In 2009, there were 6342 penguins in Isla Martillo, Argentina. The area of the island
is approximately 47 square acres. To the nearest whole number, what was the
density of the penguin population?

Answer:

1024 pages left

Step-by-step explanation:

19 pack  * 75 page/pack - 401 page =

Answer:

Given:

[tex]\begin{aligned} \textsf{Perimeter} & =\textsf{shorter leg + longer leg + hypotenuse}\\ & = (x+5)+[3(x+5)-1]+[2(x+5)+13]\\ & = x+5+3x+15-1+2x+10+13\\ & = 6x+42\end{aligned}[/tex]

[tex]\begin{aligned} \textsf{Area} & =\dfrac12\textsf{(shorter leg)(longer leg)}\\ & =\dfrac12(x+5)[3(x+5)-1]}\\ & =\dfrac12(x+5)(3x+14)\\ & = \dfrac12(3x^2+29x+70)\\ & = \dfrac32x^2+\dfrac{29}{2}x+35 \end{aligned}[/tex]

[tex]\begin{aligned} \textsf{Area} & =2.5 \sf (Perimeter)\\ \implies \dfrac32x^2+\dfrac{29}{2}x+35 & =\dfrac52(6x+42)\\ 3x^2+29x+70 & =5(6x+42)\\ 3x^2+29x+70 & =30x+210\\ 3x^2 -x-140 & =0\\ 3x^2-21x+20x-140 & =0\\ 3x(x-7)+20(x-7) &=0\\ (x-7)(3x+20)& =0\end{aligned}[/tex]

Therefore:

[tex](x-7)=0 \implies x=7[/tex]

[tex](3x+20)=0 \implies x=-\dfrac{20}{3}[/tex]

[tex]x=-\dfrac{20}{3}[/tex] is not a viable solution as when inputting this into the formula for the shorter leg, it gives a negative value:

[tex]\textsf{Shorter leg}=-\dfrac{20}{3}+5=-\dfrac53[/tex]

As distance cannot be negative, this is not a viable solution.

When x = 7:

[tex]\textsf{Shorter leg}=7+5=12[/tex]

[tex]\textsf{Longer leg}=3(7+5)-1=35[/tex]

[tex]\textsf{Hypotenuse}=2(x+5)+13=37[/tex]

[tex]\textsf{Perimeter}=6(7)+42=84[/tex]

[tex]\textsf{Area} & =\dfrac32(7)^2+\dfrac{29}{2}(7)+35=210[/tex]

Therefore, there is one viable solution.  This solution in the form (x, A) is  (7, 210)

18

Hope it helps.

Do comment if you have any query.

Answer:

1.5, so an hour and thirty minutes

Step-by-step explanation:

Simplify 3/4 as 0.75. 0.75 times 2 is 1.5.

Answer:

81

Step-by-step explanation:

65 meters plus the 16 is 81

Answer:

Step-by-step explanation:

AB represent the building. C represents the spot

The building forms right angle with the ground.

BC will be the hypotenuse and AB, AC are the legs

Use Pythagorean theorem,

AB² + AC² = BC²

AB² + 16² = 65²

AB² + 256 = 4225

          AB² = 4225 - 256

                 = 3969

          [tex]AB = \sqrt{3969} =\sqrt{63*63}[/tex]

AB = 63 m

height of the building = 63 m

Answer:

32.2 square feet

Answer:

Option D is correct

[tex]Slope[/tex] [tex]of[/tex] [tex]AC=Slope[/tex] [tex]of[/tex] [tex]DF[/tex]

Step-by-step explanation:

Given:

1.

ΔABC and ΔDEF are similar

Property of similar states that corresponding sides are in proportion.

2.

[tex]\frac{BC}{EF}=\frac{AB}{DE}[/tex] [By property of similar triangles]

Property of proportions allows you to cross multiply the equation.

then;

3.

[tex]\frac{AB}{BC}=\frac{DE}{EF}[/tex]   [Property of proportion]

Definition of slope: Slope is described as the steepness and direction of line.

then by definition of slope;

4.

[tex]Slope[/tex] [tex]of[/tex] [tex]AC=\frac{BC}{AB}[/tex]

5.

[tex]Slope[/tex] [tex]of[/tex] [tex]DF=\frac{EF}{DE}[/tex]

6.

Substitution property of equality states that:

If a = b then a can be substituted in place of b in any equation or vice-versa.

then;

[tex]Slope[/tex] [tex]of[/tex] [tex]AC= Slope[/tex] [tex]of[/tex] [tex]DF[/tex]

Therefore, the missing step in 6 we get,

[tex]Slope[/tex] [tex]of[/tex] [tex]AC= Slope[/tex] [tex]of[/tex] [tex]DF[/tex]

Answer:

195 cubic inches

Step-by-step explanation:

A fishing tackle box is 13 inches long, 6 inches wide, and inches high. What is the volume of the tackle box? SOLUTION: The volume of the tackle box is 195 cubic inches.

Answer:

x=4

Step-by-step explanation:

distributive property goes first.

you get 6x-9=15

add 9 on both sides so 9 cancells out on the left side.

you get 6x=24

divide by 6 and you get x=4

Answer:

Step-by-step explanation:

y=2x+3

y=-3x+3

**This is what's on the image.**

You need to aline the two together.

