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Irina18 [472]
2 years ago
7

You are choosing between two different cell phone plans. The first plan charges a rate of 21 cents per minute. The second plan c

harges a monthly fee of $29.95 plus 8 cents per minute. How many minutes would you have to use in a month in order for the second plan to be preferable? Round up to the nearest whole minute.
Mathematics
1 answer:
11Alexandr11 [23.1K]2 years ago
6 0

Answer:

 231 minutes

Step-by-step explanation:

Plan1:  0.21m

Plan2:  29.95 + 0.08m

0.21m > 29.95 + 0.08m

0.13m > 29.95

m > 230.38

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Write the number in standard form and expanded form. Three million four hundred eighty- seven thousand six hundred fifty-one​
snow_tiger [21]

Answer:

down below

Step-by-step explanation:

3,487, 651

(3 x 1,000,000) + (4 x 100,000) + (8 x 10,000) + ( 7 x 1,000) + (6 x 100 ) +

(5 x 10) + (1 x 1)

7 0
2 years ago
On a coordinate plane, 2 right triangles are shown. The first triangle has points A (negative 1, 3), B (negative 1, 1), C (3, 1)
drek231 [11]

Answer:

  • B and E

Step-by-step explanation:

<u>Given</u>

  • ΔABC ⇒ A(- 1, 3), B(- 1, 1), C(3, 1)
  • ΔA'B'C' ⇒ A'(2, - 2), B'(2, - 4), C'(6, - 4)

<u>Comparing the coordinates of the corresponding vertices, we see the difference:</u>

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It means the ΔABC has been translated 3 units right and 5 units down

Correct answer choices are B and E

8 0
2 years ago
Read 2 more answers
—2t(t+1),<br> t &lt; 6<br> 5t<br> g(t) =<br> =<br> ,6 6<br> 2t2 + 3t<br> t&gt; 12<br> g(12) =
yuradex [85]

Answer:to Let f(t) = 6, g(t) = −5t, and h(t) = 2t2

Step-by-step explanation:

3 0
2 years ago
Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = 9t + 9 cot(t/2), [π/4, 7π/4]
agasfer [191]

Answer:

the absolute maximum value is 89.96 and

the absolute minimum value is 23.173

Step-by-step explanation:

Here we have cotangent given by the following relation;

cot \theta =\frac{1 }{tan \theta} so that the expression becomes

f(t) = 9t +9/tan(t/2)

Therefore, to look for the point of local extremum, we differentiate, the expression as follows;

f'(t) = \frac{\mathrm{d} \left (9t +9/tan(t/2)  \right )}{\mathrm{d} t} = \frac{9\cdot sin^{2}(t)-\left (9\cdot cos^{2}(t)-18\cdot cos(t)+9  \right )}{2\cdot cos^{2}(t)-4\cdot cos(t)+2}

Equating to 0 and solving gives

\frac{9\cdot sin^{2}(t)-\left (9\cdot cos^{2}(t)-18\cdot cos(t)+9  \right )}{2\cdot cos^{2}(t)-4\cdot cos(t)+2} = 0

t=\frac{4\pi n_1 +\pi }{2} ; t = \frac{4\pi n_2 -\pi }{2}

Where n_i is an integer hence when n₁ = 0 and n₂ = 1 we have t = π/4 and t = 3π/2 respectively

Or we have by chain rule

f'(t) = 9 -(9/2)csc²(t/2)

Equating to zero gives

9 -(9/2)csc²(t/2) = 0

csc²(t/2)  = 2

csc(t/2) = ±√2

The solutions are, in quadrant 1, t/2 = π/4 such that t = π/2 or

in quadrant 2 we have t/2 = π - π/4 so that t = 3π/2

We then evaluate between the given closed interval to find the absolute maximum and absolute minimum as follows;

f(x) for x = π/4, π/2, 3π/2, 7π/2

f(π/4) = 9·π/4 +9/tan(π/8) = 28.7965

f(π/2) = 9·π/2 +9/tan(π/4) = 23.137

f(3π/2) = 9·3π/2 +9/tan(3·π/4) = 33.412

f(7π/2) = 9·7π/2 +9/tan(7π/4) = 89.96

Therefore the absolute maximum value = 89.96 and

the absolute minimum value = 23.173.

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