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3 years ago

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Explain, in complete sentences, which method you would use to solve the following system of equations and why you chose that met

hod. Show your work and provide the solution to the system.
4x + 3y = 2
3x + 2y = 1

1 answer:

svp [43]3 years ago

4 0

I would use elimination. I would multiply 4x+3y=2 by 3 so the it becomes 12x+9y=6, and I would multiply the bottom equation by 4 so that it becomes 12x+8y=4. Because I am using elimination I have to get rid of one variable, I chose to get rid of X hence that the coefficient of X in each equation is now 12. i simply subtract both equations and get y by itself. y=2. I plug in Y to find x in either of the original equations, where I get x=-1. To check my work substitute the values of x and y in the other equation. 4(-1)+3(2)=2 -------> 2=2

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Choose the equation below that represents the line passes to the point (7,-2) an the slope of -3

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Hello there!
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y-y1=m(x-x1)
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3 years ago

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Sonja [21]

Answer:

490

Step-by-step explanation:

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3 years ago

Which shapes have at least 1 right angle choose ALL that are correct Iready -click to see the shapes-

nirvana33 [79]

Answer:

Square (top right), rectangle (middle bottom), and trapezoid (bottom right)

Step-by-step explanation:

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3 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

4 years ago

Write the function to represent the total numbers or words , y, that mrs. Garcia can type in x minutes.

FrozenT [24]

Answer:

Part a) $y=70x$

Part b) $3,430\ words$

Step-by-step explanation:

Let

x------> the time in minutes

y-----> the total numbers of words

step 1

we have

$A(1,70), B(2,140)$ -----> given table

<u>Find the slope of the linear equation</u>

$m=(140-70/(2-1)=70\ words/minute$

with the slope m and the point A find the equation of the line

The equation of the line in point slope form is equal to

$y-y1=m(x-x1)$

substitute

$y-70=70(x-1)$

$y=70x-70+70$

$y=70x$ ----> This is a linear direct variation

Part b) For $x=49\ min$

substitute the value of x in the linear equation to find the value of y

$y=70(49)=3,430\ words$

7 0

3 years ago