The tens digit is two less than the units digit. If the digits are reversed, the sum of the reversed number and the original number is 154. Find the original number.

To solve this problem, let us first remember that the formula for rate is:

rate = f (n) = A (r)^(n-1)

Where,

A = the 1st term

r = fractional rate of evaporation

n = number of terms

Now let us calculate for the fraction rate of evaporation, r. Since it is stated that the evaporation is happening at a fixed rate, therefore we can use any two given f (n) values to find for r. In this case, let us use when n=1 and 2.

r = 27 / 54

r = 0.5

The first term in the series is when n = 1 and that is:

A = 54

Therefore substituting all known values to the equation:

f (n) = 54 (0.5)^(n-1)                       (ANSWER)

Answer: 5.7

I just did the test and got it correct

The only positive number that is the same as its reciprocal is 1. This is achieved by setting up the equation x = 1/x and solving it.

In mathematics, a number and its reciprocal are the same when the number is 1. If you denote the mysterious number we are looking for as 'x', then its reciprocal would be 1/x. Since the number and its reciprocal are the same, we can set up the equation x = 1/x. Solving this equation, we cross multiply to get x^2 = 1. The positive solution to this equation is x = 1, which confirms that the only positive number that is the same as its reciprocal is 1.

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The words that came from the same ancestral language and originated from the same word are called COGNATE WORDS.

In the historical linguistics tree model, a protolanguage is a hypothetical ancestral language from which several documented languages are thought to have evolved, constituting a language family. In most cases, protolanguages are unattested or, at most, only partially attested.

The languages of Norway, Sweden, Denmark, and Iceland descend from Old Norse. Numerous Indian languages, including Bengali, Hindi, Marathi, and Urdu, have their roots in Sanskrit. Each of these ancestral languages had a single common progenitor further back in time.

The term "cognates" in linguistics refers to words with the same etymological background. These are words that have the same pronunciation, spelling, and meaning in two different languages. For instance, Spanish has many words that are similar to English words.

Therefore, Words that came from the same ancestral language and originated from the same word are called COGNATE WORDS.

To know more about ancestral language:

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Answer:

Step-by-step explanation:

Answer:

3/2x+3

Step-by-step explanation:

Final answer:

To convert square feet to square meters, we multiply the number of square feet (1,420) by the conversion factor (0.092903), resulting in approximately 132 square meters as the area of the house.

Explanation:

To convert the area of a house from square feet to square meters, we use the conversion factor where 1 square foot equals 0.092903 square meters. The house in question has 1,420 square feet, so we multiply this number by the conversion factor to find the area in square meters.a

1,420 square feet  * 0.092903 square meters/square foot = 131.92186 square meters.

We can round the final result to the nearest whole number, which gives us approximately 132 square meters as the area of the house.

The discriminant of [tex]3x^2-10x=-2[/tex] is 76

To find the discriminant of [tex]3x^2-10x=-2[/tex], we have to recall the quadratic formula.

The formula of the quadratic equation can be expressed as [tex]ax^2+bx+c=0[/tex] and discriminant also expressed as [tex]D=b^2-4ac[/tex]

Using the quadratic formula, the given question can be expressed as:

[tex]3x^2-10x+2=0[/tex]

Where a = 3, b = -10, and c = 2

If we substitute the values, then the discriminant would be:

Recall the discriminant is [tex]D=b^2-4ac[/tex]

Therefore, we have

[tex]D=(-10)^2-4(3)(2)[/tex]

[tex]D=100-24[/tex]

[tex]D=76[/tex]

Thus, the discriminant of [tex]3x^2-10x=-2[/tex] is 76.

Discriminant is very helpful in quadratic equation as it helps reveals the number of real solutions to a given quadratic equation. In other words, it helps you to solve quadratic equation.  

While discriminant only tells only reveals the number of real solutions, it doesn’t reveal what the solutions are. The determinant would only give you hint as regards the number of real solution to look for.

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Answer:

The produced parts average each day were 370.75.

Step-by-step explanation:

We have to find the average of parts produced by day, to calculate it we have sum all the parts produced by day and divide it by the number of days (4 days). In the equation we have:

[tex]Average=\frac{345+298+452+388}{4}=\frac{1483}{4}=370.75[/tex]

The produced parts average each day were 370.75.

Answer: In fact tis D. Is all real numbers

Step-by-step explanation: your welcome?

Answer:

It is still 3.

Step-by-step explanation:

We only translated it, so we just moved it over to the side. Translating cannot take away length.

The amplitude, period, and phase shift are 9, [tex]\dfrac{\pi }{2} [/tex] and [tex]\dfrac{\pi }{4} [/tex] respectively.

A periodic function is a function that repeats itself after a definite time interval.

[tex]f(x) = -3cos(4x+\pi ) +6[/tex]

The cosine function is a periodic function that repeats itself in the interval of [tex]2\pi [/tex].

For maximun amplitude

[tex]cos(4x+\pi )=-1\\ [/tex]

Then

[tex]f(x)=3+6\\ f(x)= 9[/tex]

For time period

The cosine function repeats itself in the interval of [tex]2\pi [/tex].

[tex]\begin{aligned} \frac{2\pi }{T} &= 4 \\\\ T &=\dfrac{\pi }{2}\\ \end{aligned}[/tex]

For phase shift

Phase is   [tex]\dfrac{\pi }{4} [/tex]

Thus, the amplitude, period, and phase shift are 9, [tex]\dfrac{\pi }{2} [/tex] and [tex]\dfrac{\pi }{4} [/tex] respectively.

To more about the Period function link is given below.

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