Ask question

Ask question

All categories

3 years ago

9

Please help!! Local wildlife experts have begun to track the population of trout in their area. The function f represents the ap

proximate population of trout in Sky Lake, and the function g represents the approximate population of trout in Lake Cyan, where t is the number of months since experts began tracking the populations.
f(t) = 1.5t + 50

g(t) = 0.1t^2 - 4t + 70

Find the expression that describes the total trout population in the area after t months, f(t) + g(t).

A. 0.1t^2 + 5.5t +120

B. 0.1t^2 - 5.5t +120

C. 0.1t^2 - 2.5t + 120

D. 0.1t^2 + 2.5t + 120

1 answer:

jeka57 [31]3 years ago

6 0

Answer:

Option C.

Step-by-step explanation:

We know that

f(t) = 1.5t + 50

represents the approximate population of trout in Sky Lake

And

g(t) = 0.1t^2 - 4t + 70

represents the approximate population of trout in Lake Cyan

The total trout population in the area is described as

f(t) + g(t)

f(t) + g(t) = [1.5t + 50] + [0.1t^2 - 4t + 70]

f(t) + g(t) = [1.5t + 50+ 0.1t^2 - 4t + 70]

f(t) + g(t) = [0.1t^2 -2.5t + 120]

f(t) + g(t) = 0.1t^2 -2.5t + 120

Option C.

You might be interested in

The points (2, 8) and (1, 2) fall on a particular line. What is its equation in slope-intercept form?

Leona [35]

Answer:

y = 6x - 4

Step-by-step explanation:

(2, 8) & (1, 2)

First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(2 - 8) / (1 - 2)

Simplify the parentheses.

= (-6) / (-1)

Simplify the fraction.

-6/-1

= 6

This is your slope. Plug this value into the standard slope-intercept equation of y = mx + b.

y = 6x + b

To find b, we want to plug in a value that we know is on this line: in this case, I will use the second point (1, 2). Plug in the x and y values into the x and y of the standard equation.

2 = 6(1) + b

To find b, multiply the slope and the input of x(1)

2 = 6 + b

Now, subtract 6 from both sides to isolate b.

-4 = b

Plug this into your standard equation.

y = 6x - 4

This is your equation.

Check this by plugging in the other point you have not checked yet (2, 8).

y = 6x - 4

8 = 6(2) - 4

8 = 12 - 4

8 = 8

Your equation is correct.

Hope this helps!

3 0

3 years ago

A building is 30 meters tall and 50 meters on each side of its square base. What is the perimeter of the base of the building?

kobusy [5.1K]

30+30=60
50+50=100
60+100=
160 meters

7 0

3 years ago

Graph the polygon and its image after a dilation centered at C(1,1)

Grace [21]

Now we proceed to present the graphs of the polygon and its image with the help of a graphing tool. The <em>original</em> polygon is highlighted in <em>red</em> and the image is highlighted in <em>blue</em>.

DIlations are defined by the follwing operation:

$P'(x,y) = O(x,y) + k\cdot [P(x,y)-O(x,y)]$ (1)

Where:

$O(x,y)$ - Center of dilation.
$k$ - Dilation factor.
$P(x,y)$ - Original point of the polygon.
$P'(x,y)$ - Dilated point of the polygon.

If we know that $O(x,y) = (1,1)$ , $k = 0.5$ , $J(x,y) = (3,1)$ , $K(x,y) = (5, -3)$ , $L(x,y) = (5,5)$ and $M(x,y) = (3,7)$ , then the coordinates of the new polygon are:

$J'(x,y) = (1,1) + 0.5\cdot [(3,1)-(1,1)]$

$J'(x,y) = (1,1)+0.5\cdot (2,0)$

$J'(x,y) = (1,1) +(1,0)$

$J'(x,y) = (2,1)$

$K'(x,y) = (1,1) + 0.5\cdot [(5,-3)-(1,1)]$

$K'(x,y) = (1,1) +0.5\cdot (4,-4)$

$K'(x,y) = (1,1) +(2,-2)$

$K'(x,y) = (3,-1)$

$L'(x,y) = (1,1) + 0.5\cdot [(5,5)-(1,1)]$

$L'(x,y) = (1,1) + 0.5\cdot (4,4)$

$L'(x,y) = (1,1) + (2,2)$

$L'(x,y) = (3,3)$

$M'(x,y) = (1,1) + 0.5\cdot [(3,7)-(1,1)]$

$M'(x,y) = (1,1) +0.5\cdot (2,6)$

$M'(x,y) = (1,1) +(1,3)$

$M'(x,y) = (2,4)$

Now we proceed to present the graphs of the polygon and its image with the help of a graphing tool. The <em>original</em> polygon is highlighted in <em>red</em> and the image is highlighted in <em>blue</em>.

We kindly invite to check this question on dilations: brainly.com/question/13176891

6 0

3 years ago

Choose all of the equations of vertical lines.

tester [92]

Answer:

a is the answer cd

7 0

3 years ago

4 quarts= how many gallons

Vadim26 [7]

4 quarts would equal one gallon

3 0

3 years ago