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SIZIF [17.4K]
3 years ago
5

8" × 8" × 3". Which expression will give her the total volume of the pans

Mathematics
1 answer:
Zina [86]3 years ago
8 0
192 8*3= 24 and 24*8= 192
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Solve the problem algebraically. Clearly define all variables, write an appropriate equation, and solve.
hichkok12 [17]

Answer:

Y=8 and X=21

Step-by-step explanation:

The key to solving word (story) problems is to learn how to translate words and phrases into concise, precise math expressions (variables and operations).  Make a table and add to it as you do problems:

      is              means           =

    more than                        +

      twice                              2*x

      sum                               +

      of                            usually means multiply

     ...

Assign variables.  Try to assign variables to the values the problem asks you to find.

In this problem, there are two variables.   Let x = one number;   y = other numbers

Translate:

 "One number is 5 more than twice the other number"    means

            x          =    5    +        2     *      y

 "sum of the two numbers is 29"     means

      x   +   y                    = 29

Now, the easy math.

Use the value for x from the first equation and substitute that into the second equation:

    (5 + 2y)      +     y       =  29

     5 + 3y = 29                    (collect terms)

           3y = 24                (subtract 5 from both sides)

             y = 8

Now, put that value of y into either equation to solve for x  (Which equation is easier??)

     x + 8 = 29

       x  = 21                 (subtract 8 from both sides)

Checking (very important):

 Is 21 really 5 more than 2(8)?

      21 = 5+16     ?

      21  =  21? yes

 Is  21 + 8 = 29  ?

        29 = 29? yes

p.s., learn the process, don't just get the right answer;  there will be lots of problems that are solved the same way!

3 0
1 year ago
What is the volume of something if the diameter is 2cm and the height is 9cm ?
Nady [450]
28.23 is the volume of something if the diameter is 2 cm and the height is 9 cm.
7 0
3 years ago
What are the center and radius of the circle defined by the equation<br> x2 + y2 - 6x+By+21=0 ?
podryga [215]

    (x-3)2+(y+B2)2+By=-12+B24

5 0
3 years ago
I will mark brainliest IF CORRECT
umka2103 [35]

Answer:

1 - (π/6) - (√3/4)

Step-by-step explanation:

First, calculate the area of ABCD. That's just 1*1 = 1 un^{2}

Then, we are told that arcs BD and AC are circular, meaning they are portions of a circle. Therefore, let's redraw this image a little. Look below for the image.

Essentially, what I've done is created an equilateral triangle and two sectors. You may be wondering why the triangle is equilateral. Well, we firstly know it's isosceles because the two original arcs are circular and congruent. Their overlap creates two congruent lines that can be extend from point M to the vertices A and D. These two lines also happen to be radii of the quarter circles because the two sectors have AM AND AD as radii. AM and AD = 1, so AMD is an equilateral triangle.

Draw altitude OD. This is a right angle. Since equilateral triangles are also isosceles triangles, and isosceles triangles have the property of sharing the median to base and altitude to base, we can say that OD = \frac{1}{2} AD = \frac{1}{2}. MD = 1, so this triangle is a 30-60-90 triangle. Why? This is because of the 30º angle converse theorem. The shorter leg is half of the hypotenuse MD, so <OMD is a 30º angle, making <ODM a 60º angle and inevitably <MDC a 30º angle (because <D is a right angle) and <ABM as well because the two sectors are congruent.

Because m<ABM = m<MDC = 30º, these two sectors are 30/360 of the individual circles or 1/12 of the original circles, which have areas of π (because 1^2*π = π). Each is 1/12π, combined they are 1/6π.

The area of the equilateral triangle is √3/8. This is because MO can be calculated, using the 30-60-90 ratios, to be √3/2. (1 * √3/2)/2 = (√3/2)/2 = √3/4; this uses the area of a triangle. Now, time to calculate the shaded area.

The area of the square is 1, the area of the sectors π/6, and the equilateral triangle √3/4. Subtract the equilateral triangle and sectors' areas from the area of the square to be left with the remaining shaded part. 1-(π/6)-(√3/4) is your final answer. To put that a little more cleanly below in the image.

Hope this helps, have a great day.

3 0
2 years ago
a cone has a volume of 6 cubic inches. what is the volume of a cylinder that the cone fits exactly inside of
ella [17]

Answer:

= 18 cubic inches

Step-by-step explanation:

The volume of a cone is given by the formula;

V = 1/3 × base area × height

While that of cylinder is given by the formula;

Volume = Base area × height

Since we need the cylinder to fit exactly inside the cone, then it  means that their bases are the same and heights are the same.

Therefore;

The cone has three times less volume compared to the cylinder.

Thus;

Volume of the cylinder = Volume of cone × 3

                                       = 6 In³ × 3

                                       <u>= 18 cubic inches</u>

5 0
3 years ago
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