Question

*** Medal , Medal , Medal , Medal , Medal ***

24 Weeks of Homework, finished in one day here’s the ones I got stuck on . Please help even if it’s just one you can help on .

Answer 1

Part One:
12.2
Given that f(x) is a quadratic function, find the missing value in the table
X: 2, 4, 6, 8
F(x):3, -1, -6, ?
a. 0
b. -1
c. -11
d. -12
12.5
How is the graph of g(x)=2(x+1)^2 transformed from the graph of f(x)=x^2
a. The graph of f is translated 2 units left and 1 unit up
b. The graph of f is vertically compressed by a factor of (1/2) and translated 1 unit left.
c. The graph of f is vertically stretched by a factor of 2 and translated 1 unit up
d. The graph of f is vertically stretched by a factor of 2 and translated 1 unit left.
13.3
Which situation is best represented by the data?
T: 0, 0.5, 1, 1.5, 2, 2.5
F(t): 112, 108, 96, 76, 48, 12
a. the distance decreases by 4 miles for every 30 seconds traveled
b. the height of an object above the ground decreases nonlinearly over time
c. as the time increases, the speed of the car increases at a constant rate
d. as the time increases, the distance traveled decreases at a constant rate.
14.1
The length x of a rectangle is 6 feet longer than its width. What is a reasonable domain for the function that represents the area of the rectangle?
a. all real numbers
b. all positive numbers
c. x > 6
d. 0 ≤ x ≤ 6
14.3
The function p=(h-3)^2+174 models the power, in megawatts, generated between midnight and noon by a power plant, where h represents hours after midnight. How would the graph of the function change if the minimum power generated increased to 250 megawatts?
a. the vertex would change to (3, 250)
b. the vertex would change to (250, 174)
c. the graph of the function would be reflected over the x-axis
d. the graph of the function would be horizontally compressed

Answer 2

12.2:
If f(x) is a quadratic equation, the second difference would be the same.

f(x): 3 -1 -6 ?
1st difference: -4 -5 ?
2nd difference: -1

Therefore:

f(x): 3 -1 -6 -12
1st difference: -4 -5 -6
2nd difference: -1 -1

Answer 3

12.5:
One unit left: f(x) -> f(x+1)
One unit right: f(x) -> f(x-1)
One unit up: f(x) -> f(x)+1
One unit down:f(x) -> f(x)-1

Therefore to translate 2(x+1)^2 to x^2, we vertically compress it by a factor of (1/2) so that it becomes (x+1)^2, then we translate it one unit right so it becomes x^2

Answer 4

Well lesson learnt: the question may also be wrong

Answer 5

part two:
14.4
To solve the equation 0=x^2+7x-26 by completing the square, the first step is to add 26 to both sides of the equation. Which statement best describes the second step?
add (9/4) to both sides
square the product of 7 and square it
take half of 7 and square it
rewrite the perfect square trinomial as a binomial squared
15.2
Which best describes g(x)=√(2(x-1))+4 as a transformation of f(x)= √(x)
g is f horizontally compressed by a factor of (1/2) and translated left 1 unit and up 4 units
g is f horizontally stretched by a factor of 2 and translated left 1 unit and up 4 units
g is f horizontally compressed by a factor of (1/2) and translated right 1 unit and up 4 units
g is f horizontally stretched by a factor of 2 and translated left 1 unit and down 4 units
15.4
The perimeter P of a rectangle with a length of x feet and a width of y feet cannot exceed 300 feet. Which is NOT a constraint of the feasible region representing P?
x > 0
x > 300 - y
y > 0
x ≤ 150 – y
16.2
Which function best represents the data in the table
X: -2, -1, 0, 1, 2, 3
F(x): 25, 12, 5, 1, 1, 5
f(x)= 2x^2-6x+5
f(x)= -2x^2-6x+8
f(x)= x^2-6x+5
f(x)= 2x^2-9x+5
16.4
At the beginning of a basketball game, the referee tosses the ball into the air with an initial vertical velocity of 24 feet per second. The ball’s initial height is 5 feet above the floor. Which inequality can be used to find the time interval t for which the height of the ball is greater than 10 feet?
-16t^2+24t+5<10
-16t^2+24t+5>10
24t^2-16t+5>10
24t+5>10
16.5
The function P=-16(c-25)^2+10,000 models the profit the student council makes from a dance, where c is the cost per ticket in dollars. How does the graph of the function change if the maximum profit is made by selling the tickets for $40?
the graph of the function would be reflected over the y-axis
the vertex would change to (25, 40)
the vertex would change to (40, 10000)
the graph of the function would not change

Answer 6

13.3
f(t): 112 108 96 76 48 12
1st diff: -4 -12 -20 -28 -36
2nd diff: -8 -8 -8 -8

Therefore it is quadratic, so its rate of change is constant

Answer 7

14.1
The width can't be negative, so x must be greater than 6.

Answer 8

14.3
The minimum was (3,174) because (h-3)^2 is smallest when (h-3)^2 is 0 (it can't be negative). If it increases to 250, it'd become (3,250)

Answer 9

14.4
To complete the square, move the constant term to the other side, then take half of the x-coefficient and square it and add the value obtained to both sides. Now you have a perfect square trinomial; rewrite it into the square of a binomial. Rewrite the monomial into something squared. Move the monomial to the original side, making the other side 0. Now, you have something in the form of difference of square. Factor it and you'll get the factors. Set the factors to be 0 to find out the values of x.

