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3 years ago

A system of equations is graphed below. Which point represents the solution to this system?

Mathematics

1 answer:

Sergeu [11.5K]3 years ago

8 0

$\huge \bf༆ Answer ༄$

The solution of the system of equation is the coordinates of the common point on both lines !

that is ~

$\sf( - 3,2)$

Therefore the Correct choice is C

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The estimated number of organisms in a population after t days is shown in the table below. t days estimated number of organisms

Lelu [443]

Answer:

The function $n=591.68(1.2056)^t$ best models the situation.

Step-by-step explanation:

The values in the table do not lie over a straight line because their slope is not a constant; for example

$m_1=\frac{1250=860}{4-2} =195$

$m_2=\frac{1850-1250}{2}=275$

we see here that $m_1\neq m_2$ therefore a linear equation cannot represent this situation.

The values in the table are increasing exponentially , therefore the equation modeling the situation will be of the form:

$n=ab^t$

we take two points from the table for evaluating $a$ and $b$ namely points $(2,860)$ and $(4,1250)$

thus we have

(1). $860=ab^2$

(2). $1250=ab^4$

From equation (1) we solve for $a:$

$a=\frac{860}{b^2}$

and put this value into equation (2)

$1250 =\frac{860}{b^2}b^4$

$b^2=\frac{1250}{860}$

$\boxed{b=1.2056}$

with this value $b$ , we solve for $a$ in equation (1):

$860=a(1.2056)^2$

$a=\frac{860}{(1.2056)^2}$

$\boxed{a=591.68}$

Thus we have the equation

$\boxed{n=591.68(1.2056)^t}$

8 0

3 years ago

Read 2 more answers

Solve using derivatives.

Bond [772]

Answer:

Below in bold.

Step-by-step explanation:

The surface area of the box

= x^2 + 4hx where x = a side of the square base and h is the height.

So x^2 + 4hx = 8

The volume of the box

V = x^2h

From the first equation we solve for h

4hx = 8 - x^2

h = (8 - x^2) / 4x

Now we substitute for h in the formula for the volume:

V = x^2 * (8 - x^2) / 4x

V = 8x^2 - x^4 / 4x

V = 2x - 0.25x^3

Finding the derivative:

V' = 2 - 0.75x^2 = 0 for max/mimn values

x^2 = 2/ 0.75 = 2.667

x = 1.633.

So the length and width of the base is 1.633 m and the height

= ( 8 - 2.667) / (4*1.633)

= 0.816 m

The maximum volume = 0.816 * 2.667 = 2.177 m^2.

The answers are correct to the nearest thousandth.

7 0

3 years ago

5 more than the quotient of a number and 8 is 42

Zepler [3.9K]

Answer:

<u>The number is 296.</u>

Step-by-step explanation:

Let's call "x" to the number we are looking for.

Now, the problem states that "5 more than the quotient of a number and 8 is 42". This means that this number is being divided by 8, it's also being additioned 5 and the final result is 42. Therefore, the expression of this operations on this number is the following:

$\frac{x}{8}+5=42$ . Let's solve the equation to find x.