A study was done to investigate the population of a certain species of animal over time. The correlating linear model is shown below, where x represents the number of years after 1955, and y represents the number of that certain species. Interpret the y-intercept.

y = 5,000 + 500x

A. There were 1,000 of that species in 1955.
B. There were 10,000 of that species in 1955.
C. There were 500 of that species in 1955.
D. There were 5,000 of that species in 1955.

Answer:

280 ft

Step-by-step explanation:

An auditorium is in the shape of an equilateral triangle with side length as 112 ft.

The stage extends from one vertex of the triangle to the mid-segment and the seating area extends from the mid-segment to the rear wall.

*The situation is represented in the attachment.

According to the midpoint theorem, the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.

Hence, the length of the mid-segment in this case is,

[tex]\dfrac{1}{2}\times 112=56\ ft[/tex]

Therefore, the perimeter of the seating area is,

[tex]=112+56+56+56=280\ ft[/tex]

The perimeter of the seating area of an auditorium shaped as an equilateral triangle with rear wall measuring 112 feet will be 224 feet.

This is a Mathematics question related to Geometry. An equilateral triangle is a triangle where all sides are of equal length. Since the auditorium is in the shape of an equilateral triangle, all sides of the triangle will have identical measurements. In this case, it’s specified that the rear wall measures 112 feet. Thus, each side of the triangle will be 112 feet.

The question asks for the perimeter of the seating area which starts from the midsegment of the triangle and extends to the rear wall. The midsegment of an equilateral triangle splits the triangle into equivalent smaller equilateral triangles. Hence, the length of the midsegment to a vertex is half of the side of the triangle. So, the length of the seating area on each side is 112/2 = 56 feet.

Since, there are two sides that measure 56 feet (that is from the midsegment to the other two vertices of the triangle), and the rear side measures 112 feet, to calculate the perimeter, we sum up these sides. Hence, the perimeter of the seating area will be 56 + 56 + 112 = 224 feet.

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Answer:

12 days

Step-by-step explanation:

Time taken by one man = x days , and that by 1 boy = y days

work done in 1 day by one man = 1/x

work done in 1 day by one boy= 1/y

work done by 2 men in one day = 2/x

work done by 7 boys in one day = 7/y

2/x + 7/y = 1/4      -----> [ 1]

work done by 4 men in one day = 4/x

work done by 4 boys in one day = 4/y

4/x + 4/y = 1/3       ----> [2]

Multiplying  equation 1 by  , 2 ,  

2(2/x + 7/y = 1/4   )

 = 4/x + 14/y = 1/2           ---> [3]

solving equations 2 and 3

 4/x + 4/y = 1/3  

- 4/x + 14/y = 1/2  

==============

-10/y = 2-3/6

-10/y = -1/6

-1/6y = -10

y = -10 × 6/-1

  = 60 

2/x + 7/y = 1/4

2/x + 7/60 = 1/4

7/60 - 1/4 = -2/x

-8/60 = -2/x

-120 = -8x

x = -120/-8

x = 15

=================================

Time taken by 1 man to do the  whole job = 15 days

time taken by 1 boy to do the whole  job = 60 days

time taken by one boy and one man to do one day's work = 1/60 + 1/15

                                         = 1/60 + 4/60

                                         = 5/60  = 1/12

Together they can do it in 12 days !

Answer:

.7

Step-by-step explanation:

As a decimal it would be .7, easy way to do it is 7/10 is 70%, change the % to a . and move it to the left twice, leaving you with .70, 0's are place holders, and you dont have to write them if there is nothing behind it, leaving you with .7

Hope this helped, Brainliest?

Answer:

.7

Step-by-step explanation:

As a percent, this would be expressed as 70%. However, if you wanted to change 70% into a decimal, all you have to do is take 70 and divide it by 100.

Answer:

647.0625

Step-by-step explanation:

Answer:

about 11920.92896

Step-by-step explanation:

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have the points P(2, 2) ans Q(7, 4). Substitute:

[tex]|PQ|=\sqrt{(7-2)^2+(4-2)^2}=\sqrt{5^2+2^2}=\sqrt{25+4}=\sqrt{29}\approx5.4[/tex]

Answer:

-80*pi

Step-by-step explanation:

pi*-80 can be written alternatively as -80*pi.

