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DochEvi [55]
3 years ago
7

A square-based prism made of clay had dimensions of 6 by 6 by 10. A pyramid was removed from the prism as shown below so that th

e prism has no top. If the slant height of the pyramid is 10.5 units, the total surface area of the remaining clay solid is _____ square units. (Round answer to nearest whole number)
Mathematics
1 answer:
guajiro [1.7K]3 years ago
6 0

Answer:

<h2>The total surface area is 402 square units.</h2>

Step-by-step explanation:

Givens

  • The dimensions of the square-based prism are 6 by 6 by 10.(l=6, w=6 and h=10.
  • The slant height of the pyramid is 10.5 units.
  • The base of the pyramid matches the top of the square prism, so it's square-based prism.

Remember tha the slant height refers to the height of sided triangles.

Basically, the resulting form 4 rectangular faces, 1 square face, and four triangular faces.

Rectangular face area:

A_{rectangular}=6 \times 10 = 60 u^{2}

(Remember that the area of a rectangle is defined as b \times h)

Square face area (bottom):

A_{square}=6 \times 6 = 36 u^{2}

(Remember that the area of a square is l \times l)

Triangular faces area:

A_{triangular}=\frac{1}{2}bh=\frac{1}{2}(6)(10.5) =31.5u^{2}

(Remember that the area of a triangle is \frac{1}{2} bh.

Multiplying by the right number of each type, we have the total surface area of the resulting figure:

A=4(60)+36+4(31.5)=240+36+126=402 u^{2}

Therefore, the total surface area is 402 square units.

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2. After the relay race, Larry, Curly, and Moe went to the
jarptica [38.1K]

Using proportions, it is found that each of the 6 people got $0.5.

<h3>Proportions:</h3>
  • This question is solved by <em>proportions</em>, using a rule of three.
  • $3.00 is shared between 6 people, which are Larry, Curly, Moe, Alvin, Simon and Theodore. How much did each people(1 person) get?

The <em>rule of three</em> is:

$3.00 - 6 people

$x - 1 person

Applying cross multiplication:

6x = 3

x = \frac{3}{6}

x = 0.5

Each of the 6 people got $0.5.

To learn more about proportions, you can take a look at brainly.com/question/24372153

7 0
2 years ago
Solve for X<br> -5x=45<br><br> A 225 <br> B 9 <br> C -9<br> D 45
andriy [413]
X=-9

-x=9 so x=-9 since you inverse the sign
8 0
3 years ago
Can anyone explain how to solve this using %/100 = is/of?
kumpel [21]

Answer:

20%/100 = 8 peeps / 40 items in the basket

(40 total items)

Step-by-step explanation:

Let x be the total number of items in the basket. The ratio of peeps to the total item is 1/5. Therefore,

1/5 = 8/x

x = 40

40 total items

6 0
3 years ago
Consider the function,
RUDIKE [14]

Answer:

If x= 4 then f(x) = 4x -5 is 11.

Step-by-step explanation:

f(x) = 4x -5

We need to find the domain value that corresponds to the output f(x) = 11

In this question, we need to solve the expression for value of x such that the answer is 11.

if  x= 3

f(3) = 4(3) -5

     = 12 -5

    = 7

Since we want the answer 11 so we cannot take x= 3

if x = 4

f(4) = 4(4)-5

    = 16 - 5

    = 11

So, if x= 4 then f(x) = 4x -5 is 11.

5 0
3 years ago
The graph below shows the height of a tunnel f(x), in feet, depending on the distance from one side of the tunnel x, in feet:
denis23 [38]
Part A) x-intercepts simply show that when the value of the function is zero. Vertex coordinates show that when the function obtains its maximum value. When x=50, function obtains its maximum value and it's 75. The function is increasing in the interval (0, 50) and decreasing in the interval (50, 100). In regard to the height and distance of the tunnel, these numbers show that decreasing and increasing intervals are symmetric. Each number from the intervals has its own pair in the corresponding interval and they are located in the same distance from the midpoint (50,75)

Part B) In order to calculate the average rate of change, we can first write the function. Using the information about the x-intercept and the vertex coordinates, we find that our function is f(x)=-0.03x^{2}+3x.
Plugging 15 and 35 in x, we can find the values of the function, i.e. 
f(15)=38.25 and f(35)=68.25.
Then, the average change is \frac{68.25-38.25}{35-15}=1.5
4 0
3 years ago
Read 2 more answers
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