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Mathematics

1 answer:

podryga [215]4 years ago

8 0

it is 1/2 the area of a rectangle of side lengths of 4 and 3 and in the square there is 3 squares to 1/'2 which equal another square a small triangle and the quadtrilateral equal a square and another trangle and triangle equal square which equal 6 which is half of 12 whcih 3 tiims 4 equals

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Part of the proceeds from a garage sale was $470 worth of $10 and $20 bills. If there were 14 more $10 bills than $20 bills, fin

Brums [2.3K]

There are 25 $10 bills and 11 $20 bills.

Step-by-step explanation:

Given,

Worth of proceeds from garage = $470

Let,

x be the number of $10 bills

y be the number of $20 bills.

According to given situation;

10x+20y=470 Eqn 1

x = y+14 Eqn 2

Putting value of x from Eqn 2 in Eqn 1

$10(y+14)+20y=470\\10y+140+20y=470\\30y=470-140\\30y=330$

Dividing both sides by 30

$\frac{30y}{30}=\frac{330}{30}\\y=11$

Putting y=11 in Eqn 2

$x=11+14\\x=25$

There are 25 $10 bills and 11 $20 bills.

Keywords: linear equation, substitution method

Learn more about linear equations at:

#LearnwithBrainly

5 0

3 years ago

In a normal respiratory cycle the volume of air that moves into and out of the lungs is about 498 mL. The reserve and residual v

Lisa [10]

Answer:

The model is $V(t)=2239+249\sin(\frac{\pi}{2}t)$ .

Step-by-step explanation:

Consider the given information.

The volume of air inside the lungs increases or decreases so for this we will use the basic sine function $B(t)=d+a\sin[b(t+ \frac{c}{a})]$ as our parent function.

Let us assume that the phase shift is 0 it means $\frac{c}{b}=0$ .

The air that moves into and out of the lungs is about 498 mL.

It means the amplitude of the function will vary by 249(half of 498).

The reserve and residual volumes of air that remains in the lungs occupy about 1990 mL which is the minimum air in the lungs.

So, the max air will be: 1990+498 =2488 mL

And the average will be d=1990+249=2239 ml

The horizontal stretch will be $b=\frac{2\pi}{4}=\frac{\pi}{2}$ as we know that period of $y=\sin t$ is $2\pi$ and respiratory cycle for an average human takes about 4 seconds.