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expeople1 [14]
3 years ago
8

Cidnee is weighing combinations of geometric solids. She found that 4 cylinders and 5 prisms weigh 32 ounces and that 1 cylinder

and 8 prisms weigh 35 ounces. Write and solve a system of equations to determine the weight of each cylinder and prism.
Mathematics
1 answer:
vitfil [10]3 years ago
4 0

Answer:

The weights of each cylinder and prism are 3 and 4 ounces, respectively.

Step-by-step explanation:

Let be x and y the masses of a cylinder and a prism, measured in ounces, respectively. After a careful reading of the statement we get the following linear equations by interpretation:

i) <em>She found that 4 cylinders and 5 prisms weigh 32 ounces:</em>

4\cdot x +5\cdot y = 32\,oz (Eq. 1)

ii) <em>And that 1 cylinder and 8 prisms weigh 35 ounces:</em>

x + 8\cdot y = 35\,oz (Eq. 2)

Now we solve the system of linear equations algebraically:

From (Eq. 2):

x = 35 - 8\cdot y

(Eq. 2) is (Eq. 1):

4\cdot (35-8\cdot y) + 5\cdot y = 32

140-32\cdot y +5\cdot y = 32

32\cdot y - 5\cdot y = 140-32

27\cdot y = 108

y = 4\,oz

From (Eq. 2):

x = 35 - 8\cdot (4)

x = 35 - 32

x = 3\,oz

The weights of each cylinder and prism are 3 and 4 ounces, respectively.

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Dovator [93]
<h3>Answer:  B) 2</h3>

=========================================================

Explanation:

Take away the four white small squares on the left side. To balance things out, you have to add 4 black squares to the right side.

Also, take away the two white long rectangles from the right side. To balance this out, you have to add 2 gray long rectangles to the left side.

You should have:

  • 5 gray rectangles, and no squares (of any color) on the left side
  • 10 black squares, no long rectangles (of any color), on the right side

From here you'll group up the 10 black squares so that you'll have 2 black squares per gray rectangle.

This means the solution is 2.

-------------------------------------

If you're curious about the algebraic way to solve, then you could do this:

3x-4 = -2x+6

3x+2x = 6+4

5x = 10

x = 10/5

x = 2

This method doesn't require us to use the visual model.

5 0
3 years ago
8,326 x 9 =n<br>which is the answer?<br>A. 52,234<br>B.74,934<br>C.2,376<br>D.3008<br>E. none​
Kazeer [188]

Answer:

B

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
What two numbers' sum=-4 and product=-2
n200080 [17]

Let <em>a</em> and <em>b</em> be the two numbers. Then

<em>a</em> + <em>b</em> = -4

<em>a b</em> = -2

Solve the second equation for <em>b</em> :

<em>b</em> = -2/<em>a</em>

Substitute this into the first equation:

<em>a</em> - 2/<em>a</em> = -4

Multiply both sides by <em>a</em> :

<em>a</em>² - 2 = -4<em>a</em>

Move 4<em>a</em> to the left side:

<em>a</em>² + 4<em>a</em> - 2 = 0

Use the quadratic formula to solve for <em>a</em> :

<em>a</em> = (-4 ± √(4² - 4(-2))) / 2

<em>a</em> = -2 ± √6

If <em>a</em> = -2 + √6, then

-2 + √6 + <em>b</em> = -4

<em>b</em> = -2 - √6

In the other case, we end up with the same numbers, but <em>a</em> and <em>b</em> are swapped.

7 0
2 years ago
How many solutions exist for the given equation?
Tpy6a [65]

Answer:

infinitely many

Step-by-step explanation:

12x + 1 = 3(4x + 1) - 2

Distribute

12x + 1 = 12x + 3 - 2

Combine like terms

12x+1 = 12x +1

Subtract 12x from each side

1 =1

Since this is always true, we have infinite solutions

4 0
2 years ago
Read 2 more answers
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o-na [289]
Some of the possible points using this equation are...
(2,14)
(1,10)
(0,6)
(-1,2)
(-2,-2)
5 0
3 years ago
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