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Nostrana [21]
3 years ago
15

Use sigma notation to represent the sum of the first seven terms of the following sequence: 4, 10, 16, … the summation from n eq

uals 1 to 7 of negative 4 plus 6 times n the summation from n equals 1 to 7 of 4 plus 6 times n the summation from n equals 1 to 7 of 2 plus 6 times n the summation from n equals 1 to 7 of negative 2 plus 6 times n
Mathematics
1 answer:
Dominik [7]3 years ago
6 0

\bf 4~~,~~\stackrel{4+6}{10}~~,~~\stackrel{10+6}{16}~~,~~...~\hspace{10em}\stackrel{\textit{common difference}}{d = 6} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ a_1=4\\ d = 6 \end{cases} \implies a_n=4+(n-1)6 \\\\\\ a_n=4-6+6n\implies a_n=6n-2~\hfill \displaystyle\boxed{\sum\limits_{n = 1}^{7}~6n-2}

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Pls help !!!!! i'll mark brainliest
ExtremeBDS [4]

Answer:

Last year there were 550 bison in the heard and this year it is 10% larger.

10% is also 10/100 or 0.10

To find 10% of the heard last year

550 x.0.10 = 55. To find the number in the heard this year add 550 (last year) + 55 (10% growth) = 605 or,

to find how many there are now last years heard size was 100% of the heard or 1.00. To find any percent more add it to 1.00 and multiply by the starting amount.

550 x 1.10 = 605

For the second example.

If there are 550 bison in the heard this year, and this year was a decrease of 10% from last year we can express last year's number like this.

550 = (x - (x * 0.10)) simplify;

550 = 1x - 0.10x

550 = 0.90x

Divide both sides by 0.90

x = 611.11 but it's hard to have 0.11 of a bison so realistically 611 bison last year. Subtract 10% or 61 and you indeed have 550 this year.

5 0
3 years ago
Evaluate the expression <br><br> x=-4.9 and y=-1.3 <br><br> -5x+7y
Flura [38]

Answer:

15.4

Step-by-step explanation:

-5×(-4.9) +7×(-1.3)

=24.5+(-9.1)

=24.5-9.1

==15.4

8 0
3 years ago
Let f: 4 → and c(t): → 4. suppose ∇f(1, 1, π, e6) = (0, 1, 2, −4), c(π) = (1, 1, π, e6), and c'(π) = (13, 12, 0, 1). find d(f ∘
Tems11 [23]
3tt hope it helps just starting out
6 0
3 years ago
5.
adell [148]

Answer:

Solving the inequality 3x -2 < 4 we get \mathbf{x

Option D is correct option.

Step-by-step explanation:

We need to solve the inequality 3x -2 < 4 and find value of x

Solving the inequality for finding value of x, we will keep x on left side of inequality and all other terms on the right side.

3x -2 < 4

Adding 2 on both sides

3x -2+2 < 4+2\\3x < 6

Now, we will divide 3 on both sides

\frac{3x}{3}

So, we get x < 2

Solving the inequality 3x -2 < 4 we get \mathbf{x

Option D is correct option.

5 0
3 years ago
3. What three numbers are the Pythagorean triple generated by using 4 for x and 1 for y. Remember to use the formulas:
Gnom [1K]

Given:

The three equations for the three numbers are

a=x^2-y^2

b=2xy

c=x^2+y^2

To find:

The Pythagorean triple generated by using 4 for x and 1 for y.

Solution:

Substituting x=4 and and y=1 in the given equations, we get

a=4^2-1^2

a=16-1

a=15

In the same way find b and c.

b=2(4)(1)

b=8

The third number is

c=4^2+1^2

c=16+1

c=17

The required Pythagorean triple is 8, 15, and 17.

Therefore, the correct option is C.

5 0
3 years ago
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