2x+3 = -3x+3

Add 3x both sides

3x+2x+3=3

5x+3=3

Now subtract 3 from both sides

5x=3-3

x= 0

This should be a vertical line from (0,0) to above since there is no slope you should have a straight line that is vertical.

Answer:

5.25 inches or [tex]5 \frac{1}{4}[/tex] inches

Step-by-step explanation:

I believe that the question is what do they multiply to..? If so, we start by making them both in decimal form:

7 / 2 = 3.5

3 / 2 = 1.5

Now, we multiply:

3.5 * 1.5 = 5.25

If you want fraction form, we can turn .25 to 1/4.

Fraction form: [tex]5 \frac{1}{4}[/tex]

To turn something into the slope-intercept form

  ⇒ must know the slope-intercept form ⇒ [tex]y = mx +b[/tex]

To convert our current form into slope-intercept form

 ⇒ must solve for 'y'

    ⇒ (in other words) move everything to one side and 'y' by itself on the

    other

        [tex]3y - 9x = -81\\3y =9x-81\\y = 3x - 27[/tex]

     *purely extra information (not necessary for final answer)

Slope-intercept form: y = 3x - 27

Hope that helps!

hi the awnser us defiantly going to be that I 56

Step-by-step explanation:

edge

Answer:

Use points (0,12) and (1,20) on graphing paper or a program to find final answer.

Step-by-step explanation:

In the problem, I was unable to understand the equation so I am presuming the equation actually means y=8x+12

Whenever you graph a Linear Function you always need two points. The first point is always easy to acquire.

You can plug in any value for x, which will be your x cordinate and the output (solution) of the equation will be you y cordinate.

I'm plugging in 0 for X first.

y=8x+12

y=8(0) +12

y=12

We have our first point as (0,12)

Now you can plug in any other number for X other then Zero.

I choose 1 this time for X.

y=8x+12

y=8(1)+12

y=8+12

y=20

We now have our second point (1,20). Two points will be enough to graph this graph, you can graph these two points and then draw a line if on paper or use an application and get the line that way.

Answer:

Use the rise/run strategy to draw the line. Start at the y-intercept (0, 12), and count 8 up and 1 to the right to the point (1, 20). Then, draw a line through the points. Test the point (3,36) in the equation y = 8x + 12 to verify that the line is correct.

Step-by-step explanation:

got it right

Answer:

I believe it is 10!

Step-by-step explanation:

The multiples of 10 are: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200 and so on.

The only multiple between -4 and 12 is 10!

Hope this helps!!!!

The probability of the friend completing the new level in her first try is 22.5%

This is a concept that is used to talk about the likelihood or the chances of an event occuring.

For the digit 8, the frequency is 7

For the digit 9, the frequency is 11

The total number of frequencies is given as

10 + 9 + 6+ 7 + 8 + 12 + 4 + 6 + 7 + 11 = 80

7 + 11 = 18

Probability = 18/80

= 0.225 x 100

= 22.5%

Read more on probability here: https://brainly.com/question/251701

Answer:

19

Step-by-step explanation:

Answer:

420

Step-by-step explanation:

Answer:

2.

Step-by-step explanation:

it's the reciprocal

so it's gonna reflect

Answer:

triangular prism

Step-by-step explanation:

Have a great day!

The amount of sand needed = volume of rectangular pyramid = 160 cubic inches of sand.

Volume of rectangular pyramid = 1/3(base area × height of pyramid)

Given the following:

Amount of sand needed to fill each beach toy = Volume of rectangular pyramid = 1/3(48 × 10) = 160 cubic inches of sand.

Learn more about volume of rectangular pyramid on:

https://brainly.com/question/1153556

Answer:

The answer is 3

Step-by-step explanation:

Answer:

The unit rate would be 3 dollars per pound!

Answer:

yes, if this is the answer you're looking for

Step-by-step explanation:

Yes. The scale factor is 1/2 or Divide by 2

The Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex]

We're given:

Plug these measurements into the Pythagorean theorem:

[tex]a^2+b^2=c^2\\9^2+12^2=c^2[/tex]

⇒ Combine like terms:

[tex]81+144=c^2\\c^2=225[/tex]

[tex]c^2=225[/tex]

Answer:

One is 89 , the other is 33.

Step-by-step explanation:

Set up a system of 2 equations:

x + y = 122

x - 2y = 23        Subtracting:

0 + 3y = 99

y = 33.

So:

x + 33 = 122

x = 122 -33 = 89.

Answer:

first number= 89 and second number= 33

Step-by-step explanation:

here, let the first number be X and the second number be y,then

From the question,

x + y = 122 ---- eq i

x -2y = 23 ----- eq ii

From substitution method,

From eq i,

x + y = 122

or, x =122 - y

Now, putting the vale of x in eq ii,we get,

122 -y -2y = 23

or, -3y = 23-122

or, -3y = -99 (cut minus sign in both sides)

or, y=99/3

or, y = 33

Again, putting the value of y in eq i,we get,

x + 33 = 122

or, x= 122-33

or, x=89