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3 years ago

What is the answer too this (3x+3)(x+4)

1 answer:

7 0

=3x2+15x+12 you can solve this using an algebra calculator

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A class survey found that 29 students watched television on Monday, 24 on Tuesday, and 25 on Wednesday. Of those who watched TV

gizmo_the_mogwai [7]

Answer:

There were 49 students in the class

Step-by-step explanation:

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

I am going to say that:

-The set A represents the students that watched TV on Monday

-The set B represents the student that watched TV on Tuesday.

-The set C represents the students that watched TV on Wednesday.

We have that:

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

In which a is the number of students that only watched TV on Monday, $A \cap B$ is the number of adults that watched TV both on Monday and Tuesday, $A \cap C$ is the number of students that watched TV both on Monday and Wednesday, and $A \cap B \cap C$ is the number of students that watched TV on every day.

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 subsets:

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

The sums of all of this values is the number of student that were there in the class. This means that we want to find the value of T:

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

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

Solution:

12 students watched TV on all three days:

$A \cap B \cap C = 12$

14 students watched TV on both Monday and Tuesday

$A \cap B + A \cap B \cap C = 14$

$A \cap B = 14 - 12$

$A \cap B = 2$

Of those who watched TV on only one of these days, 13 choose Monday, 9 chose Tuesday, and 10 chose Wednesday.

$a = 13, b = 9, c = 10$

29 students watched television on Monday:

$A = 29$

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

$29 = 13 + 2 + (A \cap C) + 12$

$A \cap C = 29 - 27$

$A \cap C = 2$

24 on Tuesday

$B = 24$

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

$24 = 9 + (B \cap C) + 2 + 12$

$B \cap C = 24 - 23$

$B \cap C = 1$

Now we have every value needed to find T:

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

$T = 13 + 9 + 10 + 2 + 2 + 1 + 12$

$T = 49$

There were 49 students in the class

7 0

4 years ago

41) Gabriella invests $8,193 in a retirement

nataly862011 [7]

Answer:

Option C. $\$34,252.67$

Step-by-step explanation:

we know that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$t=18\ years\\ P=\$8,193\\ r=0.08\\n=6$

substitute in the formula above

$A=\$8,193(1+\frac{0.08}{6})^{6*18}=\$34,252.67$

4 0

4 years ago

Two lines, C and D. are represented by the equations given below.

Delicious77 [7]

The answer is D. (4,14) because both lines pass through this point

Explanation: You can insert (4,14) in either equation and so if you insert it into y= x+10 you get 14=4+10 which shows the x combined with 10 equals the y so it’s correct and if you plotted both lines on the graph both lines would travel through this point because it is a solution for both lines.

3 0

3 years ago

Divide (10x^3 + 19x^2 + x - 7) by (5x + 2)

Maslowich

Answer:

2x² + 3x - 1 - 5/(5x +2)

Step-by-step explanation:

2x² + 3x - 1

__________________

5x + 2 | 10x³ + 19x² + x - 7

| -10x³ - 4x²

| 15x² + x

| - 15x² - 6x

| - 5x - 7

| 5x +2

| - 5

2x² + 3x - 1 - 5/(5x +2)

6 0

3 years ago

A trail around a river is 3 1/4 miles long. What is the length, in feet, of the trail?

Law Incorporation [45]

5280 feet in a mile
3.25 x 5280 = 17160 feet

3 0

3 years ago