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soldi70 [24.7K]
3 years ago
7

If the graphs of the linear equations in a system are the same line, what does that mean about the possible solution or solution

s of the system?
Mathematics
1 answer:
Mademuasel [1]3 years ago
8 0

Answer:

If we have a system of linear equations:

y = a*x + b

y = c*x + d

And the graphs of the equations are the same line, this means that both lines have the same equation, then:

a = c and b = d.

Then we have only one equation (but repeated) and two variables, then we have infinite solutions for our system.

Another way to see this is:

When we have a system of linear equations, the solution is the point where the lines intersect.

But if both lines are the same line, then the lines intersect in infinite points, then we have infinite solutions.

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CAN SOMEONE HELP ME PLS!!!!!
ad-work [718]

Answer:

5

Step-by-step explanation:

8 0
3 years ago
A copy machine produces 40 copies in 5 minutes. How many copies can the machine make in 3 minutes? Solve and explain your soluti
hammer [34]

Answer:

24

Step-by-step explanation:

40 divided by 5 = 8

8 x 3 = 24

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7 0
3 years ago
The population of California was 29.76 million in 1990 and 33.87 million in 2000. Use the model found in part a (f(x) =29.76(1.0
NeTakaya

Answer:

The average rate of change from 1990 to 1991 is 0.387 \:\frac{million}{years}

The average rate of change from 2000 to 2001 is 0.440 \:\frac{million}{years}

Step-by-step explanation:

The average rate of change of function f(x) over the interval a\leq x\leq b is given by

\frac{f(b)-f(a)}{b-a}

It is a measure of how much the function changed per unit, on average, over that interval.

From the information given:

  • The function that models the population t years after 1990 is f(t) =29.76(1.013)^t
  • The year 1990 is t = 0 and the year 2000 is t = 10.

1. The average rate of change from 1990 to 1991 is:

The interval is 0\leq x\leq 1

\frac{29.76(1.013)^1-29.76(1.013)^0}{1-0}\\\\\frac{1.013^1\cdot \:29.76-1\cdot \:29.76}{1-0}\\\\\frac{0.38688}{1-0}\\\\0.387 \:\frac{million}{years}

2. The average rate of change from 2000 to 2001 is

The interval is 10\leq x\leq 11

\frac{29.76(1.013)^{11}-29.76(1.013)^{10}}{11-10}\\\\\frac{0.44022}{11-10}\\\\0.440 \:\frac{million}{years}

8 0
3 years ago
Hello . Please help me with theses Negative exponents please and thank you.
Tems11 [23]

Answer:

So, to work with negative exponents you need to multiply like a positive exponent, and move the decimal over double the digits place each time.

Examples:

If it is 4 with an exponent of -2, then you will multiply 4 by 4 to get 16, and then move the decimal over double the amount of digits. There are two digits, so you will move the decimal over four digits.

So the answer to 4 with an exponent of -2 would be .0016.

5 0
3 years ago
Read 2 more answers
Dillon plans to invest $16,000 part at 4% simple interest and the rest at 5% simple interest what is the most he can invest at 4
marishachu [46]

Answer:

Step-by-step explanation:

The simple interest formula is P * r * t = I, where P is the initial investment, r is the interest rate in decimal form, t is the time in years.  This problem would be best solved by making a table, one row for account 1 and one row for account 2 with the formula along the top:

              P     *     r     *     t     =     I

acct 1

acct 2

First let's fill in our years.  The words "per year" were used, so the time in each row is a 1:

            P     *      r      *      t       =      I

acct 1                                 1

acct 2                                1

Now let's fill in the interest rates as decimals:

         P     *     r     *     t     =     I

acct 1            .04          1

acct 2           .05          1

Now for the principle amount.  If all we have to invest is 16000 and we put x into one account, then all we have left to put into the other account is what's left after taking x out of 16000, or 16000 - x.

                     P      *      r      *      t      =      I

acct 1             x           .04           1

acct 2   16000 - x       .05          1

The formula tells us that we multiply the P times the r times the t to get I, so lets do that.  Multiply straight across the top to get an interest of .04x.  Multiply straight across the bottom to get an interest of .05(16000 - x) which, after distributing, is 800 - .05x:

                 P      *      r      *      t      =      I

acct 1         x           .04            1      =    .04x

acct 2   16000-x    .05            1      =   800 - .05x

We need the amount of interest that we earn from both of these accounts to equal 700, so add the last column and set it equal to 700:

.04x + 800 - .05x = 700.  Combine like terms to get

-.01x = -100 so

x = 10,000

That means that the account which has an interest rate of 4% can have 10,000 in it while the other account has 6,000 in it.

5 0
3 years ago
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