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3 years ago

What is 4.2X-1.4Y=2.1-2X

Mathematics

2 answers:

enot [183]3 years ago

7 0

4.2x - 1.4y = 2.1 - 2x

Subtract 4.2x

-1.4y = 2.1 - 6.2x

Divide by -1.4

y = -3/2 + 9/2x

Answer: y = 9/2x - 3/2

Rina8888 [55]3 years ago

6 0

In this problem, we have to solve for y.
So:
After subtracting 4.2x and dividing -1.4; you get this:
y = 9/2x - 3/2

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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

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2 years ago

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Ratio in simplest form 8 pounds to 10 pounds

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Answer:

4:5

Step-by-step explanation:

You can divide two to each number.

8 divided by 2 equals 4.

10 divided by 2 equals 5.

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3 years ago

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Find the domain of the following piece wise function

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Answer:

Step-by-step explanation:

$f(x)=\left\{\begin{array}{ccc}x+4&if&-4\leq x$

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What is the rule for the sequence with the first four terms below? 0.5, 0.25, 0, –0.25

elena55 [62]

Answer:

subtract .25 each time x-.25

Step-by-step explanation:

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3 years ago

What is the simplified expression for Negative 3 c d minus d (2 c minus 4) minus 4 d? Negative 5 c d c d minus 8 d 5 c d minus 8

Pavel [41]

Question

What is the simplified expression for Negative 3 c d minus d (2 c minus 4) minus 4 d?

a) Negative 5 c d

b) c d minus 8 d

c) 5 c d minus 8 d

d) Negative 5 c d minus 8 d

Answer:

a) Negative 5cd or -5cd

Step-by-step explanation:

The question asks:

What is the simplified expression for Negative 3 c d minus d (2 c minus 4) minus 4 d?

This is expressed mathematically as:

-3cd - d(2c - 4) - 4d

= -3cd -2cd + 4d - 4d

= -5cd + 0

= -5cd

The answer is negative 5cd(in words) or - 5cd

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