Solve for x: |x − 2| + 10 = 12 (1 point)

Since we know we only have 640 feet of fence available, we know that L + W + L = 640, $\implies$ 2L + W = 640. This allows us to represent the width, W, in terms of L: W = 640 – 2L

Remember, the area of a rectangle is equal to the product of its width and length, therefore,

$A_{\rm pigpen}=L(640-2L)\implies 640L-2L^2$

Notice that, quadratic has been vertically reflected, since the coefficient on the squared term is negative, so the graph will open downwards, and the vertex will be a maximum value for the area.

recall,

$x_{max}=-b/2a$
$f(x)_{max}=f(x_{max})$

Since our function is A(L)=640L-2L², we get

a=-2
b=640

plug in the value of a and b into the first formula:

$L_{max}=-(640)/2(-2)\implies 160$

$A(L)_{max}=640(160)-2(160)^2\implies 76800$

hence,the dimensions of the pen that will maximize the area are L=160m and W=76800/160=480m

and we're done!

3 0

2 years ago

Find the perimeter of the figure. Round all figures to the nearest hundredths place. Isosceles trapezoid

zhannawk [14.2K]

Answer:

d. 92.84

Step-by-step explanation:

The top edge overhangs the bottom edge by (39 -27)/2 = 6 ft on both ends. This makes the slant side have length

.. √((6 ft)^2 +(12 ft)^2) = 6√5 ft

Then the perimeter is

.. (39 +6√5 +27 +6√5) ft = 66 +12√5 ft

= 92.83 ft

6 0

3 years ago

Help me with these 3 and explain too thank you :))

xz_007 [3.2K]

Answer:

1) 25

2) 2

3) f(g(1)) = 42

Step-by-step explanation:

1) Given that f(x) = 4x^2 + 9

If x = -2

f(-2) = 4(-2)^2 + 9

f(-2) = 4(4) + 9

f(-2) = 16 + 9

f(-2) = 25

2) Given that f(x) = 4x - 6

y = 4x - 6

Replace y with x

x = 4y - 6

MAke y the subject of the forfmula

4y = x+ 6

y = (x+6)/4

SInce x = 2

f^(-1)(2) = (2+6)/4

f^(-1)(2) = 8/4 = 2

3) If f(x) = 6x and g(x) = x+6

f(g(x)) = f(x+6)

f(x+6) = 6(x+6)

Since x = 1

f(g(1)) = 6(1+6)

f(g(1)) = 6(7)

f(g(1)) = 42

5 0

3 years ago