Rewrite it in the form a^2 - 2ab + b^2, where a = d and b = 2

d^2 - 2(d)(2) + 2^2

Use the Square of Difference: (a - b)^2 = a^2 - 2ab + b^2

(d - 2)^2

Answer:

(d - 2)²

Step-by-step explanation:

d² - 4d + 4 ← is a perfect square of the form

(x ± a )²  = x² ± 2ax + a²

compare coefficients of like terms

- 2a = - 4 ⇒ a =  2 and a² = 4, hence

d² - 4d + 4 = (d - 2)²

Answer: D

Step-by-step explanation:

Ratio of Top:Bottom

Top/Bottom

5.5/7.5

5.5/7.5 * 2/2 = 11/15

Answer:

D

Step-by-step explanation:

You want the ratio of the width to the length

w/L = 5.5/7.5 There are no decimals in any answer except b and it looks it is wrong. The reason is that the numerator is divided by 2 to give 5.5/2 = 2.75  and the denominator is multiplied by 2 to give 15. So B is out.

C

C: is pretty close. The problem is that the ratio is stated as width to length. C does do the same things to top and bottom (multiplies both of them by 2) but this answer is upside down of right.

I don't know exactly what was done with A but it isn't right.

Answer D

Answer:

The length of the rectangle is 17 cm and the width of the rectangle is 5 cm.

Step-by-step explanation:

Given the measurements in the question, you can set up two different equations to find the length and width of the rectangle.  First, the formula for the perimeter of a rectangle is:  P = 2W + 2L, where W = width and L=length.  In this problem the L is '7 more than twice its width', this means our first equation is:

L = 2W + 7

Next, we can use this expression in our formula for perimeter to get our second equation:

P = 2W + 2(2W + 7)  or 44 = 2W + 2(2W + 7)

Distribute:  44 = 2W + 4W + 14

Combine like terms:  44 = 6W + 14

Subtract 14 from both sides:  44 - 14 = 6W + 14 - 14 or 30 = 6W

Divide 6 from both sides:  30/6 = 6W/6 or W = 5

Now, solve for L:  L = 2(5) + 7 or L = 10 + 7 = 17

So, the width is 5cm and the length is 17 cm.

The length of the rectangle is 17 cm and the width of the rectangle is 5 cm

The area of Rectangle is length times of width.

Given that perimeter of a rectangle is 44 cm.

Its length is 7 more than twice its width.

Length=2w+7

Width=w

Perimeter=2(Length+Breadth)

44=2(2w+7)+2w

Apply distributive property on right hand side

44=4w+14+2w

44=6w+14

Subtract 14 on both sides

30=6w

Divide both sides by 5

5=w

So width of rectangle is 6cm and length is 2(5)+7=10+7=17 cm

Hence, the length of the rectangle is 17 cm and the width of the rectangle is 5 cm

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Answer:

n=1.75

Step-by-step explanation:

(7-4n)*6=0

We simplify the equation to the form, which is simple to understand  

(7-4n)*6=0

Reorder the terms in parentheses

(+42-24n)=0  

Remove unnecessary parentheses

+42-24n=0

We move all terms containing n to the left and all other terms to the right.  

-24n=0-42

We simplify left and right side of the equation.  

-24n=-42

We divide both sides of the equation by -24 to get n.  

n=1.75

Answer:

42 - 24n

Step-by-step explanation:

This is an expression, not an equation.  We can simplify

(7-4n)*6

Distribute the 6

7*6 - 4n*6

42 - 24n

Answer:

90.5cm

Step-by-step explanation:

Pythagorean Theorem: a^2 + b^2 = c^2

c= 128cm. c^2= 16384

a = b in 45-45-90

a^2 = b^2 = (c^2)/2 = 8192

√8192 = 90.51

Lia saved $8.50 on a dress by purchasing it at a 10% discount from the original price of $85.

To find out how much money Lia saved on a dress that was originally $85.00 with a 10% discount, we need to calculate the amount of the discount. First, convert the percent to a decimal by dividing by 100, which gives us 0.10. Then multiply the original price by the decimal to find the amount saved.

The original price of the dress: $85.00
Discount rate: 10% or 0.10
Amount saved: $85.00 x 0.10 = $8.50
Lia saved $8.50 by buying the dress on sale.

Lia saved $8.50 by buying the dress on sale.

To calculate how much Lia saved by buying the dress on sale, we first need to find out the discount amount.

Calculate the discount: The dress is marked 10% off the original price of $85.00. To find the discount amount, we calculate 10% of $85.00.

Discount = 10% of $85.00 = 0.10 * $85.00 = $8.50

Subtract the discount from the original price: Now that we know the discount amount, we subtract it from the original price to find the sale price.

Sale Price = Original Price - Discount = $85.00 - $8.50 = $76.50

Calculate the savings: To find out how much money Lia saved by buying the dress on sale, we subtract the sale price from the original price.

Savings = Original Price - Sale Price = $85.00 - $76.50 = $8.50

So, Lia saved $8.50 by buying the dress on sale.

