MATHEMATICS MIDDLE SCHOOL

1Mom buys a rectangular rug with an area of 77 square
meters. The length of the rug is 35 meters. What is the width
of the rug?

Answers

Answer 1
Answer:

Width = area / length

Width = 77 / 35

Width = 2.2 meters
Answer 2
Answer:

The answer is w=2.2m

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When preparing the cheese for their pizzas, the cooks at Brian's pizza restaurant mix 1 kilogram of Parmesan cheese and 9 kilograms of mozzarella. At Jeff's pizza restaurant, the cooks mix 2 kilograms of Parmesan cheese and 16 kilograms of mozzarella. Which restaurant uses a lower ratio of Parmesan to mozzarella?Brian's restaurant
Jeff's restaurant
neither; the ratios are equivalent

Answers

Jeff's Restaurant uses less because if you simplify both of the ratios you get 1/9 and 1/8

The expression 1/4 X 3/4 represents a fraction of a circle that is shaded

Answers

1/4 * 3/4 = 3 /16 of a circle

Mack designed a water fountain with a square pyramid flowing into a cube. The edges of the bases of the pyramid and the cube have the same length and the heights of the pyramid and the cube are the same. Describe the relationship between the volume of the cube and the volume of the pyramid.

Please help me on this question. There are six questions in total and I did the rest (finding the volume/surface area) but this one I just don't understand. I'm willing to give up 60 of the 70 points I have for help (help that tells me the answer and explains it). Maybe even all 70. Please help if you understand. Thank you, minna.

Answers

volume of pyramid = 1/3 b2h
volume of  cube = b3

now , provided pyramid and cube have same edges and same heights.

thus, volume of pyramid = 1/3 b3
volume of cube = b3.

thus, ratio = 1/3b3/ b3 = 1/3.

Thus, volume of pyramid = 1/3volume of cube
V_(cube)=a^3\ \ \ and\ \ \ V_(pyramid)= (1)/(3) \cdot a^2\cdot h=(1)/(3)a^3\n \n (V_(pyramid))/(V_(cube)) = ((1)/(3)a^3)/(a^3)= (1)/(3)\n \n \nA_(cube)=6a^2\n \nh^2=a^2+( (1)/(2) a)^2\ \ \ \Rightarrow\ \ \ h^2= (5a^2)/(4)\ \ \ \Rightarrow\ \ \ h= (a √(5) )/(2)\n\nA_(pyramid)=a^2+4\cdot (1)/(2)ah=a^2+2a\cdot (a √(5) )/(2) =a^2(1+ √(5)) \n \n (A_(pyramid))/(A_(cube))= (a^2(1+ √(5)) )/(6a^2) = (1+ √(5))/(6)

Please help don't know how to do

Answers

Area of a triangle is (basexheight)/2

That's what your Formula, then you have to plug in the numbers

so the algebraric expression is (5xn)/2

For then end if you look at the patteren for the height it goes by 2. So the last height would be 10.
Plug that into the equation, which would be (5x10)/2=25

A rectangular pool is 20 feet wide and 50 feet long. A deck used for sunning surrounds the pool. The deck is the same width all the way around the pool. The total area of the deck is 456 square feet. How wide is the walkway?A. 2 feet
B. 3 feet
C. 4 feet
D. 5 feet

Answers

Ahh, this question goes all the way back to my year 9 test a couple years ago; which I got wrong back then - I now know how

Firstly we find the expression for the area (using x as the walk way):
>50x * 2 (the left and right) 
>20x * 2 (the top and bottom)
>4 * x^2 (the corners)

Add them all together , Area = 140x + 4x^2
Now we place the deck's area, 456 into the expression

456 = 140x + 4x^2

Solve for x
I'm a bit rusty on this i'm afraid, but I believe the only way to solve this is to factorise it
0 = 4x^2 + 140x - 456
0 = 4(x+38)(x-3)            <
x must = -38 or = +3 (the numbers inside the brackets inverted)
x must = +3 as it's logical, you can't have a negative width

The walkway is 3 feet wide, we can put this into our expression to double check this,
456 = 140*(3) + 4(3)^2
456 = 420 + 4*9
456 = 420 + 36
456 = 456
Yes, 3 feet wide is correct.


*Note, I tried to keep this simple, please let me know if I didn't go into enough detail anywhere
The answer is b. 3 ft

What are exponents and how do I do them?

Answers

Exponents are actually really simple. They are the little numbers on top of numbers and represents powers, so if it was 2 to the power of 2 you multiply 2*2 since there is 2 2s.(
an exponent is the little number above a different number 

10^((2)This 2 Is The Exponent)

10*2= 10+10=20

10^(2)=10*10=100

here is another example

4^(6)=4*4*4*4*4*4=4096
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