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1 year ago

4* - 5(2) + 4 = 0, u = 2 [Note: 4* = (2*)^2 Use the substitution given

Mathematics

1 answer:

KengaRu [80]1 year ago

5 0

Answer:

x = 0, 2

Step-by-step explanation:

${4}^{x} - 5( {2}^{x} ) + 4 = 0 \\ {({2}^{x})}^{2} - 5( {2}^{x} ) + 4 = 0 \\ {u}^{2} - 5u + 4 = 0 \\ (u - 1)(u - 4) = 0 \\ u = 1 \: or \: u = 4 \\ {2}^{x} = 1 \: or \: {2}^{x} = 4 = {2}^{2} \\ x = 0 \: or \: x = 2$

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I do not understand the process/steps to do this.

VARVARA [1.3K]

Answer:

Step-by-step explanation:

Remark

An angle bisector sets up a triangle ratio that looks like the following proportion.

3x - 3 5x

====== = ====== Cross multiply

24 44

44*(3x-3) = 24*5x Remove the brackets on the left

132x - 132 = 24*5x Combine the right side

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3 years ago

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3 years ago

Is this the right answer?

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3 years ago

A scale model of an office building is 3' x 2' x 5' (length, width, height). If the actual building has a length of 45 feet, wha

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Answer:

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Step-by-step explanation:

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3 years ago

A pan of warm water (46∘ Celsius) was put in a refrigerator. After 15 minutes, the water's temperature was 27∘ C; 15 minutes aft

Cloud [144]

Answer:

The refrigerator was at around 13 ∘C

Step-by-step explanation:

Newton's Law of Cooling:

The rate of change of a body temperature (amount of heat loss/time of loss) is directly proportional to the difference between its own temperature and the surroundings.

$\frac{T(t2)-T(t1)}{t2-t1} = -h (T(t2) - Tenv)$

T ⇒ temperature

t ⇒ time

Tenv ⇒refrigerator temperature

$\frac{T(t2)-T(t1)}{t2-t1}$ ⇒ rate of change of he temperature

-h ⇒ constant of proportionality (negative because the temperature is decreasing inside the refrigerator)

We have 3 points:

time (minutes) - Temperature (∘ C)

0 (when the pan was put in the refrigerator) - 46

15 (after 15 minutes) - 27

30 (15 minutes after the first 15 minutes) - 19

$\frac{27 - 46}{15 - 0}$ = -h (27 - Tenv)

$\frac{19 - 27}{15 - 0}$ = -h (19 - Tenv)

Now we have a system of two equations and two variables

$\frac{-19}{15} = -h (27 - Tenv)\\ \frac{19}{15} = h (27 - Tenv)\\ \frac{19}{15(27 - Tenv)} = h$

$\frac{19 - 27}{15 - 0} = -h (19 - Tenv)\\\frac{-8}{15} = -h (19 - Tenv)\\\frac{8}{15} = h (19 - Tenv)\\\frac{8}{15} = \frac{19}{15(27 - Tenv)} (19 - Tenv)\\8(27 - Tenv) = 19 (19 - Tenv)\\216 - 8 Tenv = 361 - 19 Tenv\\19 Tenv - 8 Tenv = 361 - 216\\11 Tenv = 145 \\Tenv = 145/ 11\\Tenv = 13. 18$

The refrigerator was at around 13 ∘C

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2 years ago

4* - 5(2*) + 4 = 0, u = 2* [Note: 4* = (2*)^2 Use the substitution given

4* - 5(2) + 4 = 0, u = 2 [Note: 4* = (2*)^2 Use the substitution given