18. The 5 only needs to be "distributed" to terms that are inside the parentheses where 5 is on the outside. Here, the only term in the parentheses is 2x. Anne apparently also multiplied -3 by 5, erroneously. The -3 term is not inside the parentheses, so should be left alone when "distributing" the 5.

The left side of the equation simplifies to 10x -3, so Anne should have had ...

10x -3 = 20x +15

-18 = 10x . . . . . . . . . add -15-10x

-1.8 = x . . . . . . . . . . divide by 10.

The solution is x = -1.8.

___

19. Procedure: Subtract the right side of the equation from both sides. Use the distributive property as many times as necessary to eliminate parentheses. Collect terms. Divide by the coefficient of x. Subtract the constant.

5[3(x+4) -2(1 -x)] -x -15 = 14x +45 . . . . . . . original equation

5[3(x+4) -2(1 -x)] -x -15 -14x -45 = 0 . . . . . right side subtracted

5[3x+12 -2 +2x] -x -15 -14x -45 = 0 . . . . . . inner parentheses eliminated

15x +60 -10 +10x -x -15 -14x -45 = 0 . . . . . outer parentheses eliminated

(15 +10 -1 -14)x +(60 -10 -15 -45) = 0 . . . . . like terms associated

10x -10 = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . simplified

x - 1 = 0 . . . . . . . . . divide by the coefficient of x

x = 1 . . . . . . . . . . . . subtract -1 (same as add 1)

The solution is x = 1.

5 0

4 years ago

In the diagram below, ΔPQR ≅ ΔSTR. Complete the statement RQ⎯⎯⎯⎯⎯⎯⎯⎯≅ R Q ¯ ≅ ___

pantera1 [17]

Based on the CPCTC theorem, the complete statement is: RQ ≅ RT.

<h3>What is the CPCTC Theorem?</h3>

According to the CPCTC theorem, if two triangles are said to be congruent, then all the corresponding parts of both triangles are congruent.

Given that ΔPQR ≅ ΔSTR, RQ corresponds to RT. Therefore, both sides are congruent to each other.

Thus, the complete statement is: RQ ≅ RT.

Learn more about the CPCTC theorem on:

brainly.com/question/14706064

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3 0

2 years ago

The sides of the base of a right square pyramid are 4 m in length , and its slant height is 8 m. If the lengths of the sides of

hram777 [196]

Answer:

Step-by-step explanation:

We have that the total surface area of a regular pyramid is the sum of the areas of its lateral faces and its base, therefore it would be equal to:

As = 1/2 * p * h + l ^ 2

where l are the sides that measure 4, p is the perimeter that is the sum of the sides, and since there are 4 sides then it would be 16 (4 * 4), h the inclined height is 8, replacing we are left with:

As = 1/2 * 16 * 8 + 4 ^ 2

Ace = 80

Now, they say that the sides and the tilt height are multiplied by 4, the sides now measures 16, therefore the perimeter is 64 (4 * 16), the height would be 32, replacing would be:

As = 1/2 * 64 * 32 + 16 ^ 2

As = 1280

Therefore the factor would be:

1280/80 = 16

This means that to calculate the new surface area, it must be multiplied by the square of the number by which the sides and the inclined height are multiplied, that is, 4 ^ 2 = 16.

5 0

3 years ago

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