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3 years ago

Find the common difference and the next three terms of the arithmetic sequence. 1/4,1/2,3/4,1,5/4

Mathematics

1 answer:

andriy [413]3 years ago

3 0

Hi there! :)

Answer:

$\large\boxed {\frac{1}{4}}$ Common difference

$\large\boxed{\frac{3}{2}, \frac{7}{4}, 2}$ Next three terms

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Find the common difference by subtracting the previous term from a term. We can use the terms 1/4 and 1/2:

Convert 1/2 into a fraction over 4:

1/2 · 2/2 = 2/4

Find the common difference by subtracting the fractions:

2/4 - 1/4 = 1/4. This is the common difference.

Find the next 3 terms by adding 1/4:

5/4 + 1/4 = 6/4 (Reduce fraction) = 3/2

6/4 + 1/4 = 7/4

7/4 + 1/4 = 8/4 (Reduce fraction)

Therefore, the next 3 terms are 3/2, 7/4 and 2.

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please help me!!!!!

Lana71 [14]

Answer: 194

Step-by-step explanation:

1. Square both sides to get (b+2)=14^2=196

2. Subtract 2 from both sides to get b=194

4 0

3 years ago

South wind vineyard uses 100 acres to plant Chardonnay and riesling grapes the venter knows the profit will be greatest by plant

GuDViN [60]

Answer:

let riesling=x=340

let chardonnay=x+140=480

Step-by-step explanation:

x+x+140=820

2x=680

x=340

6 0

3 years ago

Acellus... can you help please

Vedmedyk [2.9K]

Based on the image we can see that angle B and angle E will be the same so we can write this into an equation.

x + 4 = 48°

Now, we can solve for x.

x + 4 - 4 = 48 - 4

x = 44 (answer)

Best of Luck!

8 0

3 years ago

Explain the process of changing rational exponents to radical form

hoa [83]

The formula that describes the transformation of rational exponents to radical form is:

$a^{\frac{n}{m}} = \sqrt[m]{a^n}$

<h3>Transformation of rational exponents to radical form:</h3>

A rational exponent is represented by: $a^\frac{m}{n}$ .

That is, the exponent is a fraction, in which m is the numerator and n is the denominator.

In the conversion to radical form, the numerator will be power(also exponent), while the denominator will be the root.

Hence, the formula for the transformation is:

$a^{\frac{n}{m}} = \sqrt[m]{a^n}$

You can learn more about the transformation of rational exponents to radical form at brainly.com/question/7296346

3 0

3 years ago

!!HELP!! algebra two!! multiply and combine like terms to write as the sum of difference of monomials!! a-i !!!explanation, if p

vazorg [7]

Answer:

a. 10a + 8a²

c. 12z + 3z²

e. -20 + x + x²

g. -64 + 9z⁴

i. y¹⁰⁰¹ + 8y¹³²⁰⁰

Step-by-step explanation:

According to the Six Exponential Rules, whenever you divide terms, you subtract the exponents, and of course whenever you multiply terms, you add the exponents.

a. The variables have an invisible degree term of 1, so when multiplied, you get 8a².

c. ⅛ of 24 and 96 means dividing both numbers by its multiplicative inverse, which is 8: ⅛[24] → 24 ÷ 8; 3; ⅛[96] → 96 ÷ 8; 12. Then of course, you still have to follow the exponential procedure.

e. This is just like the Quadratic Equation, y = Ax² + Bx + C. All you have to do is do what I like to call FOIL:

F - Multiply the first terms in each set of parentheses FARTHEST TO THE LEFT

O [Outermost] - Multiply the first term in the first set of parentheses FARTHEST TO THE LEFT by the last term in the second set of parentheses FARTHEST TO THE RIGHT

I [Innermost] - Multiply the last term in the first set of parentheses FARTHEST TO THE RIGHT by the first term in the second set of parentheses FARTHEST TO THE LEFT

L - Multiply the last terms in each set of parentheses FARTHEST TO THE RIGHT

Doing this will give you the above answer.

g. See explanation letter e.

i. Now, as I mentioned before, when you multiply terms, you add the exponents. In addition, that decimal in the far right corner, is equivalent to ⅛, and ⅛ of 8 is 1, so we know that 1 is our INVISIBLE coefficient next to the y, then you just add 1 to 1000 in the exponents because of the invisible degree of 1.

If you are ever in need of assistance, do not hesitate to let me know by subscribing to my You-Tube channel [USERNAME: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.

**I have a video that talks about the Six Exponential Rules. It is titled "Six Exponential Procedures". Go check out the channel to watch it and gain more assistance.

4 0

3 years ago