Question 4 (Essay Worth 10 points)

(05.06 MC)

The distance, y, in centimeters, of an ant from a hole in the tree for a certain amount of time, x, in seconds, is shown in the graph:

A graph titled Motion of Ant is shown. The graph shows time in seconds on the x-axis and the Distance from Hole in centimeters on the y-axis. The scale on the x-axis is shown from 0 to 7 at increments of 1, and the scale on the y-axis is shown from 0 to 24 at increments of 4. The graph has 3 straight lines. The first line is labeled A and joins ordered pairs 0, 0 and 2, 16. The second line is labeled B and joins ordered pairs 2, 16 and 4, 16. The third line is labeled C and joins ordered pairs 4, 16 and 6, 0.

Part A: Is the graph linear or nonlinear? Explain your answer. (2 points)
Part B: In which segments is the graph increasing, decreasing, and constant? (3 points)
Part C: In your own words, describe the motion of the ant, as shown on the graph. (5 points)

Source
StylesFormat

Answer:

Step-by-step explanation:

Degrees   Radians   tangent

60°      π/3         √3

45°            π/4                     1

30°           π/6                 1/√3

0°            0                   0

Answer:

1 term

Step-by-step explanation:

Writing an expression of 5 terms such that all 5 terms are like terms ;

Using the analogy :

x, 2x, 4x, 3x, 5x

Writing as an expression :

x + 2x + 4x - 3x + 5x

7x - x + 5x

6x + 5x

11x

The least number of terms in its equivalent expression is 1 ;

As the expression x + 2x + 4x - 3x + 5x is equivalent to 11x

Answer:

the answer will be

184.31

Answer:

10/3 days  or 3 1/3 days

Step-by-step explanation:

Let d = number of days total

75% of the days is 10

.75 d = 10

d = 10/.75

d = 40/3 days

We want to know how man is 25% of d

d * 25%

(40/3) *.25

10/3 days

Answer:

C

Step-by-step explanation:

Answer:

3.1

Step-by-step explanation:

5 x5 =25

25+3=28

the other children are 4 years old

Answer:

c = 9.7

Step-by-step explanation:

Using the law of sines

sin 55       sin 82

---------- = ---------------

8                    c

Using cross products

c sin 55 = 8 sin 82

c = 8 sin 82 / sin 55

c=9.67115

To the nearest tenth

c = 9.7

Answer:

She bought 6 first class tickets and 1 coach ticket

Step-by-step explanation:

1060(6)= 6360 and 6960-6360=300 and 300 is the price for a coach ticket.

Answer:

1/3

Step-by-step explanation:

Slope is rise over run

your rise is 1 (because you only go up one block each time)

your run is 3 ( because you go right three times)

so 1/3

Answer:

Option C, sin Y = 38/63

Step-by-step explanation:

sin Y = Opposite/Hypotenuse

sin Y = 38/63

Answered by GAUTHMATH

Answer:

BC = 6.8

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta =opp /adj

tan C = AB / BC

tan 45 = 6.8/ BC

BC = 6.8 / tan 45

BC = 6.8 / 1

BC = 6.8

Answer: Choice D. 6.8

Step-by-step explanation:

45,45,90 triangles, memorize that the short sides are equal to each other in length and are [tex]\frac{1}{\sqrt{2} }[/tex] the length of the long side.

Answer:

C

Step-by-step explanation:

Answer:

Step-by-step explanation:

6 and 4 : LCM is 12

6 and 8: LCM is 24

6 and 10 LCM is 30.

Answer:

1508527.582 cm³/min

Step-by-step explanation:

The net rate of flow dV/dt = flow rate in - flow rate out

Let flow rate in = k. Since flow rate out = 6800 cm³/min,

dV/dt = k - 6800

Now, the volume of a cone V = πr²h/3 where r = radius of cone and h = height of cone

dV/dt = d(πr²h/3)/dt = (πr²dh/dt)/3 + 2πrhdr/dt (since dr/dt is not given we assume it is zero)

So, dV/dt = (πr²dh/dt)/3

Let h = height of tank = 12 m, r = radius of tank = diameter/2 = 3/2 = 1.5 m, h' = height when water level is rising at a rate of 21 cm/min = 3.5 m and r' = radius when water level is rising at a rate of 21 cm/min

Now, by similar triangles, h/r = h'/r'

r' = h'r/h = 3.5 m × 1.5 m/12 m = 5.25 m²/12 m = 2.625 m = 262.5 cm

Since the rate at which the water level is rising is dh/dt = 21 cm/min, and the radius at that point is r' = 262.5 cm.

