226.19 divided by 2/3

Find the domain of the function (f/g)(x) given f (x)=x^2-4x-5 and g(x)=x^2-25

stealth61 [152]

Answer:

all real numbers except ±5.

Step-by-step explanation:

Each function (f(x), g(x)) has a domain that is all real numbers. Their quotient (f(x)/g(x)) must exclude values that make g(x) = 0. The quotient is undefined when the denominator is zero. Those excluded values are x = ±5.

The domain of (f/g)(x) is all real numbers except ±5.

___

Of course you recognize x^2 -25 = 0 has solutions x = ±√25 = ±5. You can get there two ways:

add 25 and take the square root: x^2=25; x=±√25.
factor the difference of squares and set the factors to zero: (x-5)(x+5)=0 has solutions x-5=0 and x+5=0, that is, x = ±5.

5 0

3 years ago

mary has 39 square feet of patio bricks. each square brick has sides 1 foot long. what is the greatest perimeter of a rectangle

bearhunter [10]

-- The smallest perimeter you can make with a certain area
is a circle.

-- The NEXT smallest perimeter with the same area is a square.

   With 1-ft by 1-ft square bricks, the shortest perimeter she could
make would be by using her bricks to make it as square as possible.
Without cutting bricks into pieces, the best she could do would be

       (13 bricks) x (3 bricks) .

= (13-ft) x (3-ft)

   Perimeter = (2 x length) + (2 x width)

   = (2 x 13-ft) + (2 x 3-ft)

   =      (26-ft) + (6-ft) = 32 feet <== shortest perimeter.

-- Then, the more UNSQUARE you make it, the more perimeter
it takes to enclose the same area. That means Mary has to make
a rectangle as long and skinny as she can.

The longest perimeter she can make (without cutting bricks into
pieces) is (39 bricks) x (1 brick) .

      = (39-ft) x (1-ft) .

Perimeter = (2 x length) + (2 x width)

   = (2 x 39-ft) + (2 x 1-ft)

   =    (78-ft) + (2-ft) = 80 feet .

What she'll have then is a brick path, 39 feet long and 1 foot wide,
and when you walk on it, you'll need to try hard to avoid falling off
because it's only 1 foot wide.

7 0

3 years ago

What is the total surface area of the pyramid below?

mel-nik [20]

Answer:I guess 6 ft as you gave same options

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Determine the distance between -10 and 5. HELP

kow [346]

Answer: 15

Step-by-step explanation: Good luck! :D

7 0

3 years ago

Read 2 more answers

Uninhibited growth can be modeled by exponential functions other than A(t) =Upper A 0 e Superscript kt. For example, if an i

laila [671]

The question is incomplete. Here is the complete question.

Uninhibited growth can be modeled by exponential functions other than $A(t)=A_{0}e^{kt}$ . for example, if an initial population P₀ requires n units of time to triple, then the function $P(t)=P_{0}(3)^{\frac{t}{n} }$ models the size of the population at time t. An insect population grows exponentially. Complete the parts a through d below.

a) If the population triples in 30 days, and 50 insects are present initially, write an exponential function of the form $P(t)=P_{0}(3)^{\frac{t}{n} }$ that models the population.

b) What will the population be in 47 days?

c) When wil the population reach 750?

d) Express the model from part (a) in the form $A(t)=A_{0}e^{kt}$ .

Answer: a) $P(t)=50(3)^{\frac{t}{30} }$