Solve the system of linear equations by substitution.<br> y = x<br> y = 2x

Without using trignometery tables find value of , cos70/sin20+cos57.cosec33 - 2cos60

Helen [10]

Here is some thoughts on this:

cos 57 = sin (90-57) = sin 33

so cos 57 . cosec 33 = cos 57 / sin 33 = sin 33 / sin33 = 1

2 cos 60 = 2 * 1/2 = 1

so the last 2 parts work out to 0

now we have to find cos 70 / sin 20

sin 20 = cos 70 so this comes to 1

so finally the answer is 1

4 0

2 years ago

There are some Nichols dimes and quarters in a large piggy bank for every two nickels there a sweetheart forever to Diane’s ther

grigory [225]

Answer:

There are 80 nickels, 120 dimes and 300 quarters in the piggy bank.

All coins in the piggy bank worth $91.

Step-by-step explanation:

Please consider the complete question:

There are some nickels, dimes, and quarters in a large piggy bank. For every 2 nickels there are 3 dimes. For every 2 dimes there are 5 quarters. There are 500 coins total. How many nickels, dimes, and quarters are in the piggy bank? Explain your reasoning. How much are the coins in the piggy bank worth?

Let n, d, q represent number of nickles, dimes and quarters respectively.

For every 2 nickels there are 3 dimes. We can represent this information in an equation as:

$\frac{2}{n}=\frac{3}{d}...(1)$ or

$n=\frac{2d}{3}...(1)$

For every 2 dimes there are 5 quarters. We can represent this information in an equation as:

$\frac{2}{d}=\frac{5}{q}...(2)$ or

$q=\frac{5d}{2}...(2)$

There are 500 coins total. We can represent this information in an equation as:

$n+d+q=500...(3)$

We will use substitution method to solve our given system.

Upon substituting equation (1) and equation (2) in equation (3), we will get:

$\frac{2d}{3}+d+\frac{5d}{2}=500$

Multiply the equation by 6:

$\frac{2d}{3}*6+d*6+\frac{5d}{2}*6=500*6$

$2d*2+6d+5d*3=3000$

$4d+6d+15d=3000$

$25d=3000$

$\frac{25d}{25}=\frac{3000}{25}$

$d=120$

Therefore, there are 120 dimes in the piggy bank.

Upon substituting $d=120$ in equation (1), we will get:

$n=\frac{2(120)}{3}$

$n=2(40)$

$n=80$

Therefore, there are 80 nickels in the piggy bank.

Upon substituting $d=120$ in equation (2), we will get:

$q=\frac{5d}{2}$

$q=\frac{5(120)}{2}$

$q=5(60)$

$q=300$

Therefore, there are 300 quarters in the piggy bank.

Now, we need to find the value of all coins.

We know 1 quarter is worth $0.25, so 300 quarters will be worth $\$0.25\times 300=\$75$ .

We know 1 dime is worth $0.10, so 120 dimes will be worth $\$0.10\times 120=\$12$ .

We know 1 nickel is worth $0.05, so 80 nickels will be worth $\$0.05\times 80=\$4$ .

$\text{All coins worth}=\$75+\$12+\$4$

$\text{All coins worth}=\$91$

Therefore, all coins in the piggy bank worth $91.

7 0

3 years ago

The intensity, I, of a sound varies inversely with the square of the distance, r, from the source of the sound. Write an equatio

charle [14.2K]

Answer:The equation relating I, r, and k is I =K/r²

Step-by-step explanation:

The intensity, I, of a sound varies inversely with the square of the distance, r, from the source of the sound can be written as

I ∝ 1/r²

Introducing the constant of proportionality, K we have that

I =K x 1/r²

Therefore , the equation relating I, r, and k is I =K/r²

7 0

2 years ago

(Scientific Notation LC)

vlada-n [284]

Answer:

21,800

Step-by-step explanation:

I'm assuming you meant 2.18 x 10^4

Since the exponent is positive, you will move the decimal point 4 spaces to the right.

5 0

1 year ago

Read 2 more answers

What is the perimeter of the contest area on the judo mat?

Rus_ich [418]

How big is the judo mat,

3 0

2 years ago

Read 2 more answers

Solve the system of linear equations by substitution. y = x y = 2x - 1