots
</span><span>Create and interpret line plots with fractions
</span><span>Create frequency tables
</span><span>Interpret bar graphs
</span><span>Create bar graphs
</span><span>Interpret double bar graphs</span><span>
</span></span><span>
</span></span>
Answer:
Choices A, C, E
Step-by-step explanation:
The prices are proportional, so divide any price by the corresponding number of pounds to find the unit cost.
$1.47/(3 lb) = $0.49/lb
The unit cost is $0.49 per lb.
Now we look in the choices to see which choice has a unit price of $0.49/lb.
We divide each price by its number of pounds to fund each unit cost. Every choice with a unit cost of $0.49/lb is an answer.
A $0.98/(2 lb) = $0.49/lb Choice A works
B $4.45/(7 lb) = $0.64/lb Choice B does not work
C $2.94/(6 lb) = $0.49/lb Choice C works
D $0.54/(1 lb) = $0.54/lb Choice D does not work
E $3.92/(8 lb) = $0.49/lb Choice E works
Answer: Choices A, C, E