Answer:

     r+5                 r^2+4r-21

-------------- /   --------------------

r^2+5r-14               r-2

         r+5                     r-2

= --------------  x   --------------------

   r^2+5r-14           r^2+4r-21

         r+5                     r-2

= --------------  x   --------------------

   (r+7)(r-2)           (r+7)(r-3)

         r+5                     

= -----------------

   (r+7)^2 (r-3)          

hope it helps

Step-by-step explanation:

Answer:

The average weight is 7 1/8 pounds

Step-by-step explanation:

To find the average, we add them up and then divide by how many

average = (b1+b2+b3)/3

             = (8 1/4 + 6 1/2+ 6 5/8) /3

Let look at the sum

(8 1/4 + 6 1/2+ 6 5/8)

We need to get a common denominator of 8

8 1/4 *2/2 + 6 1/2 *4/4 + 6 5/8

8 2/8 + 6 4/8 + 6 5/8

20 11/8

20 + 1 3/8

21 3/8

average = (21 3/8) /3

Now we divide by 3

We need to change the mixed number to an improper fraction

21 3/8 = (8*21+3) /8 = 171/8

average = (171/8) /3

We can use copy dot flip

171/8 * 1/3

171/24

We need to change it back to a mixed number

24 goes into 171  7 times with 3 left over

7 3/8

7 1/8

Answer:

He saw 4 more

Step-by-step explanation:

There were 5 sparrows and 1 blue jay 5 - 1 = 4

let's say the breakfast price was "x", so that's the 100%, and we know she gave 20% of that and that is 1.80.

so, 1.80 is 20%, and "x" is the 100%, what is "x"?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 1.80&20\\ x&100 \end{array}\implies \cfrac{1.80}{x}=\cfrac{20}{100}\implies \cfrac{1.8}{x}=\cfrac{1}{5} \\\\\\ 9.0=x\implies 9=x[/tex]

Answer:

$9

Step-by-step explanation:

Answer:

Step-by-step explanation:

The ratio of the total cost to the number of yards is always 4.35 cents

[tex]Money/Yards = 4.35 dollars/1 yard[/tex]

Answer: 8n

==========================================================

Explanation:

The two sides 4n+5 and 5n+6 have the terms 4n and 5n which add to 9n. We need 8n to add onto this so that we end up with 17n. In other words, 4n+5n+8n = 9n+8n = 17n

So that is why the answer is 8n. We don't have anything added or subtracted to it because the "+5" and "+6" in the two given expressions (4n+5 and 5n+6) add up to 5+6 = 11 which is what we want in the perimeter expression 17n+11

Side 1 = 4n+5

Side 2 = 5n+6

Side 3 = 8n

Perimeter = (side1) + (side2) + (side3)

Perimeter = (4n+5) + (5n+6) + (8n)

Perimeter = 4n+5 + 5n+6 + 8n

Perimeter = (4n+5n+8n) + (5+6)

Perimeter = 17n+11

So that confirms we have the proper expression for the third missing side.

Question

The expression 17n+11 represents the perimeter of a triangle. The other two sides measure 4n+5 and 5n+6. A simplified expression that represents the measure of the third side would be...?

Answer:

Step-by-step explanation:

you simply take off the misure of the know sides from the perimeter

(17n + 11) - (4n +5 - 5n + 6) =

8n

Answer:

65,81,97,113,129

Step-by-step explanation:

she has 65 water bottles and she is buying boxes of water bottles (x) that hold 16 water bottles each. She can only buy up to 5 water bottles.

f(x) = 16x + 65...where f(x) = total water bottles and x = number of boxes

x < = 5 here is ur restriction

the range is ur f(x) values which represent the total number of water bottles...keep in mind, she can only buy 5. Therefore, the numbers that can be subbing in for x are 0 thru 5.

So when subbing in 0 thru 5 for x, the results for f(x) are :

{ 65,81,97,113,129 }

Half Tens is a way of multiplying where we have to find the value of given numbers. First we double any 'one' of the two given numbers and multiply both to get an answer. Then we divide that answer by '2' to get the answer.

Lets take two numbers as 16 and 340

[tex]16\times340=?[/tex]

Double the number 16

[tex]32\times340=10880[/tex]

Now we will divide this by 2

[tex]\frac{10880}{2}= 5440[/tex]

So, if we check [tex]16\times340=?[/tex] , it is 5440.

Similarly if we double the number 340, we get 680

Now, [tex]16\times680=10880[/tex]

And 10880/2 = 5440

Hence, in both ways the answer is 5440.

In Half-Tens method first, double the first number then multiply that number with the second number, and then divide that value by 2 the result obtained is the required result.

Given :

Noah loves the Half-Tens facts and often uses them to solve multiplication problems.

It is given that make up a 2-digit by 3-digit multiplication problem for which using Half Ten facts is efficient.

So, let the two numbers be 56 and 362 then multiply both the numbers by using the Half-Tens method.

First, double the two-digit number:

[tex]=56\times2[/tex]

= 112

Then multiply the above number by 362.

