Farmer John looks out on his farm. One pen has chickens and pigs. John counted 12 heads and 34 legs. How many of each animal did he see? EXPLAIN your reasoning. I DO WANT YOU TO EXPLAIN AND ANSWER QUICKLY PLEASE

Answers

Answer 1

Answer: 34 legs and 12 heads

Chicken has 2 legs and Pig has 4 legs, both got one head

7 chicken heads, 7 x 2= 14 chicken legs

5 pig heads, 5 x 4= 20 pig legs

7 chicken heads + 5 pig heads = 12 heads

14 chicken legs + 20 pig legs = 34 legs

Answer: He saw 7 chickens and 5 pigs

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Carmen rolls a cube with sides labeled A, B, C, D, E, and F.What is the number of possible outcomes?

Answers

The cube may come to rest with any one of its sides upright. So there are six (6) possible outcomes of a single roll. Technically, there is also some finite probability that the cube will come to rest standing on one of its edges, or on one corner. These probabilities are so small that these additional possible outcomes are almost always ignored, and not counted.

there are six outcomes. so , you would put 1 over 6 for all of them and add them together, which results in 6 possibilities.

A boat costs $12,050 and decreases in value by 12% per year. How much will the boat be worth after 9 years?A $33,415.60
B $3,813.56
C $11,942.00
D $3,355.94

Answers

B $3,813.56 is the correct answer

1 year = $10,604
2 years = $9,331.52
3 years = $8,211.74
4 years = $7,226.33
5 years = $6,359.17
6 years = $5,596.07
7 years = $4,924.54
8 years = $4,333.60
9 years = $3,813.56

For this case we have the following expression:

$y = A (b) ^ x$

Where,

A: initial value
b: rate of change
x: number of years
y: future value

Therefore, replacing values we have:

$y = 12050 * (0.88) ^ 9\ny = 3813.56$

Answer:

The boat will be worth after 9 years about:

B $ 3,813.56

What is the elapsed time between 10:30 p.m. and 1:15 a.m.?3 hours
3 hours and 15 minutes
2 hours and 45 minutes
2 hours and 30 minutes

Answers

If you would like to find the elapsed time between 10:30 p.m. and 1:15 a.m., you can calculate this using the following steps:

12:00 p.m. - 10:30 p.m. = 1:30
00:00 a.m. + 1:15 a.m. = 1:15

1:30 + 1:15 = 2:45 = 2 hours and 45 minutes

The correct result would be 2 hours and 45 minutes.

In winter, the price of apples suddenly went up by$0.75 per pound. Sam bought 3 pounds of apples at the new price for a total of $5.88. Write an equation to determine the original price per pound (p) and then find the original price per pound.

Answers

From the information given, the original price per pound was increased by $ 0.75
Let the original price be x, so the new price is x + 0.75

Sam bought 3 pounds of apples at new price and it cost him 5.88

so we form an equation:

3 (x + 0.75) = 5.88

3x + 2.25 = 5.88

3x = 5.88 - 2.25

3x = 3.63

x = 3.63 / 3

x = 1.21

Therefore the original price per pound is 1.21 dollars

Answer:

1.21=x

Step-by-step explanation:

3 (x + 0.75) = 5.88

then 3x + 2.25 = 5.88

then 3x = 5.88 - 2.25

to 3x = 3.63

and last of allx = 3.63 / 3

The line y=mx is tangent to the curve y^2 = X-C. Show that c = 1/ (4m^2)

Answers

Hello,
Let (a,b) the intersection of the tangent and the curve.
That point must be double.

So
b=m*a
b²=a-c
==>(ma)²-a+c=0
==>m²a²-a+c=0 roots must be equal
Δ=(-1)²-4*m²c=0 => 4m²c=1==>c=1/(4m²)

Can atriangle be formed with side lengths of 5cm. 10cm and 15cm

Answers

Theorem of cosine:
a²=b²+c²-2bc(cos α) ⇒cos α=-(a²-b²-c²) / 2bc

In this case:
a=15 cm
b=10 cm
c=5 cm

cos α=-(15²-10²-5²) / 2*10*5
cos α=-100 / 100
cos α=-1

A=arc cos -1=180º This is impossible, because:

A+B+C=180º; then B=C=0º This is impossible for make a triangle (B>0 and C>0 if we want to make a triangle).

Therefore: it is not possible can make a triangle with side lengths of 5 cm, 10 cm and 15 cm.

remember
longest side must be less than the sum of the other 2 sides because if it is eqal than you get a line, and if it is longer, then you cannot connect the points

longest side is 15
15<10+5
15<15
fasle

no triangle can be formed

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