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3 years ago

Which of the following sequences of numbers are arithmetic sequences?

Mathematics

2 answers:

serg [7]3 years ago

5 0

Hello,

A:no
B:no
C,D,E :yes

All you have to do : is the difference of next term and the term must be constant.

Zigmanuir [339]3 years ago

4 0

Answer:

C), D) and E)

Step-by-step explanation:

First let's see what an arithmetic sequence is.

A arithmetic sequence is series of numbers where the difference between the successive terms must be a constant.

For example,

2, 4, 6, 8, 10.....

If you find the difference between the successive terms, it will be the same constant.

4 -2 = 2

6 -4 = 2

8 -6 = 2

This is called arithmetic sequence.

A and B are not the arithmetic sequence. The different is not the same constant.

C) 345, 346, 347, 348, 349....

Difference = 1 between the two successive terms.

So it is an arithmetic sequence.

D) 54, 71, 88, 105, 122...

Difference = 71 - 54 = 17

88 - 71 = 17

So it is an arithmetic sequence.

E) -3, -10, -17, -24, -31...

Difference = -10 -(-3) = -10 + 3 = -7

Difference of -10 and -17 is -17 -(-10) = -17 +10 = -7

So it is an arithmetic sequence.

Answer: C), D) and E)

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Find a rational number that's between 5.2 and 5.5

Andrei [34K]

Answer:

5.3 or 5.4

Step-by-step explanation:

A rational number is a number that can be expressed as a fraction.

A decimal can be a rational number when it repeats or ends.

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3 years ago

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A particular restaurant can legally have only 150 people in it at one time. The tables in the restaurant can seat 4 people at a

astra-53 [7]

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3 years ago

Rewrite the quadratic function in vertex form.<br> Y=2x^2+4x-1

Fantom [35]

Answer:

$\large\boxed{y=2(x+1)^2-3}$

Step-by-step explanation:

The vertex form of an equation of a parabola:

$y=a(x-h)^2+k$

(h, k) - vertex

We have

$y=2x^2+4x-1=2\left(x^2+2x-\dfrac{1}{2}\right)$

We must use the formula: $(a+b)^2=a^2+2ab+b^2\qquad(*)$

$2\left(x^2+2(x)(1)-\dfrac{1}{2}\right)=2\bigg(\underbrace{x^2+2(x)(1)+1^2}_{(*)}-1^2-\dfrac{1}{2}\bigg)\\\\=2\left((x+1)^2-1-\dfrac{1}{2}\right)=2\left((x+1)^2-\dfrac{3}{2}\right)$

Use the distributive formula a(b + c) = ab + ac

$2(x+1)^2+2\left(-\dfrac{3}{2}\right)=2(x+1)^2-3$

5 0

3 years ago

Please help, i don’t understand this at all.

zubka84 [21]

So, standard form basically takes the shape of Ax+By=C. You want all of your variables to be on the left side and your constant on the right. There can also be no fractions!

In your case, since you didn't mention a y value for y, your line is y=-3/2x+6

first we get rid of the fraction by multiplying both sides of the equation by 2:
(2)y= (-3/2x+6)(2) and get
2y=-3x+12
now all there is left to do is get x to the other side by adding it to both sides:
3x+2y=12 is your final answer

8 0

3 years ago

What is the solution of this system of linear equations? 3y=3/2x+6 1/2y-1/4x=3.

tensa zangetsu [6.8K]

Answer:

No solution

Step-by-step explanation:

Please, separate equations with a comma, or the word "and," or a semicolon.

Next, determine the LCD and multiply both equations by it, so as to elimiinate the fractional coefficients.

3y=3/2x+6 1/2y-1/4x=3

should be written as the system

3y=(3/2)x+6 Use parentheses around the fraction for clarity

(1/2)y-(1/4)x=3 Same: use parentheses

The LCDs here are 2 (for the first equation) and 4 (for the second equation). Multiply the first equation by 2 to eliminate the fractions:

3y=(3/2)x+6 → 6y = 3x + 12, and

4[ (1/2)y-(1/4)x=3 ] → 2y - x = 12

Let's use the substitution method to solve this system. Solve the 2nd equation for x, obtaining x = 2y - 12. Substitute 2y - 12 for x in the 1st equation 6y = 3x + 12:

6y = 3(2y - 12) + 12, or

6y = 6y - 36 + 12

This reduces to 0 = -24, which is never true. Thus,

this system has NO solution.

5 0

3 years ago