Answer 10

15.2
√x => √(2x) => √(2(x-1)) => √(2(x-1))+4
compress right1 up4

Answer 11

15.4
The perimeter is 2(x+y).
2(x+y)≤300
x+y≤150
And the dimensions must be positive

Answer 12

16.2
x=0 eliminated B
x=1 eliminated C and D

Answer 13

part 3 :
17.1
The school’s ticket office sells adult and stident tickets to a musical. The auditorium normally holds no more than 2500 people. There can be no more than 1200 student tickets and no more than 1800 adult tickets sold. If x represents the number of student tickets sold and y represents the number of adult tickets sold, which system of linear inequalities represents the possible combinations of students and adult tickets that can be sold.
{█(x+y>2500@x+y≤1200@y≤1800)┤
{█(x+y≥2500@x≥1200@y≥1800)┤
{█(x+y≤1200@x≤2500@y≤1800)┤
{█(x+y≤2500@x≤1200@y≤1800)┤
17.2
in chemistry, pH=-log[H+], where [H+] is the hydrogen ion concentration of a solution in moles per liter. What is [H+] of a carbonated soda if its pH is 1.5?
10^(-1.5)
10^(1.5)
–log1.5
–log(-1.5)
17.3
Charade randomly bought 5 bags of popcorn. One out of every 10 bags is buttered popcorn. What is the probability that Charade bought 2 bags of buttered popcorn?
0.2048
0.1458
0.0729
0.0081
18.1
The area of a rectangle parking lot with a length of 1500 feet can be no more than 3,000,000 square feet. Which is the most reasonable domain of the function representing the parking lot’s area A in square feet in terms of its width w in feet?
0<w≤1500
0<w≤2000
1500<w≤2000
1500<w≤3,000,000

Answer 14

16.4
Since you're not in a physics class, gravity is not concerned

Answer 15

16.5
Currently the profit is maximum when c=25 because -16(c-25)^2 is greatest when c=25 (it can't be positive). The current vertex is (25,10000)

Answer 16

17.1
just convert everything into notation

Answer 17

17.2
So you have pH=-log[H+} and pH=1.5
1.5=-log[H+]
10^-1.5=[H+]

Answer 18

17.3
Binomial distribution huh...
\(\Large P=C_r^np^r(1-p)^{n-r}=C_2^50.1^20.9^3=...\)

Answer 19

18.1
So the area of the rectangle is 1500w and it must be smaller than or equal to 3,000,000...

Answer 20

part 4 (3 q's after this) :
18.4
Which function represents the graph of f(x)= lnx translated 2 units right and 5 units up?
g(x)=ln⁡(x+2)-5
g(x)=ln⁡(x+5)-2
g(x)=ln⁡(x-2)+5
g(x)=ln⁡(x-5)+2
19.5
Which correlation coefficient shows the strongest correlation for a set of data?
r=0.09
r=0.78
r=-0.17
r=-0.82
20.1
The speed of a sound wave travelling through a thin rod is given by the formula v=√(Y/P) , where v is the speed of the waves in meters per second, y is 8.0×10^(10) pascals, and p is the density of the rod in kilograms per cubic meter. If you know the value of v, which equations can you use to determine p?
p=√(y/v)
p=y/(v^(2))
p=√y/v
p=(yv)^(2)
20.5
What is the 11th term of the arithmetic sequence with a (subscript 4)= 13 and a(subscript 7)=25?
1
4
31
41
21.1
the range of a quadratic function is {y|y≤4}. What is the range of the same function after translation 3 units up?
{y|y≤1}
{y|y≥1}
{y|y≤7}
{y|y≥7}
21.2
which function represents a translation of f(x)=2^(x) six units up?
g(x)=2^(x)-6
g(x)=2^(x-6)
g(x)=2^(x)+6
g(x)=2^(x+6)

Answer 21

18.4
2 units right: g(x)=f(x-2)
5 units up: g(x)=f(x-2)+5

Answer 22

19.5
Linear correlation has r=1.00

Answer 23

20.1
Just literal equations

Answer 24

part 4 (YAY THIS IS THE END) :
22.2
Bobby is on a biking trip that consists of 55 miles on paved roads and 18 miles on unpaved roads. He is able to bike twice as fast on paved roads as on unpaved roads. Which function represents the total time T in hours that Bobby need to complete the trip in terms of his average speed on unpaved roads x in miles per hour?
T(x)=(55/x)+(18/2x)
T(x)=(55/2x)+(18/x)
T(x)=(55/x)-(37/2x)
T(x)=(55/x)-(18/2x)
23.5
How many ways can the athletic boosters pick a president, vice president, treasurer, and secretary from a group of 15 people?
455
1365
2730
32,760
24.2
The function y=2sin(π/2)x represents the position of a surfer in the ocean where x is the time in seconds and y is the height in feet above or below sea level. How long will it take the surfer to complete one full cycle as she rides the waves in the ocean?
2 seconds
4 seconds
8 seconds
16 seconds

Answer 25

20.5
a_4 = a+3d
a_7 = a+6d
Find the values of a and d and plug it into the equation below
a_11=a+10d

Answer 26

21.1
If y was 4, y is now 7.

Answer 27

21.2
6 units up: g(x)=f(x)+6

Answer 28

22.2
d=st
t=d/s
s=d/t
His speed on paved roads is 2x

Answer 29

23.5
Choose 4 in 15 with permutation: \(\Large P_4^{15}=\frac{15!}{(15-4)!}\)

Answer 30

24.2
The period of sine is 2π
Divide this by the coefficient of x inside the sine

Answer 31

YAY THIS IS THE END

Answer 32

YAY thank you so so so SOOOOO much !