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3 years ago

12

the library fine for an overdue book is $0.30 plus $0.07 for every day it is late. express the fee as a function of days. how mu

ch would it cost if your book is 10 days overdue.

1 answer:

kolezko [41]3 years ago

4 0

1$ 0.07 time 10 is 0.70+0.30=1

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Mark's soup recipe makes 66 servings and uses 44 carrots and 22 potatoes. how to make 15 serves

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10 carrots
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The domain and the range of the reciprocal function are the set of all real numbers. True or false?.

Elodia [21]

False. All real numbers, with the exception of 0 because f (0) = 1 0, fall inside the reciprocal function's domain and range. Y cannot be 0 if x cannot, either.

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2 years ago

A triangle with sides 7.5, 10, and 12.5 is a right triangle.

liq [111]

Answer:

Yes

Step-by-step explanation:

$( {12.5)}^{2} = 156.25...(1) \\ ( {7.5)}^{2} + ( {10)}^{2} \\ = 56.25 + 100 = 156.25...(2) \\ from \: equations \: (1) \: and \: (2) \\ ( {12.5)}^{2} =( {7.5)}^{2} + ( {10)}^{2} \\ \therefore \: given \: side \: lengths \: form \: right \: \\triangle \\ (by \: converse \: of \: pythagorean \: \\ theorem)$

4 0

4 years ago

PLEASE HELP ITS DUE IN 5 MINUTES

babunello [35]

Y - 18 = -1.5(x - 12)

I hope this helped out! Have a nice day :)

(Good luck!)

8 0

3 years ago

Find an equation of the sphere containing all surface points P = (x, y, z) such that the distance from P to A(−3, 6, 3) is "twic

Marina86 [1]

Answer:

Equation of Sphere = $x^{2}$ + $y^{2}$ + $z^{2}$ - 18x - 4/3y +10z + 142/3 = 0

Step-by-step explanation:

Data Given:

P = (x,y,z)

Distance from P to A (-3,6,3) = Twice the distance from P to B(6,2,-3)

Solution:

Find the equation of the sphere:

It is given that:

PA = 2PB

Squaring both sides:

$(PA)^{2} = (2PB)^{2}$

$(PA)^{2} = 4 (PB)^{2}$

$(x - (-3))^{2}$ + $(y - 6)^{2}$ + $(z-3)^{2}$ = 4 x $(x-6)^{2}$ + $(y-2)^{2}$ + $(z-(-3))^{2}$

Solving the above equation:

$(x + 3))^{2}$ + $(y - 6)^{2}$ + $(z-3)^{2}$ = 4 x { $(x-6)^{2}$ + $(y-2)^{2}$ + $(z + 3))^{2}$ }

$x^{2}$ + 9 + 6x + $y^{2}$ + 36 - 12y + $z^{2}$ + 9 - 6z = 4 { $x^{2}$ + 36 - 12x + $y^{2}$ + 4 - 4y + $z^{2}$ + 9 + 6z}

$x^{2}$ + 9 + 6x + $y^{2}$ + 36 - 12y + $z^{2}$ + 9 - 6z = 4 $x^{2}$ + 144 - 48x +4 $y^{2}$ + 16 - 16y + 4 $z^{2}$ + 36 + 24z

Putting the right hand side = 0 and solving the equation:

$x^{2}$ - 4 $x^{2}$ + $y^{2}$ - 4 $y^{2}$ + $z^{2}$ - 4 $z^{2}$ + 6x + 48x - 12y +16y -6z - 24z + 9 + 36 + 9 -144 - 16 - 36 = 0

-3 $x^{2}$ - 3 $y^{2}$ -3 $z^{2}$ + 54x + 4y -30z -142 = 0

Taking (-) common

- ( 3 $x^{2}$ + 3 $y^{2}$ + 3 $z^{2}$ - 54x - 4y +30z + 142) = 0

3 $x^{2}$ + 3 $y^{2}$ + 3 $z^{2}$ - 54x - 4y +30z + 142 = 0

dividing the whole equation by 3

$x^{2}$ + $y^{2}$ + $z^{2}$ - 54/3x - 4/3y +30/3z + 142/3 = 0

$x^{2}$ + $y^{2}$ + $z^{2}$ - 54/3x - 4/3y +30/3z + 142/3 = 0

$x^{2}$ + $y^{2}$ + $z^{2}$ - 18x - 4/3y +10z + 142/3 = 0

7 0

3 years ago