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4 years ago

Use the substitution method to solve the following system of equations:

Mathematics

1 answer:

horsena [70]4 years ago

5 0

Answer:

(6, - 3 )

Step-by-step explanation:

Given the 2 equations

3x + 5y = 3 → (1)

x + 2y = 0 → (2)

Rearrange (2) expressing x in terms of y by subtracting 2y from both sides

x = - 2y → (3)

Substitute x = - 2y into (1)

3(- 2y) + 5y = 3

- 6y + 5y = 3

- y = 3 ( multiply both sides by - 1 )

y = - 3

Substitute y = - 3 into (3) for corresponding value of x

x = - 2(- 3) = 6

Solution is (6, - 3 )

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A bale of hay measures 2 feet by 2 feet by 3 feet. Hay weighs 8 pounds per cubic foot. How much does the bale of hay weigh?

Inga [223]

Answer:

$96lb$

Step-by-step explanation:

$2 \times 2 \times 3 = 12 \\ 12 \times 8 = 96$

3 0

3 years ago

Kevin and Randy Muise have a jar containing 78 coins, all of which are either quarters or nickels. The total value of the coins

gregori [183]

Answer:

50 quarters and 28 nickels

Step-by-step solution:

We have two variables we are solving for. We will call them Q for the number of quarters and N for the number of nickels.

We know that the total number of coins is equal to 78, and we know that the total amount the coins are worth is equal to $13.90. With this information, we can set up a system of equations:

Q + N = 78

0.25Q + 0.05N = 13.90

Now we can solve for either Q or N in the first equation and solve by substitution by plugging the value into the second equation. Let's solve for Q:

Q = 78 - N

Now plug in 78-N for Q:

0.25(78-N) + 0.05N = 13.90

Distribute and combine like terms:

19.50 - 0.25N + 0.05N = 13.90

19.50 - 0.20N = 13.90

-0.20N = -5.60

N = 28

Now we know that there are 28 nickels. We can plug this into one of the original equations to solve for Q:

Q + 28 = 78

Q = 50

There are 50 quarters. We can verify our answer by plugging the values for A and N into the other equation (optional step to check work):

0.25(50) + 0.05(28) = 13.90

12.5 + 1.40 = 13.9

13.9 = 13.9

Our answer is correct.

5 0

3 years ago

If x^2=-1, What is the value of x?

vodomira [7]

Answer:

-1

Step-by-step explanation:

-1^2 = -1

7 0

3 years ago

Suppose (ideally) a hammer claw moves a distance of 0.10 meters to remove a nail. If a resistance force of 1500 N is exerted by

dusya [7]

Answer:

7500 N

Step-by-step explanation:

Given that,

A hammer claw moves a distance of 0.10 meters to remove a nail.

Resistance force, F = 1500 N

The person move the handle of the hammer 0.5 m

We need to find the effort force. Let it is F'. The mechanical advantage is given by :

$m=\dfrac{effort}{resistance}=\dfrac{d_i}{d_o}$

Where $d_i\ \text{and}\ d_o$ are input and output distance respectively.

$m=\dfrac{F'}{F}=\dfrac{0.1}{0.5}\\\\\dfrac{1500}{F}=\dfrac{0.1}{0.5}\\\\\dfrac{1500}{F}=0.2\\\\F=7500\ N$

So, the effort force is 7500 N.

4 0

3 years ago

Places A and B are 100km apart from each other on a highway. A car starts from A and another from B at the same time. If they mo

Mashutka [201]

Answer:

Speed of the first car = x = 35km/hr

Speed of the second car = 25km /hr

Step-by-step explanation:

The calculation of speeds of the cars is given below:-

Assume that the speed of the 1st car which is opening from A = x km/hr

and assume the Speed of the 2nd car which is starting from B

= y km/hr

As we know that

Time = Distance ÷ Speed

So, the distance lies between two places i.e. A and B are

80km d = 80 km

1. now when the car moves in the similar direction

So, the corresponding speed of them = (x + y)km/hr

Time = 8hr

d = 80km

$8 = \frac{80}{(x + y)}\\\\x + y = \frac{80}{8}\\\\x + y = 10 ..... (i)$

2. when two cars moving in the inverse direction,

So, the corressponding speed = (x - y) km / hr

Time = 1 hr 20 minutes

That means

= (1 + 20 ÷ 60) hr

= (80 ÷ 60)

= 4/3 hr

d = 80km

Now

4 ÷ 3 = 80 ÷ (x -y)

x -y = (80 × 3) ÷ 4

x - y = 60 ..... (ii)

Now, we will sum equation 1 and equation 2 we will get

2x = 70

x = 35

now, Put x = 35 in (i) we will get

y = 25

Speed of the first car = x = 35km/hr

Speed of the second car = 25km /hr

8 0

4 years ago