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3 years ago

Which step shows the result of applying the subtraction property of equality?

Mathematics

1 answer:

Scilla [17]3 years ago

7 0

Answer:

First step

Step-by-step explanation:

Subtract the 4 to the other side making the equation

(12x+8)+4=3

12x+8=-1

12x=-9

x=-3/4

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The liquid base of an ice cream has an initial temperature of 86°C before it is placed in a freezer with a constant temperature

Karolina [17]

The temperature of the ice cream 2 hours after it was placed in the freezer is 37.40 °C

From Newton's law of cooling, we have that

$T_{(t)}= T_{s}+(T_{0} - T_{s})e^{kt}$

Where

$(t) = \ time$

$T_{(t)} = \ the \ temperature \ of \ the \ body \ at \ time \ (t)$

$T_{s} = Surrounding \ temperature$

$T_{0} = Initial \ temperature \ of \ the \ body$

$k = constant$

From the question,

$T_{0} = 86 ^{o}C$

$T_{s} = -20 ^{o}C$

∴ $T_{0} - T_{s} = 86^{o}C - -20^{o}C = 86^{o}C +20^{o}C$

$T_{0} - T_{s} = 106^{o} C$

Therefore, the equation $T_{(t)}= T_{s}+(T_{0} - T_{s})e^{kt}$ becomes

$T_{(t)}=-20+106 e^{kt}$

Also, from the question

After 1 hour, the temperature of the ice-cream base has decreased to 58°C.

That is,

At time $t = 1 \ hour$ , $T_{(t)} = 58^{o}C$

Then, we can write that

$T_{(1)}=58 = -20+106 e^{k(1)}$

Then, we get

$58 = -20+106 e^{k(1)}$

Now, solve for $k$

First collect like terms

$58 +20 = 106 e^{k}$

$78 =106 e^{k}$

Then,

$e^{k} = \frac{78}{106}$

$e^{k} = 0.735849$

Now, take the natural log of both sides

$ln(e^{k}) =ln( 0.735849)$

$k = -0.30673$

This is the value of the constant $k$

Now, for the temperature of the ice cream 2 hours after it was placed in the freezer, that is, at $t = 2 \ hours$

From

$T_{(t)}=-20+106 e^{kt}$

Then

$T_{(2)}=-20+106 e^{(-0.30673 \times 2)}$

$T_{(2)}=-20+106 e^{-0.61346}$

$T_{(2)}=-20+106\times 0.5414741237$

$T_{(2)}=-20+57.396257$

$T_{(2)}=37.396257 \ ^{o}C$

$T_{(2)} \approxeq 37.40 \ ^{o}C$

Hence, the temperature of the ice cream 2 hours after it was placed in the freezer is 37.40 °C

Learn more here: brainly.com/question/11689670

6 0

2 years ago

Read 2 more answers

Can somebody tell me how too simplify this expression 3(5*+2)

Pie

Answer:

15+6

Step-by-step explanation:

You would need to multiply 3*5 then 3*2 and then put 15+6

6 0

2 years ago

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Can someone help me pls

Drupady [299]

Answer:

150 degrees

Step-by-step explanation:

75 -----> 75 out of 360

360-75=285

285-75 will be divided by 2

210 divided by 2 equals 105

105 is the measure of the angle I think (lmk if its wrong)

4 0

2 years ago

I need helpppppppppppppp

zalisa [80]

Answer:

Since this is a graph, I don't know how to help you sorry-

Its on your computer and I don't know how to put an answer down for you.

8 0

2 years ago

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HELP WILL GIVE BRANLIEST!

Natali5045456 [20]

Answer:

Since it is vertical angles, 4x - 12 = 88.

Answer is 25

Step-by-step explanation:

88 + 12 = 100

100 / 4 = 25

6 0

2 years ago