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3 years ago

Solve by the linear combination method (with or without multiplication).

Mathematics

1 answer:

Dima020 [189]3 years ago

5 0

The first step is to name the equations to make the process of solving them easy.

$6x+7y=-4....(1)\\5x-3y=-21....(2)$

The second step is to multiply each of the equations by the coefficient of the x term in the other equation. In this case, we will multiply equation (1) by 5 to get equation (3) and then multiply equation (2) by 6 to get equation (4).

$-30x-35y=20...(3)\\30x-18y=-126...(4).$

The next step is to add equation equation(3) and (4) together to get equation (5) as shown below;

$-53y=-106....(5)\\=> y= 2.$

The next step is to take the value of y and substitute it into any of the equations above. For this solution, I pick equation (1). The work done to solve for x is shown below.;

$6x+7y=-4\\=>6x+7(2)=-4\\=>6x=-18\\=>x=-3$

The solution for this system of equations is $(-3,2)$

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Suppose that $2000 is placed in a savings account at an annual rate of 4.6%, compounded quarterly. Assuming that no withdrawals

LenaWriter [7]

Answer:

It will take 35.46 quarters for the account to grow to $3000.

Step-by-step explanation:

Since the annual rate is compounded quarterly, this can be calculated using the formula for calculating the future value as follows:

FV = PV * (1 + r)^n ............................ (1)

Where;

FV = future value or the amount the deposit expected to grow to = $3,000

PV = Present value or the amount place in the savings = $2,000

r = Quarterly rate = Annual rate / 4 = 4.6% / 4 = 0.046 / 4 = 0.0115

n = number of quarters it will take for the loan to grow to $3000 = ?

Substituting the values into equation (1) and solve for n, we have:

$3,000 = $2,000 * (1 + 0.0115)^n

$3,000 / $2,000 = (1.0115)^n

1.50 = (1.0115)^n

Loglinearise both sides, we have:

log(1.50) = n log(1.0115)

0.176091259055681 = n * 0.00496588710682352

n = 0.176091259055681 / 0.00496588710682352

n = 35.4601816891322

Rounding to the nearest hundredth, which also implies to rounding to 2 decimal places, we have:

n = 35.46

Since the the annual rate is compounded quarterly, it will therefore take 35.46 quarters for the account to grow to $3000.

3 0

3 years ago

10 minus three times a number is no more than 61

Elena L [17]

Answer:

n ≥ -17

Step-by-step explanation:

Writing a symbolic inequality, we get:

10 - 3n ≤ 61

Solve this for 3n by adding 3n to both sides of this equation:

10 ≤ 61 + 3n

Solve for n by subtracting 61 from both sides and then dividing all of the resulting terms by 3:

-51 ≤ 3n (divide both sides by 3):

-17 ≤ n, or

n ≥ -17

8 0

3 years ago

The runner has to race for 21km. She has to finish race before 1h 40min. What avarage speed She has to run to gain such goal?

abruzzese [7]

Answer:

The rate of the runner is 3.5 meters per second.

Step-by-step explanation:

To get this answer in meters per second, we first have to convert each of the terms into either meters or seconds. We can do that by multiplying by unit rates.

21 km * 1000 = 21,000 meters

1 hour * 3600 = 3,600 seconds

40 minutes * 60 = 2,400 seconds

Now we divide the meters by the total number of seconds to get the rate.

21,000 meters / (3,600 + 2,400) secs

21,000 meters / 6,000 secs

3.5 meters per second.

7 0

3 years ago

PLEASE HELP! BRAINLIEST! AND EXTRA POINTS

Rom4ik [11]

Answer:

The discount is $0.8d.

Step-by-step explanation:

Given that,

The original cost of Tamara's purchase is d dollars.

Tamara uses a coupon to save 20% off her purchase at the bookstore.

Discount = 20%

Discount is applied to the original cost.

Discount = d-(20/100)d

Discount = 0.8 d

Hence, the discount is $0.8d.

8 0

3 years ago

The table shows the amount it costs to rock climber an indoor rock climbing facility based on the number of hours. What is the r

FinnZ [79.3K]

within each hour, the amount goes up by $8

6 0

3 years ago