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jeka94
3 years ago
13

3.

Mathematics
2 answers:
Mazyrski [523]3 years ago
8 0
Answer: A

Explanation:
lana66690 [7]3 years ago
3 0

Answer:

a

Step-by-step explanation:

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Fernando has two equally-sized containers of clay which he is using to build a pyramid-like structure. The finished structure wi
evablogger [386]

Answer:

Fernando does not have enough clay to finish the structure since, the expressions for the volume left are not the same.

Step-by-step explanation:

Let w be the length of the longest slab. Since each slab is 2 inches less than the one beneath it, we have the width of the other 3 slabs as w - 2, w - 2 - 2 = w - 4 and w - 4 - 2 = w - 6 respectively.

Since the base of each slab is a square and has thickness 2 inches, the volume of each slab from largest to smallest is thus 2w², 2(w - 2)², 2(w - 4)² and 2(w - 6)² respectively.

We have that we have half of the container of clay left after forming the first two slabs(which are the bottom-most slabs). Let V be the volume of each clay container. Since we have half left, that is V/2, we have used 2V - V/2 = 3V/2 to make the two bottom-most slabs.

So, 3V/2 = 2w² + 2(w - 2)²

= 2w² + 2(w² - 4w + 4)

= 2w² + 2w² - 8w + 8

= 4w² - 8w + 8

= 4(w² - 2w + 2)   (1)

Also we want to know if V/2 is equal to the volume of the two top-most slabs.

So, V/2 = 2(w - 4)² + 2(w - 6)²

= 2(w² - 8w + 16) + 2(w² - 12w + 36)

= 2w² - 16w + 32 + 2w² - 24w + 72

= 4w² - 40w + 104

= 4(w² - 10w + 26)

From (1) V/2 = 4(w² - 2w + 2)/3 ≠ 4(w² - 10w + 26)

<u>Since the expressions for the remaining volume are not the same, Fernando does not have enough clay to finish the structure.</u>

4 0
3 years ago
How many solutions would there be for the following systems of equations <br>y=3x-5<br>6x-2y=10​
Ann [662]

Answer:

So the solution would be (1,-2). Remember you can always validate that the solution is correct by plugging it into both equations. But this is the same as the first equation, y=3x-5. Since they are the SAME line they will have infinite solutions.

Step-by-step explanation:

6 0
3 years ago
Use the midpoint formula to estimate the sales of Cars, Inc. in 2009, given the sales in 2008 and 2010. Assume that the sales of
lana [24]

Answer:

<em>The estimated sales were $260 million</em>

Step-by-step explanation:

Assume the endpoints of a segment are (x1,y1) and (x2,y2).

The midpoint (xm,ym) is calculated as follows:

\displaystyle x_m=\frac{x_1+x_2}{2}

\displaystyle y_m=\frac{y_1+y_2}{2}

The sales ov Cars, Inc. were (2008,240 million) and (2010,280 million). We need to use the midpoint to estimate the sales in 2009:

\displaystyle x_m=\frac{2008+2010}{2}=2009

\displaystyle y_m=\frac{240+280}{2}=260

The estimated sales were $260 million

5 0
3 years ago
The profit y (in dollars) for a business from selling x coats is represented by y=56x . Graph the equation.
Agata [3.3K]

Answer:

The graph of the equation is also attached.

From the graph, it is clear that at x = 0, the value of y = 0

Hence, the line passes through the origin with the y-intercept 0.

Step-by-step explanation:

The slope-intercept form of the line equation

y = mx+b

where

  • m is the slope
  • b is the y-intercept

Given that the profit y (in dollars) for a business from selling x coats is represented by the equation

y=56x

comparing with the slope-intercept form of the line equation

m = 56

<u>Determining the y-intercept</u>

We know that the value of the y-intercept can be determined by setting x = 0 and determining the corresponding value of y.

substitute x = 0 in the equation

y = 56(0)

y = 0

Thus, the y-intercept b = 1

Thus,

The equation y = 5x has:

  • The slope m = 56
  • The y-intercept b = 1

The graph of the equation is also attached.

From the graph, it is clear that at x = 0, the value of y = 0

Hence, the line passes through the origin with the y-intercept 0.

4 0
3 years ago
How many terms are in the following expression?<br> 2x+4y+8-2
sashaice [31]

Answer:

3

Step-by-step explanation:

In this expression, the first term is <em>2x</em>, then <em>4y, </em>then 8-2 (which simplifies to 6).

3 0
2 years ago
Read 2 more answers
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