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vlabodo [156]
3 years ago
14

Match the following expression 12(x-3)+18=4(2x-3) with the number of solutions below.

Mathematics
2 answers:
notka56 [123]3 years ago
8 0

Answer:

3/2, one solution.

Step-by-step explanation:

12(x-3)+18=4(2x-3)

12x-36+18=8x-12

12x-8x-18=-12

4x-18=-12

4x=-12+18

4x=6

x=6/4

simplify

x=3/2

vfiekz [6]3 years ago
4 0
12(x-3) + 18 = 4(2x-3)

12x-36+18 = 8x-12

12x -18 = 8x-12

12x-8x = -12 + 18

4x = 6

x = 6/4 or 3/2

one solution A

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What is the value of x?
adelina 88 [10]

This is an equilateral triangle, which is a triangle that has 3 congruent/equal sides and 3 congruent angles.


To find "x", you can set the sides equal to each other because they are suppose to be the same length (you can just do two sides because all of the sides are the same)

[Side AB = Side BC]

4x - 10 = 3x + 2     Subtract 3x on both sides

x - 10 = 2         Add 10 on both sides

x = 12


[proof]

Side AB:

4x - 10    Plug in 12 for x

4(12) - 10 = 48 - 10 = 38


Side BC:

3x + 2     Plug in 12 for x

3(12) + 2 = 36 + 2 = 38


Side AC:

5x - 22      Plug in 12 for x

5(12) - 22 = 60 - 22 = 38




This is also an equilateral triangle (the tick marks show that the sides are the same)

A triangle is 180°. So the three angles add up to 180°.

Since this is an equilateral triangle, all the angles should be the same.

Each angle is 60°

[60° + 60° + 60° = 180°   or you could have divided 180 by 3 = 60]


Now that you know each angle is 60°, you can do:

(2x - 4)° = 60°

2x - 4 = 60    Add 4 on both sides

2x = 64    Divide 2 on both sides

x = 32


4 0
2 years ago
27. Use Structure Use the table at the right. Yolanda is planning a party that will take place in three rooms. a. Write an expre
BabaBlast [244]

Answer:

25t+95 or 5(5t + 19)

Step-by-step explanation:

The total of the sound fee = $25

The total of the rental fee = $95

Write is as an equation and you can get 25t + 95 or 5(5t + 19)

5 0
2 years ago
What is the surface area of this figure?
disa [49]

Answer:

72 sq. mi

Step-by-step explanation:

Breaking this down, we have 2 right triangles with sides of 3, 4, and 5 miles, and 3 rectangles with dimensions 3 x 5, 4 x 5, and 5 x 5 miles. Remember that the area of a triangle is 1/2 x b x h , where b and h are the triangle's base and height. The base and height of the triangles at the bases of the figure are 3 and 4, so each triangle has an area of 1/2 x 3 x 4 = 1/2 x 12 = 6 sq. mi, or 6 + 6 = 12 sq. mi together.

Onto the rectangles, we can find their area by multiplying their length by their width. Since the width of these rectangles is the same for all three - 5 mi - we can make our lives a little easier and just "glue" the lengths together, giving us a longer rectangle with a length of 3 + 4 + 5 = 12 mi. Multiplying the two, we find the area of the rectangles to be 5 x 12 = 60 sq. mi.

Adding this area to the triangle's area gives us a total area of 12 + 60 = 72 sq. mi.

7 0
3 years ago
Read 2 more answers
jim is building a model of a square pyramid for a class project the side length of the square base is 12 inches and the slant he
yulyashka [42]
Surface area of a square pyramid is the area of the base + 4 times the area of one of the slanted sides.
Area of base = side length * side length
Area of side = (1/2) * side length * slant height
Don't forget that you have to multiply the area of the side by 4!

Step 1: 12 x 12 = 144
Step 2: 12 x 20 = 240 divided by 2 = 120
Step 3: 144 + 120 x 4
4 0
3 years ago
Read 2 more answers
Suppose a 5x8 coefficient matrix for a system has pivot columns. Is the system​ consistent? Why and Why not?
Lyrx [107]

Step-by-step explanation:

All the 5 rows of the coefficient matrix (since it is of order 5×8) will have a pivot position. The augmented matrix obtained by adding a last column of constant terms to the 8 columns of the coefficient matrix will have nine columns and will not have a row of the form [0 0 0 0 0 0 0 0 1]. So the system is consistent.

7 0
3 years ago
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