The net rate of increase of water is dV/dt = (πr'²dh/dt)/3

dV/dt = (π(262.5 cm)² × 21 cm/min)/3

dV/dt = (π(68906.25 cm²) × 21 cm/min)/3

dV/dt = 1447031.25π/3 cm³

dV/dt = 4545982.745/3 cm³

dV/dt = 1515327.582 cm³/min

Since dV/dt = k - 6800 cm³/min

k = dV/dt - 6800 cm³/min

k = 1515327.582 cm³/min - 6800 cm³/min

k = 1508527.582 cm³/min

So, the rate at which water is pumped in is 1508527.582 cm³/min

Answer:

A =27 cm^2

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh  where b is the base and h is the height

A = 1/2 (9) (6)

A =27 cm^2

Answer:

I assure you the person above is perfectly right. The area of a triangle is:

A = 1/2bh

Step-by-step explanation:

Have a good day.

Answer:

5

Step-by-step explanation:

Given: i = 5¹

5¹ = 5

Therefore, the correct option is 5

Answer: Choice C. 110ft

Step-by-step explanation:

Near a 30,60,90 triangle, multiply by [tex]\sqrt{3}[/tex] to approximate the distance from point B to the tree.

Answer:

82

Step-by-step explanation:

I want to say 82 but i am not positive

Answer:

B. 4

Step-by-step explanation:

54 - 4 = 50

50 - 4 = 46

46 - 4 = 42

42 - 4 = 38

Answer: D. -4

Step-by-step explanation: took the quiz and got it right.

Answer:

I am not sure on the answer but i think its $9,000

Step-by-step explanation:

11,000x0.20=2,200

2,200+11,000=13,200

22,200-13,200=9,000

which would mean she got $9,000 from commissions.

if you did 100,000x0.03=3,000

9,000/3,000= 3

so she would have had 3 commissions worth over 100,000

Answer:

y + 1 = 2/3 (x - 8)

Step-by-step explanation:

y2 - y1 / x2 - x1          -5 - (-1) / 2 - 8      -4/-6      2/3

y + 1 = 2/3 (x - 8)

Answer:

System of equations:

20x + 30y = 650

x + y = 25

Time underwater = 10 hours

Time at the surface = 15 hours

Step-by-step explanation:

Let x = time underwater at 20 km/h.

Let y = time on the surface at 30 km/h.

speed = distance/time

distance = speed * time

distance underwater: 20x

distance on the surface: 30y

total distance: 650

20x + 30y = 650

total time: x + y

total time: 25

x + y = 25

20x + 30y = 650

x + y = 25

20x + 30y = 650

-20x - 20y = -500

--------------------------------

          10y = 150

              y = 15

x + y = 25

x + 15 = 25

x = 10

Hi there!

[tex]\large\boxed{r\approx 10.6 cm}[/tex]

Solve for the radius using the pythagorean theorem:

a² + b² = c²

We know the lengths of the hypotenuse and one leg, so:

a = 12

b = ?

c = 16

Plug these into the equation:

12² + b² = 16²

Simplify:

144 + b² = 256

Subtract both sides by 144:

b² = 112

Take the square root:

b ≈ 10.6

Thus the radius is about 10.6 cm.

Answer:

um 1/4

Step-by-step explanation:

Answer:

The probability that the two rats are from the first litter is 14.28%, and the probability that the two rats are from the second litter is 34.28%.

Step-by-step explanation:

Since a cage holds two litter of rats, and one litter comprises one female and five males, while the other litter comprises seven females and two males, and a random selection of two rats is done, to find the probability that the two rats are from the same litter the following calculation must be performed:

6/15 x 5/14 = 0.1428

9/15 x 8/14 = 0.3428

Therefore, the probability that the two rats are from the first litter is 14.28%, and the probability that the two rats are from the second litter is 34.28%.

Answer:

domain [-1, ∞)

range [ -3, ∞)

Step-by-step explanation:

Answer:

$1.05 per yard

Step-by-step explanation:

5.25 ÷ 5 = 1.05

Answer:

$1.05 per yard.

Step-by-step explanation:

find unit rate; (cost / quantity)

5.25 / 5 = 1.05

Answer:

45in³

Step-by-step explanation:

6 x 5 x 3 = 90/2 = 45in³

Answer:

i think the answet is 0.625