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Olin [163]
3 years ago
12

Find the nth term of this quadratic sequence 4,7,12,19,28

Mathematics
1 answer:
olga55 [171]3 years ago
7 0

Answer:

nth term = n^2 + 3.

Step-by-step explanation:

                      4    7   12   19   28

Differences       3    5    7     9

Differences          2    2    2

So the nth term contains n^2.

                          4   7   12   19   28

Values of n^2    1   4    9    16   25

Differences       3   3    3    3     3

So the nth term = n^2 + 3.

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Explain how to determine which numbers must be excluded from the domain of a rational expression. Please provide an example with
Katarina [22]

Answer:

  • When we are having a rational expression i.e. a expression of the type:

\dfrac{f(x)}{g(x)}

Where f(x) and g(x) are polynomial functions.

Now the domain of this rational expression is whole of the real numbers except the points where the function g(x) will be zero.

Hence we have to exclude the points where the given denominator quantity is zero.

  • Let us consider an example as:

  Let R(x) denote the rational function as:

R(x)=\dfrac{x^2}{(x-2)(x-3)}

Now the domain of this rational function will be whole of the real line minus the points where the denominator is zero.

We know that (x-2)(x-3) is zero when x=2 or x=3.

Hence, the domain of R(x) is: R- {2,3}.

7 0
3 years ago
3.50 plus an additional 6% tax.what is the price after the tax?
Sonja [21]

.3.50 plus additional 6%= to 3.71 after the tax

3 0
3 years ago
how many gallons of 80% antifreeze solution must be mixed with 100 gallons of 10% antifreeze to get a mixture that is 70% antifr
ololo11 [35]
Let's say we'll mix "x" amount of the 80% solution, how much antifreeze is in it? well is just 80% of antifreeze, and the rest is something else.... what's 80% of "x"? so is (80/100)*x, or 0.8x.

likewise, the mixture will be a 70% solution, and let's say it adds up to "y" amount, so how much antifreeze is in it? well (70/100) * y or 0.7y.

\bf \begin{array}{lccclll}
&\stackrel{gallons}{amount}&\stackrel{\%}{quantity}&\stackrel{antifreeze}{quantity}\\
&------&------&------\\
\textit{80\% sol'n}&x&0.80&0.8x\\
\textit{10\% sol'n}&100&0.10&10\\
------&------&------&------\\
mixture&y&0.70&0.7y
\end{array}

so whatever "x" is, we know that x + 100 = y.

and we know that 0.8x + 10 = 0.7y.

\bf \begin{cases}
x+100=\boxed{y}\\
0.8x+10=0.7y\\
----------\\
0.8x+10=0.7\left( \boxed{x+100} \right)
\end{cases}
\\\\\\
0.8x+10=0.7x+70\implies 0.8x-0.7x=70-10\implies 0.1x=60
\\\\\\
x=\cfrac{60}{0.1}\implies x=600
6 0
3 years ago
Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AB = 8
Delicious77 [7]

Answer:

x = 32

Step-by-step explanation:

∠BCA = ∠DBA (90 - ∠DBC)

∠A = ∠A

ΔABD similar to ΔACB

AC/AB = AB/AD

x / 8 = 8 / 2

x = 32

4 0
3 years ago
Two hundred people were asked to choose their favorite of the following ice cream flavors: vanilla, chocolate, or strawberry. Ho
Lyrx [107]

Answer:

Vanilla Percentage = 34%

Therefore the number of people who choose vanilla is :

34% x 200 = 68 people

Formula:

Percentage of Object x Total number = Number of Object

8 0
3 years ago
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