How can you use functions to solve real world problems ??

The ratio of the number of boys to the number of girls at Liam's school is 4:5. There are 270 students at his school. Statement

Aleks04 [339]

Answer:

"statement 1: The number of boys at the school is $\frac{4}5$ of the number of girls." is true.

Step-by-step explanation:

Given:

Ratio of Number of boys to the number of girls = 4 : 5

Total number of students = 270

To find:

Number of boys in terms of number of girls = ?

Solution:

As per given statement,

Let, Number of boys = $4x$

Let, Number of girls = $5x$

Total number of students = Number of boys + Number of girls = 270

$\Rightarrow 4x+5x =270\\\Rightarrow 9x=270\\\Rightarrow \bold{x = 30}$

Therefore, number of boys = 4 $\times$ 30 = 120

And, number of girls = 5 $\times$ 30 = 150

As per Statement 1:

Finding $\frac{4}5$ of the number of girls:

$\dfrac{4}{5}\times 150 = 4 \times 30 = 120$ = Number of boys.

Finding $\frac{4}9$ of the total number of students:

$\frac{4}{9}\times 270= 4 \times 30 = 120$ = Number of boys.

Number of boys is equal to $\frac{4}9$ of total number of students.

So, "statement 1: The number of boys at the school is $\frac{4}5$ of the number of girls." is true.

6 0

3 years ago

The community of Yontsville is having a town hall meeting to discuss the damage a recent storm did to their community. It is an

svet-max [94.6K]

Answer:

Trees can help stop erosion by managing runoff. Their leaf canopies help reduce erosion caused by falling rain. They also provide surface area where rain water lands and evaporates. Roots take up water and help create conditions in the soil that promote infiltration.

7 0

3 years ago

Which two tables represent the same function?

topjm [15]

Answer:

The 1st and the 5th tables represent the same function

Step-by-step explanation:

* Lets explain how to solve the problem

- There are five tables of functions, two of them are equal

- To find the two equal function lets find their equations

- The form of the equation of a line whose endpoints are (x1 , y1) and

(x2 , y2) is $\frac{y-y_{1}}{x-x_{1}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

* Lets make the equation of each table

# (x1 , y1) = (4 , 8) and (x2 , y2) = (6 , 7)

∵ x1 = 4 , x2 = 6 and y1 = 8 , y2 = 7

∴ $\frac{y-8}{x-4}=\frac{7-8}{6-4}$

∴ $\frac{y-8}{x-4}=\frac{-1}{2}$

- By using cross multiplication

∴ 2(y - 8) = -1(x - 4) ⇒ simplify

∴ 2y - 16 = -x + 4 ⇒ add x and 16 for two sides

∴ x + 2y = 20 ⇒ (1)

# (x1 , y1) = (4 , 5) and (x2 , y2) = (6 , 4)

∵ x1 = 4 , x2 = 6 and y1 = 5 , y2 = 4

∴ $\frac{y-5}{x-4}=\frac{4-5}{6-4}$

∴ $\frac{y-5}{x-4}=\frac{-1}{2}$

- By using cross multiplication

∴ 2(y - 5) = -1(x - 4) ⇒ simplify

∴ 2y - 10 = -x + 4 ⇒ add x and 10 for two sides

∴ x + 2y = 14 ⇒ (2)

# (x1 , y1) = (2 , 8) and (x2 , y2) = (8 , 5)

∵ x1 = 2 , x2 = 8 and y1 = 8 , y2 = 5

∴ $\frac{y-8}{x-2}=\frac{5-8}{8-2}$

∴ $\frac{y-8}{x-2}=\frac{-3}{6}=====\frac{y-8}{x-2}=\frac{-1}{2}$

- By using cross multiplication

∴ 2(y - 8) = -1(x - 2) ⇒ simplify

∴ 2y - 16 = -x + 2 ⇒ add x and 16 for two sides

∴ x + 2y = 18 ⇒ (3)

# (x1 , y1) = (2 , 10) and (x2 , y2) = (6 , 14)

∵ x1 = 2 , x2 = 6 and y1 = 10 , y2 = 14

∴ $\frac{y-10}{x-2}=\frac{14-10}{6-2}$

∴ $\frac{y-10}{x-2}=\frac{4}{4}======\frac{y-10}{x-2}=1$

- By using cross multiplication

∴ (y - 10) = (x - 2)

∴ y - 10 = x - 2 ⇒ add 2 and subtract y in the two sides

∴ -8 = x - y ⇒ switch the two sides

∴ x - y = -8 ⇒ (4)

# (x1 , y1) = (2 , 9) and (x2 , y2) = (8 , 6)

∵ x1 = 2 , x2 = 8 and y1 = 9 , y2 = 6

∴ $\frac{y-9}{x-2}=\frac{6-9}{8-2}$

∴ $\frac{y-9}{x-2}=\frac{-3}{6}======\frac{y-9}{x-2}=\frac{-1}{2}$

- By using cross multiplication

∴ 2(y - 9) = -1(x - 2) ⇒ simplify

∴ 2y - 18 = -x + 2 ⇒ add x and 18 for two sides

∴ x + 2y = 20 ⇒ (5)

- Equations (1) and (5) are the same

∴ The 1st and the 5th tables represent the same function

3 0

4 years ago

Evaluate 2/3x + 1/2 for x=3/4 (I just copied the exact question)

Travka [436]

Answer:

1

Step-by-step explanation:

(⅔)(¾) + ½

½ + ½

= 1

6 0

3 years ago

Find the value of X (Gotta choose at least 2) x = 52 x = 2 x = 3 x = 33

Ad libitum [116K]

Answer:

Before this problem gets an answer, can you define "gotta." Does this work mean isosceles?

Step-by-step explanation:

8 0

3 years ago

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