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otez555 [7]
2 years ago
12

If f(3x − 1) = 6x − 1, find f(x) and f(0)

Mathematics
1 answer:
klio [65]2 years ago
5 0

f(3x - 1) = 6x - 1

Rewrite 6x - 1 as a function of 3x - 1:

6x - 1 = 6x - 2 + 1 = 2(3x - 1) + 1

That is,

f(3x - 1) = 2(3x - 1) + 1

which means

f(x) = 2x + 1

and so

f(0) = 2*0 + 1 = 1

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Solve for θ. <br>sin(74) = cos(θ) <br><br>1. 6° <br>2. 74° <br>3. 36° <br>4. 16° ​
Marianna [84]

Sin74 = Cos16

cause 16 + 74 = 90

Whenever the sum of two angles is equal with 90, the Sin of one is equal with the Cos of the other like :

Sin(30) = Cos(60)

and also

Tan(30) = Cot(60)

5 0
3 years ago
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A student tries out for the track team and runs a lap in 45 seconds. The coach tells her she will have to cut her time by 50% to
Fiesta28 [93]
Cutting her time by 50% means reducing her time by half. Half of 45 seconds is 22.5 seconds. Therefore, to make the team, she must run a lap in 22.5 seconds.
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In the △ABC, the height AN = 24 in, BN = 18 in, AC = 40 in. Find AB and BC. Consider all possible cases. Case 1 : N∈BC, AB = __,
aivan3 [116]

Answer:

Case 1:

AB = 30

BC = 50

Case 2:

AB = 15.9

BC = 36.7

Case 3: Not possible

Step-by-step explanation:

Given

See attachment for illustration of each case

Required

Find AB and BC

Case 1:

Using Pythagoras theorem in ANB, we have:

AB^2 = AN^2 + BN^2

This gives:

AB^2 = 24^2 + 18^2

AB^2 = 576 + 324

AB^2 = 900

Take square roots of both sides

AB = \sqrt{900

AB = 30

To calculate BC, we consider ANC, where:

AC^2 = AN^2 + NC^2

40^2 = 24^2 + NC^2

1600 = 576 + NC^2

Collect like terms

NC^2 = 1600 - 576

NC^2 = 1024

Take square roots

NC = \sqrt{1024

NC = 32

So:

BC = NC + BN

BC = 32 + 18

BC = 50

Case 2:

Using Pythagoras theorem in ANB, we have:

AN^2 = AB^2 + BN^2

This gives:

24^2 = AB^2 + 18^2

576 = AB^2 + 324

Collect like terms

AB^2 = 576 - 324

AB^2 = 252

Take square roots of both sides

AB = \sqrt{252

AB = 15.9

To calculate BC, we consider ABC, where:

AC^2 = AB^2 + BC^2

40^2 = 252 + BC^2

1600 = 252 + BC^2

Collect like terms

BC^2 = 1600 - 252

BC^2 = 1348

Take square roots

BC = \sqrt{1348

BC = 36.7

Case 3:

This is not possible because in ANC

The hypotenuse AN (24) is less than AC (40)

3 0
2 years ago
Troy's family is going to the beach for vacation. They plan to drive at the posted speed limit of 65 miles per hour and drive 5
Elena-2011 [213]
The answer is A) the number of miles
4 0
2 years ago
PLEASE HELP ME! NO LINKSSSSSS!!!
Andrews [41]

In 4 days your family drive 5/7 of a trip. Your rate of travel is the same throughout the trip. The total trip is 1250 miles. How many more days until you reach your destination?

Find the amount traveled in one day by dividing

(5/7)/4 = 5/28 of the trip

How many days would it take to add up to 1

1/(5/28) = 5.6 days total

since we already traveled for 4 days, we have 1.6 more days to go

7 0
3 years ago
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