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3 years ago

15

A biologist determined that there were 42 oak trees in a 5-acre forest. How many oak trees would be expected on 40 acres of iden

tical habitat?

1 answer:

klio [65]3 years ago

6 0

Answer:

336

Step-by-step explanation:

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Please Help! 30 POINTS! Given the following three points, find by hand the quadratic function they represent. (−1,−8), (0,−1),(1

ycow [4]

Answer:

(1) B

(2) D

Step-by-step explanation:

(1)

Let the quadratic function be:

$y = ax^{2} + bx + c$

For the point, (0,-1),

$y = ax^{2} + bx + c$

$-1=(a\times0)+(b\times0}+c\\-1=c\\c=-1$

Then the equation is:

$y = ax^{2} + bx -1$

For the point (-1, -8) ,

$y = ax^{2} + bx -1$

$-8=(a\times (-1)^{2})+(b\times -1)-1\\-8=a-b-1\\a-b=-7...(i)$

For the point (1, 2) ,

$y = ax^{2} + bx -1$

$2=(a\times (1)^{2})+(b\times 1)-1\\2=a+b-1\\a+b=3...(ii)$

Add the two equations and solve for <em>a</em> as follows:

$a-b=-7\\a+b=3\\\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\2a = -4\\a = -2$

Substitute <em>a</em> = -2 in (i) and solve for <em>b</em> as follows:

$a-b=-7\\-2-b=-7\\b=5$

Thus, the quadratic function is:

$f(x)=-2x^{2}+5x-1$

The correct option is (b).

(2)

The ordered pairs are:

(5, 7), (7, 11), (9, 14), (11, 18)

Represent them in an XY table as follows:

X : 5 | 7 | 9 | 11

Y : 7 | 11 | 14 | 18

Compute the difference between the <em>Y</em> values as follows:

Diff = 11 - 7 = 4

Diff = 14 - 11 = 3

Diff = 18 - 14 = 4

Now compute the difference between the Diff values:

d = 3 - 4 = -1

d = 4 - 3 = 1

Since the differences between the differences of the y-values is not consistent, the ordered pairs do not represent a quadratic equation.

The correct option is D.

8 0

3 years ago

Lady bird [3.3K]

Answer:

19 1-point shots and 32 2-point shots

Step-by-step explanation:

Let x be the amount of 1-point shots they made and y be the amount of 2-point shots they made then...

x+y=51

x+2y=83

We can solve this equation using elimination. In this case, we can eliminate x be subtracting the two equations.

-y=-32

Divide both sides by -1

y=32

Plug this back into the equation to solve for x

x+32=51

Subtract 32 from both sides

x=19

They scored 19 1-point shots and 32 2-point shots.

8 0

3 years ago

Can someone please help me with this? It’s the last problem I need to turn in a test, I will mark brainliest :(

stiks02 [169]

Answer:

33b - 8

Step-by-step explanation:

You solve for the perimeter like you would for any other shape by adding all the sides

The perimeter is side A + side B + side C.

so it's 9b+8 + 12b-8 + 12b-8

Add all the like terms

9b + 12 b + 12b = 33b

8 - 8 - 8= -8

= 33b -8

3 0

3 years ago

A)Three out of my four brothers play soccer. What percent of my brothers do not play soccer?

exis [7]

A. 1)25%
B. 2)7
C. 3)48

7 0

4 years ago

Read 2 more answers

Round 21.333 to the nearest minute

QveST [7]

Answer: 21

Step-by-step explanation: 21 because we have to round to the nearest minute, also known as a whole number. 21.333 can be rounded to 21 since 3 is less than 5.

5 0

3 years ago

Read 2 more answers