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3 years ago

Solve for x: 10 - 2x = -5x - 5 (1) X = -5 (3) X= 4 (2) x 15 (4)x= -15

Mathematics

2 answers:

Alekssandra [29.7K]3 years ago

7 0

10 - 2x = -5x -5
+2x +2x
10 = -3x -5
+5 +5
15= -3x
X= -5

topjm [15]3 years ago

3 0

First you add 5x on both sides:

10−2x+5x=−5

=
10+3x=−5

Then you subtract 10 from both sides:

3x=−5−10
=
3x=-15

Then you divide both sides by 3

X= -15/3

X= -5

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Answer:

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Where x and y are the numerator and denominator of our new fraction respectively.

Also given is that x + y = 24

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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.

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