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Step2247 [10]
2 years ago
11

Point J is located at (-4,4)

Mathematics
1 answer:
rewona [7]2 years ago
4 0
What is the question?
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The surface area of the prism below is 264 square units . Find the missing dimensions of this prism. ( picture is in the picture
nignag [31]

Answer:

The missing dimension is 4 units.

Step-by-step explanation:

In the given prism,

Of all the surfaces,

There are three rectangular surfaces and two triangular surfaces

<h2>Analyzing areas of rectangular surfaces:</h2>

1)The two rectangles with dimensions of 15 units and 5 units:

The area of each rectangle = Length of rectangle \times Breadth of rectangle

From the diagram,

Length of rectangle = 15 units,

Breadth of rectangle = 5 units.

Area of each rectangle = 15\times 5 ;

Area of each rectangle = 75 square units.

Sum of areas of the two rectangles = 2\times 75

Sum of areas of the two rectangles = 150 square units (equation 1)

2) The rectangle with the dimensions 15 units and 6 units:

The area of thus rectangle=  Length of rectangle \times Breadth of rectangle

From the diagram,

Length of rectangle = 15 units,

Breadth of rectangle = 6 units.

Area of the rectangle = 15\times 6 ;

Area of the rectangle = 90 square units. (equation 2)

From equation 1 and equation 2,

Therefore sum of areas of all rectangles in the prism = 150 + 90

Sum of areas of rectangles = 240 square units.

We also know,

Total surface area of the prism = Sum of areas of triangles + Sum areas of rectangles

Given, Total surface area of prism = 264 square units.

Therefore from the formula,

Sum of areas of triangles = Total surface area - sum of areas of reactangles

Sum of areas of triangles = 264 - 240

Sum of areas of triangles = 24 square units. (equation 3)

Let the missing dimension be 'h units'

<h2>Calculating sum of areas of triangles:</h2>

From diagram,both triangles are congruent,hence have the same area

Area of a triangle = \frac{1}{2}\times base\times height

From diagram,

Base = 6 units,

Height = h units.

Area of a triangle =\frac{1}{2}\times 6\times h = 3h square units.

Sum of the areas of both triangles = 3h+3h = 6h square units.

Using equation 3, we get

6h = 24;

h = \frac{24}{6}

Therefore,

h = 4 units.

Therefore,

The missing dimension is 4 units.

4 0
3 years ago
Gino studied 3/4 hour for his test on Monday. He studied another 2/4 hour on Tuesday. How long did he study in all?
dybincka [34]
Gino studied for 5/4 hours in all. To get this, do 3+2 for the numerator and just put 4 as the denominator. (Four just stays the same the denominator is all fours. If you want more details just put it on comments.) Now you have the answer: 5/4 hours. 
8 0
2 years ago
Someone please help me with d.
Sav [38]
X=0.2
All you have to do is simplify both sides of the equation. Add 3x to both sides. Then subtract 0.8 from both sides.
8 0
2 years ago
Read 2 more answers
2. Aaron baked two identical cakes. He cut one into 9 equal slices and the other into 19 equal slices.
Svetlanka [38]

2/3 x 9 = 6 slices

1/3 x 18 = 6 slices

Hence they give the same number of slices.

5 0
2 years ago
Solve the equation for x by graphing.
olchik [2.2K]
Answer:
x ≈ -0.24

Explanation:
Using a graphing tool to graph the given equation, we will end up with the graph shown in the attached image.

Now, to solve the equation means to find the x-intercept.

Taking a look at the graph, we would find that the x-intercept is somewhere between the -0.2 and the -0.3

This means that the best choice is x ≈ -0.24

We can check using algebraic substitution:
-3x + 2 = -3(-0.24) + 2 = 2.72
4ˣ +2 = 4⁻⁰.²⁴ + 2 = 2.7169
We can note that the two values are almost equal.

Hope this helps :)

6 0
3 years ago
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