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anastassius [24]

3 years ago

13

A biologist studying the relationship between tilapia and catfish in a pond finds that the ratio of tilapia to catfish is 6:20.

If the pond has 30 catfish, how many tilapia are in the pond?

1 answer:

Neko [114]3 years ago

5 0

Answer: 9 tilapia

Step-by-step explanation:

The ratio of 6:20 for tilapia to catfish means that for every six tilapia, there are 20 catfish in the pond.

If there are 30 catfish, use direct proportion to find out the number of tilapia:

6 : 20

x : 30

Cross multiply:

20x = 180

x = 180 / 20

x = 9 tilapia

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This circle is centered at the origin, and the length of its radius is 8. What is

Kitty [74]

$\quad \huge \quad \quad \boxed{ \tt \:Answer }$

$\qquad \tt \rightarrow \: x² + y² = 64$

____________________________________

$\large \tt Solution \: :$

Standard equation of circle is :

$\qquad \tt \rightarrow \: (x - h) {}^{2} + (y - k) {}^{2} = {r}^{2}$

$\textsf{h = x - coordinate of centre of circle}$

$\textsf{k = y - coordinate of centre of circle}$

$\textsf{r = radius= 8}$

Since the circle is centered at origin, h = k = 0

$\qquad \tt \rightarrow \: (x - 0) {}^{2} + (y - 0) {}^{2} = {8}^{2}$

$\qquad \tt \rightarrow \: {x}^{2} + {y}^{2} = 64$

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4 0

2 years ago

Can you answer both please !

ddd [48]

First one is 2= x -3 and second is -4= 3x -4

6 0

3 years ago

What is the GCF of 12x3 - 9x2

Oksanka [162]

Answer:

I would probably say 4

Step-by-step explanation:

6 0

4 years ago

II. Let f(x) = 9 – x , g(x) = x2 + x, and h(x) = x – 2. Compute the following:

Neko [114]

Answer:

$h(g(x))=x^2+x-2$

$h(g(f(x))= x^2-19x+88$

Step-by-step explanation:

<u>Composite Function</u>

Suppose f(x) and g(x) are real functions, the composite function named $(f\circ g)(x)$ is defined as:

$(f\circ g)(x)=f(g(x))$

The composite function can be found by substituting g into f.

We are given these functions:

$f(x)=9-x$

$g(x)=x^2+x$

$h(x)=x-2$

Find:

a) h(g(x))

Substituting g into h:

$h(g(x))=x^2+x-2$

b) h(g(f(x))

First we find g(f(x)):

$g(f(x))=(9-x)^2+(9-x)$

Operating:

$g(f(x))=81-18x+x^2+9-x$

Simplifying:

$g(f(x))=90-19x+x^2$

Now find h(g(f(x)) replacing the above equation into h:

$h(g(f(x))= 90-19x+x^2-2$

Simplifying and rearranging:

$h(g(f(x))= 88-19x+x^2$

$h(g(f(x))= x^2-19x+88$

3 0

3 years ago

What type of triangle is defined by the following set of side lengths

NARA [144]

Answer:

<u>ACUTE</u><u> </u><u>TRIANGLE</u><u> </u>

Step-by-step explanation:

If the sum of the squares of the two shorter sides of a triangle is greater than the square of the longest side, the triangle is acute. However, if the sum of the squares of the two shorter sides of a triangle is smaller than the square of the longest side, the triangle is obtuse.

Therefore, the triangle with sides 11, 9, and 7 is an acute triangle since 9² + 7² is greater than 11²

${9}^{2} \: + \: {7}^{2} > \: {11}^{2} \\ 130 > 121$

8 0

3 years ago