I need help with 40-51

In the barn, there are horses and chickens. There are 11 heads and 32 legs altogether. How many chickens are there?

Masteriza [31]

Answer:

6 Chickens

Step-by-step explanation:

Let H represent the number of horses and C represent the number of chickens. Since there are 32 legs altogether this means that on equation to use would be given by:

2C + 4 H = 32 (Eq. 1)

Another equation can be made from the fact that there are 11 heads or 11 animals altogether which can be written as:

C + H = 11 (Eq. 2)

From Eq. 2, solve for the number of chickens:

C + H = 11

C = 11 - H (Eq. 3)

Substituting Eq. 3 in Eq. 1, the number of horses can be determined:

2 C + 4 H = 32

2 ( 11 − H ) + 4 H = 32

22 − 2 H + 4 H = 32

2H = 32 − 22

2 H = 10

H = 5 Eq.4

Putting Eq.4 in Eq.1

2C + 4*5 = 32

2C = 32 - 20

2C = 12

C = 12/2

C = 6

8 0

3 years ago

Evaluate the expression.<br> 38 +16 - 12 - 2 - (302)<br> Enter your answer in the box.

masha68 [24]

Answer:

-262

Step-by-step explanation:

Evaluate Subtraction & Addition from right to left [or left to right, as long as you know what you are doing]:

38 + 16 - 12 - 2 - 302

|_______||____________|

$44 - 316 = -262$

I am joyous to assist you anytime.

5 0

3 years ago

Which is the standard form of the equation of the parabola that has a vertex of (3, 1) and a directric of x = -2?

vagabundo [1.1K]

Check the picture below. So,the parabola looks like so, notice the distance "p". since the parabola is opening to the right, then "p" is positive, thus is 5.

$\bf \textit{parabola vertex form with focus point distance}\\\\
\begin{array}{llll}
\boxed{(y-{{ k}})^2=4{{ p}}(x-{{ h}})} \\\\
(x-{{ h}})^2=4{{ p}}(y-{{ k}}) \\
\end{array}
\qquad 
\begin{array}{llll}
vertex\ ({{ h}},{{ k}})\\\\
{{ p}}=\textit{distance from vertex to }\\
\qquad \textit{ focus or directrix}
\end{array}\\\\$

$\bf -------------------------------\\\\
\begin{cases}
h=3\\
k=1\\
p=5
\end{cases}\implies (y-1)^2=4(5)(x-3)\implies (y-1)^2=20(x-3)
\\\\\\
\cfrac{1}{20}(y-1)^2=x-3\implies \boxed{\cfrac{1}{20}(y-1)^2+3=x}$

8 0

3 years ago

Read 2 more answers

Find the surface area of the prism formed by the net

Lunna [17]

ANSWER

$T.S.A=1960m^2$

EXPLANATION

The diagram represents the net of a rectangular prism.

The dimensions are,

$l=42m$

$w = 14m$

and

$h = 7m$

The total surface area of a rectangular prism is given by:

$T.S.A=2(lw + lh + wh)$

We substitute the values to obtain,

$T.S.A=2(42 \times 14 + 42 \times 7 + 14 \times 7)$

$T.S.A=2(980)m^2$

$T.S.A=1960m^2$

3 0

3 years ago

Your interest rate is compounded annually. Beginning Balance: $1,166.40. Annual Interest Rate: 8% How much will you earn in inte

konstantin123 [22]

Answer:

93.31200 dollars

Step-by-step explanation:

8% of 1166.40

4 0

3 years ago