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Brut [27]
3 years ago
13

Which numbers are irrational? Select each correct answer. 101 − − − √ 101 2.25 − − − − √ 2.25 − 4 √ −4 5 √

Mathematics
1 answer:
stepan [7]3 years ago
5 0
All Real Numbers that are NOT Rational Numbers; cannot be expressed as fractions, only non-repeating, non-terminating decimals −√2 , −√5 3 , √21, √81 3 , √101 
 *Even roots (such as square roots) that don’t simplify to whole numbers are irrational.
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Two cities are building bicycle paths. Charles City has built 5km of bicycle paths by the end of the first month, and the total
sergey [27]

Answer:

Month 4

Step-by-step explanation:

To solve this problem we must propose an equation that models the number of kilometers of bicycle trails made monthly in Charles City and in Tinsel Town

<em>For Charles City </em>we know that the number of kilometers built in the first month is 5, and it doubles every month. Then we have an exponential equation, in base 2, whose initial value is 5.

This equation has the following form:

y = C_1 (2^{x-1})

Where:

C_1 is the number of kilometers built in month 1

x is the number of months: {1, 2, 3, 4, 5 ... x}

x = 1 represents month 1.

So:

Charles\ City\ (km) = 5(2^{x-1})

<em>For Tinsel Town</em> we know that the number of kilometers built in the first month is 21 and increases at a fixed rate of 5 kilometers per month. This can be modeled by a linear equation.

Tinsel\ Town\ (km) = 21 + 5(x-1)

Where x is the number of months. x: {1, 2, 3, 4, 5 ...}

We want to know at the end of what month the total length of the cycle lanes in Charles City first exceeds the length in Tinsel Town

Then we equal both equations and clear x.

5 (2^{x-1}) = 21 + 5(x-1)\\\\5 (2^{x-1}) - (21 + 5(x-1)) = 0

Clearing x from this equation is very difficult, so to find x, we iterate until we get the value of x that causes the equation to approach 0.

For x = 3

5(2^{3-1}) - (21 +5(3-1)) = 0\\\\20- 31= -11

For x = 4

5(2^{4-1}) - (21 +5(4-1)) = 0\\\\40 - 36 = 4

<em>The value must be between x = 3 and x = 4</em>

For x = 3.8

5 (2^{3.8-1}) - (21 +5(3.8-1)) = 0\\\\34.82 - 35 = 0.18

Then x ≈ 3.8 months.

Finally we have that By the end of the fourth month the total length of the cycle lanes in Charles City exceeds the length in Tinsel Town

6 0
3 years ago
Q is directly proportional to r.<br> Q is 76 when r is 20.<br> Work out q when r is 45
r-ruslan [8.4K]

Answer:

171

Step-by-step explanation:

Q~r

find k (k is the constant)

Q=kr

76=k×20

76=20k divide 20 on both sides giving you

k=3.8

then Q=k×r

Q=3.8×45

Q=171

3 0
3 years ago
Solve this using substitution method. Many many thanks
In-s [12.5K]

Answer:

y=2 and x=1

Step-by-step explanation:

sub 2 into 1

3(15-7y) + 4y= 11

45 - 21y +4y =11

-21y+4y= 11-45

-17y= - 34

y=2

Therefore sub y into x equation

x=15-7(2)

x= 1

8 0
3 years ago
Read 2 more answers
What is the Circumference of this circle
Gelneren [198K]

Answer:

81.68 is the correct answer. Hoped this helped.

6 0
2 years ago
Point S is on line segment RT given ST=3x-8, RT = 4x, and RS = 4x - 7, determine the numerical length of RT
seraphim [82]

Answer:

20

Step-by-step explanation:

Segment ST is half and RS is the other half. RT is the whole line so adding ST and RS will get you RT. 4x-7+3x-8=4x. solve for x which will get you 5. Replace the x with 5 in 4x (for segment RT) will get you an answer of 20 for the whole line.

8 0
3 years ago
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