MATHEMATICS HIGH SCHOOL

What is the average of the integers from 25 to 41?
27, 33, 36, 66 ?

Answers

Answer 1
Answer: a=(25+26+27+...+41)/(17)=(561)/(17)=33

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Find the domain and range of this function f(x)=1/squareroot of (x-4)

Answers

In this exercise we have assumption:
x-4>0
x>4
from this we know domain : x∈(4,+infinity)
range y∈R

Answer:

x is greater than or equal to -6

Step-by-step explanation:

3. Through what angle does the minute hand of a clock turn in 12 minutes of time?

Answers

60 minutes=360º
Then:

360º---------------60 minutes
x--------------------12 minutes

x=(360º * 12 minutes) / 60 minutes=72º

answer: 72º
60 minutes=360º
Then:

360º---------------60 minutes
x--------------------12 minutes

x=(360º * 12 minutes) / 60 minutes=72º

answer: 72º

Please help me with this explain!!!!!

Answers

Given:
Cylinder: radius = 8 yd; height = 4 yd
Surface Area = 2 π r h + 2 π r²
SA = 2 * 3.14 * 8 yd * 4yd + 2 * 3.14 * (8yd)²
SA = 200.96 yd² + 401.92 yd²
SA = 602.88 yd²
Volume = π r² h
V = 3.14 * (8yd)² * 4yd
V = 803.84 yd³

Dimension is cut in half. radius = 4yds ; height = 2yds
S.A = 2 * 3.14 * 4yd * 2yd + 2 * 3.14 * (4yd)²
S.A = 50.24 yd² + 100.48 yd²
SA = 150.72 yd²
V = 3.14 * (4yd)² * 2yd
V = 100.48 yd³

SA = 602.88 yd² - 150.72yd² = 452.16 yd²
V = 803.84 yd³ - 100.48 yd³ = 703.36 yd³

If a laptop that is regularly priced
at $1240 is 2  off, how much does it cost?
                                                                 5

Answers

2/5 off basically means that it is 40% off 

1240 * 40% = 496

1240 - 496 =

744
2/5 is 40 0/0 off take 2÷5 = .4 then 1.00-.4= .6  1240×.6=744

Karla is riding vertically in a hot air balloon, directly over a point P on the ground. Karla spots a parked car on the ground at an angle of depression of 30o. The balloon rises 50 meters. Now the angle of depression to the car is 35 degrees. How far is the car from point P?

Answers

Answer:

407 m

Step-by-step explanation:

Refer the attached figure

Karla spots a parked car on the ground at an angle of depression of 30° i.e. ∠BDP = 30°

Now the balloon rises 50 meters.i.e. AB = 50 m

So, the angle of depression to the car is 35 degrees. i.e.∠ADP = 35°

Let DP be the distance of the car prom point P

Let BP be x

In ΔBDP

Tan\theta = (Perpendicular)/(Base)

Tan 30^(\circ) = (BP)/(DP)

(1)/(√(3))= (x)/(DP)

DP= (x)/((1)/(√(3)))  --1

In ΔADP

Tan\theta = (Perpendicular)/(Base)

Tan 35^(\circ) = (AP)/(DP)

0.70020= (50+x)/(DP)

DP= (50+x)/(0.70020)  --2

So, equating 1 and 2

(50+x)/(0.70020) = (x)/((1)/(√(3)))

(50+x)/(x) = (0.70020)/((1)/(√(3)))

(50+x)/(x) =1.21278

50+x =1.21278x

50 =1.21278x-x

50 =0.21278x

(50)/(0.21278)=x

(50)/(0.21278)=x

x=234.982

Substitute the value of x in 1

DP= (234.982)/((1)/(√(3)))

DP= 407.0007

Hence the car is at a distance of approximately 407 m from point P
We form 2 similar rt. triangles:

Triangle #1.
X = Hor. side = dist. from P to the car.
Yi = Ver. side.
A = 30o.

Triangle #2.
X = Hor. side = Dist. from P to the car.
Y2 = Y1+50 = Ver. side.
A = 35o.

Use aw of Sines.
sin30/Y1 = sin35/(Y1+50).
Cross multiply:
(Y1+50)sin30 = Y1*sin35
Y1/2+25 = 0.574Y1
Multiply both sides by 2:
Y1+50 = 1.148Y1
1.148Y1-Y1 = 50
0.148Y1 = 50
Y1 = 337.8 m.

tan30 = Y1/X = 337.8/X
X = 337.8/tan30 = 585 m. 714 feet away hope that helps if not tell me.

The distributive property combines (blank) and (blank) to make multiplying whole numbers simpler.

Answers

I am not too sure whether there were options, but one way to approach this is to fill it with "multiplication" and "addition" - the distributive property combines addition and multiplication to make multiplying whole numbers simpler.The gain is that you don't have to make one difficult multiplication, but a couple of simpler ones and then you can add them up.
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