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Harman [31]
3 years ago
10

TEN POINTS:

Mathematics
1 answer:
neonofarm [45]3 years ago
3 0

Answer:

81/16 = 5 1/16

Step-by-step explanation:

-4(square root of x) -3 = -12

Add 3 to both sides

-4(square root of x) = -12 +3 = -9

Divide both sides by -4

(square root of x) = -9/-4

-/- equals +

(square root of x) = 9/4

Square both sides to cancel the square root

x = (9/4)^2 = 81/16 = 5 1/16

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Kala purchased a prepaid phone card for $15. Long distance calls cost $12 a minute using this card. Kala Use her card only once
irina [24]

Kala call lasted for 0.36 minutes

<em><u>Solution:</u></em>

Given that Kala purchased a prepaid phone card for $15

Long distance calls cost $12 a minute using this card.

If the remaining credit on her card is $10.68

To find: Number of minutes her call lasted

Let "x" be the number of minutes her call lasted

Cost of 1 minute = $ 12

Total balance = $15

Remaining balance = $ 10.68

So we can frame a equation as:

Total balance = Remaining balance + Cost of 1 minute x number of minutes her call lasted

15 = 10.68 + 12 \times x\\\\15 - 10.68 = 12x\\\\4.32 = 12x\\\\x = 0.36

So her call lasted for 0.36 minutes

4 0
3 years ago
A plane flying horizontally at an altitude of 2 mi and a speed of 540 mi/h passes directly over a radar station. Find the rate a
Rasek [7]

Answer:

The plane's distance from the radar station will increase about 8 miles per minute when it is 5 miles away from it.

Step-by-step explanation:

When the plane passes over the radar station, the current distance is the altitude h = 2. Then it moves b horizontally so that the distance to the station is 5. We can form a rectangle triangle using b, h and the hypotenuse 5. Therefore, b should satisfy

h²+b² = 5², since h = 2, h² = 4, as a result

b² = 25-4 = 21, thus

b = √21.

Since it moved √21 mi, then the time passed is √21/540 = 0.008466 hours, which is 0.51 minutes. Note that in 1 minute, the plane makes 540/60 = 9 miles.

The distance between the plane and the radar station after x minutes from the moment that the plane passes over it is given by the function

f(x) = \sqrt{((9x)^2 + 2^2)} = \sqrt{(81x^2+4)}

We have to compute the derivate of f in x = 0.51. The derivate of f is given by

f'(x) = \frac{162x}{2\sqrt{81x^2+4}}

also,

f'(0.51) = \frac{162*0.51}{2\sqrt{81*0.51^2+4}} = 8.2486

The plane's distance from the station will increase about 8 miles per minute.

4 0
3 years ago
Write the two statements that create the biconditional: There is traffic on the freeway if and only if there are a lot of cars o
MariettaO [177]

Answer:

there is traffic on the freeway

a lot of cars on the freeway

Step-by-step explanation:

5 0
3 years ago
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zlopas [31]
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4 0
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