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2 years ago

.−3(4x + 3) + 4(6x + 1) = 43 What is the solution?

Mathematics

1 answer:

maks197457 [2]2 years ago

6 0

Answer:

x = 4

Step-by-step explanation:

After you simplify the left side by eliminating parentheses and collecting terms, you have a 2-step linear equation.

-3(4x +3) +4(6x +1) = 43 . . . . . . given

-12x -9 +24x +4 = 43 . . . . . eliminate parentheses

12x-5 = 43 . . . . . . . . . . . collect terms (now a 2-step equation)

12x = 48 . . . . . . . . . . step 1, add the opposite of the unwanted constant

x = 4 . . . . . . . . . . . step 2, divide by the coefficient of x

The solution is x = 4.

<em>Check</em>

-3(4·4 +3) +4(6·4 +1) = 43 . . . . substitute for x

-3(16 +3) +4(24 +1) = 43

-3(19) +4(25) = 43

-57 +100 = 43 . . . . . true

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When the members of a family discussed where their annual reunion should take place, they found that out of all the family mem

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Answer:

The total number of family members is 21.

Step-by-step explanation:

To solve this problem, we must build the Venn's Diagram of these sets.

I am going to say that:

-The set A represents those that would not go to a park.

-The set B represents those who would not go to a beach.

-The set C represents those who would not go to the family cottage.

The value d represents those who would go to all three places.

We have that:

$A = a + (A \cap B) + (A \cap C) + (A \cap B \cap C)$

In which a are those that would only not go to a park, $A \cap B$ are those who would not got to a park or to the beach, $A \cap C$ are those who would not go to a park or to the famili cottage. And $A \cap B \cap C$ are those that would not go to any of these places.

By the same logic, we have:

$B = b + (B \cap C) + (A \cap B) + (A \cap B \cap C)$

$C = c + (A \cap C) + (B \cap C) + (A \cap B \cap C)$

This diagram has the following values:

$a,b,c,d,(A \cap B), (A \cap C), (B \cap C), (A \cap B \cap C)$

The total number of family members is the sum of all these values:

$T = a + b + c + d + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C)$

We start finding the values from the intersection of the three sets

5 would not go to a park or a beach or to the family cottage.

This means that $A \cap B \cap C = 5$

1 would go to all three places. This means that $d = 1$ .

8 would go to neither a park nor the family cottage

This means that:

$A \cap C + (A \cap B \cap C) = 8$

$A \cap C = 3$

8 would go to neither a beach nor the family cottage

$B \cap C + (A \cap B \cap C) = 8$

$B \cap C = 3$

7 would go to neither a park nor a beach

$A \cap B + (A \cap B \cap C) = 7$

$A \cap B = 2$

15 would not go to the family cottage

$C = 15$

$C = c + (A \cap C) + (B \cap C) + (A \cap B \cap C)$

$15 = c + 3 + 3 + 5$

$c = 4$

12 would not go to a beach

$B = 12$

$B = b + (B \cap C) + (A \cap B) + (A \cap B \cap C)$

$12 = b + 3 + 2 + 5$

$b = 2$

11 would not go to a park

$A = 11$

$A = a + (A \cap B) + (A \cap C) + (A \cap B \cap C)$

$11 = a + 2 + 3 + 5$

$a = 1$

Now, we can find the total number of family members.

$T = a + b + c + d + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C)$

$T = 1 + 2 + 4 + 1 + 2 + 3 + 3 + 5$

$T = 21$

The total number of family members is 21.

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Answer:

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3 years ago

Read 2 more answers

Given the expression ‘6 more than twice a number’, what is the value of the expression if the number is equal to 5?

stepan [7]

Answer:

Expression: $2x + 6$

Value of the expression when $x = 5$ : $16$

Step-by-step explanation:

Let's first focus on the expression: '6 more than twice a number'. Twice a number is the same as saying two times a number. Let's have that number be represented by $x$ . Twice a number would mean $2x$ , and 6 more than that would just be $2x + 6$ .

We'll then plug in 5 for $x$ to get the value of the expressinn:

$2(5) + 6 = 10 + 6 = 16$

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3 years ago