Write the exponential function represented by the tables below

Butoxors [25]

It’s 0.775x +2.5 =correct

6 0

2 years ago

Solve the following: Three times the 1st number plus the 2nd number plus twice the 3rd is 5. If three times the 2nd number is su

Karolina [17]

Three times the 1st number plus the 2nd number plus twice the 3rd is 5 is the same as 3x+y+2z=5. If three times the 2nd number is subtracted from the sum of the 1st and three times the 3rd number, the result is 2 is just x+3z-3y=2. And if the 3rd number is subtracted from two times the 1st number and three times the 2nd, giving a result of 1 means 2x+3y-z=1. Then you use substition on these equations to get a equation where one variable equals 2 others, like using the first to get y=5-2z-3x and then this can be substituted into the other two to get x+3z-3(5-2z-3x)=2 and 2x+3(5-2z-3x)-z=1 we can then simplify and subtract the equations. After simplification we have 10x+9z=17 and 7z+7x=16 which can be turned into 70x+63z=119 and 70x+70z=160 which can be then subtracted to get that 7z=41 and z=41/7. Now we backtrack to a two variable equation like 7z+7x=16 and plug in to find x. So after plugging in we get 41+7x=16 and 7x=-25 so x=-25/7. Now we choose a 3 variable equation and plug in. So taking y=5-2z-3x we plug in 41/7 for z and -25/7 for x to get y=5-82/7+75/7 and y=5-7/7 and y=4. Therefore x = -25/7 y = 4 and z = 41/7.

3 0

3 years ago

Under the translation T(-5, -2) the point (1, 6) will become (-4, -4).<br><br> True<br><br> False

Butoxors [25]

Step-by-step explanation:

<h3>It's False</h3>

Because (-5+ 1, - 2 + 6) = (- 4, 4) which is not equal to (-4, - 4).

7 0

3 years ago

Read 2 more answers

Solve the system of equations by graphing. x+y=-9 4x+y=-19

shutvik [7]

For this case we have the following system of equations:

$x + y = -9\\4x + y = -19$

We multiply the first equation by -4:

$-4x-4y = 36$

We have the following equivalent system of equations:

$-4x-4y = 36\\4x + y = -19$

We add the equations:

$-4x + 4x-4y + y = 36-19\\-3y = 17\\y = - \frac {17} {3}$

We find the value of the variable "x":

$x = -9-yx = -9 - (- \frac {17} {3})\\x = -9 + \frac {17} {3}\\x = \frac {-27 + 17} {3}\\x = - \frac {10} {3}$

Thus, the solution of the system is:

$(x, y): (- \frac {10} {3}, - \frac {17} {3})$

See the graphic in the attached image

ANswer:

$(x, y): (- \frac {10} {3}, - \frac {17} {3})$

See the graphic in the attached image

4 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

2 years ago