MATHEMATICS HIGH SCHOOL

Which second degree polynomial function has a leading coefficient of –1 and root 4 with multiplicity 2f(x) = x3 – x2 – 4x + 4
f(x) = x4 – 3x2 – 4
f(x) = x4 + 3x2 – 4
f(x) = x3 + x2 – 4x – 4

Answers

Answer 1
Answer: Hello,

ANSWER B (x^4-3x²-4) [roots are i,-i,2,-2]
Answer 2
Answer: Your answer is f(x) = x4 – 3x2 – 4

Hope this helps.

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An adult elephant eats about 300 pounds of food each day. Write an expression to represent the number of pounds of food a heard of 12 elephants eats in 5 days.

Answers

Answer:

Your answer would be 18,000.

Step-by-step explanation:

You would need to multiply 300 by 12 to get 3,600. Then you would multilpy that by 5 to get your answer.

What number should be added to both sides of the equation to complete the square?x2 + 12x = 11

Answers

given:
x² + 12x = 11

perfect square:

a² + 2ab + b²

a² = x² ⇒ x * x
2ab = 12x ⇒ 2(6)x
b² = 6² ⇒ 36

x² + 12x + 36 = 11 + 36

(x+6)(x+6) = 47

Both sides must be added with 36.

Answer:

36.

Step-by-step explanation:

We have been given an equation x^2+12x=11 and we are asked to find the number that should be added to both sides of the equation to complete the square.

To complete the square we divide the constant with x term by two and add the square of that number to both sides of equation to complete the square.

((b)/(2))^2

We can see that constant of x term is 12, so let us divide 12 by 2.

(12^2)/(2^2)

(144)/(4)

36

Therefore, we should add 36 to both sides of our equation to complete the square.

After adding 36 to both sides of our equation we will get,

x^2+12x+36=11+36

x^2+12x+6^2=47

(x+6)^2=47

The population of the country of Oz was 600,000 in the year 2010. The population is expected to grow by a factorof 5% annually. The annual food supply of Oz is currently sufficient for a population of 700,000 people and is
increasing at a rate that will supply food for an additional 10,000 people per year.
c. At what point does the population exceed the food supply? Justify your response.

Answers

Answer:

After 5 years (2015)

Step-by-step explanation:

The population is increasing 5% per year, so the first year it will be 1.05 of the initial, the next year 1.05x1.05 of the initial, and then  successively, so, for n years:

P(n) = 600,000*(1.05)ⁿ

The food suply increase 10,000 people per year, so the first year will be 10,000 + the initial, the next year 10,000 + 10,000 + the initial, and then  successively, so, for n years:

F(n) = 70,000 + 10,000*n

So

P(n) > F(n)

600,000*(1.05)ⁿ > 70,000 + 10,000*n

(1.05)ⁿ > 1.167 + 0.0167n

Solving in a computer:

n > 4.42

So, after 5 years the population exceed the food supply.

FUNCTIONS

h(x)= 3^x

a) Solve the equation h^-1(x)= 2

Answers

Because the inverse of function h(x) = 3^x is h^-1 ( x ) = log 3 ( x ) , we solve the equation log 3 ( x ) = 2 ;
3^2 = x;
x = 9 ;
Use the property of inverse functions:
h(h^(-1)(x))=x \n \n\hbox{if} \n h^(-1)(x)=2 \n \hbox{then} \nh(2)=x \n\Downarrow \nh(x)=3^x \nh(2)=3^2 \nh(2)=9 \n \n\boxed{x=9}

The map below shows the length of a proposed land bridge at Phil Hardberger Park. The length of the land bridge is represented by PHin the map below.
P(2,55)
H(32, 15)
On the map, each unit represents 1 yard. To the nearest yard, what is the actual length of the land bridge from P to H?
A 50 yards
B. 150 yards
C. 78 yards
D. 234 yards

Answers

Answer:

A; the actual length of the land bridge from P to H is 50 yards

Step-by-step explanation:

Here in this case, given the coordinates of P and H, we want to calculate the actual length of the distance between the two points.

Mathematically, to calculate this distance, we make use of the distance formula;

D = √(x2-x1)^2 + (y2-y1)^2

In this case, (x1,y1) = (2,55) while (x2,y2) = (32,15)

Substituting these values

D = √(32-2)^2 + (15-55)^2

D = √(-30)^2 + (-40)^2

D = √(900 + 1600)

D = √(2,500)

D = 50 units

Now, we know that each units represent 1 yard, thus 50 units will represent 50 * 1 = 50 yards

What is the reciprocal of 4? A.
–4

B.
-1/4

C.
1/4

D.
4

Answers

the answer is 0.25. o work it out and this is what i came up with. I hope this helps
it is .25, which converted to a fraction would be 1/4.  your answer should be C.
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