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3 years ago

What is the remainder when x 3 − 7x + 5 is divided by x + 3 ?

Mathematics

1 answer:

baherus [9]3 years ago

5 0

Answer:

the remainder is - 1

Step-by-step explanation:

when (x ³ - 7x + 5) is divided by (x + 3) the remindeer is f( -3 )

x + 3 = 0 => x = - 3

f(-3) = (-3)³ - 7(-3) + 5

= - 27 + 21 + 5

= - 1

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A pigpen is to be enclosed using 640 m of fencing along three of its sides, the fourth side being a barn. Determine the dimensio

Basile [38]

Answer:

$W_{max}=480m\\ L_{max}=160m$

Step-by-step explanation:

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

What are the domain and range of the function below?

irina1246 [14]

I think the answer is

domain : (- infinity , infinity )

range : [ -2 , infinity )

i am sorry if my answer was wrong

8 0

3 years ago

Read 2 more answers

A roll of steel is manufactured on a processing line. The anticipated number of defects in a 10-foot segment of this roll is two

Vikentia [17]

Answer:

the probability of no defects in 10 feet of steel = 0.1353

Step-by-step explanation:

GIven that:

A roll of steel is manufactured on a processing line. The anticipated number of defects in a 10-foot segment of this roll is two.

Let consider β to be the average value for defecting

So;

β = 2

Assuming Y to be the random variable which signifies the anticipated number of defects in a 10-foot segment of this roll.

Thus, y follows a poisson distribution as number of defect is infinite with the average value of β = 2

i.e

$Y \sim P( \beta = 2)$

the probability mass function can be represented as follows:

$\mathtt{P(y) = \dfrac{e^{- \beta} \ \beta^ \ y}{y!}}$

where;

y = 0,1,2,3 ...

Hence, the probability of no defects in 10 feet of steel

y = 0

$\mathtt{P(y =0) = \dfrac{e^{- 2} \ 2^ \ 0}{0!}}$

$\mathtt{P(y =0) = \dfrac{0.1353 \times 1}{1}}$

P(y =0) = 0.1353

4 0

2 years ago

Two separate bacteria populations grow each month and are represented by the

ASHA 777 [7]

Answer:

Option 4.) month 4

Step-by-step explanation:

we have

$f(x)=3^{x}$ ----> equation A

$g(x)=7x+6$ ----> equation B

Solve the system by graphing

Remember that the solution is the intersection point both graphs

The solution is the point (3,27)

That means -----> For x=3 months, the populations in both functions are the same (the bacteria populations is 27)

therefore

For x> 3 months the f(x) population is greater then the g(x) population

5 0

2 years ago

Find the minimum or maximum value of the function. What is the H? (Desmos)

beks73 [17]

Answer:

Minimum: (2,4)

Step-by-step explanation:

h(x)=3( $x^{2}$ -4x)+16

=3( $x^{2}$ -4x+4-4)+16 (- For the balance of equation, and attention 1)

=3 $(x-2)^{2}$ -3*4+16

=3 $(x-2)^{2}$ +4

<h3>Attention:</h3>

1. $(a-b)^{2}=a^{2} -2ab+b^{2}$

2. The formula for the vertex form is y = $a(x-h)^{2}+k$ , the vertex is (h,k)

4 0

2 years ago