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hichkok12 [17]
2 years ago
10

Simplify.

Mathematics
1 answer:
Kazeer [188]2 years ago
3 0
(1/2)^2 = 1/4
2-2/3 = 6/3 - 2/3 = 4/3

OK so:
(1/2)^2 - 6(2-2/3) = 1/4 - 6(4/3)
= 1/4 - 8
= 1/4 - 32/4
= -31/4
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Ms. May has to pay $5 for each bag of flour to make her cookies. She needs to buy 20 bags of flour. How much will she have to pa
xenn [34]
$100 dollars will be the end price.
5 0
3 years ago
Rewrite the following in the form log(c). log(4) - log(2)
Elis [28]

Answer:

log(2)

Step-by-step explanation:

log(4) − log(2)

log(4/2)

log(2)

3 0
3 years ago
George and Paula are running around a circular track. George starts at the westernmost point of the track, and Paula starts at t
arsen [322]

Answer:

George is 43.20 ft East of his starting point.

Step-by-step explanation:

Let Paula's speed be x ft/s

George's speed = 9 ft/s

Note that speed = (distance)/(time)

Distance = (speed) × (time)

George takes 50 s to run a lap of the track at a speed of y ft/s

Meaning that the length of the circular track = y × 50 = 50y ft

George and Paula meet 14 seconds after the start of the run.

Distance covered by George in 14 seconds = 9 × 14 = 126 ft

Distance covered by Paula in 14 seconds = y × 14 = 14y ft

But the sum of the distance covered by both runners in the 14 s before they first meet each other is equal to the length of the circular track

That is,

126 + 14y = 50y

50y - 14y = 126

36y = 126

y = (126/36) = 3.5 ft/s.

Hence, Paula's speed = 3.5 ft/s

Length of the circular track = 50y = 50 × 3.5 = 175 ft

So, in 4 minutes (240 s), with George running at 9 ft/s, he would have ran a total distance of

9 × 240 = 2160 ft.

2160 ft around a circular track of length 175 ft, means that George would have ran a total number of laps (2160/175) = 12.343 laps.

Breaking this into 12 laps and 0.343 of a lap from the starting point. 0.343 of a lap = 0.343 × 175 = 60 ft

So, 60 ft along a circular track subtends an angle θ at the centre of the circle.

Length of an arc = (θ/360°) × 2πr

2πr = total length of the circular track = 175

r = (175/2π) = 27.85 ft

Length of an arc = (θ/360) × 2πr

60 = (θ/360°) × 175

(θ/360°) = (60/175) = 0.343

θ = 0.343 × 360° = 123.45°

The image of this incomplete lap is shown in the attached image,

The distance of George from his starting point along the centre of the circular track = (r + a)

But, a can be obtained using trigonometric relations.

Cos 56.55° = (a/r) = (a/27.85)

a = 27.85 cos 56.55° = 15.35 ft

r + a = 27.85 + 15.35 = 43.20 ft.

Hence, George is 43.20 ft East of his starting point.

Hope this Helps!!!

6 0
3 years ago
The original price for the shirt is $30.00. The shirt is on sale for 10% off. What is the sale price of the shirt?
Xelga [282]

Answer:

$3 off which is $27

Step-by-step explanation:

10% of 30 is 3 so you would subtract 30 - 3

and you get $27

8 0
2 years ago
The perimeter of a swimmingpool is 78 feet. The difference between four times the length and the width is 73.5 feet. What are th
Marianna [84]

Answer:

Length is 22.5 ft

Width is 16.5 ft

Step-by-step explanation:

4L-w=73.5

4L=73.5+w

L=(73.5+w)/4

P=78

P=2L+2w

78=2[(73.5+w)/4]+2w

78=(73.5+w)/2+2w

78=(73.5+w+4w)/2

2•78=73.5+5w

156=73.5+5w

156-73.5=5w

82.5=5w

82.5/5=w

16.5=w

L=(73.5+w)/4

=(73.5+16.5)/4

=90/4

L=22.5

3 0
3 years ago
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