[tex]=112\times 362[/tex]

= 40544

Then divide the above number by 2.

[tex]=\dfrac{40544}{2}[/tex]

= 20272

Now, check : [tex]56\times 362= 20272[/tex]

Now, similarly double the number 362.

[tex]=362\times 2[/tex].

= 724

Then multiply the above number by 56.

[tex]=724\times 56[/tex]

= 40544

Then divide the above number by 2.

[tex]=\dfrac{40544}{2}[/tex]

= 20272

Now, check : [tex]56\times 362= 20272[/tex]

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Answer:

x=5/2

Step-by-step explanation:

We can use ratios of similar triangles to help solve the problem.

side                    x                       5

--------              = --------------- = ---------------

hypotenuse               4                   8

Using cross products

x*8 = 4 * 5

8x = 20

Divide each side by 8

8x/8 = 20/8

x = 5/2

Answer:

1/12 = 24/12 = 2

pea: 12/24

haz: 4/24

alm: 8/24

cash: 18/24

pec: 6/24

how to do it: find a common denominator, or write it how and scan it with photo math and it will show you how to work it out!

hope this helped or was right, thanks <3

Answer:

the answer is d

Step-by-step explanation:

Answer:

HELLO :

the slope is : (5-1)/(-2-3)) = 4/-5 = -4/5  ( answer : d)

Answer:2 whole sandwiches and 3/4 of another one

Step-by-step explanation:

Answer:

Step-by-step explanation:

So first draw a table then messure it out or you can draw out a box into 3 parts then shade in 2 of the 3 then shade a small portion for 3/4.

Answer:$7.50

Step-by-step explanation:

multiply 2.50 by three because four goes into 12 three times.

Answer:

30.00$

Step-by-step explanation:

All you have to do is multiply 2.50 by 4 and that equals 10.00

And then know how much a dozen is which equals 12.

And last multiply 2.50 by 4, 3 times and you will get 30.00

Answer:

17. 6

18. 18 (as shown)

19. 10/3 = 3 1/3

20. 20/3 = 6 2/3

Step-by-step explanation:

17. For this, you can subtract the given length GB=12 from the length you found for problem 18, BF=18. Doing that tells you FG = 18-12 = 6, as you have marked on the diagram.

19. As with median BF, the point G divides it into two parts that have the ratio 1:2. The distance from G to D is the shorter of the distances, so you have ...

... GD = (1/3) CD = (1/3)·10 = 10/3

... GD = 3 1/3

20. You can subtract GD from CD to get CG, or you can multiply CD by 2/3. The result is the same either way.

... CG = CD -GD = 10 -3 1/3

... CG = 6 2/3

_____

Comment on centroid and median

The centroid (G) divides each median into parts in the ratio 1:2. Hence the shorter of those parts is half the length of the longer one, or 1/3 the total length of the median.

The longer of the parts is double the length of the shorter one, or 2/3 the total length of the median.

Your marking of median BF seems to show an understanding of these relationships. (Total length: 18; length of parts: 6 and 12.)

When you multiply an exponent directly into another exponent, you multiply the exponents

(for a fraction, you multiply the exponent to both the numerator and denominator)

For example:

[tex](x^{2})^5=x^{2(5)}=x^{10}[/tex]

[tex](\frac{x^3}{y^2} )^5=\frac{x^{3(5)}}{y^{2(5)}} =\frac{x^{15}}{y^{10}}[/tex]

[tex](\frac{7}{4})^{11}=(\frac{7^1}{4^1})^{11}=\frac{7^{11}}{4^{11}}[/tex]

Your answer is A

Answer:

[tex](\frac{7^{11}}{4^{11}})[/tex]

Step-by-step explanation:

[tex](\frac{7}{4})^{11}[/tex]

To simplify this fractional exponent we apply exponential property

[tex](\frac{x}{y})^m=\frac{x^m}{y^m}[/tex]

As per this property , we multiply the exponent inside the fraction

Multiply the exponent 11 inside the fraction

Multiply the exponent 11 with 7 and then 4

[tex](\frac{7}{4})^{11}[/tex]

[tex](\frac{7^{11}}{4^{11}})[/tex]

Answer:

Bruh no one has still answered u?!

Step-by-step explanation:

Answer:

Answer??

Step-by-step explanation:

Answer:

25 nautical miles

Step-by-step explanation:

We need to find the rate.  We can do so using the formula, distance = rate * time

d= rt

We know the distance and the time, so we need to solve for the rate

d/t = rate

d= 150 nautical miles

t = 6 hours

d/t = 150 nautical miles /6 hours

rate = 25 nautical miles per hour

So in 1 hour we can go 25 nautical miles

Answer:

25 nautical miles.

Step-by-step explanation:

Givens

Equation

Solution